1. L. Gracia, M. Marqués, A. Beltrán, A. Martín Pendás, and J. M. Recio, We present the results of a theoretical study of the response of molecular CO_{2}I and CO_{2}III, and polymeric CO_{2}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 intramolecular 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 CO_{2}III as the first precursor phase of a polymeric carbon fourfold 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 highpressures. 

2. W. Paszkowicz, R. Minikayev, P. Piszora, M. Knapp, C. Bahtz, J. M. Recio, M. Marqués, P. MoriSánchez, L. Gerward, and J. Z. Jiang, The lattice parameter and the thermal expansion coefficient (TEC) for a spineltype Si_{3}N_{4} phase prepared under high pressure and high temperature conditions are determined for 14 < T < 302~K by Xray diffraction, at a synchrotronradiation source, and for 0 < T < 1683~K by firstprinciples calculations. The lowT and highT 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. MoriSánchez, J. M. Recio, and R. Pandey, We report the results of a theoretical study of structural, electronic, and pressureinduced phase transitions properties in ZnTe. Total energies of several highpressure polymorphs are calculated using the density functional theory (DFT) formalism under the nonlocal approximation. Thermal effects are included by means of a nonempirical Debyelike model. In agreement with optical absorption data, the lowest direct gap of the zincblende polymorph is found to follow a nonlinear pressure dependence that turns into linear behavior in terms of the decrease in the lattice parameter. The pressure stability ranges of cubic (zincblende and rocksalt), trigonal (cinnabar), and orthorhombic (Cmcm) polymorphs are computed at static and room temperature conditions. Our calculations agree with the experimental observed zincblende  cinnabar  Cmcm pressureinduced 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 cubiclike compression of its shortest ZnTe bonds. The qualitative trend shows a crystal that becomes relatively less compressible in the highpressure phases. 

4. A. Waskowska, L. Gerward, J. Staun Olsen, M. Feliz, L. Gracia, M. Marqués, and J. M. Recio, The highpressure structural behavior of CdCr_{2}Se_{4} (space group $Fd\bar3m$) and CdGa_{2}Se_{4} ($I\bar4$) 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 firstprinciples calculations based on the Density Functional Theory formalism. The calculated bulk modulus for CdGa_{2}Se_{4} in hypothetical cubic spinel structure ($Fd\bar3m$) is 84.8 GPa. This value together with the experimental and theoretical results for CdCr_{2}Se_{4} suggest that seleniumbased cubic spinels have a uniform response to hydrostatic pressure, like their oxygenbased 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, Highquality atomic electron densities are often approximated by limitedsize 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 gaussianexponential sets. We report approximate densities of this type for the ground state of neutral atoms HeXe 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 MoriSánchez, Aurora Costales, Miguel A. Blanco, and A. Martín Pendás, Download a reprint: JCP1196341ovLM2003alkalinemetals.pdf. The topological properties of the electron density of bcc alkaline metals (LiCs) is examined by means of HartreeFock 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, Download a reprint: JCP1197643ovPL2003bcurvatures2.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, Download a reprint: JCP1197633ovPL2003acurvatures1.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 GaussBonnet 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, Download a reprint: PRB6814110ovMF2003polarization.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 B1B33 transformation over the B1B2 one in NaBr and NaI and (ii) the potential appearance of the orthorhombic phase at high pressures in lithium halide crystals. 

10. Paula MoriSánchez, Miriam Marqués, Armando Beltrán, J. Z. Jiang, L. Gerward, and J. M. Recio, Download a reprint: PRB6864115ovMM2003nitridespinels.pdf. doi locator: doi:10.1103/PhysRevB.68.064115. A microscopic investigation of firstprinciples electron densities of $\gamma$A_{3}N_{4} (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 $\gammaC_{3}N_{4} and different degrees of ionic polarization in \gammaSi_{3}N_{4} and \gamma$Ge_{3}N_{4}, (ii) nitrogen is the lowest compressible atom controlling the trend in the bulk modulus of the solids, and (iii) the groupIV 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, Download a reprint: JPCB1074508ovCK2003nitrideclusters.pdf. doi locator: 10.1021/jp022417s. We report the results of a theoretical study of M_{n}N_{n} (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 Al_{n}N_{n} clusters, whereas it affected significantly the lowest energy configurations of Ga_{n}N_{n} and In_{n}N_{n} clusters. This may be attributed to the dominance of NN bonds in Ga_{n}N_{n} and In_{n}N_{n} clusters in contrast to the dominance of AlN bonds in Al_{n}N_{n} 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 MoriSánchez, and A. Martín Pendás, Download a reprint: JPCB1074912ovLC2003danburite.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 metaloxide 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 OO long distance bonds (up to 11 different types of OO 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, Download a reprint: PRB6764110ovFB2003spinodal.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 TiO_{2}. We show that results of ab initio Perturbed Ion calculations and very recent Xray 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 roomtemperature experimental data. Overall, we find highly consistent results and good theoryexperiment agreement for a significant series of observables, including structural parameters, pV 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, Download a reprint: JPCA107191ovCP2003IIInitrides.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 IIInitrides 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 HOMOLUMO 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, Download a reprint: PRB66224114ovGB02MgAl2O4.pdf. doi locator: doi:10.1103/PhysRevB.66.224114. The equations of state and phases diagram of the cubic spinel and two highpressure polymorphs of MgAl_{2}O_{4} have been investigated up to 65 GPa using Density Functional Theory, the spacefilling polyhedral partition of the unit cell, and the static approximation. Energyvolume curves have been obtained for the spinel, the recently observed calcium ferritetype and calcium titanitetype phases, and the MgO+$\alpha$Al_{2}O_{3} mixture. Zeropressure unit lengths and compressibilities are well described by the theoretical model, that predicts static bulk moduli about 215 GPa for all the highpressure 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 pressureinduced 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, Download a reprint: CPL362210ovCP2002InAs.pdf. doi locator: 10.1016/S00092614(02)01076X. First principles study of the small InAs_{n} 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 MoriSánchez, A. Martín Pendás, and V. Luaña, Download a reprint: JACS12414721ovMP2002triangle.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 ArkelKetelaar diagrams. 

