Site Map Universidad de Oviedo Oviedo's Quantum Chemistry Group Departamento de Química Física y Analítica Universidad de Oviedo Oviedo's Quantum Chemistry Group

1. L. Gracia, M. Marqués, A. Beltrán, A. Martín Pendás, and J. M. Recio,
Bonding and compressibility in molecular and polymeric phases of CO2,
J. Phys. Condens. Matter xx (2003) xxxx-xxxx.

We present the results of a theoretical study of the response of molecular CO2-I and CO2-III, and polymeric CO2-V polymorphs to hydrostatic pressure. Total energy calculations and geometry optimizations have been performed under the local density functional approximation combining a pseudopotential and planewave scheme as implemented in the VASP code. Using the Atoms in Molecules theory, the network of inter- and intra-molecular chemical bonds of the different phases are rigorously characterized in terms of the values of the electron density and its Laplacian at the bond critical points. The chemical graph reveals CO2-III as the first precursor phase of a polymeric carbon four-fold coordinated structure. In addition, the bulk compressibility is decomposed into atomic and molecular contributions with the aim to provide a better understanding of the reasons that explain the emergence of low compressible polymorphs at high-pressures.

2. W. Paszkowicz, R. Minikayev, P. Piszora, M. Knapp, C. Bahtz, J. M. Recio, M. Marqués, P. Mori-Sánchez, L. Gerward, and J. Z. Jiang,
Thermal expansion of spinel-type Si3N4,
Appl. Phys. Lett. xx (2003) xxxx-xxxx.

The lattice parameter and the thermal expansion coefficient (TEC) for a spinel-type Si3N4 phase prepared under high pressure and high temperature conditions are determined for 14 < T < 302~K by X-ray diffraction, at a synchrotron-radiation source, and for 0 < T < 1683~K by first-principles calculations. The low-T and high-T experimental TEC data are in excellent agreement with present and previous calculations. The temperature dependence of these two quantities can be accurately represented by polynomials over the complete T range. Our results demonstrate that the linear expansion coefficient tends to vanish for T<100~K.

3. R. Franco, P. Mori-Sánchez, J. M. Recio, and R. Pandey,
Theoretical compressibilities of high-pressure ZnTe polymorphs,
Phys. Rev. B xx (2003) xxxx-xxxx.

We report the results of a theoretical study of structural, electronic, and pressure-induced phase transitions properties in ZnTe. Total energies of several high-pressure polymorphs are calculated using the density functional theory (DFT) formalism under the non-local approximation. Thermal effects are included by means of a non-empirical Debye-like model. In agreement with optical absorption data, the lowest direct gap of the zincblende polymorph is found to follow a non-linear pressure dependence that turns into linear behavior in terms of the decrease in the lattice parameter. The pressure stability ranges of cubic (zincblende and rock-salt), trigonal (cinnabar), and orthorhombic (Cmcm) polymorphs are computed at static and room temperature conditions. Our calculations agree with the experimental observed zincblende --- cinnabar --- Cmcm pressure-induced phase sequence. Linear and bulk compressibilities are evaluated for the four polymorphs and reveal an anisotropic behavior of the cinnabar structure, which contrasts with the cubic-like compression of its shortest Zn-Te bonds. The qualitative trend shows a crystal that becomes relatively less compressible in the high-pressure phases.

4. A. Waskowska, L. Gerward, J. Staun Olsen, M. Feliz, L. Gracia, M. Marqués, and J. M. Recio,
High-pressure behavior of selenium based spinels and related structures - an experimental and theoretical study,
J. Phys. Condens. Matter xx (2003) xxxx-xxxx.

The high-pressure structural behavior of CdCr2Se4 (space group $Fd\bar3m$) and CdGa2Se4 ($I\bar4$) has been investigated experimentally and theoretically in order to understand the large difference in compressibility between the two selenides. The experimental values of the bulk modulus for these compounds are 103(3) GPa and 50(1) GPa, respectively. These values compare well with 92.0 GPa and 44.3 GPa obtained from first-principles calculations based on the Density Functional Theory formalism. The calculated bulk modulus for CdGa2Se4 in hypothetical cubic spinel structure ($Fd\bar3m$) is 84.8 GPa. This value together with the experimental and theoretical results for CdCr2Se4 suggest that selenium-based cubic spinels have a uniform response to hydrostatic pressure, like their oxygen-based conterparts. Also the observed difference in compressibility between the cubic and tetragonal structures can be understood in terms of polyhedral analysis.

5. E. Francisco, L. Pueyo, and A. Martín Pendás,
Reduced size representations of high-quality atomic densities. The hybrid gaussian-exponential case,
Theor. Chem. Acc. xx (2003) xxxx-xxxx.

High-quality atomic electron densities are often approximated by limited-size expansions able to reproduce particular features of a reference function. Recent examples are the exponential sets of Koga (Theor. Chim. Acta 95, 113 (1997)) and the gaussian core densities of Cioslowski \em et al. (J. Chem. Phys. 106, 3607 (1997)). Since atomic densities have a rich structure and should obey theoretical conditions, the approximation procedure must be flexible enough to secure useful results. Here we present an extension of the algorithm used by Koga that gives uniformly accurate densities even for hybrid gaussian-exponential sets. We report approximate densities of this type for the ground state of neutral atoms He-Xe that exactly copy the reference density and its first and second derivatives at r=0, describe accurately the finer details of the density convex structure, reproduce its most significant moments, and give a faithful description of the Z dependence of density functionals like $\langle \rho-1/3\rangle$ or the Shannon entropy.

6. Víctor Luaña, Paula Mori-Sánchez, Aurora Costales, Miguel A. Blanco, and A. Martín Pendás,
Non-nuclear maxima of the electron density on alkaline metals,
J. Chem. Phys. 119 (2003) 6341-6350.

Download a reprint: JCP119-6341-ov-LM2003-alkaline-metals.pdf.

The topological properties of the electron density of bcc alkaline metals (Li-Cs) is examined by means of Hartree-Fock and Density Functional calculations. Our best results indicate that lithium is the only alkaline metal showing Non Nuclear Maxima (NNM) at the room pressure and temperature experimental geometry. Sodium and potassium, but not rubidium and cesium, would also present NNM under an appropriate compression, even though the NNM in potassium would be residual at best and contain a negligible amount of electrons. Despite these differences, all five alkaline metals share a common tendency towards topological change that makes their behavior clearly distinct from what is typical in ionic, covalent and molecular crystals. When examined in a wide range of interatomic distances, the electron density of every metal follows a well defined topological sequence, with strong similarities across the five metals.

7. A. Martín Pendás, and Víctor Luaña,
The curvature of interatomic surfaces. II. Origin and systematics,
J. Chem. Phys. 119 (2003) 7643-7650.

Download a reprint: JCP119-7643-ov-PL2003b-curvatures2.pdf.

doi locator: doi:10.1063/1.1607964.

We investigate in this paper the origin of the local curvatures of the interatomic surfaces of the Theory of Atoms in Molecules. The analytic expressions obtained in the previous work are used as a basic guide to this end, and several simplified models of the electron density between a pair of interacting atoms demonstrate that the stiffness difference in the atomic densities near the bond critical points control their signs and magnitudes. Some steps toward a systematic evaluation of the curvatures of simple molecules have also been taken, and a number of correlations between these curvatures and chemically relevant atomic properties are presented.

8. A. Martín Pendás, and Víctor Luaña,
The curvature of interatomic surfaces. I. Fundamentals,
J. Chem. Phys. 119 (2003) 7633-7642.

Download a reprint: JCP119-7633-ov-PL2003a-curvatures1.pdf.

doi locator: doi:10.1063/1.1607963.

Some basic aspects regarding the geometry of the interatomic surfaces of the theory of Atoms in Molecules are considered. After showing that the global Gauss-Bonnet theorem poses severe difficulties on the calculation of the total gaussian curvatures of unbounded interatomic surfaces, we propose the use of the local value of the gaussian curvature at the bond critical point as a better suited indicator of the geometry of the surfaces. To that end, we report analytical expressions for the curvatures of gradient lines and interatomic surfaces at critical points.

9. M. Marqués, M. Flórez, M. A. Blanco, and J. M. Recio,
Role of polarization effects in the prediction of an orthorhombic pressure-induced phase in alkali halides,
Phys. Rev. B 68 (2003) 014110-1-8.

Download a reprint: PRB68-14110-ov-MF2003-polarization.pdf.

doi locator: doi:10.1103/PhysRevB.68.014110.

Ab initio static atomistic simulations are performed to investigate the stability under pressure of cubic (B1 and B2) and orthorhombic (B33) structures of NaBr, NaI, and LiBr crystals. The calculated unit cell geometries, equations of state parameters, and phase transitions properties show systematic trends controlled by the ionic sizes and compare successfully with available experimental data. A microscopic analysis of the crystal energy identifies the anionic polarization contribution as essential to explain: (i) the preference of the recently observed B1---B33 transformation over the B1---B2 one in NaBr and NaI and (ii) the potential appearance of the orthorhombic phase at high pressures in lithium halide crystals.

10. Paula Mori-Sánchez, Miriam Marqués, Armando Beltrán, J. Z. Jiang, L. Gerward, and J. M. Recio,
Origin of the low compressibility in hard nitride spinels,
Phys. Rev. B 68 (2003) 064115-1-5.

Download a reprint: PRB68-64115-ov-MM2003-nitride-spinels.pdf.

doi locator: doi:10.1103/PhysRevB.68.064115.

A microscopic investigation of first-principles electron densities of $\gamma$-A3N4 (A:C,Si,Ge) spinels reveals a clear relationship between the compressibility and the chemical bonding of these materials. Three striking findings emanate from this analysis: (i) the chemical graph is governed by a network of highly directional strong bonds with covalent character in $\gamma-C3N4 and different degrees of ionic polarization in \gamma-Si3N4 and \gamma$-Ge3N4, (ii) nitrogen is the lowest compressible atom controlling the trend in the bulk modulus of the solids, and (iii) the group-IV counterions show strong site dependent compressibilities enhancing the difficulty in the synthesis of the spinel phases of these nitrides.

11. Aurora Costales, Anil K. Kandalam, and Ravindra Pandey,
Theoretical study of neutral and anionic Group III nitride clusters: MnNn (M= Al, Ga, and In; n=4-6),
J. Phys. Chem. B 107 (2003) 4508-4514.

Download a reprint: JPCB107-4508-ov-CK2003-nitride-clusters.pdf.

doi locator: 10.1021/jp022417s.

We report the results of a theoretical study of MnNn (M = Al, Ga, and In; m = 4, 5, 6) neutral and anionic clusters, focusing on the changes in structural and electronic properties upon the addition of an electron to the corresponding neutral clusters. Overall, the extra electron did not induce significant structural changes in AlnNn clusters, whereas it affected significantly the lowest energy configurations of GanNn and InnNn clusters. This may be attributed to the dominance of N-N bonds in GanNn and InnNn clusters in contrast to the dominance of Al-N bonds in AlnNn clusters. The atomic charge analysis showed that the extra electron is localized on the metal atoms, irrespective of the lowest energy structural configurations of these clusters.

12. Víctor Luaña, Aurora Costales, Paula Mori-Sánchez, and A. Martín Pendás,
Ions in crystals: the topology of the electron density in ionic materials. IV. The danburite (CaB2Si2O8) and the occurrence of oxide-oxide bonds in crystals.,
J. Phys. Chem. B 107 (2003) 4912-4921.

Download a reprint: JPCB107-4912-ov-LC2003-danburite.pdf.

We have obtained the electron density of danburite by means of ab initio Perturbed Ion (aiPI) quantum mechanical calculations and fully characterized its topological features as required for the analysis of crystal bonding in the ligth of Bader's Atoms In Molecules (AIM) theory. Our theoretical results do compare with the experimental determination by Downs and Swope (J. Phys. Chem. 96 (1992) 4834) of the metal-oxide bond properties and the features of the laplacian of electron density. Each B and Si ion is bound to its four nearest oxide ions in a deformed tetrahedral disposition, whereas Ca is bonded to seven oxide ions. Bonding is prototypically ionic, with positive laplacians at the bond critical points, outmost valence shell disappeared in the cations and topological charges approaching the nominal oxidation states. The existence of O-O long distance bonds (up to 11 different types of O-O bonds are present in danburite) is examined in several crystalline oxides and gas phase molecules. The occurrence of bonds is not simply due to the distance between atoms, but rather is a consequence of the molecular and crystal geometry. It is shown that the electron density at the bond critical point decreases exponentially as the distance between atoms increases. This relationship groups together molecules and crystals, neutral oxygen and oxide ions, bonds from 1.2 to 3.2~Å, covalent and ionic bonds. This behavior is, we believe, a firm proof of the true existence of the long distance bonds that the AIM theory predicts in some molecules and crystals.

13. E. Francisco, M. Bermejo, V. García Baonza, L. Gerward, and J. M. Recio,
Spinodal Equation of State for Rutile TiO2,
Phys. Rev. B 67 (2003) 064110-1-8.

Download a reprint: PRB67-64110-ov-FB2003-spinodal.pdf.

doi locator: doi:10.1103/PhysRevB.67.064110.

We present a general computational scheme to extend the spinodal equation of state [Garc\'\i a Baonza et al. (Phys. Rev. B 51, 28 (1995))] to the interpretation of the cell parameters response to hydrostatic pressure in orthogonal lattices. As an important example, we analyze the pressure (p)-volume(V)-temperature(T) data of the rutile phase of TiO2. We show that results of ab initio Perturbed Ion calculations and very recent X-ray diffraction experiments of isothermal compression on this system closely follow the spinodal conduct. The computational scheme permits the incorporation of temperature effects in the static calculation as well as in the room-temperature experimental data. Overall, we find highly consistent results and good theory-experiment agreement for a significant series of observables, including structural parameters, p-V diagram, bulk modulus, linear compressibilities, and thermal expansion coefficient. The observed discrepancies in the pressure first derivative of the bulk modulus can be traced back to the difference between the theoretical and the experimental spinodal pressure.

14. Aurora Costales, and Ravindra Pandey,
Density Functional Calculations of Small Anionic Clusters of Group III Nitrides.,
J. Phys. Chem. A 107 (2003) 191-197.

Download a reprint: JPCA107-191-ov-CP2003-III-nitrides.pdf.

doi locator: 10.1021/jp022202i.

In this paper, we study the changes in structural, vibrational, bonding and electronic properties of small clusters of the group III-nitrides when an electron is added to the neutral clusters. The results, based on first principles calculations, reveal that addition of an electron induces significant structural changes in the neutral cluster configurations. The atomic charge analysis suggests that the added electron is located over the metallic atoms in dimers and trimers, and equally shared by metal and nitrogen atoms in monomers. We have computed the electron affinities and the HOMO-LUMO gap of these clusters and the values are comparable to available results.

15. L. Gracia, A. Beltrán, J. Andrés, R. Franco, and J. M. Recio,
Quantum-mechanical simulation of MgAl2O4 under high-pressure,
Phys. Rev. B 66 (2002) 224114-1-7.

Download a reprint: PRB66-224114-ov-GB02-MgAl2O4.pdf.

doi locator: doi:10.1103/PhysRevB.66.224114.

The equations of state and phases diagram of the cubic spinel and two high-pressure polymorphs of MgAl2O4 have been investigated up to 65 GPa using Density Functional Theory, the space-filling polyhedral partition of the unit cell, and the static approximation. Energy-volume curves have been obtained for the spinel, the recently observed calcium ferrite-type and calcium titanite-type phases, and the MgO+$\alpha$-Al2O3 mixture. Zero-pressure unit lengths and compressibilities are well described by the theoretical model, that predicts static bulk moduli about 215 GPa for all the high-pressure forms. Computed equations of state are also in good agreement with the most recent experimental data for all compounds and polymorphs considered. We do not find a continuous pressure-induced phase sequence but the static simulations predict that the oxide mixture, the ferrite phase, and the titanite phase become more stable than the spinel form at 15, 35, and 62 GPa, respectively. A microscopic analysis in terms of polyhedral and bond compressibilities leads to identify the ionic displacements accompanying the phase transformations and to an appealing interpretation of the spinel response to compression.