18. M. Flórez, J. M. Recio, E. Francisco, M. A. Blanco, and A. Martín Pendás, Download a reprint: PRB66144112ovFR2002B1B2.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 HartreeFock 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 quantummechanical contributions. 

19. E. Francisco, M. A. Blanco, and P. Palacios, We have determined the equation of state (EOS) of SrF_{2} in the cubic (C1, Fm3m) and orthorhombic (C23, Pbnm) phases using Electron Gas Interionic Potentials (EGIP) that incorporate manybody energy components. Thermal effects are included by means of a quasiharmonic Debye model. The zero pressure unit cell length (a_{0}), lattice energy (E$_{\mathrmlatt}$), bulk modulus (B_{0}), 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 $\eta/\eta_{0}p$ data ($\eta=a,b,c$) to linear forms of the Vinet EOS reveal that SrF_{2} (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 p_{t}=3.92 GPa, which is between the observed direct ($p_{t}=5.0$ GPa) and reverse C1 ($p_{t}=1.7$ GPa) phase transitions. 

20. J. Z. Jiang, H. Lindelov, L. Gerward, K. Stahl, J. M. Recio, P. MoriSánchez, S. Carlson, M. Mezouar, E. Dooryhee, A. Fitch, and D. J. Frost, Download a reprint: PRB65161202ovJL2002Si3N4.pdf. The compressibility and thermal expansion of the cubic silicon nitride (cSi_{3}N_{4}) phase have been investigated by performing insitu Xray powder diffraction measurements using synchrotron radiation, complemented with computer simulations by means of first principles calculations. The bulk compressibility of the cSi_{3}N_{4} phase originates from the average of both SiN 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 SiN and NN bond lengths with temperature, while the lengths for the tetrahedral SiN and NN bonds remain almost unchanged in the temperature range of 2951075 K. 

21. A. Martín Pendás, V. Luaña, L. Pueyo, E. Francisco, and Paula MoriSánchez, Download a reprint: JCP1171017ovPL2002Hirshfeld.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, Download a reprint: JCP117965ovPendas2002pressure.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, Download a reprint: JPCA106335ovFP2002MgF2clusters.pdf. doi locator: doi:10.1021/jp012347+. HartreeFock (RHF) and secondorder M\ollerPlesset (MP2) first principles calculations have been performed to study the structures, stabilities, harmonic vibrational frequencies, and bonding properties of MgF_{2} dimers and trimers, complementing our previous work (J. Phys. Chem. 2001, 105, 4126) on the MgF_{2} monomer. The less energetic isomers found for (MgF_{2})_{2} and (MgF_{2})_{3} are the bridged F(Mg_{2}F_{2})F (D$_{\mathrm2h}$) and FMgF_{2}MgF_{2}MgF (D$_{\mathrm2d}$) structures, respectively. A new C_{s} trimer structure has been found and characterized. Correlation energy corrections increase the MgF distances by a 1.21.4 % and do not modify appreciably the MgFMg and FMgF angles. The dissociation energy per magnesium difluoride unit (DE) of (MgF_{2})_{n} increases with n. MP2 frequencies for the (MgF_{2})_{2} D$_{\mathrm2h}$ isomer are around 1.0 % lower than their RHF equivalents. The whole set of computed frequencies for (MgF_{2})_{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 (MgF_{2})_{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 polarizableions 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, Download a reprint: JPCB1061940ovCK200235clusters.pdf. doi locator: 10.1021/jp013906f. The structure, geometry, and vibrational frequencies of several isomers of small IIIV (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 D_{3h} structure like the nitride, but the gallium and indium trimers exhibit a three dimensional structure of C_{s} symmetry. The existence of strong XX 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, Download a reprint: JACS1244116ovCB2002bonding3N.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 NN bond dominated small clusters to the MN bond dominated crystals, with the aim of explaining how the strong multiple bond of N_{2} 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 NN 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 NN bond is weakest in them. The nitrogen atom charge is seen to be proportional to the metal coordination, being thus a bondrelated property, and dependent on the MN 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, Download a reprint: JPCB1061945ovKB20023Nclusters.pdf. We report the results of a theoretical study of Al_{n}N_{n}, Ga_{n}N_{n}, and In_{n}N_{n} (with $n=4,5,6$) clusters, focusing on their structural properties, stability, and electronic structure. For Al_{n}N_{n} clusters, the metalnitrogen bond is found to dominate the lowest energy configurations, with a transition from planar to bulklike three dimensional structures, as the cluster size increases from Al_{4}N_{4} to Al_{6}N_{6}. However, for Ga_{n}N_{n} and In_{n}N_{n} clusters, the lowest energy configurations are mostly planar, and they are dominated either by N_{3}^{} or N_{2} subunits. It strongly suggests that Nsegregation 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, A theoretical investigation of the MgAl_{2}O_{4} crystal response to highpressure conditions has been carried out to determine its stability against decomposition towards MgO and $\alpha$Al_{2}O_{3} and towards recently observed orthorhombic phases. We have evaluated total energy versus volume curves using the density functional formalism under the nonlocal 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 MgO_{4} and AlO_{6} 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, 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 HartreeFock 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, doi locator: doi:10.1080/08957950290008747. The pressureinduced polymorphism of NaBr has been investigated by means of a quantummechanical HartreeFock 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 P2_{1}/m unit cell are also reported. 