16. Aurora Costales, and Ravindra Pandey,
A Theoretical Study of Structural, Vibrational, and Electronic Properties of Neutral, Positive, and Negative Indium Arsenide Clusters, InnAsn (n=1,2,3),
Chem. Phys. Lett. 362 (2002) 210-216.

Download a reprint: CPL362-210-ov-CP2002-InAs.pdf.

doi locator: 10.1016/S0009-2614(02)01076-X.

First principles study of the small InAsn clusters is performed to investigate the changes in structural, vibrational and electronic properties, when an electron is either added or removed from the corresponding neutral clusters. The calculated results reveal that the addition of an electron to the neutral clusters induce significant structural changes relative to the case when an electron is removed. The changes in vibrational properties can be explained in terms of the variation of the interatomic distances upon removing or adding the electron. The calculated values of electron affinity and ionization potential are comparable to those calculated in GaAs and InP clusters.

17. Paula Mori-Sánchez, A. Martín Pendás, and V. Luaña,
A classification of covalent, ionic and metallic solids based on the electron density,
J. Am. Chem. Soc. 124 (2002) 14721-14723.

Download a reprint: JACS124-14721-ov-MP2002-triangle.pdf.

The electron density of crystals contains all the information required to complete a classification of their bonding types. We propose here a set of three different indexes, flatness, charge transfer and molecularity, easily obtained from the experimental or theoretical electron density, which give rise to a classification in close resemblance to the classical van Arkel-Ketelaar diagrams.

18. M. Flórez, J. M. Recio, E. Francisco, M. A. Blanco, and A. Martín Pendás,
First-principles study of the rock salt-cesium chloride relative phase stability in alkali halides,
Phys. Rev. B 66 (2002) 144112/1-8.

Download a reprint: PRB66-144112-ov-FR2002-B1B2.pdf.

doi locator: doi:10.1103/PhysRevB.66.144112.

We present a detailed investigation of observable properties associated with the relative stability of the rock salt (B1) and cesium chloride (B2) phases in the AX (A: Li, Na, K, Rb, Cs; X: F, Cl, Br, I) crystal family. Thermodynamic B1 --- B2 transition pressures and $\Delta Y = Y\rm (B2)-Y\rm (B1)$ differences in total energies, volumes, and bulk moduli at zero and transition pressures are computed following a localized Hartree-Fock method. The arrangement of the data in clear trends is shown to be mainly dominated by the cation atomic number. This behavior is well interpreted in terms of a variety of microscopic arguments that emerge from: (i) the evaluation of the energy Hessian at the B1 and B2 points, and (ii) the decomposition of the energy, pressure, and bulk modulus in anionic and cationic classical and quantum-mechanical contributions.

19. E. Francisco, M. A. Blanco, and P. Palacios,
Atomistic simulation of the equation of state of SrF2 using electron gas interionic potentials,
High Pressure Res. 22 (2002) 227-230.

We have determined the equation of state (EOS) of SrF2 in the cubic (C1, Fm3m) and orthorhombic (C23, Pbnm) phases using Electron Gas Interionic Potentials (EGIP) that incorporate many-body energy components. Thermal effects are included by means of a quasi-harmonic Debye model. The zero pressure unit cell length (a0), lattice energy (E$\mathrmlatt$), bulk modulus (B0), and EOS of the C1 phase are predicted in good agreement with the observed data. Moreover, the computed EOS satisfy very well the empirical Vinet EOS. Fittings of $\eta/\eta0-p$ data ($\eta=a,b,c$) to linear forms of the Vinet EOS reveal that SrF2 (C23) is more compressible along the b and c axes than along the a direction. Finally, the C1 --- C23 transition is predicted to occur at pt=3.92 GPa, which is between the observed direct ($pt=5.0$ GPa) and reverse C1 ($pt=1.7$ GPa) phase transitions.

20. J. Z. Jiang, H. Lindelov, L. Gerward, K. Stahl, J. M. Recio, P. Mori-Sánchez, S. Carlson, M. Mezouar, E. Dooryhee, A. Fitch, and D. J. Frost,
Compressibility and thermal expansion of cubic silcon nitride,
Phys. Rev. B 65 (2002) R161202-1-4.

Download a reprint: PRB65-161202-ov-JL2002-Si3N4.pdf.

The compressibility and thermal expansion of the cubic silicon nitride (c-Si3N4) phase have been investigated by performing in-situ X-ray powder diffraction measurements using synchrotron radiation, complemented with computer simulations by means of first principles calculations. The bulk compressibility of the c-Si3N4 phase originates from the average of both Si-N tetrahedral and octahedral compressibilities where the octahedral polyhedra are less compressible than the tetrahedral ones. The origin of the unit cell expansion is revealed to be due to the increase of the octahedral Si-N and N-N bond lengths with temperature, while the lengths for the tetrahedral Si-N and N-N bonds remain almost unchanged in the temperature range of 295-1075 K.

21. A. Martín Pendás, V. Luaña, L. Pueyo, E. Francisco, and Paula Mori-Sánchez,
Hirshfeld Surfaces as approximations to Interatomic Surfaces,
J. Chem. Phys. 117 (2002) 1017-1023.

Download a reprint: JCP117-1017-ov-PL2002-Hirshfeld.pdf.

doi locator: doi:10.1063/1.483851.

A simple algebraic model is used to show that Hirshfeld surfaces in condensed phases may be understood as approximations to the interatomic surfaces of the Theory of Atoms in Molecules. The conditions under which this similarity is valid are explored, and both kinds of surfaces are calculated in the LiF crystal to illustrate the main results. The link between Hirshfeld and interatomic surfaces provides a physical ground to understand the usage of the former to visualize intermolecular interactions.

22. A. Martín Pendás,
Stress, Virial, and Pressure in the Theory of Atoms in Molecules,
J. Chem. Phys. 117 (2002) 965-979.

Download a reprint: JCP117-965-ov-Pendas2002-pressure.pdf.

The Quantum Theory of Stress (QTS) is developed within the Atoms in Molecules (AIM) framework. The complete local stress field is introduced and integrated within atomic basins, and it is shown that the kinetic term gives rise to the atomic virial theorem. The role of the potential part of the stress field in the AIM theory is discussed, and its necessary consideration in order to define atomic pressures presented. These atomic pressures are shown to tend to the thermodynamic limit as the size of the system grows. A link between the AIM theory and the Theory of Electronic Separability has also been found. A set of simple examples illustrates our results.

23. E. Francisco, A. Martín Pendás, and A. Costales,
Structure and bonding in magnesium difluoride clusters: The (MgF2)n (n=2-3) clusters,
J. Phys. Chem. A 106 (2002) 335-344.

Download a reprint: JPCA106-335-ov-FP2002-MgF2-clusters.pdf.

doi locator: doi:10.1021/jp012347+.

Hartree-Fock (RHF) and second-order M\oller-Plesset (MP2) first principles calculations have been performed to study the structures, stabilities, harmonic vibrational frequencies, and bonding properties of MgF2 dimers and trimers, complementing our previous work (J. Phys. Chem. 2001, 105, 4126) on the MgF2 monomer. The less energetic isomers found for (MgF2)2 and (MgF2)3 are the bridged F-(Mg2F2)-F (D$\mathrm2h$) and F-MgF2MgF2Mg-F (D$\mathrm2d$) structures, respectively. A new Cs trimer structure has been found and characterized. Correlation energy corrections increase the Mg-F distances by a 1.2-1.4 % and do not modify appreciably the Mg-F-Mg and F-Mg-F angles. The dissociation energy per magnesium difluoride unit (DE) of (MgF2)n increases with n. MP2 frequencies for the (MgF2)2 D$\mathrm2h$ isomer are around 1.0 % lower than their RHF equivalents. The whole set of computed frequencies for (MgF2)n has allowed us to perform a critical analysis of the experimental vibrational data, where some spectral assignments remained uncertain. The Atoms in Molecules analysis of the electron density reveals that (MgF2)n clusters are highly ionic, with almost nominal net atomic charges (q$\mathrmMg\simeq +$1.8 $\verte\vert and q\mathrmF\simeq -$0.9 $\verte\vert$). Our previous polarizable-ions model accounts fairly well for the properties of these clusters, rationalizing the energy ordering of trimers in a physically sound way.

24. Aurora Costales, A. K. Kandalam, Ruth Franco, and Ravindra Pandey,
Theoretical Study of Structural and Vibrational Properties of (AlP)n, (AlAs)n, (GaP)n, (GaAs)n, (InP)n, and (InAs)n clusters with n=1,2,3,
J. Phys. Chem. B 106 (2002) 1940-1944.

Download a reprint: JPCB106-1940-ov-CK2002-3-5-clusters.pdf.

doi locator: 10.1021/jp013906f.

The structure, geometry, and vibrational frequencies of several isomers of small III-V (MX)n clusters ($n=1,2,3$; M= Al, Ga, In; X= P, As) have been investigated using density functional theory. The results reveal the same behavior as in the nitride clusters for monomers and dimers. The Al trimers exhibit a D3h structure like the nitride, but the gallium and indium trimers exhibit a three dimensional structure of Cs symmetry. The existence of strong X-X bonds dominates both the structure and the vibrations of the Ga and In trimers.

25. A. Costales, M. A. Blanco, A. Martín Pendás, A. K. Kandalam, and R. Pandey,
Chemical bonding in the group III nitrides,
J. Am. Chem. Soc. 124 (2002) 4116-23.

Download a reprint: JACS124-4116-ov-CB2002-bonding-3-N.pdf.

doi locator: doi:10.1021/ja017380o.

We analyze in this article the evolution of the chemical bonding in the group III nitrides (MN, M = Al, Ga, In), from the N-N bond dominated small clusters to the M-N bond dominated crystals, with the aim of explaining how the strong multiple bond of N2 is destabilized with the increase in coordination. The picture that emerges is that of a partially ionic bond in the solid state, which is also present in all the clusters. The covalent N-N bond, however, shows a gradual decrease of its strength due to the charge transfer from the metal atoms. Overall, Al clusters are more ionic than Ga and In clusters, and thus the N-N bond is weakest in them. The nitrogen atom charge is seen to be proportional to the metal coordination, being thus a bond-related property, and dependent on the M-N distance. This explains the behavior observed in previous investigations, and can be used as a guide in predicting the structures and defects on semiconductor quantum dot or thin film devices of these compounds.

26. A. K. Kandalam, M. A. Blanco, and R. Pandey,
Theoretical study of AlnNn, GanNn, and InnNn ($n=4,5,6$) clusters,
J. Phys. Chem. B (106) 1945-53.

Download a reprint: JPCB106-1945-ov-KB2002-3-N-clusters.pdf.

We report the results of a theoretical study of AlnNn, GanNn, and InnNn (with $n=4,5,6$) clusters, focusing on their structural properties, stability, and electronic structure. For AlnNn clusters, the metal-nitrogen bond is found to dominate the lowest energy configurations, with a transition from planar to bulk-like three dimensional structures, as the cluster size increases from Al4N4 to Al6N6. However, for GanNn and InnNn clusters, the lowest energy configurations are mostly planar, and they are dominated either by N3- or N2 sub-units. It strongly suggests that N-segregation may occur during quantum dot or thin film deposition processes, due to the low atomic coordination and abundance of dangling bonds.

27. L. Gracia, R. Franco, A. Beltrán, J. Andrés, and J. M. Recio,
Stability of MgAl2O4 under high-pressure conditions,
High Pressure Res. 22 (2002) 447-450.

A theoretical investigation of the MgAl2O4 crystal response to high-pressure conditions has been carried out to determine its stability against decomposition towards MgO and $\alpha-$Al2O3 and towards recently observed orthorhombic phases. We have evaluated total energy versus volume curves using the density functional formalism under the non-local B3LYP approximation as i implemented in the CRYSTAL package. Numerical and analytical fittings have been carried out to determine the equilibrium unit cell geometry and equation of state parameters for all the structures and compounds involved in the phase diagram. The macroscopic compressibility of the spinel phase is interpreted considering the compressibility of its elementary MgO4 and AlO6 coordination polyhedra, and implications to understand the phase stability diagram are suggested.

28. J. M. Recio, M. Flórez, E. Francisco, M. A. Blanco, and A. Martín Pendás,
Microscopic study of the rock salt-caesium chloride phase stability in alkali halides,
High Pressure Res. 22 (2002) 443-446.

In this work we present a microscopic study of observable magnitudes linked to the relative stability of the rock salt (B1) and cesium chloride (B2) phases in the AX (A: Li, Na, K, Rb, Cs; X: F, Cl, Br, I) crystal family. Transition pressures and $\Delta Y = Y\rm (B2)-Y\rm (B1)$ differences in total energies, volumes, and bulk moduli at zero and transition pressures are computed following a localized Hartree-Fock scheme. The arrangement of the data in clear trends is shown to be dominated by the cation atomic number, being weaker the dependence of the data on the anion. These systematics are well interpreted in terms of a variety of microscopic arguments that emerge from the decomposition of the energy, pressure, and bulk modulus in anionic and cationic contributions.

29. M. Marqués, M. Flórez, M. A. Blanco, and J. M. Recio,
Role of polarization effects in the prediction of an orthorhombic high-pressure phase in NaBr,
High Pressure Res. 22 (2002) 439-442.

doi locator: doi:10.1080/08957950290008747.

The pressure-induced polymorphism of NaBr has been investigated by means of a quantum-mechanical Hartree-Fock localized scheme implemented in the ab initio Perturbed Ion code. Polarization effects are included using a semiclassical model and considering constant and volume dependent ionic polarizabilities. The equilibrium cell geometry, the bulk modulus and its pressure derivative have been evaluated for the B1, B2, and B33 phases. The relative merits of several polarization models in the static description of the B33 structural parameters and phase stability diagram are analyzed. Preliminary results describing the B1 and B33 phases using a common monoclinic P21/m unit cell are also reported.

30. M. Calatayud, Paula Mori-Sánchez, A. Beltrán, A. Martín Pendás, E. Francisco, J. Andrés, and J. M. Recio,
Quantum-mechanical analysis of the equation of state of anatase TiO2,
Phys. Rev. B 64 (2001) 184113-1-9.

Download a reprint: PRB64-184113-ov-CM2001-TiO2.pdf.

doi locator: doi:10.1103/PhysRevB.64.184113.

Quantum-mechanical simulations have been performed to investigate pressure effects on the crystal geometry, the chemical bonding, and the electronic structure of anatase TiO2. Total energy calculations are carried out using the density functional formalism under the non-local B3LYP approximation. The optimized unit cell equilibrium parameters, and the bulk and linear compressibilities are determined in good agreement with recent experimental data. The topology of the electron density is examined by means of the Atoms in Molecules (AIM) theory. Computed AIM charges and topological properties of the bond critical points reveal a partially ionic behavior of the crystal that complements the description obtained from the band structure and the projected density of states analysis. A microscopic interpretation of the crystal response to hydrostatic pressure is given in terms of the elementary polyhedra and the AIM atomic volumes that fill the unit cell space.

31. Paula Mori-Sánchez, J. M. Recio, Bernard Silvi, C. Sousa, A. Martín Pendás, V. Luaña, and F. Illas,
Rigorous characterization of oxygen vacancies in ionic oxides,
Phys. Rev. B 66 (2002) 075103-1-6.

Download a reprint: PRB66-075103-ov-MR2002-F-MgO.pdf.

Charged and neutral oxygen vacancies in the bulk and on perfect and defective surfaces of MgO are characterized as quantum-mechanical subsystems chemically bonded to the host lattice and containing most of the charge left by the removed oxygens. Attractors of the electron density appear inside the vacancy, a necessary condition for the existence of a subsystem according to the Atoms in Molecules theory. The analysis of the Electron Localization Function also shows attractors at the vacancy sites, which are associated to a localization basin shared with the valence domain of the nearest oxygens. This polyatomic superanion exhibits chemical trends guided by the formal charge and the coordination of the vacancy. The topological approach is shown to be essential to understand and predict the nature and chemical reactivity of these objects. There is not a vacancy but a core-less pseudoanion that behaves as an activated host oxygen.

32. Ruth Franco, Anil K. Kandalam, Ravindra Pandey, and Udo C. Pernisz,
Theoretical Study of Structural and Electronic Properties of Methyl-Silsesquioxanes,
J. Phys. Chem. B 106 (2002) 1709-1713.

Calculations based on density functional theory (DFT) were performed on various structural isomers of methyl-silsesquioxanes, [MeSiO3/2]n where n = 4, 6, 8, 10, 12, 14 and 16 to study their structural and electronic properties. The calculated results find the stabilty of methyl-silsesquioxanes, except [MeSiO3/2]4, against fragmentation and hydrolysis. The most stable isomers are found to prefer configurations with a larger ring-size. The deformation density plots show that chemical bonding in methyl-silsesquioxan es is mainly determined by the building block unit, (CH3SiO3/2) as also see n in hydro-silsesquioxanes (HSQ). However, unlike HSQ, phenyl-silsesquioxanes predicted to be insulator without a presence of a midgap state in their HOMO-LUMO gap.

33. R. Pandey, B. K. Rao, P. Jena, and M. A. Blanco,
Electronic structure and properties of transition metal benzene complexes,
J. Am. Chem. Soc. 123 (2001) 7744-7744.

Download a reprint: JACS123-7744-ov-PR2001b-MBenz-corr.pdf.

34. R. Pandey, B. K. Rao, P. Jena, and M. A. Blanco,
Electronic structure and properties of transition metal benzene complexes,
J. Am. Chem. Soc. 123 (2001) 3799-3808.

Download a reprint: JACS123-3799-ov-PR2001-MBenz.pdf.

A comprehensive theoretical study of the geometries, energetics, and electronic structure of neutral and charged 3-d transition metal atoms (M) interacting with benzene molecules (Bz) is carried out using density functional theory and generalized gradient approximation for the exchange-correlation potential. The variation of the metal-benzene distances, dissociation energies, ionization potentials, electron affinities, and spin multiplicities across the 3-d series in MBz complexes differs qualitatively from those in M(Bz)2. For example, the stability of Cr(Bz)2 is enhanced over that of CrBz by almost a factor of 30. On the other hand, the magnetic moment of Cr(Bz)2 is completely quenched although CrBz has the highest magnetic moment, namely 6~$\muB$, in the 3-d metal-benzene series. In multi-decker complexes involving V2(Bz)3 and Fe2(Bz)3, the metal atoms are found to couple antiferromagnetically. In addition, their dissociation energies and ionization potentials are reduced from those in corresponding M(Bz)2 complexes. All these results agree well with available experimental data and demonstrate the important role the organic support can play on the properties of metal atoms clusters.

35. A. K. Kandalam, M. A. Blanco, and R. Pandey,
Theoretical study of structural and vibrational properties of Al3N3, Ga3N3, and In3N3,
J. Phys. Chem. B 105 (2001) 6080-6084.

Download a reprint: JPCB105-6080-ov-KB2001-Nclusters.pdf.

We report the results of a theoretical study of the nitride trimers (i.e. M3N3 with M = Al, Ga, In) focusing on their structure, stability, and vibrational properties. The calculated results reveal a distinct structural difference between the most stable isomers of Al and those of Ga and In, which can be explained in terms of the evolution of the relative strengths of metal-nitrogen and metal-metal bonds in going from Al to Ga to In. It is also shown that the strength of the nitrogen-nitrogen bond still dominates the preferred fragmentation path for these clusters, and that fragmentation occurs at a lower energy than ionization. Assignments to the frequencies of the various normal modes are made in terms of those of the MN monomers (Al3N3), or in terms of those of weakly bonded M3 and N3 subunits (Ga3N3 and In3N3).

36. V. Luaña, J. M. Recio, A. Martín Pendás, M. A. Blanco, L. Pueyo, and R. Pandey,
Practical Embedding for Ionic Materials. I. Crystal adapted pseudopotentials for the MgO crystal,
Phys. Rev. B 64 (2001) 104102-1-11.

Download a reprint: PRB64-104102-ov-LR2001-caps1.pdf.

We present a new method of deriving Effective Core Potentials (ECP) for negative and positive ions. The new ECPs are adapted to ionic crystals and can be used as components of an embedding model in most Quantum Chemistry codes. Cluster-in-the-lattice calculations of several defects and impurity centers in MgO are examined as a test.

37. E. Francisco, A. Costales, and A. Martín Pendás,
Structure and bonding in magnesium difluoride clusters: The MgF2 molecule,
J. Phys. Chem. A 105 (2001) 4126-4135.

Download a reprint: JPCA105-4126-ov-FC2001-MgF2.pdf.

doi locator: doi:10.1021/jp0041656.

We have calculated the ground state geometry, vibrational frequencies, and bonding properties of MgF2 at the Hartree-Fock (HF), second-order (MP2), and fourth-order M\oller-Plesset (MP4(SDTQ)) levels of calculation. Several high-quality basis sets have been used, with special attention on the influence of polarization and diffuse functions on the above properties. The best HF and MP2 calculations predict that MgF2 is a linear molecule. MP2 and MP4 results are very similar. The MP2 symmetric ($\nu1$) and asymmetric ($\nu3$) stretching frequencies are about 5-7 % smaller than the HF values and agree well with the observed data. The MP2 $\nu2$ (bending) frequency is close to that found in other ab initio calculations and the experimental gas-phase value, but is 80 cm-1 smaller than the value observed in the IR spectrum of MgF2 trapped in solid argon. Polarization functions shorten noticeably the magnesium-fluorine equilibrium distance and increase $\nu1 and \nu3$. An Atoms in Molecules (AIM) analysis of the wavefuncions reveals that MgF2 is a highly ionic molecule, the net charge of Mg being about +1.8 e, and that most basis set effects are due to the poor convergence properties of the atomic electron dipole moments. This suggests a polarizable ions model that is shown to account for the trends found in most of the properties studied. The origin of the bending problem in these compounds is traced back to the polarizability of the cation.

38. Paula Mori-Sánchez, R. Franco, A. Martín Pendás, V. Luaña, and J. M. Recio,
Microscopic analysis of the compressibility in the spinel phase of Si3N4,
Europhys. Lett. 54 (2001) 760-766.

Quantum mechanical static simulations of the high-pressure spinel phase of Si3N4 have been performed to determine the unit cell geometry and the equation of state from 0 to 50 GPa. The application of the Bader theory to the ab initio electron density leads to quantum consistent atomic charges and volumes, the crystalline bonding graph, and the prediction of a highly ionic bonding. The computed thermodynamic properties have been interpreted in terms of the local behaviour of the Si and N quantum subgroups and constitutive unit cell polyhedra. We show that: (i) the bulk compressibility can be estimated from the average of the tetrahedral and octahedral compressibilities, and (ii) the N response to pressure controls the macroscopic behaviour. The conclusions of this work can be useful in the search of very hard, N-based materials.

39. J. M. Recio, R. Franco, A. Martín Pendás, Miguel A. Blanco, L. Pueyo, and Ravindra Pandey,
Theoretical explanation of the uniform compressibility behavior observed in oxide spinels,
Phys. Rev. B 63 (2001) 184101-1-7.

Download a reprint: PRB63-184101-ov-RF2001-UniformCompress.pdf.

doi locator: doi:10.1103/PhysRevB.63.184101.

Simple algebraic equations show that the bulk compressibility in spinel-type compounds can be expressed by means of cation-oxide polyhedra compressibilities and a term that accounts for the pressure effect on the internal oxygen position in the unit cell. The equations explain (i) the difference of compressibilities at octahedral and tetrahedral sites, (ii) why the macroscopic bulk modulus can be estimated as the average of these polyhedra bulk moduli, and (iii) the uniform behavior found in oxide spinels under hydrostatic pressure. Quantum-mechanical ab initio Perturbed Ion (aiPI) results on the MgAl2O4, ZnAl2O4, ZnGa2O4, and MgGa2O4 direct spinels and on the MgGa2O4 inverse spinel are reported to illustrate the interpretative capabilities of the proposed equations.

40. Paula Mori-Sánchez, A. Martín Pendás, and V. Luaña,
Polarity inversion in the electron density of BP crystal,
Phys. Rev. B 63 (2001) 125103-1-4.

Download a reprint: PRB63-125103-ov-MP2001-BP.pdf.

A rigorous analysis of the electron density of the BP crystal in the light of the Atoms in Molecules theory reveals very unusual properties. The standard polarity, B$\delta+P\delta-$, found at the zinc-blende equilibrium geometry suffers a reversal under the application of hydrostatic pressure. The inversion occurs through an intermediate situation in which the P valence shell is transferred to a non-nuclear maximum before being caught by the B atom.

41. V. Luaña, A. Martín Pendás, A. Costales, Gabino A. Carriedo, and Francisco J. García-Alonso,
Topological analysis of chemical bonding in cyclophosphazenes,
J. Phys. Chem. A 105 (2001) 5280-5291.

Download a reprint: JPCA105-5280-ov-LP2001-Phosphazenes.pdf.

Chemical bonding in the cyclophosphazenes is studied from the point of view of Bader's Atoms in Molecules (AIM) theory. To that end, HF/6-31G** ab initio calculations are done on a collection of (NPX2)3 derivatives for a wide set of -X substituents, and its electron density, $\rho(\vecr)$, and pair density, $\rho(2)(\vecr1,\vecr2)$, are obtained and analyzed. The (NP)3 ring geometry and bonding properties are basically maintained along the cyclotriphosphazenes. The PN distance and the bond critical point properties (electron density, Laplacian, etc) lie in between those of XNPX3, formally a double NP bond, and those of X2NPX4, formally a single NP bond, being much closer to the former than to the latter. The Laplacian of the electron density shows the PN bond to be highly polar, with a clear tendency of the P atoms to lose almost all of their five valence electrons, and a significant concentration of charge along the PN line, even though within the N basin. The charge on the ring N basins, $\calQ$(N), remains almost invariant, $-2.3~e$, in all cyclotriphosphazenes, whereas the charge of the ring P basin, $\calQ$(P), varies from $+2.9 to +4.0~e$, depending on the electronegativity of the -X group. There is an inverse correlation between $\calQ$(P) and the PN distance, the more electronegative -X groups shrinking the (NP)3 ring more, even though only slightly. The partition of the pair densities indicates that some 0.63 electron pairs are shared between each P and its two N neighbors in the ring, this value being typical of a polar but largely ionic bonding situation. The three N atoms in the ring share 0.20 electron pairs per N-N group, a small but significant amount, even though no bond path line occurs linking them. The 3D contour surfaces of $\nabla2\rho$ clearly depict the molecular regions having a Lewis basic or acidic character. Ring N atoms behave as weak Lewis bases, whereas ring P atoms are preferred sites for a nucleophillic attack tending to remove, perhaps ionically, a -X group. These topological properties do explain the chemistry of cyclophosphazenes and agree well with the available experimental densities. The AIM analysis supports the main conclusions from the traditional Dewar's model of phosphazenes.

42. E. Francisco, M. A. Blanco, and G. Sanjurjo,
Atomistic simulation of SrF2 polymorphs,
Phys. Rev. B 63 (2001) 094107-1-9.

doi locator: doi:10.1103/PhysRevB.63.094107.

Atomistic simulations using crystal consistent electron gas interionic potentials (CCEGIP) have been performed to determine the geometrical structure and the equation of state (EOS) of the fluorite (C1) and orthorrombic (C23) crystalline phases of SrF2. Thermal effects are taken into account by means of a quasi-harmonic Debye model. The results for the zero pressure cell parameter (a0), lattice energy (E$\mathrmlatt$), and bulk modulus (B0) of the C1 phase are in excellent agreement with the experiment. Regarding the C23 phase, we report for the first time the optimized cell parameters and six internal coordinates for presssures (p) from 0 to 20 GPa. At zero-p, the results agree very well with those determined trough the ab initio Perturbed Ion model.

43. Ravindra Pandey, M. C. Ohmer, Aurora Costales, and J. M. Recio,
Modelling of the properties of dopants in the NLO semiconductor CdGeAs2,
Mat. Res. Soc. Symp. Proc. 607 (2000) 471-476.

The results of a shell-model study on CdGeAs2 doped with Cu, Ag, B, Al, Ga, and In are presented here. The pairwise interatomic potential terms representing the interaction of dopants with the host lattice ions are derived using first principle methods while empirical fitting methods are used for the host-lattice potentials. Defect calculations based on Mott-Littleton methodology predict small binding energies for Cu and Ag substituting Cd in the lattice which are in agreement with the available experimental data. The group III dopants (i.e. B. Al, Ga, and In) at the Ge site are predicted to have large binding energies for a hole placing acceptor levels in the middle of the band gap.

44. A. Martín Pendás, A. Costales, M. A. Blanco, J. M. Recio, and V. Luaña,
Local compressibilities in crystals,
Phys. Rev. B. 62 (2000) 13970-13978.

Download a reprint: PRB62-13970-ov-PC2000-local-compress.pdf.

The application of the Atoms in Molecules theory to the partition of static thermodynamical properties in condensed systems is presented. Attention is focused on the definition and the behavior of atomic compressibilities. Bulk moduli are found to be simple weighted averages of atomic compressibilities, and two kind of systems are investigated as examples: four related oxide spinels and the alkali halides family. Our analyses show that the puzzling constancy of the bulk moduli of these spinels is a statement of the value of the compressibility of an oxide ion. A functional dependence between ionic bulk moduli and ionic volume is also proposed.

45. Miguel A. Blanco, J. M. Recio, A. Costales, and and Ravindra Pandey,
Transition path for the B3---B1 phase transformation in semiconductors,
Phys. Rev. B 62 (2000) R10599-10602.

A symmetry-based, non-displacive mechanism for the first-order B3---B1 phase transition exhibited by many binary semiconductors is proposed. Using a single-molecule R3m unit cell, the energetic and dynamical features of the transformation are disclosed along a transition path characterized by the internal coordinate, the lattice constant, and the rhombohedral angle. First-principles calculations on the wide-gap semiconductor ZnO are performed to illustrate the attainments of the proposed mechanism. Computed potential energy surfaces and Bader analysis of the electronic density are used to describe the atomic rearrangements, the energy profile along the transition coordinate, and the effects of the external pressure on this profile. The geometry and energy of the transition state are determined, and the bonding details of the transformation identified. The proposed mechanism explains the change in coordination from 4 (B3) to 6 (B1), the less covalent Zn-O bond in the B1 structure, and the transformation of ZnO from a direct-gap (B3) to an indirect-gap (B1) material.

46. M. A. Blanco, A. Costales, A. Martín Pendás, and V. Luaña,
Ions in crystals: The topology of the electron density in ionic materials. V. The B1-B2 phase transition in alkali halides,
Phys. Rev. B. 62 (2000) 12028-12039.