30. M. Calatayud, Paula MoriSánchez, A. Beltrán, A. Martín Pendás, E. Francisco, J. Andrés, and J. M. Recio, Download a reprint: PRB64184113ovCM2001TiO2.pdf. doi locator: doi:10.1103/PhysRevB.64.184113. Quantummechanical simulations have been performed to investigate pressure effects on the crystal geometry, the chemical bonding, and the electronic structure of anatase TiO_{2}. Total energy calculations are carried out using the density functional formalism under the nonlocal 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 MoriSánchez, J. M. Recio, Bernard Silvi, C. Sousa, A. Martín Pendás, V. Luaña, and F. Illas, Download a reprint: PRB66075103ovMR2002FMgO.pdf. Charged and neutral oxygen vacancies in the bulk and on perfect and defective surfaces of MgO are characterized as quantummechanical 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 coreless pseudoanion that behaves as an activated host oxygen. 

32. Ruth Franco, Anil K. Kandalam, Ravindra Pandey, and Udo C. Pernisz, Calculations based on density functional theory (DFT) were performed on various structural isomers of methylsilsesquioxanes, [MeSiO_{3/2}]_{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 methylsilsesquioxanes, except [MeSiO_{3/2}]_{4}, against fragmentation and hydrolysis. The most stable isomers are found to prefer configurations with a larger ringsize. The deformation density plots show that chemical bonding in methylsilsesquioxan es is mainly determined by the building block unit, (CH_{3}SiO_{3/2}) as also see n in hydrosilsesquioxanes (HSQ). However, unlike HSQ, phenylsilsesquioxanes predicted to be insulator without a presence of a midgap state in their HOMOLUMO gap. 

33. R. Pandey, B. K. Rao, P. Jena, and M. A. Blanco, Download a reprint: JACS1237744ovPR2001bMBenzcorr.pdf. 

34. R. Pandey, B. K. Rao, P. Jena, and M. A. Blanco, Download a reprint: JACS1233799ovPR2001MBenz.pdf. A comprehensive theoretical study of the geometries, energetics, and electronic structure of neutral and charged 3d transition metal atoms (M) interacting with benzene molecules (Bz) is carried out using density functional theory and generalized gradient approximation for the exchangecorrelation potential. The variation of the metalbenzene distances, dissociation energies, ionization potentials, electron affinities, and spin multiplicities across the 3d 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~$\mu_{B}$, in the 3d metalbenzene series. In multidecker complexes involving V_{2}(Bz)_{3} and Fe_{2}(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, Download a reprint: JPCB1056080ovKB2001Nclusters.pdf. We report the results of a theoretical study of the nitride trimers (i.e. M_{3}N_{3} 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 metalnitrogen and metalmetal bonds in going from Al to Ga to In. It is also shown that the strength of the nitrogennitrogen 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 (Al_{3}N_{3}), or in terms of those of weakly bonded M_{3} and N_{3} subunits (Ga_{3}N_{3} and In_{3}N_{3}). 

36. V. Luaña, J. M. Recio, A. Martín Pendás, M. A. Blanco, L. Pueyo, and R. Pandey, Download a reprint: PRB64104102ovLR2001caps1.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. Clusterinthelattice calculations of several defects and impurity centers in MgO are examined as a test. 