We have applied Bader's topological analysis to the study of the B1-B2 phase transition in the alkali halides. Our results shed a new light upon the phase stability rules of the traditional ionic model: by using topological ionic radii, a connection between the topologies of the electron density and the energy surface is found. The topological description of the transition that emerges puts an emphasis on the creation of two new bond points in passing from coordination 6 to 8, and makes a unique definition of structural change. As we have found in previous papers, topological isomerization, as a case of structural change, is mainly dominated by geometric relations involving topological ionic radii. Further relations between the structural diagram and the energy surface features are also investigated.

47. H. Jiang, A. Costales, M. A. Blanco, Mu Gu, R. Pandey, and J. D. Gale,
Theoretical study of native and rare-earth defect complexes in $\beta$-PbF2,
Phys. Rev. B. 62 (2000) 803-809.

doi locator: doi:10.1103/PhysRevB.62.803.

Native and rare-earth-doped point-defects in $\beta$-PbF2 are studied in the framework of the pair-potential approximation coupled with the shell model description of the lattice ions. For the perfect lattice, a new set of potential parameters are obtained which reproduce structure, elastic and dielectric constants of PbF2 very well. The calculated formation energies for native defects suggest that the anion Frenkel disorder is preferred over the cation Frenkel and Schottky-like disorder in PbF2. The computed temperature behavior of the ionic conductivity agrees very well with the available experimental data. In the rare-earth doped PbF2, a site-preference of the charge-compensating fluorine interstitial appears to change from nearest to next-nearest neighbor with the increase in the rare-earth ionic radius.

48. T. Arlt, M. Bermejo, M. A. Blanco, L. Gerward, J. Z. Jiang, J. Staun Olsen, and J. M. Recio,
High-pressure polymorphs of Anatase TiO2,
Phys. Rev. B. 61 (2000) 14414-14419.

Download a reprint: PRB61-14414-ov-AB2000-TiO2.pdf.

doi locator: doi:10.1103/PhysRevB.49.69.

The equation of state of anatase TiO2 has been determined experimentally -- using polycrystalline as well as single-crystal material -- and compared with theoretical calculations using the ab initio Peturbed Ion model. The results are highly consistent, the zero-pressure bulk modulus being 179(2) GPa from experiment and 189 GPa from theory. Single-crystal tetragonal anatase transforms to the orthorhombic $\alpha$-PbO2 structure at about 4.5 GPa. This transition is suppressed in the polycrystalline material at room temperature, probably due to the presence of grain boundaries and other crystal defects. Polycrystalline anatase is found to transform to the monoclinic baddeleyite structure at about 13 GPa. Upon decompression, the baddeleyite phase transforms to the $\alpha$-PbO2 phase at about 7 GPa. The experimental zero-pressure bulk moduli are 258(8) GPa for the $\alpha$-PbO2 phase and 290(10) GPa for the baddeleyite phase.

49. A. Costales, A. K. Kandalam, A. Martín Pendás, M. A. Blanco, J. M. Recio, and R. Pandey,
First principles study of polyatomic clusters of AlN, GaN, and InN. Part II - Chemical bonding,
J. Phys. Chem. B 104 (2000) 4368-4374.

Download a reprint: JPCB104-4368-ov-CK2000-Nclusters.pdf.

doi locator: doi:10.1021/jp994309k.

In this paper we study the chemical bonding of the small (monomer, triatomic, and dimer) neutral clusters of AlN, GaN, and InN presented earlier in paper I. It includes the analysis of the topology of the electron density and its Laplacian, together with relevant atomic properties, in the light of the Theory of Atoms in Molecules. The most prominent feature of the bonding here, the existence of strong N-N bonds, is seen to diminish with the increase of the number of metal atoms and the degree of ionicity. The Al-N bond shows a large transfer of charge, but also a significant deformation of the Al electron shells, so it can be understood as a highly polar shared interaction. On the other hand, Ga-N and In-N bonds are non-shared interactions, with smaller charge transfers and polarizations. In all the cases, the existence of a N-N bond weakens the metal-N bond. The bonding picture that emerges depends only on the reliability of the electron densities, and it is consistent with the conclusions of our previous work in paper I.

50. A. K. Kandalam, R. Pandey, M. A. Blanco, A. Costales, J. M. Recio, and J. M. Newsam,
First principles study of polyatomic clusters of AlN, GaN, and InN. Part I - Structure, Stability, Vibrations and Ionization,
J. Phys. Chem. B 104 (2000) 4361-4367.

Download a reprint: JPCB104-4361-ov-KP2000-Nclusters.pdf.

First principles calculations based on the non-local density approximation to the density functional theory were performed to study structures, stabilities and vibrational properties of small (monomer, triatomic and dimer) neutral and ionized clusters of AlN, GaN, and InN. As a general trend, triatomic isomers prefer doublet spin states whereas triplets are predicted for the monomer and the linear dimer clusters. Both nitrogen-excess and metal-excess triatomic clusters show minimum energy configurations to be approximately linear. The most stable isomer of Al2N2 and Ga2N2 is a rhombus with a singlet spin state, though In2N2 is predicted to be not stable against dissociation into In2 and N2. A strong dominance of the N-N bond over the metal-nitrogen and metal-metal bonds appears to control the structural skeletons and the chemistry of these clusters. This is manifested in the dissociation of neutral and singly-ionized clusters where the loss of metal atoms is shown to be the most likely fragmentation channel, except in the case of the dimer, in which the formation of two homonuclear diatomics is favored. The vibrational modes and frequencies are also explained in terms of the different bond strengths found in the diatomic clusters.

51. A. Costales, M. A. Blanco, R. Pandey, and J. M. Recio,
Theoretical characterization of the high pressure phases of PbF2,
Phys. Rev. B 61 (2000) 11359-11362.

doi locator: doi:10.1103/PhysRevB.61.11359.

Ab initio Perturbed Ion calculations were performed for the cubic, orthorhombic, hexagonal, and monoclinic phases of PbF2. A complete characterization of these phases was achieved in terms of the potential energy surfaces, the equations of state, and the phase-transition pressures. Thermal effects were included via a quasi-harmonic non-empirical Debye model. The internal parameters of the unit cell of each phase were reoptimized at each volume to generate the energy surface. The calculated results are in good agreement with the experimental data available for the cubic and orthorhombic phases. The results predict the hexagonal phase to be the high-pressure post-cotunnite structure for PbF2, since the monoclinic phase is seen to collapse into the hexagonal phase during the optimization at high pressures.

52. K. Xiang, R. Pandey, J. M. Recio, E. Francisco, and J. M. Newsam,
A theoretical study of the cluster vibrations in Cr2O2, Cr2O3, and Cr2O4,
J. Phys. Chem. A 104 (2000) 990-994.

We report the results of first principles calculations on the Cr$\rm{2}O\rm{2}$, Cr$\rm{2}O\rm{3}$, and Cr$\rm{2}O\rm{4}$ clusters for which some of the considered configurations were proposed in the recent infrared spectroscopy experiments (J. Chem. Phys. 107, 2798 (1997)). Both linear and ring-like isomers are predicted to be equally probable for Cr2O2 while the (Cr2O2)O isomer is preferred over the chain-like (OCrOCrO) isomer for Cr2O3. For Cr2O4, a clear preference for the O(Cr2O2)O isomer over the (CrO2)2 isomer is predicted. Calculations of the vibrational frequencies for the lowest-energy isomers of these clusters yield the stretching mode involving the stronger Cr-O bond to be around 900-1000 cm-1 and the bending mode involving the puckered-ring to be around 550-700 cm-1. Overall, the calculated normal modes of the cluster vibrations provide a very satisfactory description of the observed IR spectrum of the chromia clusters.

53. P. Zapol, Ravindra Pandey, M. Seel, J. M. Recio, and M. C. Ohmer,
Density functional study of the structure, thermodynamics, and electronic properties of CdGeAs2,
J. Phys.: Condens. Matter. 11 (1999) 4517-4526.

Structural, thermodynamic and electronic properties of CdGeAs2 with chalcopyrite structure are investigated in the framework of density functional theory. We employ the linear combination of atomic orbitals method with the Gaussian basis sets and present the results for the equation of state, the Gruneisen constant, the electronic band structure and the pressure coefficients of the valence and conduction levels in CdGeAs2.

54. Ravindra Pandey, Julian D. Gale, Suresh K. Sampath, and J. M. Recio,
Atomistic simulation study of spinel oxides: zinc aluminate and zinc gallate,
J. Amer. Ceram. Soc. 82 (1999) 3337-3341.

Stoichiometric zinc aluminate (ZnAl2O4) and zinc gallate (ZnGa2O4) are simulated in the framework of the shell model for wich a new set of two-body interatomic potential parameters were developed. Using these parameters, a reasonable prediction is made for elastic and dielectric constants of ZnAl2O4 and ZnGa2O4. Both oxides are found to be stable against the decomposition to the component oxides. The fitting of the potential energy surface of these oxides to equation of state yields the bulk modulus and its pressure derivatives. The bulk modulus is predicted higher in ZnAl2O4 as compared to that of ZnGa2O4, whereas its pressure derivative remains the same in both oxides. On the other hand, the octahedral and tetrahedral volumes of ZnGa2O4 are higher than those of ZnAl2O4. These differences in the compressibility behavior can be attributed to the size difference between Al+3 and Ga+3 in the spinel oxides considered here. The calculated formation energies of native defects suggest the preference of disorder in the cation sublattice over the Schottky and Frenkel defects. Although the degree of disorder is expected to be small, it is likely to influence the vacancy population in the lattice. Finally, deviations from stoichiometric are considered in which a preference for the dissolution of Al2O3/Ga2O3 via the formation of zinc vacancies is predicted relative to that of ZnO in ZnAl2O4/ZnGa2O4.

55. V. Luaña, A. Costales, A. Martín Pendás, and L. Pueyo,
Ionic properties of perovskites derived from topological analysis of their wave function,
J. Phys.: Condens. Matter 11 (1999) 6329-6336.

We present in this work a discussion on the quantitative bonding information that can be deduced from the topological analysis of the crystal wave function of 120 alkali halide perovskites. The formalism, recently presented, is a development of the theory of atoms in molecules of Bader into the domain of crystalline materials. We discuss the shape of the ions and show how the classical picture in terms of slightly deformed spheres is contained in the topological description. The nature of the chemical bond in these systems is depicted by means of graphical representation of the electron density and its Laplacian along the surfaces of the attraction basins. The ionicity of the crystals and the behaviour of the ionic radii are also briefly reviewed.

56. A. Martín Pendás, Miguel A. Blanco, A. Costales, Paula Mori-Sánchez, and V. Luaña,
Non-nuclear maxima of the electron density,
Phys. Rev. Lett. 83 (1999) 1930-1933.

Download a reprint: PRL83-1930-ov-PB99-NNM.pdf.

Simple arguments and quantum mechanical calculations are used to analyze the occurrence of non-nuclear maxima (NNMs) in the electron density of crystals and molecules. The recent controversy concerning the experimental detection of NNMs in Be and Si is thus clarified, and they are shown to be a normal step in the evolution of chemical bonding of homonuclear groups as internuclear distances decrease.

57. M. A. Blanco, J. M. Recio, E. Francisco, A. Costales, V. Luaña, and A. Martín Pendás,
Strategies for determining and using ab initio interionic potentials,
Radiation Effects and Defects in Solids 151 (1999) 223-228.

In this contribution, we discuss two techniques for determining interionic potentials from quantum-mechanical descriptions of ions in crystals. The first one is based on the use of the energy expressions supplied by the Theory of Electronic Separability, as implemented in the ab initio Perturbed Ion (\it{ai\/}PI) method. The second one relies on the ionic electron densities generated by means of the \it{ai\/}PI model and the Electron Gas theory of Gordon and Kim. \par In ionic solids, the many body contributions mainly arise due to the changes of the ionic electron densities in passing from the gas-phase to the crystal. We present several schemes to deal with these self-energy terms, both as a separate contribution to the total energy and as an implicit term in the pair potentials. Finally, we compare the results of the different schemes, showing that the inclussion of the self-energy dependence on crystal strains is crucial in the determination of sensible properties like phase transition pressures.

58. Ravindra Pandey, M. C. Ohmer, Aurora Costales, and J. M. Recio,
Atomistic calculations of dopant binding energies in ZnGeP2,
Mat. Res. Soc. Symp. Proc. 484 (1998) 525-530.

Atomistic modelling has been applied to study various cation dopants, namely Cu, Ag, B, Al, Ga and In in ZnGeP2. The pairwise interatomic potential terms representing the interaction of dopants with the host lattice ions are derived using first principle methods. Defect calculations based on Mott-Littleton methodology predict small binding energies for Cu and Ag substituting Zn in the lattice which are in agreement with the available experimental data. The group III dopants (i.e. B, Al, Ga and In) at the ge site are predicted to have large binding energies for a hole except B which shows a distinct behavior. This may be due to large mismatch in atomic sizes of B and Ge. At the Zn site, the calculated binding energies of the group III dopants place donor levels in the middle of the band gap.

59. Sundar Veliah, Kai-hua Xiang, Ravindra Pandey, J. M. Recio, and John M. Newsam,
Density Functional Study of Chromium Oxide Clusters: Structures, Bonding, Vibrations and Stability,
J. Phys. Chem. B 102 (1998) 1126-1135.

We report the results of density functional theory calculations on chromium oxide clusters responding to the formula Cr$\rm mO\rm n$ (m=1-2, n=1-3). Double numeric basis sets supplemented by polarization functions have been used in both the local and non-local spin density approximation. Geometry optimizations of different spin states have been performed at the unrestricted spin level for the selected initial configurations. We have found that the covalent polarized Cr-O bonds dominate the chemical description of the CrO$\rm n$ series, while for the Cr2O$\rm n$ series the presence of the Cr-Cr bond reduces the metal to oxygen charge transfer yielding much softer clusters, as reflected by the smaller HOMO-LUMO gaps. The stability of all the isomers has been checked by computing their harmonic vibrational frequencies and the energetics of different fragmentation paths. The calculations reveal that the linear isomers are not true minima and that the oxygen-rich clusters are preferred over the metal-rich clusters. Overall, our results show good agreement with the available experimental data in terms of geometrical parameters, vibrational frequencies, atomization energies and fragmentations for the CrO$\rm n$ clusters. For the Cr2O series, our computed values are discussed in connection with recent infrared spectroscopy measurements and with available data in analogous metal oxide clusters.

60. J. M. Recio, M. A. Blanco, V. Luaña, R. Pandey, L. Gerward, and J. Staun Olsen,
Compressibility of the high-pressure rock-salt phase of ZnO,
Phys. Rev. B. 58 (1998) 8949-8954.

Download a reprint: PRB58-8949-ov-RB98-ZnO.pdf.

We report the results of a combined experimental and theoretical investigation on the stability and the volume behavior under hydrostatic pressure of the rock-salt (B1) phase of ZnO. Synchrotron-radiation X-ray powder diffraction data are obtained from 0 to 30 GPa. Static simulations of the ZnO B1 phase are performed using the ab initio Perturbed Ion method and the local and non-local approximations to the density functional theory. After the pressure induced transition from the wurtzite phase, we have found that a large fraction of the B1 high-pressure phase is retained when pressure is released. The metastability of this ZnO polymorph is confirmed through the theoretical evaluation of the Hessian eigenvalues of a nine parameter potential energy surface. This allows to treat the experimental and theoretical pressure-volume data on an equal basis. In both cases, we have obtained values of the bulk modulus in the range of 160-194 GPa. For its zero pressure first derivative, the experimental and theoretical data yield a value of 4.4$\pm$1.0. Overall, our results show that the ZnO B1 phase is slightly more compressible than previously reported.

61. A. Martín Pendás, Aurora Costales, and Víctor Luaña,
Ions in crystals: the topology of the electron density in ionic materials .III. Geometry and ionic radii,
J. Phys. Chem. B 102 (1998) 6937-6948.

We present the application of Bader's topological analysis of the electron density to geometric properties in ionic materials. Particular attention is paid to the concept of ionic radius, in relation to the shapes of ions in crystals, and to the various correlations among atomic properties, i.e. electronegativities, deformabilities, etc, that it induces. Using a simple model to fit our results to a theoretical frame, we show that ionic bonds display properties in complete parallelism to those known in covalent bonds. This allows us to define unambiguosly the strength of an ionic bond, which is found to correspond to Pauling's bond valence.

62. R. Franco, J. M. Recio, and L. Pueyo,
Ab initio perturbed ion description of the equation of state and a high pressure phase transition of Al2O3,
J. Mol. Struct. (Theochem) 426 (1998) 233-240.

The electronic structure, equilibrium geometry, and equation of state of Al2O3 in the $\alpha$-Al2O3 and Rh2O3(II) phases have been determined by means of the ab initio Perturbed Ion method augmented by a recently developed non-empirical Debye-like model for describing the vibrational thermal effects. A systematic multidimensional optimization of the structural parameters has been completed for the two phases from zero to 2200~K, and pressures up to 70~GPa for the $\alpha$-Al2O3 phase, and 20~GPa for the high pressure phase. our structural results are in good agreement with the experimental information available. Although the $\alpha$-Al2O3 phase is more stable in the static (p=T=0) description, a pressure-induced phase transition is detected at room temperature near 4~GPa. The critical pressure pc increases very slightly with temperature, being about 5.5~GPa at 1000~K. This value is consistent with the phase transition found in Rh2O3 by Shannon and Prewitt [Journal of Solid State Chemistry \textbf2, (1970) 134] at pc 6.5~GPa. Furthermore, the $\alpha$-Al2O3 phase shows a slight pressure-induced anisotropy, since the c/a ratio decreases from 2.638 at zero pressure, to 2.474 at 70~GPa. Also, according to our calculations, the crystal maintains its symmetry and reduces moderately its compressibility in the high temperature regime. The present methodology gives detailed structural information on phase transitions of the type described in this work, as well as a meaningful description of the high pressure phase, a task rather difficult to undertake in the laboratory.

63. E. Francisco, J. M. Recio, M. A. Blanco, A. Martín Pendás, and A. Costales,
Quantum-Mechanical Study of Thermodynamic and Bonding Properties of MgF2,
J. Phys. Chem. A 102 (1998) 1595-1601.

doi locator: doi:10.1021/jp972516j.

The structural and thermodynamic properties of MgF2 have been investigated in a wide range of pressures (0-80 GPa) and temperatures (0-850 K) by coupling quantum-mechanical Ab Initio Perturbed Ion calculations with a quasi-harmonic Debye model. The room-T, zero-p structural parameters and lattice energy are computed with errors smaller than 2% when correlation energy corrections are incorporated in the calculation. Our computed equation of state (EOS) is compatible with direct measurements of the bulk modulus and obeys universal p-V relations. We have simulated the rutile-to-fluorite phase transition during the loading process and have found lower ($\simeq $4 GPa) and upper ($\simeq$ 45 GPa) bounds for the transition pressure by means of thermodynamic and mechanical criteria for phase stability. Bonding properties and their change with pressure have been derived through a topological analysis of the electron density using Bader's \em Atoms in Molecules theory. This analysis reveals that MgF2 is a highly ionic compound. Its ionicity decreases linearly with increasing pressure and, as in other ionic compounds, the crystal shows anion-anion bonds.

64. A. Martín Pendás, J. M. Recio, E. Francisco, and Víctor Luaña,
Universal-binding-energy relations across the rock-salt cesium-chloride phase transition in alkali halides,
Phys. Rev. B 56 (1997) 3010-3015.

Download a reprint: PRB56-3010-ov-PR97-uber.pdf.

The fulfillment of universal-binding-energy relations across the rock-salt (B1) cesium chloride (B2) phase transition in alkali halides is analyzed from a first principles point of view. We show that extensive ab initio quantum-mechanical calculations fully support the existence of universality in both intraphase intersystem and intrasystem interphase phenomena. For the latter problems, it is found that the fundamental requirement for a universal law to simultaneously describe both phases and the unstable intermediate steps along the transition path is the topological equivalence of the Gibbs energy profile at the B1 and B2 points. Several simple relations between thermodynamic quantities of both phases are put forward and discussed in reference to our theoretical data and their interest in experimental research.

65. A. Martín Pendás, A. Costales, and V. Luaña,
Ions in crystals: the topology of the electron density in ionic materials. I. Fundamentals,
Phys. Rev. B 55 (1997) 4275-4284.

Download a reprint: PRB55-4275-ov-PC97-AIM1.pdf.

The topological theory of Atoms in Molecules is applied to periodic crystalline ionic systems. A systematic investigation of the fundamental properties of the topology of the charge density in crystals is undertaken, and several basic facts, peculiar to the solid state, and not previously explored, are put forward. We also show how the theory allows us to define unambiguously very important concepts of solid state theory, like the coordination index or the coordination polyhedron of an ion in a solid. We particularize our results by means of the detailed study of an example crystal, the rock-salt phase of LiI. It is shown that this crystal is best described as made up of 18-fold coordinated iodides and 6-fold coordinated lithiums, contrary to the usual 6-6 description.

66. V. Luaña, A. Costales, A. Martín Pendás, M. Flórez, and V. M. García Fernández,
Structural and chemical stability of halide perovskites,
Solid State Commun. 104 (1997) 47-50.

The ab initio Perturbed Ion (aiPI) quantum mechanical method is used to study the solid state reaction: AX + MX2 --- AMX3 from a thermodynamical point of view. The reaction energy is first determined by means of static calculations (i.e. at null absolute temperature) on the ideal cubic structures of the components. The very difficult problem of determining the most stable crystal structure of a compound is then undertaken by examining the differences in energy among many structures reported for AX, MX2 and AMX3 compounds. Finally, the reaction reaction energy is again examined in the light of those corrections, and the results are used to analyze the experimental data available on the synthesis of perovskites.

67. V. Luaña, A. Costales, and A. Martín Pendás,
Ions in crystals: the topology of the electron density in ionic materials. II. The cubic alkali halide perovskites,
Phys. Rev. B 55 (1997) 4285-4297.

Download a reprint: PRB55-4285-ov-LC97-AIM2.pdf.

We present here the topological (Bader) analysis of the electronic structure for 120 cubic perovskites AMX3 (A: Li, Na, K, Rb, Cs; M: Be, Mg, Ca, Sr, Ba, Zn; X: F, Cl, Br, I). The perovskite being perhaps the simplest and most abundant structure for ternary compounds, we have found up to seven different topological schemes for the electronic density. Those schemes can be simply arranged and explained in terms of ratios of topologically defined ionic radii. However, no set of empirical radii, or even of best fitted radii, can accomplish the same objective. All crystals do present M-X and A-X bonds, many have X-X too, and only CsSrF3 and CsBaF3 have A-A bonds. The topology and geometry of the electronic density has been further analyzed by depicting the shape of the attraction basins of the ions. Basins have polyhedral shapes and can be simply predicted, in most cases, after the knowledge of the bonds that the ion forms. M2+ basins do present, however, bizarre nearly bidimensional wings on those topological schemes lacking X-X bonds. Lattice energy has been found to be dominated by coulombic interactions and determined by the crystal size more than by the electronic topological scheme, although the influence of the electronic density at the M-X bond critical point is also observed. The stability of the perovskite structure with respect to the decomposition into MX2 + AX has been found to be mostly governed by the M2+ cation, the crystals having small M2+ and large A+ ions being the most stable ones. There is also a clear tendency for the crystals lacking X-X bonds, and having bizarre M2+ shapes, to decompose.

68. M. A. Blanco, V. Luaña, and A. Martín Pendás,
Quantum mechanical cluster calculations of ionic materials: Revision 10 of the ab initio Perturbed Ion program,
Comput. Phys. Commun. 103 (1997) 287-302.

69. M.A. Blanco, M. Flórez, and M. Bermejo,
Evaluation of the rotation matrices in the basis of real spherical harmonics,
J. Mol. Struct. (Theochem) 419 (1997) 19-27.

Download a reprint: Theochem419-19-ov-BF97-rotation-matrices.pdf.

Rotation matrices (or Wigner D functions) are the matrix representations of the rotation operators in the basis of the spherical harmonics. They are the key entities in the generation of symmetry-adapted functions by means of projection operators. Although their expression in terms of ordinary (complex) spherical harmonics and Euler rotation angles is well known, an alternative representation using real spherical harmonics is desirable. The aim of this contribution is to obtain a general algorithm to compute the representation matrix of any point-group symmetry operation in the basis of the real spherical harmonics, paying attention to the use of recurrence relations that allow the treatment of functions with high angular momenta.

70. R. Franco, M. A. Blanco, A. Martín Pendás, E. Francisco, and J. M. Recio,
Atomistic simulation of the pressure-temperature-volume diagram in $\alpha-$Al2O3,
Solid State Commun. 98 (1996) 41-44.

We report the results of a theoretical investigation that explores for the first time temperature effects on the pressure-volume relationship in corundum. The ionic interactions within the $\alpha$-Al2O3 crystal are modelized using the electron gas formalism along with electronic wavefunctions that are allowed to relax with crystal strains. A non-empirical Debye model is applied to account for the thermal contributions. Our study reveals that the crystal responds isotropically under both high-temperature and high-pressure conditions. Good agreement with hydrostatic and quasi-hydrostatic experimental data is achieved.

71. M. A. Blanco, A. Martín Pendás, E. Francisco, J. M. Recio, and R. Franco,
Thermodynamical properties of solids from microscopic theory: applications to MgF2 and Al2O3,
J. Mol. Struct. (Theochem) 368 (1996) 245-255.

72. A. Martín Pendás, J. M. Recio, M. Flórez, M. A. Blanco, and E. Francisco,
Stability of B1 and B2 phases from electronic density topology considerations,
Radiation Effects and Defects in Solids 134 (1995) 201-203.

It is preliminary reported how the consideration of the topology of the electronic density of B1 and B2 phases of alkali halides, obtained via quantum mechanical simulation, makes it possible to connect the stability or metastability of the lattices with geometrical factors. The latter turn out to validate the classical ionic model and some of the most controversial critics posed against it over the years.

73. V. Luaña, M. A. Blanco, M. Flórez, A. Martín Pendás, and L. Pueyo,
Static simulations of Cu+ centers in alkali halides,
Radiation Effects and Defects in Solids 134 (1995) 47-50.

Quantum-mechanical calculations and atomistic simulations were used to characterize the local geometry, stability and resonant vibrations of CuA centers in alkali halides.

74. D. J. Groh, R. Pandey, and J. M. Recio,
Local Relaxations and Optical Properties of Cr+3 in MgO,
Radiation Effects and Defects in Solids 134 (1995) 127-131.

75. R. Franco, J. M. Recio, A. Martín Pendás, E. Francisco, V. Luaña, and L. Pueyo,
Theoretical study of the coordination of the Cr+3 ion in $\alpha$-Al2O3,
Radiation Effects and Defects in Solids 134 (1995) 123-126.

The local arrangement of a substitutional Cr+3 ion for an Al+3 ion in corundum was studied by first-principles pairwise simulations and quantum-mechanical ab initio Perturbed Ion calculations The authors' study is organized in two steps. First, the authors determine the cohesive properties of the host lattice by calculating the set of four crystal parameters that makes minimum the total energy of corundum. Secondly, the authors solve cluster models of increasing complexity centered at the Cr+3 site and embedded in the previously computed crystal potential. This is a consistent strategy that contributes to determine the local geometry of Cr+3 in $\alpha$-Al2O3.

76. E. Francisco, J. M. Recio, and A. Martín Pendás,
Inference of crystal properties from cluster magnitudes,
J. Chem. Phys. 103 (1995) 432-439.

doi locator: doi: 10.1063/1.469609.

Using ab initio pairwise potentials, we have minimized the total energy of cube-like neutral clusters of NaCl containing from eight up to eight thousand ions. Different size coordinates have been used to describe the progressive emergence of the crystalline behavior of the lattice parameter, cohesive energy, bulk modulus, surface energy, and surface tension. Our analysis has revealed that the crystal limit may also be succesfully obtained from relatively small clusters, provided that only the atoms displaying the coordination index found in the crystal are used to compute the magnitude examined. The validity of both approaches has been demonstrated by atomistic simulations in the NaCl crystal using the same interatomic potentials.

77. E. Francisco, J. M. Recio, M. A. Blanco, and A. Martín Pendás,
Modeling the O-2-O-2 interaction for atomistic simulations,
Phys. Rev. B 51 (1995) 11289-11295.

doi locator: doi:10.1103/PhysRevB.51.11289.

A first-principles general scheme to generate crystal-consistent interatomic potentials is applied to model the ionic interactions within the MgO crystal. Our procedure makes use of the electron-gas formalism, and introduces quantum-mechanical ionic electron densities that are allowed to relax with the crystal geometry. The many-body energetic contributions that appear due to the deformation suffered by the ions upon crystal formation are also incorporated in the potentials. A complete characterization of the static behavior and the crystal stability of MgO under hydrostatic pressure reveals the suitability of the new set of interatomic potentials.

78. E. Francisco, J. M. Recio, M. A. Blanco, A. Martín Pendás, and L. Pueyo,
Derivation of electron gas interatomic potentials from quantum-mechanical descriptions of ions in crystals,
Phys. Rev. B 51 (1995) 2703-2714.

doi locator: doi:10.1103/PhysRevB.51.2703.

The Electron Gas Model theory is critically examined by means of new interatomic potentials developed from ab initio quantum-mechanical descriptions of ions embedded in a crystalline environment and from the basic hypotheses of the model, namely: spherically symmetric and additive ionic electron densities, plus energy functionals for an homogeneous electron gas. We have found that the quantum-mechanical crystal potential enhances the deformation of the ionic wavefunctions induced by the crystal formation with respect to the self-consistent, crystal-adapted densities previously used in Electron Gas simulations. Since these differences are dependent on the crystal strain, it is shown that some of the good results obtained in earlier Electron Gas based computations may be partially due to a cancellation effect between the assumptions of the model and the approximate description of the constitutive ions. For the test case explored here, the NaCl equation of state and the B1-B2 pressure induced transition phase, the overall agreement with the experimental data is recovered when the electronic densities and the energetic interactions are both computed quantum-mechanically.

79. E. Francisco, J. M. Recio, M. A. Blanco, A. Martín Pendás, and L. Pueyo,
Effects of a quantum crystal potential on the derivation of electron gas interionic energies,
Radiation Effects and Defects in Solids 134 (1995) 197-200.

Taking the NaCl crystal as a test sample, the authors analyze the performance of the Electron Gas model of Gordon and Kim with ionic electron densities obtained from the localized quantum-mechanical descriptions of the ions embedded in a quantum crystal potential. They also rationalize the potential answers of rigid and relaxed interionic potentials in terms of the charge densities used in their derivation.

80. M. Flórez, J. M. Recio, A. Martín Pendás, E. Francisco, and V. Luaña,
Energetics of the RbF + CaF2 --- RbCaF3 solid state reaction: A first-principles study,
Radiation Effects and Defects in Solids 134 (1995) 193-6.

The preliminary results of a theoretical calculation of relevant thermodynamical magnitudes involved in the RbF+CaF2$\longrightarrow$RbCaF3 solid state reaction are reported. Pairwise and quantum-mechanical simulations are combined to determine the static equations of state for the three crystals involved in this heterogeneous reaction. The standard enthalpy and volume of the reaction ($\DeltaH0$, $\DeltaV0$) and the dependence of $\DeltaH and \DeltaV$ with pressure are computed. Finally, the influence of crystal polymorphism in these magnitudes is examined.