37. E. Francisco, A. Costales, and A. Martín Pendás, Download a reprint: JPCA1054126ovFC2001MgF2.pdf. doi locator: doi:10.1021/jp0041656. We have calculated the ground state geometry, vibrational frequencies, and bonding properties of MgF_{2} at the HartreeFock (HF), secondorder (MP2), and fourthorder M\ollerPlesset (MP4(SDTQ)) levels of calculation. Several highquality 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 MgF_{2} is a linear molecule. MP2 and MP4 results are very similar. The MP2 symmetric ($\nu_{1}$) and asymmetric ($\nu_{3}$) stretching frequencies are about 57 % smaller than the HF values and agree well with the observed data. The MP2 $\nu_{2}$ (bending) frequency is close to that found in other ab initio calculations and the experimental gasphase value, but is 80 cm^{1} smaller than the value observed in the IR spectrum of MgF_{2} trapped in solid argon. Polarization functions shorten noticeably the magnesiumfluorine equilibrium distance and increase $\nu_{1} and \nu_{3}$. An Atoms in Molecules (AIM) analysis of the wavefuncions reveals that MgF_{2} 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 MoriSánchez, R. Franco, A. Martín Pendás, V. Luaña, and J. M. Recio, Quantum mechanical static simulations of the highpressure spinel phase of Si_{3}N_{4} 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, Nbased materials. 

39. J. M. Recio, R. Franco, A. Martín Pendás, Miguel A. Blanco, L. Pueyo, and Ravindra Pandey, Download a reprint: PRB63184101ovRF2001UniformCompress.pdf. doi locator: doi:10.1103/PhysRevB.63.184101. Simple algebraic equations show that the bulk compressibility in spineltype compounds can be expressed by means of cationoxide 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. Quantummechanical ab initio Perturbed Ion (aiPI) results on the MgAl_{2}O_{4}, ZnAl_{2}O_{4}, ZnGa_{2}O_{4}, and MgGa_{2}O_{4} direct spinels and on the MgGa_{2}O_{4} inverse spinel are reported to illustrate the interpretative capabilities of the proposed equations. 

40. Paula MoriSánchez, A. Martín Pendás, and V. Luaña, Download a reprint: PRB63125103ovMP2001BP.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 zincblende 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 nonnuclear maximum before being caught by the B atom. 

41. V. Luaña, A. Martín Pendás, A. Costales, Gabino A. Carriedo, and Francisco J. GarcíaAlonso, Download a reprint: JPCA1055280ovLP2001Phosphazenes.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/631G** ab initio calculations are done on a collection of (NPX_{2})_{3} derivatives for a wide set of X substituents, and its electron density, $\rho(\vecr)$, and pair density, $\rho^{(2)}(\vecr_{1},\vecr_{2})$, 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 XNPX_{3}, formally a double NP bond, and those of X_{2}NPX_{4}, 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 NN group, a small but significant amount, even though no bond path line occurs linking them. The 3D contour surfaces of $\nabla^{2}\rho$ 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, 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 SrF_{2}. Thermal effects are taken into account by means of a quasiharmonic Debye model. The results for the zero pressure cell parameter (a_{0}), lattice energy (E$_{\mathrmlatt}$), and bulk modulus (B_{0}) 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 zerop, 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, The results of a shellmodel study on CdGeAs_{2} 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 hostlattice potentials. Defect calculations based on MottLittleton 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, Download a reprint: PRB6213970ovPC2000localcompress.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, A symmetrybased, nondisplacive mechanism for the firstorder B3B1 phase transition exhibited by many binary semiconductors is proposed. Using a singlemolecule 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. Firstprinciples calculations on the widegap 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 ZnO bond in the B1 structure, and the transformation of ZnO from a directgap (B3) to an indirectgap (B1) material. 

46. M. A. Blanco, A. Costales, A. Martín Pendás, and V. Luaña, We have applied Bader's topological analysis to the study of the B1B2 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, doi locator: doi:10.1103/PhysRevB.62.803. Native and rareearthdoped pointdefects in $\beta$PbF_{2} are studied in the framework of the pairpotential 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 PbF_{2} very well. The calculated formation energies for native defects suggest that the anion Frenkel disorder is preferred over the cation Frenkel and Schottkylike disorder in PbF_{2}. The computed temperature behavior of the ionic conductivity agrees very well with the available experimental data. In the rareearth doped PbF_{2}, a sitepreference of the chargecompensating fluorine interstitial appears to change from nearest to nextnearest neighbor with the increase in the rareearth ionic radius. 