81. A. Ayuela, J. M. López, J. A. Alonso, and V. Luaña,
Theoretical study of (NaCl)n clusters,
Physica B 212 (1995) 329-342.

doi locator: doi:10.1016/0921-4526(95)00395-P.

In this paper we present the theoretical results obtained for (NaCl)n clusters with n$\leq$19, using the ab initio perturbed-ion (PI) model. That model was first developed for the study of ionic crystals and it has been adapted here to study clusters. Within the PI model we can determine the total energy of the cluster as a function of the position of the atoms in the cluster and minimizing the total energy with respect to those positions we can obtain the ground state geometry and other related properties. The results for the equilibrium geometries are compared with calculations using pair potentials and with other ab initio results. The study of the relative stabilities of clusters with different numbers of molecules shows that the clusters are especially stable for n = 4,6,9,12,15,16 and 18 molecules, in good agreement with experimental results. We also study some electronic properties, as for instance ionization potentials.

82. A. Sutjianto, R. Pandey, and J. M. Recio,
Structure and Stability of BN Microclusters - Ab initio calculations for (BN)n (n=2-4),
Int. J. Quant. Chem. 52 (1994) 199-210.

83. A. Martín Pendás, J. M. Recio, M. Flórez, V. Luaña, and M. Bermejo,
Static simulations of CaF2 polymorphs,
Phys. Rev. B 49 (1994) 5858-5868.

Download a reprint: PRB49-5858-ov-PR94-CaF2.pdf.

doi locator: doi:10.1103/PhysRevB.49.5858.

Combined first-principles pairwise simulations and quantum-mechanical ab initio perturbed ion (AIPI) calculations were extensively performed to determine the static equations of state (EOS) of the cubic (fluorite-type) and orthorhombic ($\alpha$-PbCl2-type) polymorphs of CaF2. This theoretical study covers the range of pressures experimental available (0-45 GPa). The elastic behavior and the equilibrium crystal parameters were accurately determined by efficient numerical procedures involving a Richardson-iterated, finite-difference formula for the derivatives and the combination of downhill simplex and modified Powell methods for the multidimensional optimizations. For the bulk modulus and the effective elastic constants of the cubic phase, the simulations and AIPI calculations give increasing functions of pressure with small negative curvatures. Besides, the zero-pressure AIPI computations agree with the values of Catlow et al. [J. Phys. C 11, 3197 (1978)] for the bulk modulus and the elastic constants The computed EOS also reproduces quantitatively the most recent experimental p-V data for the cubic phase. For the orthorhombic phase, the authors optimize 9 crystal parameters for each value of pressure. This set provides a full structural characterization of this phase, as well as a global description of the p-V relation that is consistent with the synchrotron-radiation x-ray-diffraction study of Gerward et al. (1992). The simulation techniques are able to detect a first-order phase transition from the low-pressure fluorite-type to the high-pressure $\alpha$-PbCl2-type polymorph. The computed thermodynamical transition pressure lies below the experimental values, as it should for this kind of structural transformation exhibiting large pressure hysteresis.

84. A. Martín Pendás, V. Luaña, J. M. Recio, M. Flórez, E. Francisco, M. A. Blanco, and L. N. Kantorovich,
Pressure-induced B1-B2 phase transition in alkali halides: General aspects from first-principles calculations,
Phys. Rev. B 49 (1994) 3066-3074.

Download a reprint: PRB49-3066-ov-PL94-B1B2.pdf.

A first principles, general study of the thermodynamical and kinetic aspects of the B1-B2 phase transition in alkali halides is presented. Particular attention is paid to (a) how to construct models of increasing complexity to be used with generic quantum-chemical techniques and (b) the topological and symmetry-dependent features of the energetic and the Gibbs potential surfaces analyzed. The transition may be thought of as involving the simultaneous opening of the rhombohedral angle in the primitive B1 crystallographical cell while a contraction of the lattice parameter takes place. Transition paths depend strongly on pressure and show large and asymetrical Gibbs barriers that qualitatively account for many of the empirical facts around the phenomenon of hysteresis.

85. L. Kantorovich, and P. B. Zapol,
Theoretical investigation of the self-trapped hole in alkali halides. 1. Long-range effects within the model hamiltonian approach,
Phys. Status Solidi B 183 (1994) 201-221.

86. L. Kantorovich, A. Stashans, E. Kotomin, and P. W. M. Jacobs,
Quantum chemical simulations of hole self-trapping in semi-ionic crystals,
Int. J. Quant. Chem. 52 (1994) 1177-1198.

87. D. J. Groh, R. Pandey, and J. M. Recio,
Embedded-quantum-cluster study of local relaxations and optical properties of Cr+3 in MgO,
Phys. Rev. B 50 (1994) 14860-14866.

88. M. Flórez, M. A. Blanco, V. Luaña, and L. Pueyo,
Local geometries and stabilities of Cu+ centers in alkali halides,
Phys. Rev. B 49 (1994) 69-75.

Download a reprint: PRB49-69-ov-FB94-CuAX.pdf.

doi locator: doi:10.1103/PhysRevB.49.69.

The local geometry, energy stabilization, and pseudo-local t1u vibration mode of the Cu+ impurity in the alkali halide crystals were investigated with the ab initio perturbed ion cluster-in-the lattice methodology The electronic structure of different clusters, containing up to 179 ions, was computed for 9 Cu:AX systems (A = Li, Na, K; X = F, Cl, Br). The calculations clearly show that the nearest-neighbor relaxations induced by impurity substitution are essentially determined by the substituted cation, the anion playing a rather minor role. In contrast with predictions deducible from empirical ionic radii, negligible or very small relaxations for Cu:LiX systems, and inward relaxations of about -0.1 Å for Cu:NaX systems [in very good agreement with recent extended x-ray absorption fine-structure (EXAFS) measurements on Cu:NaCl] were found. For the Cu:KX family inward relaxations as large as -0.3 Å were found. The stabilization energy associated to the substitution reaction ranges from -0.2 to -1.8 eV, with a remarkable dependence upon the substituted cation. The t1u frequencies, computed without including the intershell coupling, decrease with increasing cationic size, showing a trend that agrees with the experimental data reported by D. S. McClure abd S. C. Weaver (1991) for Cu:LiCl, Cu:NaF, and Cu:NaCl. The methodology, in its present form, does not reproduce the off-center equilibrium position of the Cu+ ion observed in Cu:NaBr, Cu:KCl, and Cu:KBr.

89. A. Beltrán, A. Flores Riveros, J. Andrés, V. Luaña, and A. Martín Pendás,
Local relaxation effects in the crystal structure of vanadium-doped zircon - An ab initio Perturbed Ion calculation,
J. Phys. Chem. 98 (1994) 7741-7744.

A theoretical description of local relaxation effects induced by the presence of impurity centers V+4 at the tetrahedral and dodecahedral sites of ZrSiO4 is presented. The crystal structure is analyzed via optimization of local equilibrium geometries and computation of the force constant associated with the symmetrical vibrational mode at each impurity center. The theoretical study is carried out using an extension of the ab initio perturbed ion method. The relative stability of vanadium-substituted vacancies in ZrSiO4 is examined in light of previous results reported by the present authors and the vibrational analysis here addressed. Local geometries were optimized by relaxing various sets of ions around each substituted center. An increased substitution energy together with a pronounced decrease of the breathing vibrational mode on the 4-fold-coordinated site shows that this substitution is unstable while that on the 8-fold-coordinated ion site is energetically favorable and the local geometry is minimally relaxed. Selective doping on each center leads to a decreased force constant as compared to that obtained for the pure crystal structure.

90. A. Ayuela, J. M. López, J. A. Alonso, and V. Luaña,
Theoretical study of the electronic and structural properties of small (NaCl)n clusters,
Anales de Física (1994) 190-196.

Cluster studies can provide valuable information on the development of the properties of condensed matter from those of isolated atoms or molecules. One of the most important questions in the study of clusters is the determination of the equilibrium geometry and the understanding of the so called magic numbers, that is, clusters with a number n of atoms or molecules that are more stable than the n+1 and n-1 clusters. In this communication we present the theoretical results obtained for small (NaCl)n clusters with $n \leq 10$. The calculations were performed using the ab initio Perturbed Ion (PI) model. That model was first developed for the study of ionic crystals and we have adapted it to study small clusters. Within the PI method we can determine the total energy of the cluster as a function of the position of the atoms in the cluster, that is, as a function of the geometry, and minimizing the total energy with respect to the positions of the atoms we can obtain the ground state geometry and other related properties. The results obtained for the equilibrium geometries are in good agreement with theoretical calculations using pair potentials. The study of the relative stabilities of clusters with different numbers of molecules show that for $n=4,6,9$ molecules the clusters are specially stable.

91. J. Andrés, A. Beltrán, A. Flores-Riveros, J. A. Igualada, V. Luaña, J. B. L. Martins, G. Monrós, and A. Martín Pendás,
Ab initio cluster-in-the-lattice calculations of the impurity centers V+4:ZrSiO4,
Anales de Física 90 (1994) 181-186.

A theoretical description of crystal effects induced by the presence of impurity centers V+4 entering the dodecahedral and tetrahedral sites of ZrSiO4 is presented. The computation of the electronic structure and equilibrium geometry of the impurity center in the ionic crystal is carried out using an extension of the ab initio perturbed ion method. This theoretical model consists of a new type of cluster-in-the-lattice scheme that involves the rigorous quantum mechanical solution of clusters of varying size embedded in a quantum crystal lattice. The electronic wavefunction of the doped crystal is expressed as an antisymmetrical product of group functions where each represents an ion in the crystal. The crystal is partitioned into active (C) and lattice (L) sets where the positions and wavefunctions of all ions in C are optimized while those in L are kept frozen. Numerical results are compared with experimental data to analyze the relative stability of V+4 occupying the two sites of ZrSiO4. Our findings indicate more stability of the structure and less sensible influence of the crystal lattice for substitutions occurring at the eightfold-coordinated ion site.

92. B. P. Zapol, and L. Kantorovich,
An operator technique for calculations using non-orthogonal electron group functions,
Latv. J. Phys. Tech. Sci. 5 (1993) 18-22.

93. J. M. Recio, A. Martín Pendás, E. Francisco, M. Flórez, and V. Luaña,
Low- and high-pressure ab initio equations of state for the alkali chlorides,
Phys. Rev. B 48 (1993) 5891-5901.

Download a reprint: PRB48-5891-ov-RP93-AX.pdf.

Ab-initio, perturbed-ion calculations were done for the rock salt (B1) and cesium chloride (B2) phases of the alkali (A) chloride (ACl) crystals. Zero-temperature (T), and pressure (P) lattice energies and equilibrium distances were calculated with errors less than 5%. From the static calculations, zero-temperature equations of state (EOS) were obtained in the ranges of 0-80 GPa for LiCl, 0-60 GPa for NaCl and KCl, 0-10 GPa for RbCl, and 0-5 GPa for CsCl. Since experimental data are a critical test of the performance of a theoretical methodology, we have placed particular emphasis on (a) comparison between calculated and experimental trends, and (b) consistency with the behavior observed in real materials. We have found that our theoretical modeled solids obey the Vinet universal EOS, and match the experimental behavior in temperature-scaled EOS diagrams. We have also analyzed the phase stability of the ACl crystals from a thermodynamical point of view. The hydrostatic pressure necessary to produce the B1-B2 phase transition was calculated to decrease with the cation size, in agreement with the experimental observation. Our prediced value of the (not yet measured) B1-B2 transition pressure for LiCl is close to 80 GPa. Finally, our calculations, based on the combined kinetic-thermodynamical model proposed by X. Li and R. Jeanloz (1987) for the NaCl transition phase, predict that the hysteresis pressure range of the B1-B2 transition decreases from LiCl to RbCl.

94. J. M. Recio, R. Pandey, A. Ayuela, and A. B. Kunz,
Molecular orbital calculations on (MgO)n and (MgO)n+ clusters (n=1-13),
J. Chem. Phys. 98 (1993) 4783.

95. J. M. Recio, R. Pandey, and V. Luaña,
Quantum-mechanical modelling of the high pressure state equations of ZnO and ZnS,
Phys. Rev. B 47 (1993) 3401-3403.

Download a reprint: PRB47-3401-ov-RP93-ZnO-ZnS.pdf.

Equations of state (EOS) for the high-pressure phases of ZnO and ZnS were determined by carrying out ab initio perturbed-ion calculations. The results were used to examine different empirical EOS formalisms proposed for experimental P-V data. The generalized Vinet EOS is highly sensitive to the uncertainties in experimental data, thus providing a poor extrapolation for the properties at zero pressure. Contrarily, the modified Birch-Murnaghan EOS predicts zero-pressure properties that agree with ab initio calculations.

96. J. M. Recio, and R. Pandey,
Ab initio study of neutral and ionized microclusters of MgO,
Phys. Rev. A 47 (1993) 2075-2082.

97. J. M. Recio, E. Francisco, M. Flórez, and A. Martín Pendás,
Ab initio pair potentials from quantum mechanical atoms-in-crystals calculations,
J. Phys.: Cond. Matter 5 (1993) 4975-4988.

A new technique for deriving pairwise potentials from ab initio quantum-mechanical calculations of atoms in crystals is presented. The total energy of the crystal referred to the infinitely separated atoms is partitioned into 2 components: (i) a monocentric deformation energy arising from the changes of atomic electron density in passing from the free atom to the crystal state, and (ii) a bicentric energy due to the atomic interactions in the crystal. The 1st component can be meaningfully separated into pairwise contributions. The new technique is used to derive Buckingham-type potentials for the alkali chloride crystals that (a) reproduce the ab initio crystal energy, (b) predict good static equations of state and defect properties, and (c) give a realistic description of the crystal binding.

98. J. M. Recio, A. Ayuela, R. Pandey, and A. B. Kunz,
Quantum mechanical calculations of stoichiometric MgO clusters,
Z. Phys. D-Atoms, Molecules and Clusters 26 (1993) 237.

99. U. Puntambekar, J. M. Recio, and R. Pandey,
Defect energy calculations of alkali chlorides using derived ab initio potentials,
Solid State Comm. 85 (1993) 423-425.

100. V. Luaña, A. Martín Pendás, J. M. Recio, E. Francisco, and M. Bermejo,
Quantum mechanical cluster calculations on ionic materials: The ab initio Perturbed Ion (version 7) program,
Comput. Phys. Commun. 77 (1993) 107-134.

doi locator: doi:10.1016/0010-4655(93)90041-A.

The computational implementation is described of the ab initio perturbed ion method, a self-consistent calculation of the electronic structure and energy of a system under the assumption that the total wave function can be written as an antisymmetrical product of local ionic (or atomic) wave functions. Large bases of Slater-type orbitals are supported on every center. Very large, realistic, models of ionic materials can be efficiently solved. The program is provided with an easy-to-use and easy-to-learn interface, with special orders for three-dimensional solids, either pure and defective, and for isolated clusters.

101. V. Luaña, M. Flórez, and L. Pueyo,
Local geometry and resonant vibrations of Cu+:NaF. Results of ab initio Perturbed Ion, cluster-in-the-lattice calculations involving clusters of 179 ions,
J. Chem. Phys. 99 (1993) 7970-7982.

Download a reprint: JCP99-7970-ov-LF93-Cu-NaF-vibrations.pdf.

doi locator: doi:10.1063/1.466214.

The ground state electronic structure and energy of a CuF92Na86-5 cluster (Cu+ plus 12 shells of neighbors) embedded into a quantum lattice representing the NaF crystal are determined by using the ab initio perturbed ion (aiPI) method, with unrelaxed Coulomb-Hartree-Fock (uCHF) correlation energy corrections. Parallel calculations are performed on the CuF92Na86-5 cluster of the pure crystal to identify the changes induced by the impurity and to estimate the systematic errors in the calculations The geometry of the first 4 shells (32 ions) is allowed to relax by following symmetrical breathing modes. An inwards relaxation of -0.12 Å is predicted for the nearest neighbors (nn) shell, but negligible relaxations are found for the outer shells. The substitution of the Na+ ion by the Cu+ impurity is favored by -1.03 eV. The Cu+ ion is found to occupy an on-center octahedral position. The 138 independent Oh force constants corresponding to the vibration of the Cu+ and its first 4 shells of neighbors are then numerically computed from the aiPI energy using a Richardson iterated, finite-difference limit formula. These force constants give the vibrational modes of the impurity center. Strong couplings are found among vibrational modes of adjacent shells. Vibration frequencies characteristic of the doped system are obtained at 206 cm-1 (1a1g), 108 cm-1 (1t1u), and 173 cm-1 (1eg) determined mainly by the motions of the CuF6 octahedron.

102. L. Kantorovich, A. I. Livshicz, and G. M. Fogel,
Thermoluminiscence kinetic in the case of a continuous distribution of trap centers over their activation energies,
J. Phys. Condens. Matter 5 (1993) 7503-7514.

103. M. Bermejo, J. M. Recio, V. Luaña, and L. Pueyo,
Stability of transition-metal impurities in ionic fluorides from approximate Hartree-Fock cluster calculations,
J. Solid State Chem. 102 (1993) 226-235.

doi locator: doi:10.1006/jssc.1993.1026.

The location of the 3d levels of 10 transition-metal impurities in the band gaps of 4 ionic fluorides was studied by independent Hartree-Fock (HF) cluster calculations on open-shell MF6-n systems [M = Crz+ (z = 1-3), Mnz+ (z = 1-3), Fez+ (z = 1-2), and Vz+ (z = 2-3)] and closed = shell AF6-n systems (A = Li+, Na+, Mg+2, and Zn+2). The variation of the 3d orbital energies of the impurities with the M-F distance was deduced from the corresponding MF6-n calculations at different cluster sizes. The band gap edges for LiF, NaF, KMgF3, and KZnF3 were estimated from the AF6-n calculations: the highest occupied level was estimated from HF orbital energies of the 1Ag ground state, and the lowest unoccupied level, from HF orbital energies of the first excited 3T1u state. These orbital energies were combined to preparate approximated energy-distance diagrams that describe the location of the 3d impurity levels relative to the band gap of the host crystal. The diagrams give very valuable information on the stability of the 3d impurity in the host and the probable lattice relaxation induced upon impurity substitution. Such information is difficult to obtain either experimental or by large-scale quantum-mechanical calculations.

104. A. Beltrán, S. Bohm, A. Flores-Riveros, J. A. Igualada, G. Monrós, J. Andrés, V. Luaña, and A. Martín Pendás,
Ab initio Cluster-in-the-lattice description of vanadium-doped zircon. Analysis of the impurity centers V+4:ZrSiO4,
J. Phys. Chem. 97 (1993) 2555-2559.

A theoretical description of crystal effects induced by the presence of impurity centers V+4 entering the dodecahedral and tetrahedral sites of ZrSiO4 is presented. The computation of the electronic structure and equilibrium geometry of the impurity center in the ionic crystal is carried out using an extension of the ab initio perturbed ion method. This theoretical model consists of a new type of cluster-in-the-lattice scheme that involves the rigorous quantum mechanical solution of clusters of varying size embedded in a quantum crystal lattice. The electronic wavefunction of the doped crystal is expressed as an antisymmetrical product of group functions where each represents an ion in the crystal. The crystal is partitioned into active (C) and lattice (L) sets where the positions and wavefunctions of all ions in C, and the positions of some of them, are optimized while those in L are kept frozen. Numerical results are compared with experimental data to analyze the relative stability of V+4 occupying the 2 possible sites of ZrSiO4. The evolution of the lattice energy in the crystal was examined in terms of the cluster size and the stability property studied by locally optimizing geometries that involve relaxation of various active sets of ions around the substituted centers. Substitution on the 8-fold-coordinated ion site is energetically favorable, whereas that on the 4-fold-coordinated site being unstable and very sensitive to the geometry relaxations considered in the calculation.

105. A. Ayuela, J. M. López, J. A. Alonso, and V. Luaña,
Theoretical study of NaCl clusters,
Z. Phys. D 26 (1993) 213-215.

doi locator: doi:10.1016/0166-1280(88)80439-1.

The authors present the theoretical results obtained for (NaCl)n clusters with $n\leq{}19$. The calculations were performed using the ab-initio Perturbed-Ion (PI) model. That model was first developed for the study of ionic crystals and the authors have adapted it to study clusters. Within the PI method the authors can determine the total energy of the cluster and minimizing the total energy with respect to the positions of the atoms the authors can obtain the ground state geometry and other related properties. The results obtained for the equilibrium geometries are in good agreement with theoretical calculations using pair potentials. The study of the relative stabilities of clusters with different numbers of molecules show that the clusters are specially stable for n=4, 6, 9, 12, 15, 16 and 18 molecules, in good agreement with experimetal results.

106. A. Martín Pendás, E. Francisco, V. Luaña, and L. Pueyo,
Electronic structure and electronic excitations of solid neon from an ab initio atom-in-the-lattice approach,
J. Phys. Chem. 96 (1992) 2301-2307.

The electronic structure of the ground state and the lowest electronic excited state of fcc Ne was calculated with an ab initio atom-in-the-lattice approach consistent with the theory of electronic separability of many-electron systems. The Hartree-Fock-Roothaan equations are solved for a reference atom in the field created by the rest of the lattice. The solutions of these equations are then used to describe the quantum effects of the lattice atoms in an iterative process leading to atom-lattice consistency. The equilibrium geometry, the cohesive energy, and the lowest electronic transition energy were computed in agreement with the experimental data. The calculation gives also AO's for the Ne atom that are consistent with the crystal environment. These crystal orbitals show a contraction that increases with applied pressure, with respect to the gas-phase orbitals.

107. A. Martín Pendás, E. Francisco, and J. M. Recio,
Exact versus truncated spectrally-resolved exchange in ab initio calculations,
J. Chem. Phys. 97 (1992) 452-458.

doi locator: doi:10.1063/1.463590.

We show how stating the exchange matrix elements in terms of projected functions over the subspace subtended by the exact exchange operator provides a means to extract valuable information about the quality of the approximation Special interest is paid on two-center exchange interactions with truncated monocentric spectral resolution (TMSR) of the operator. We have undertaken numerical studies of the exact and TMSR exchange for the Li+-Li+, Li+-Cl-, Cl-Li+, Cl-Cl-, and He-He closed-shell pairs with an special attention to the fictituous asymmetry introduced by the approximation Our main conclusions are: (a) the TMSR approximation for two-center exchange interactions deviates monotonically from the exact exchange with increasing internuclear distance; (b) the TMSR matrix elements are more accurate as more diffuse the primitive functions are; (c) for a particular pair of dislike ions, the approximation works better when the expansion center contains the most contracted primitive functions.

108. V. Luaña, and M. Flórez,
Ab initio calculation of the local geometry of Cu+:NaF and Cu+:NaCl,
J. Chem. Phys. 97 (1992) 6544-6548.

A new description of the nature and scope of the impurity centers Cu:NaF and Cu:NaCl emerges when the local equilibrium geometry and wave function are obtained from cluster-in-the-lattice calculations involving clusters from 7 to 33 ions. The numerical results reveal the importance of simulating the defects by means of clusters having, at least, a boundary shell of fixed ions whose wave functions can follow the geometrical changes in the cluster inner shells. Inward relaxations of 0.089 Å for Cu:NaF and 0.085 Å for Cu:NaCl are deduced from the best calculations, in agreement with recent measurements on the last system.

109. E. Francisco, A. Martín Pendás, and W. H. Adams,
Generalized Huzinaga building-block equations for nonorthogonal electronic groups: Relation to the Adams-Gilbert theory,
J. Chem. Phys. 97 (1992) 6504-6508.

doi locator: doi:10.1063/1.463679.

The Huzinaga building-block equations for many-electron systems, derived under the hypothesis of strong orthogonality among the system groups, can be also deduced as a particular case of the Adams-Gilbert formalism, in which the strong orthogonality cannot be fully achieved in most practical cases due to basis-set truncation. Incomplete orthogonality leads to nonzero expectation values of the projection operators appearing in the Fock Hamiltonian (projection energy). This fact raises some conceptual problems since the projection energy has been used to interpret several important physical effects in recent investigations. The present work clarifies several practical aspects relative to the incomplete fulfilment of the strong-orthogonality hypothesis, in particular (a) the analytical relationship between the projection energy and the intergroup overlap energy involving weakly overlapping groups; (b) the required values for the projection constants in cases of incomplete orthogonality; and (c) how the effects of basis-set truncation can be analyzed unambiguously.

110. J. M. Recio, V. Luaña, E. Francisco, and L. Pueyo,
Theoretical d-d spectrum of Cr+3:MgO,
Radiation Effects and Defects in Solids 119-121 (1991) 437-438.

A theoretical analysis is presented of the spin-orbit effects on the lower electronic state of the Cr+3:MgO system. The study is based on the calculation of the electronic structure of the CrO69- cluster and includes a rigorous determination of the spin-orbit constants Also discussed are the effects of the external lattice on the cluster electron density, and the variation of the d-d spectrum with the metal-ligand separation The calculation steps are described.

111. L. Pueyo, A. Martín Pendás, J. M. Recio, E. Francisco, and V. Luaña,
Local wave functions for multinegative ions in solids,
Radiation Effects and Defects in Solids 119-121 (1991) 727-728.

112. L. Pueyo, V. Luaña, M. Flórez, E. Francisco, J. M. Recio, and M. Bermejo,
Theoretical calculation of d-d spectra in ionic crystals,
Reviews of Solid State Science 5 (1991) 197-222.

Some important problems of the theoretical analysis of the d-d electronic transitions in ionic crystals are presented and discussed. The work is limited to the wave-functional description of the cluster approximation The selection of the topics considered has been made in view of recent quantitative results. The problems examined include: (a) cluster definition and embedding procedures; (b) delocalization of the mainly-d states; (c) electron correlation and quantitative spectral prediction; (d) variation of the electronic transitions with the cluster geometry, and (e) spin-orbit effects. The paper ends with a brief comment on the usefulness of the ab initio analyses and a reflection on future developments.

113. A. Martín Pendás, V. Luaña, and L. Pueyo,
The Theory of Electronic Separability and the properties of impurities and defects in ionic crystals,
Radiation Effects and Defects in Solids 119-121 (1991) 443-444.

A general model is given for the properties of impurities and defects in ionic crystals (IC). Results are presented concerning the electronic levels and stability of 3d transition metal impurities, vacants and F-type centers in KMgF3, MgO and ZnS.

114. A. Martín Pendás, and E. Francisco,
Overlap, Effective-potential, and Projection Operator Bicentric Integrals over Complex Slater Type Orbitals,
Phys. Rev. A 43 (1991) 3384-3391.

doi locator: doi:10.1103/PhysRevA.43.3384.

115. V. Luaña, M. Flórez, J. M. Recio, L. Pueyo, M. Bermejo, and R. M. Pitzer,
Simulation of transition metal ions in ionic crystals,
Radiation Effects and Defects in Solids 119-121 (1991) 287-299.

116. E. Francisco, and L. Pueyo,
Theoretical Computation of the Gyromagnetic Factor for the Cr+3 and V+2 ions in KMgF3,
Radiation Effects and Defects in Solids 119-121 (1991) 725-726.

117. M. Flórez, V. Luaña, M. Bermejo, and L. Pueyo,
Perturbed-Ion atomic-like orbitals for ions in cubic fluoroperovskites,
Radiation Effects and Defects in Solids 119-121 (1991) 439-440.

The electronic structures of the KMgF3 and KZnF3 cubic perovskites have been calculated with the ab initio perturbed ion (PI) method, a scheme drived from the theory of electronic separability of multi-electron systems and the ab initio model potential approach of Huzinaga.

118. M. Bermejo, J. M. Recio, V. Luaña, and L. Pueyo,
Stability diagrams of 3d transition ions in ionic crystals,
Radiation Effects and Defects in Solids 119-121 (1991) 441-442.

We use the Hartree-Fock-Roothaan method of J. W. Richardson et al. (1971), augmented with core-projection operators and including renormalization corrections, to compute the $R(M-F) distance evolution of the electronic structure of several MF6$ octahedral clusters.

119. Richard B. Ross, Víctor Luaña, Walter C. Ermler, Russell M. Pitzer, and C. William Kern,
Modeling bulk systems through large-scale ab initio calculations,
Visions 3.2 (1990) 12-15.

120. R. B. Ross, W. C. Ermler, V. Luaña, R. M. Pitzer, and C. W. Kern,
Ab initio Models for Be81 and Be87 Metal Clusters,
Int. J. Quantum Chem.: Chem. Symp. 24 (1990) 225-240.

121. J. M. Recio, V. Luaña, L. Pueyo, and M. Bermejo,
Theoretical calculation of bulk properties of ionic crystals from the cluster approach. Application to NaF,
J. Solid State Chem. 89 (1990) 39-59.

The Theory of Electronic Separability is applied to the calculation of the ground state total energy and related bulk properties of simple ionic crystals. The work is based on a general equation of this theory that gives the total energy of the crystal in terms of additive energies of conjugate clusters. The properties of the NaF crystal analyzed in this work include equilibrium geometry, cohesive energy, elastic constants, and external pressure effects on these quantities.

122. V. Luaña, J. M. Recio, and L. Pueyo,
Quantum-mechanical description of ions in crystals: Electronic structure of magnesium oxide,
Phys. Rev. B 42 (1990) 1791-1801.

Download a reprint: PRB42-1791-ov-LR90-MgO.pdf.

doi locator: doi:10.1103/PhysRevB.42.1791.

123. V. Luaña, and L. Pueyo,
Simulation of ionic crystals: the ab initio Perturbed-Ion method and application to alkali hydrides and halides,
Phys. Rev. B 41 (1990) 3800-3814.

Download a reprint: PRB41-3800-ov-LP90-aiPI.pdf.

doi locator: doi:10.1103/PhysRevB.41.3800.

124. J. M. Recio, V. Luaña, and L. Pueyo,
Ionic crystals and electrostatics,
J. Chem. Educ. 66 (1989) 307-310.

125. V. Luaña, and L. Pueyo,
Simulation of ionic transition-metal crystals: the cluster model and the cluster-lattice interaction in the light of the Theory of Electronic Separability,
Phys. Rev. B 39 (1989) 11093-11112.

Download a reprint: PRB39-11093-ov-LP89-cluster-lattice.pdf.

doi locator: doi:10.1103/PhysRevB.39.11093.

126. V. Luaña, M. Bermejo, M. Flórez, J. M. Recio, and L. Pueyo,
Effects of a quantum-mechanical lattice on the electronic structure and d-d spectrum of the MnF6-4 cluster in Mn+2:KZnF3,
J. Chem. Phys. 90 (1989) 6409-6421.

doi locator: doi:10.1063/1.456307.

127. G. Fernández Rodrigo, and L. Pueyo,
Bonding and stability of the Cr(+) ion in octahedral fluoride lattices: results of approximate Hartree-Fock-Roothaan calculations,
J. Solid State Chem. 75 (1988) 313-331.

128. J. M. Recio, and L. Pueyo,
A study of simple ionic crystals by a cluster-model approach. Application to the NaF,
J. Mol. Struct. (Theochem) 166 (1988) 209-214.

doi locator: doi:10.1016/0166-1280(88)80438-X.

129. J. F. van der Maelen, M. Bermejo, and L. Pueyo,
Theoretical calculation of the lower electronic states of the MnF65- ion,
J. Mol. Struct. (Theochem) 166 (1988) 229-234.

doi locator: doi:10.1016/0166-1280(88)80441-X.