48. T. Arlt, M. Bermejo, M. A. Blanco, L. Gerward, J. Z. Jiang, J. Staun Olsen, and J. M. Recio, Download a reprint: PRB6114414ovAB2000TiO2.pdf. doi locator: doi:10.1103/PhysRevB.49.69. The equation of state of anatase TiO_{2} has been determined experimentally  using polycrystalline as well as singlecrystal material  and compared with theoretical calculations using the ab initio Peturbed Ion model. The results are highly consistent, the zeropressure bulk modulus being 179(2) GPa from experiment and 189 GPa from theory. Singlecrystal tetragonal anatase transforms to the orthorhombic $\alpha$PbO_{2} 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 $\alpha$PbO_{2} phase at about 7 GPa. The experimental zeropressure bulk moduli are 258(8) GPa for the $\alpha$PbO_{2} 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, Download a reprint: JPCB1044368ovCK2000Nclusters.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 NN bonds, is seen to diminish with the increase of the number of metal atoms and the degree of ionicity. The AlN 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, GaN and InN bonds are nonshared interactions, with smaller charge transfers and polarizations. In all the cases, the existence of a NN bond weakens the metalN 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, Download a reprint: JPCB1044361ovKP2000Nclusters.pdf. First principles calculations based on the nonlocal 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 nitrogenexcess and metalexcess triatomic clusters show minimum energy configurations to be approximately linear. The most stable isomer of Al_{2}N_{2} and Ga_{2}N_{2} is a rhombus with a singlet spin state, though In_{2}N_{2} is predicted to be not stable against dissociation into In_{2} and N_{2}. A strong dominance of the NN bond over the metalnitrogen and metalmetal bonds appears to control the structural skeletons and the chemistry of these clusters. This is manifested in the dissociation of neutral and singlyionized 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, doi locator: doi:10.1103/PhysRevB.61.11359. Ab initio Perturbed Ion calculations were performed for the cubic, orthorhombic, hexagonal, and monoclinic phases of PbF_{2}. A complete characterization of these phases was achieved in terms of the potential energy surfaces, the equations of state, and the phasetransition pressures. Thermal effects were included via a quasiharmonic nonempirical 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 highpressure postcotunnite structure for PbF_{2}, 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, 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 ringlike isomers are predicted to be equally probable for Cr_{2}O_{2} while the (Cr_{2}O_{2})O isomer is preferred over the chainlike (OCrOCrO) isomer for Cr_{2}O_{3}. For Cr_{2}O_{4}, a clear preference for the O(Cr_{2}O_{2})O isomer over the (CrO_{2})_{2} isomer is predicted. Calculations of the vibrational frequencies for the lowestenergy isomers of these clusters yield the stretching mode involving the stronger CrO bond to be around 9001000 cm^{1} and the bending mode involving the puckeredring to be around 550700 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, Structural, thermodynamic and electronic properties of CdGeAs_{2} 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 CdGeAs_{2}. 

54. Ravindra Pandey, Julian D. Gale, Suresh K. Sampath, and J. M. Recio, Stoichiometric zinc aluminate (ZnAl_{2}O_{4}) and zinc gallate (ZnGa_{2}O_{4}) are simulated in the framework of the shell model for wich a new set of twobody interatomic potential parameters were developed. Using these parameters, a reasonable prediction is made for elastic and dielectric constants of ZnAl_{2}O_{4} and ZnGa_{2}O_{4}. 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 ZnAl_{2}O_{4} as compared to that of ZnGa_{2}O_{4}, whereas its pressure derivative remains the same in both oxides. On the other hand, the octahedral and tetrahedral volumes of ZnGa_{2}O_{4} are higher than those of ZnAl_{2}O_{4}. 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 Al_{2}O_{3}/Ga_{2}O_{3} via the formation of zinc vacancies is predicted relative to that of ZnO in ZnAl_{2}O_{4}/ZnGa_{2}O_{4}. 

55. V. Luaña, A. Costales, A. Martín Pendás, and L. Pueyo, 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 MoriSánchez, and V. Luaña, Download a reprint: PRL831930ovPB99NNM.pdf. Simple arguments and quantum mechanical calculations are used to analyze the occurrence of nonnuclear 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, In this contribution, we discuss two techniques for determining interionic potentials from quantummechanical 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 gasphase to the crystal. We present several schemes to deal with these selfenergy 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 selfenergy 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 modelling has been applied to study various cation dopants, namely Cu, Ag, B, Al, Ga and In in ZnGeP_{2}. 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 MottLittleton 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, Kaihua Xiang, Ravindra Pandey, J. M. Recio, and John M. Newsam, We report the results of density functional theory calculations on chromium oxide clusters responding to the formula Cr$_{\rm m}O_{\rm n}$ (m=12, n=13). Double numeric basis sets supplemented by polarization functions have been used in both the local and nonlocal 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 CrO bonds dominate the chemical description of the CrO$\rm _{n}$ series, while for the Cr_{2}O$\rm _{n}$ series the presence of the CrCr bond reduces the metal to oxygen charge transfer yielding much softer clusters, as reflected by the smaller HOMOLUMO 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 oxygenrich clusters are preferred over the metalrich 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 Cr_{2}O 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, Download a reprint: PRB588949ovRB98ZnO.pdf. We report the results of a combined experimental and theoretical investigation on the stability and the volume behavior under hydrostatic pressure of the rocksalt (B1) phase of ZnO. Synchrotronradiation Xray 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 nonlocal 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 highpressure 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 pressurevolume data on an equal basis. In both cases, we have obtained values of the bulk modulus in the range of 160194 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, 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, The electronic structure, equilibrium geometry, and equation of state of Al_{2}O_{3} in the $\alpha$Al_{2}O_{3} and Rh_{2}O_{3}(II) phases have been determined by means of the ab initio Perturbed Ion method augmented by a recently developed nonempirical Debyelike 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 $\alpha$Al_{2}O_{3} phase, and 20~GPa for the high pressure phase. our structural results are in good agreement with the experimental information available. Although the $\alpha$Al_{2}O_{3} phase is more stable in the static (p=T=0) description, a pressureinduced phase transition is detected at room temperature near 4~GPa. The critical pressure p_{c} increases very slightly with temperature, being about 5.5~GPa at 1000~K. This value is consistent with the phase transition found in Rh_{2}O_{3} by Shannon and Prewitt [Journal of Solid State Chemistry \textbf2, (1970) 134] at p_{c} 6.5~GPa. Furthermore, the $\alpha$Al_{2}O_{3} phase shows a slight pressureinduced 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, doi locator: doi:10.1021/jp972516j. The structural and thermodynamic properties of MgF_{2} have been investigated in a wide range of pressures (080 GPa) and temperatures (0850 K) by coupling quantummechanical Ab Initio Perturbed Ion calculations with a quasiharmonic Debye model. The roomT, zerop 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 pV relations. We have simulated the rutiletofluorite 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 MgF_{2} is a highly ionic compound. Its ionicity decreases linearly with increasing pressure and, as in other ionic compounds, the crystal shows anionanion bonds. 

64. A. Martín Pendás, J. M. Recio, E. Francisco, and Víctor Luaña, Download a reprint: PRB563010ovPR97uber.pdf. The fulfillment of universalbindingenergy relations across the rocksalt (B1) cesium chloride (B2) phase transition in alkali halides is analyzed from a first principles point of view. We show that extensive ab initio quantummechanical 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, Download a reprint: PRB554275ovPC97AIM1.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 rocksalt phase of LiI. It is shown that this crystal is best described as made up of 18fold coordinated iodides and 6fold coordinated lithiums, contrary to the usual 66 description. 

66. V. Luaña, A. Costales, A. Martín Pendás, M. Flórez, and V. M. García Fernández, The ab initio Perturbed Ion (aiPI) quantum mechanical method is used to study the solid state reaction: AX + MX_{2}  AMX_{3} 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, MX_{2} and AMX_{3} 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, Download a reprint: PRB554285ovLC97AIM2.pdf. We present here the topological (Bader) analysis of the electronic structure for 120 cubic perovskites AMX_{3} (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 MX and AX bonds, many have XX too, and only CsSrF_{3} and CsBaF_{3} have AA 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. M^{2+} basins do present, however, bizarre nearly bidimensional wings on those topological schemes lacking XX 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 MX bond critical point is also observed. The stability of the perovskite structure with respect to the decomposition into MX_{2} + AX has been found to be mostly governed by the M^{2+} cation, the crystals having small M^{2+} and large A^{+} ions being the most stable ones. There is also a clear tendency for the crystals lacking XX bonds, and having bizarre M^{2+} shapes, to decompose. 

68. M. A. Blanco, V. Luaña, and A. Martín Pendás, 

69. M.A. Blanco, M. Flórez, and M. Bermejo, Download a reprint: Theochem41919ovBF97rotationmatrices.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 symmetryadapted 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 pointgroup 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, We report the results of a theoretical investigation that explores for the first time temperature effects on the pressurevolume relationship in corundum. The ionic interactions within the $\alpha$Al_{2}O_{3} crystal are modelized using the electron gas formalism along with electronic wavefunctions that are allowed to relax with crystal strains. A nonempirical Debye model is applied to account for the thermal contributions. Our study reveals that the crystal responds isotropically under both hightemperature and highpressure conditions. Good agreement with hydrostatic and quasihydrostatic experimental data is achieved. 

71. M. A. Blanco, A. Martín Pendás, E. Francisco, J. M. Recio, and R. Franco, 

72. A. Martín Pendás, J. M. Recio, M. Flórez, M. A. Blanco, and E. Francisco, 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, Quantummechanical calculations and atomistic simulations were used to characterize the local geometry, stability and resonant vibrations of Cu_{A} centers in alkali halides. 

74. D. J. Groh, R. Pandey, and J. M. Recio, 

75. R. Franco, J. M. Recio, A. Martín Pendás, E. Francisco, V. Luaña, and L. Pueyo, The local arrangement of a substitutional Cr^{+3} ion for an Al^{+3} ion in corundum was studied by firstprinciples pairwise simulations and quantummechanical 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 $\alpha$Al_{2}O_{3}. 

76. E. Francisco, J. M. Recio, and A. Martín Pendás, doi locator: doi: 10.1063/1.469609. Using ab initio pairwise potentials, we have minimized the total energy of cubelike 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, doi locator: doi:10.1103/PhysRevB.51.11289. A firstprinciples general scheme to generate crystalconsistent interatomic potentials is applied to model the ionic interactions within the MgO crystal. Our procedure makes use of the electrongas formalism, and introduces quantummechanical ionic electron densities that are allowed to relax with the crystal geometry. The manybody 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, 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 quantummechanical 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 quantummechanical crystal potential enhances the deformation of the ionic wavefunctions induced by the crystal formation with respect to the selfconsistent, crystaladapted 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 B1B2 pressure induced transition phase, the overall agreement with the experimental data is recovered when the electronic densities and the energetic interactions are both computed quantummechanically. 