130. V. Luaña, and L. Pueyo,
The ab initio perturbed-ion model: a novel approach to the study of crystalline effects on atoms and ions. Application to NaF,
J. Mol. Struct. (Theochem) 166 (1988) 215-220.

131. E. Francisco, and L. Pueyo,
Theoretical spin-orbit coupling constants for 3d ions in crystals,
Phys. Rev. B 37 (1988) 5278-5288.

doi locator: doi:10.1103/PhysRevB.37.5278.

132. E. Francisco, V. Luaña, J. M. Recio, and L. Pueyo,
The coulombic lattice potential of ionic compounds: the cubic perovskites,
J. Chem. Educ. 65 (1988) 6-9.

133. V. M. García Fernández, G. Fernández Rodrigo, and L. Pueyo,
Theoretical calculation of the electronic structure of the FeF6-3 ion,
J. Mol. Struct. (Theochem) 166 (1988) 241-246.

doi locator: doi:10.1016/0166-1280(88)80443-3.

134. M. Bermejo, V. Luaña, J. M. Recio, and L. Pueyo,
Electronic structure of closed-shell hexafluorides,
J. Mol. Struct. (Theochem) 166 (1988) 235-240.

doi locator: doi:10.1016/0166-1280(88)80442-1.

135. M. T. Barriuso, J. A. Aramburu, M. Moreno, M. Flórez, G. Fernández Rodrigo, and L. Pueyo,
Dependence of the covalency of the MnF6-4 complex ion upon the Mn+2-F- distance,
Phys. Rev. B 38 (1988) 4239-4249.

doi locator: doi:10.1103/PhysRevB.38.4239.

136. G. Fernández Rodrigo, and L. Pueyo,
Electronic structure of Cr+, Fe+, and Ni+ in octahedral fluoride lattices,
J. Chim. Phys. 84 (1987) 821-827.

137. G. Fernández Rodrigo, L. Pueyo, M. Moreno, and M. T. Barriuso,
Determination of the equilibrium Cr+-F- distance in Cr+:NaF and Cr+:KMgF3,
J. Solid State Chem. 67 (1987) 64-69.

138. G. Fernández Rodrigo, M. Flórez, L. Pueyo, M. Moreno, and M. T. Barriuso,
Determination of R(M-F) for Cr+, Fe+, Ni+, and Mn+2 in ionic fluoride lattices from the isotropic superhyperfine constant,
Cryst. Latt. Def. and Amorph. Mat. 16 (1987) 281-287.

139. J. F. van der Maelen, C. Pérez Llera, and L. Pueyo,
Linear representations of an empirical correlation energy correction for transition-metal ions,
J. Chim. Phys. 84 (1987) 699-703.

140. V. Luaña, G. Fernández Rodrigo, M. Flórez, E. Francisco, J. M. Recio, J. F. van der Maelen, L. Pueyo, and M. Bermejo,
Theoretical calculation of equilibrium geometries of 3d transition-metal ions in fluoride lattices,
Cryst. Latt. Def. and Amorph. Mat. 15 (1987) 19-26.

141. V. Luaña, G. Fernández Rodrigo, E. Francisco, L. Pueyo, and M. Bermejo,
Core projection effects in near ab initio valence calculations. II. Ground state geometry of octahedral chromium (I,II,III,IV) hexaflourides,
J. Solid State Chem. 66 (1987) 263-282.

142. V. Luaña, and L. Pueyo,
Core projection effects in atomic frozen-core calculations: a numerical analysis,
Int. J. Quantum Chem. 31 (1987) 975-988.

143. V. Luaña, E. Francisco, M. Flórez, J. M. Recio, and L. Pueyo,
A new model for the cluster-lattice interaction in cluster-type calculations of transition-metal ions in crystals,
J. Chim. Phys. 84 (1987) 863-869.

144. M. Flórez, L. Seijo, and L. Pueyo,
Erratum: Theoretical calculation of the pure electronic spectrum of MnF6-4 in vacuo and in RbMnF3,
Phys. Rev. B 35 (1987) 2474.

doi locator: doi:10.1103/PhysRevB.35.2474.2.

145. E. Francisco, L. Seijo, and L. Pueyo,
Basis sets generation: relation between Adamowicz's and the maximum overlap method,
Int. J. Quantum Chem. 31 (1987) 279-285.

146. E. Francisco, L. Seijo, and L. Pueyo,
Reduction of orbital sets,
Comput. Phys. Commun. 43 (1987) 269-277.

147. E. Francisco, and L. Pueyo,
Accurate calculation of spin-orbit coupling constants for 3d atoms and ions with effective core potentials and reduced basis sets,
Phys. Rev. A 36 (1987) 1978-1982.

doi locator: doi:10.1103/PhysRevA.36.1978.

148. E. Francisco, V. Luaña, and L. Pueyo,
Electronic deformation density maps for manganese and chromium hexafluoride ions,
J. Chim. Phys. 84 (1987) 871-874.

149. E. Francisco, M. Flórez, Z. Barandiarán, G. Fernández Rodrigo, V. Luaña, J. M. Recio, M. Bermejo, L. Seijo, and L. Pueyo,
Theoretical d-d spectrum and spectral parameters of Crz+ (z = 1-4), Mn+2, and V+2 in fluoride lattices,
Cryst. Latt. Def. and Amorph. Mat. 15 (1987) 45-51.

150. M. Flórez, G. Fernández Rodrigo, E. Francisco, V. Luaña, J. M. Recio, J. F. van der Maelen, L. Pueyo, M. Bermejo, M. Moreno, J. A. Aramburu, and M. T. Barriuso,
On the RML dependence of the covalency in octahedral hexafluorides of Transition Metal Ions,
Cryst. Latt. Def. and Amorph. Mat. 15 (1987) 53-58.

151. M. Flórez, M. Bermejo, V. Luaña, E. Francisco, J. M. Recio, and L. Pueyo,
3d-4s and 3d-4p electronic transitions in M+2:NaF and M+2:KMgF3 (M = V, Cr, and Mn). Results of a cluster-model calculation,
J. Chim. Phys. 84 (1987) 855-861.

152. L. Seijo, M. Flórez, and L. Pueyo,
Matrix linearization,
Comput. Phys. Commun. 42 (1986) 127-136.

doi locator: doi:10.1016/0010-4655(86)90237-7.

153. L. Seijo, Z. Barandiarán, V. Luaña, and L. Pueyo,
Core-projection effects in near ab initio valence calculations of the electronic ground state of the octahedral CrF6-4,
J. Solid State Chem. 61 (1986) 269-276.

154. L. Pueyo, Z. Barandiarán, G. Fernández Rodrigo, M. Flórez, E. Francisco, V. Luaña, J. M. Recio, F. J. van der Maelen, M. Bermejo, and L. Seijo,
Algunos problemas en el cálculo de la estructura electrónica de iones de transición en redes iónicas,
Studia Chemica 11 (1986) 285-301.

155. V. Luaña, Z. Barandiarán, and L. Pueyo,
Model potentials suitable for calculations with Slater-type basis for Sc through Zn,
J. Solid State Chem. 61 (1986) 277-292.

Model potentials appropriate for molecular calculations with Slater-type (ST) basis sets have been generated for the first-row transition-metal atoms. Two sets of model potentials are presented. The first one has been optimized using standard 2 zeta ST basis sets. The second is consistent with a reduced ST basis set. The reduced bases have been obtained by means of a new algorithm, whose results are compared to those found with the method of Y. Sakai and S. Huzinaga. The comparison shows that the new approach leads to significant improvements in the overall results. Two different valence shells have been investigated, one formed by the 3s, 3p, 3d, and 4s AOs (SPDS), and the other one formed by the 3d and 4s AOs (DS). The model potentials presented here describe these valence shells in good agreement with the all-electron calculations taken as reference, the SPDS calculations being uniformly more accurate. Special attention has been paid to the transferability of the model potentials to electronic states with different orbital occupation. It is shown that the reported potentials have a wide transferability of this sort, being thus suitable for calculating the electronic structure of transition-metal compounds with STO 2 zeta quality. 58 references, 3 figures, 12 tables.

156. M. Flórez, L. Seijo, and L. Pueyo,
Theoretical calculation of the pure electronic spectrum of MnF6-4 in vacuo and in RbMnF3,
Phys. Rev. B 34 (1986) 1200-1214.

doi locator: doi:10.1103/PhysRevB.34.1200.

The pure electronic d-d spectrum of the MnF6-4 complex ion has been computed at different values of the Mn2+-F- distance R along the a1g$ vibration mode, following an open-shell self-consistent-field-molecular-orbital (SCF-MO) methodology. Both cluster-in-vacuo and cluster-in-the-lattice (RbMnF3) calculations have been performed in terms of rigid-lattice and partially-relaxed-lattice models. Theoretical spectral parameters have been obtained from the SCF results, and the evolution of the 3d splitting and the d-d repulsion with R has been examined. The lattice effects on the computed spectrum turned out to be very small in the present calculation. The overall description of the pure electronic single- and double-excitation transitions is rather good: sixteen transition energies are calculated with an rms deviation smaller than 1.9 kilokaysers (kK). This energy calculation partially supports the assignment of the peaks at (42-44) kK to double excitations. The energy splitting of the 4A1g, 4Eag states and its relationship with the electronic delocalization of the 3d MO's have been analyzed. The present calculation predicts, for MnF6-4, a variation of the 10Dq with R as $R-3.6$ ($1.7 \leq R \leq 2.3$ Å), in agreement with the thermal expansion of the RbMnF3 lattice, the red shifts shown by the lower quartets upon cooling, and the results of other theoretical calculations. Conversely, the Racah parameters B and C show a very slight and opposite variation with R.

157. E. Francisco, L. Seijo, and L. Pueyo,
The maximum overlap method: a general and efficient scheme for reducing basis sets. Application to the generation of approximate AO's for the 3d transition metal atoms and ions,
J. Solid State Chem. 63 (1986) 391-400.

158. J. A. Sordo, and L. Pueyo,
High-quality Hartree-Fock-Roothaan wave functions for molecular calculations,
J. Mol. Struct. (Theochem) 120 (1985) 9-13.

doi locator: doi:10.1016/0166-1280(85)85086-7.

A set of Hartree-Fock-Roothaan (HFR) wave functions $\alphai$i=1-6$ for the nickel atom (3d84s2:3F) has been constructed by simply adding one STO (Slater Type Orbital) to the $2\zeta$, Clementi-Roetti basis set. The application of several quality tests and the calculation of some atomic properties show that some of the wave functions obtained, $\alphai$i=2,4,5,6$, are comparable with the high-quality multi-term HFR basis sets. The intermediate size of the $\alphai$i=2,4,5,6$ wave functions makes them specially appropriate for molecular calculations.

159. Z. Barandiarán, L. Seijo, and L. Pueyo,
On the importance of an accurate representation of the Ewald potential throughout the cluster volume in the calculation of the cluster-lattice interaction,
J. Solid State Chem. 55 (1984) 236.

160. Z. Barandiarán, and L. Pueyo,
Lattice effects on bonding, covalency, and transferred hyperfine interaction in K2NaCrF6 and CrF3,
J. Chem. Phys. 80 (1984) 1597.

doi locator: doi:10.1063/1.446858.

161. Z. Barandiarán, and L. Pueyo,
Effects of a partial relaxation on the crystal lattice on the calculation of the electronic structure of CrF6-3 in ``isolated-clusters'' and ``shared-cluster'' crystals,
J. Chem. Phys. 79 (1983) 1926.

doi locator: doi:10.1063/1.445971.

162. Z. Barandiarán, L. Pueyo, and F. Gómez-Beltrán,
The cluster-lattice interaction in the calculation of the electronic structure of CrF6-3 in K2NaCrF6,
J. Chem. Phys. 78 (1983) 4612-4168.

doi locator: doi:10.1063/1.445303.

The cluster-lattice interaction involving the CrF3-6 in K2NaCrF6 has been analyzed, in the way proposed by Pueyo and Richardson [J. Chem. Phys. 67, 3583 (1977)] by computing the lattice potential with the Ewald method and introducing an analytical representation of it in the cluster Fock matrix before self-consistency. Many different expressions have been tested in order to obtain the best representation of the Ewald results. All of them have been centered in the metal site. The partition of this interaction in core-lattice and valence-lattice portions reveals that the earlier procedure of centering the lattice potential function on the ligand site is inappropriate for improving the cluster in-vacuo calculation of the equilibrium metal-ligand distance. The new results go in the required direction, but the effects of the interaction are now uniformly small. These effects have been examined in several properties, including the 10Dq, the ground state vibrational frequency $\bar\nu(a1g)$, the horizontal displacement of the 4T2g with respect to the 4A2g, the vertical Stokes shift associated with these two states and the ligand-to-metal charge transfer originated in the SCF process.

163. L. Pueyo, and J. W. Richardson,
Erratum: Improved calculation of electronic excitation energies of transition-metal compounds by a correlation energy correction: Application to CrF6-3 and NiF6-4,
J. Chem. Phys. 74 (1981) 2081.

doi locator: doi:10.1063/1.441768.

164. L. Pueyo, and J. W. Richardson,
Improved calculation of electronic excitation energies of transition-metal compounds by a correlation energy correction: Application to CrF6-3 and NiF6-4,
J. Chem. Phys. 67 (1977) 3577-3582.

doi locator: doi:10.1063/1.435334.

Correlation energy as an empirical correction is introduced into otherwise ab initio-type calculations of the electronic structure of trnasition metal complexes. The strong field MO electronic states are expanded in a series of free-ion LS terms and cluster correlation energies for the $S\Gamma$ states are calculated from the coefficients of such expansions and atomic spectral data. Numerical results are presented for NiF6-4 and CrF6-3. The effects of this correction on calculated spectra in these two cases are discussed in comparison with the limited (dn) configuration interaction. In both clusters the calculated spectra are significantly improved: the mean deviations (in cm-1) from all observed transitions are reduced from 3420 to 680 in NiF6-4 and from 2980 to 450 in CrF6-3. An analysis of the influence of the electronic delocalization on the calculated spectra suggests that the charge-transfer states might be not very significant in an extended CI treatment of the correlation energy problem in these clusters.

165. L. Pueyo, and J. W. Richardson,
Optical spectrum of Cr+3 in octahedral fluoride lattices: Refinements of an open-shell SCF MO calculation,
J. Chem. Phys. 67 (1977) 3583-3591.

doi locator: doi:10.1063/1.435357.

The six lower electronic transitions observed in octahedral fluoride compounds containing Cr+3 are calculated in the framework of an open-shell SCF MO methodology. An initial, isolated-cluster description is presented and compared with a more elaborate representation which includes the external lattice potential, a cluster correlation energy correction, and spin-orbit and configuration interactions. When these refinements are included, the six transition energies observed in K2NaCrF6 are computed with a mean deviation of 0.6 kK (600 cm-1), a sixth of the initial value. The theoretical equilibrium distance is only 0.014 Å removed from experiment. CI and cluster correlation energies play a competitive role in locating the t3 doublets; the calculation places t3-2T1g above t3-2Eg and below t2e-$4T2g. Due to the variation of spin-orbit interaction with distance, these levels change in character so rapidly that a more realistic procedure than the usual Franck-Condon approximation has been employed in the calculation of the transition intensity pattern via the magnetic dipole mechanism. Surprisingly, the equilibrium distance of $1\Gamma7-4T2g$ is computed only 0.01 Å greater than that of the ground state, but this small separation still allows at least one vibrational overtone to have observable intensity. Some of our results may be related to cubic oxide compounds and in this context quantitative discussions are presented about the doublet-quartet mixing, the structure of the 4A2g --- 2T2g broad band, and the Stokes shift observed in the emission spectra of those crystals.


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