79. E. Francisco, J. M. Recio, M. A. Blanco, A. Martín Pendás, and L. Pueyo, 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 quantummechanical 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, The preliminary results of a theoretical calculation of relevant thermodynamical magnitudes involved in the RbF+CaF2$\longrightarrow$RbCaF_{3} solid state reaction are reported. Pairwise and quantummechanical 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 ($\DeltaH^{0}$, $\DeltaV^{0}$) 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, doi locator: doi:10.1016/09214526(95)00395P. In this paper we present the theoretical results obtained for (NaCl)_{n} clusters with n$\leq$19, using the ab initio perturbedion (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, 

83. A. Martín Pendás, J. M. Recio, M. Flórez, V. Luaña, and M. Bermejo, Download a reprint: PRB495858ovPR94CaF2.pdf. doi locator: doi:10.1103/PhysRevB.49.5858. Combined firstprinciples pairwise simulations and quantummechanical ab initio perturbed ion (AIPI) calculations were extensively performed to determine the static equations of state (EOS) of the cubic (fluoritetype) and orthorhombic ($\alpha$PbCl_{2}type) polymorphs of CaF_{2}. This theoretical study covers the range of pressures experimental available (045 GPa). The elastic behavior and the equilibrium crystal parameters were accurately determined by efficient numerical procedures involving a Richardsoniterated, finitedifference 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 zeropressure 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 pV 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 pV relation that is consistent with the synchrotronradiation xraydiffraction study of Gerward et al. (1992). The simulation techniques are able to detect a firstorder phase transition from the lowpressure fluoritetype to the highpressure $\alpha$PbCl_{2}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, Download a reprint: PRB493066ovPL94B1B2.pdf. A first principles, general study of the thermodynamical and kinetic aspects of the B1B2 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 quantumchemical techniques and (b) the topological and symmetrydependent 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, 

86. L. Kantorovich, A. Stashans, E. Kotomin, and P. W. M. Jacobs, 

87. D. J. Groh, R. Pandey, and J. M. Recio, 

88. M. Flórez, M. A. Blanco, V. Luaña, and L. Pueyo, Download a reprint: PRB4969ovFB94CuAX.pdf. doi locator: doi:10.1103/PhysRevB.49.69. The local geometry, energy stabilization, and pseudolocal t1u vibration mode of the Cu^{+} impurity in the alkali halide crystals were investigated with the ab initio perturbed ion clusterinthe 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 nearestneighbor 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 xray absorption finestructure (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 offcenter 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, A theoretical description of local relaxation effects induced by the presence of impurity centers V^{+4} at the tetrahedral and dodecahedral sites of ZrSiO_{4} 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 vanadiumsubstituted vacancies in ZrSiO_{4} 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 4foldcoordinated site shows that this substitution is unstable while that on the 8foldcoordinated 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, 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 n1 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. FloresRiveros, J. A. Igualada, V. Luaña, J. B. L. Martins, G. Monrós, and A. Martín Pendás, A theoretical description of crystal effects induced by the presence of impurity centers V^{+4} entering the dodecahedral and tetrahedral sites of ZrSiO_{4} 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 clusterinthelattice 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 ZrSiO_{4}. Our findings indicate more stability of the structure and less sensible influence of the crystal lattice for substitutions occurring at the eightfoldcoordinated ion site. 

92. B. P. Zapol, and L. Kantorovich, 

93. J. M. Recio, A. Martín Pendás, E. Francisco, M. Flórez, and V. Luaña, Download a reprint: PRB485891ovRP93AX.pdf. Abinitio, perturbedion calculations were done for the rock salt (B1) and cesium chloride (B2) phases of the alkali (A) chloride (ACl) crystals. Zerotemperature (T), and pressure (P) lattice energies and equilibrium distances were calculated with errors less than 5%. From the static calculations, zerotemperature equations of state (EOS) were obtained in the ranges of 080 GPa for LiCl, 060 GPa for NaCl and KCl, 010 GPa for RbCl, and 05 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 temperaturescaled 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 B1B2 phase transition was calculated to decrease with the cation size, in agreement with the experimental observation. Our prediced value of the (not yet measured) B1B2 transition pressure for LiCl is close to 80 GPa. Finally, our calculations, based on the combined kineticthermodynamical model proposed by X. Li and R. Jeanloz (1987) for the NaCl transition phase, predict that the hysteresis pressure range of the B1B2 transition decreases from LiCl to RbCl. 

94. J. M. Recio, R. Pandey, A. Ayuela, and A. B. Kunz, 

95. J. M. Recio, R. Pandey, and V. Luaña, Download a reprint: PRB473401ovRP93ZnOZnS.pdf. Equations of state (EOS) for the highpressure phases of ZnO and ZnS were determined by carrying out ab initio perturbedion calculations. The results were used to examine different empirical EOS formalisms proposed for experimental PV 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 BirchMurnaghan EOS predicts zeropressure properties that agree with ab initio calculations. 

96. J. M. Recio, and R. Pandey, 

97. J. M. Recio, E. Francisco, M. Flórez, and A. Martín Pendás, A new technique for deriving pairwise potentials from ab initio quantummechanical 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 Buckinghamtype 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, 

99. U. Puntambekar, J. M. Recio, and R. Pandey, 

100. V. Luaña, A. Martín Pendás, J. M. Recio, E. Francisco, and M. Bermejo, doi locator: doi:10.1016/00104655(93)90041A. The computational implementation is described of the ab initio perturbed ion method, a selfconsistent 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 Slatertype orbitals are supported on every center. Very large, realistic, models of ionic materials can be efficiently solved. The program is provided with an easytouse and easytolearn interface, with special orders for threedimensional solids, either pure and defective, and for isolated clusters. 

101. V. Luaña, M. Flórez, and L. Pueyo, Download a reprint: JCP997970ovLF93CuNaFvibrations.pdf. doi locator: doi:10.1063/1.466214. The ground state electronic structure and energy of a CuF_{92}Na_{86}^{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 CoulombHartreeFock (uCHF) correlation energy corrections. Parallel calculations are performed on the CuF_{92}Na_{86}^{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 oncenter 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, finitedifference 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} (1a_{1g}), 108 cm^{1} (1t_{1u}), and 173 cm^{1} (1e_{g}) determined mainly by the motions of the CuF_{6} octahedron. 

102. L. Kantorovich, A. I. Livshicz, and G. M. Fogel, 

103. M. Bermejo, J. M. Recio, V. Luaña, and L. Pueyo, doi locator: doi:10.1006/jssc.1993.1026. The location of the 3d levels of 10 transitionmetal impurities in the band gaps of 4 ionic fluorides was studied by independent HartreeFock (HF) cluster calculations on openshell MF_{6}^{n} systems [M = Cr^{z+} (z = 13), Mn^{z+} (z = 13), Fe^{z+} (z = 12), and V^{z+} (z = 23)] and closed = shell AF_{6}^{n} systems (A = Li^{+}, Na^{+}, Mg^{+2}, and Zn^{+2}). The variation of the 3d orbital energies of the impurities with the MF distance was deduced from the corresponding MF_{6}^{n} calculations at different cluster sizes. The band gap edges for LiF, NaF, KMgF_{3}, and KZnF_{3} were estimated from the AF_{6}^{n} calculations: the highest occupied level was estimated from HF orbital energies of the 1A_{g} ground state, and the lowest unoccupied level, from HF orbital energies of the first excited 3T_{1u} state. These orbital energies were combined to preparate approximated energydistance 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 largescale quantummechanical calculations. 

104. A. Beltrán, S. Bohm, A. FloresRiveros, J. A. Igualada, G. Monrós, J. Andrés, V. Luaña, and A. Martín Pendás, A theoretical description of crystal effects induced by the presence of impurity centers V^{+4} entering the dodecahedral and tetrahedral sites of ZrSiO_{4} 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 clusterinthelattice 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 ZrSiO_{4}. 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 8foldcoordinated ion site is energetically favorable, whereas that on the 4foldcoordinated 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, doi locator: doi:10.1016/01661280(88)804391. The authors present the theoretical results obtained for (NaCl)_{n} clusters with $n\leq{}19$. The calculations were performed using the abinitio PerturbedIon (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, The electronic structure of the ground state and the lowest electronic excited state of fcc Ne was calculated with an ab initio atominthelattice approach consistent with the theory of electronic separability of manyelectron systems. The HartreeFockRoothaan 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 atomlattice 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 gasphase orbitals. 

107. A. Martín Pendás, E. Francisco, and J. M. Recio, 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 twocenter 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, ClLi+, ClCl, and HeHe closedshell pairs with an special attention to the fictituous asymmetry introduced by the approximation Our main conclusions are: (a) the TMSR approximation for twocenter 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, 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 clusterinthelattice 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, doi locator: doi:10.1063/1.463679. The Huzinaga buildingblock equations for manyelectron systems, derived under the hypothesis of strong orthogonality among the system groups, can be also deduced as a particular case of the AdamsGilbert formalism, in which the strong orthogonality cannot be fully achieved in most practical cases due to basisset 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 strongorthogonality 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 basisset truncation can be analyzed unambiguously. 

110. J. M. Recio, V. Luaña, E. Francisco, and L. Pueyo, A theoretical analysis is presented of the spinorbit 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 CrO_{6}^{9} cluster and includes a rigorous determination of the spinorbit constants Also discussed are the effects of the external lattice on the cluster electron density, and the variation of the dd spectrum with the metalligand separation The calculation steps are described. 

111. L. Pueyo, A. Martín Pendás, J. M. Recio, E. Francisco, and V. Luaña, 

112. L. Pueyo, V. Luaña, M. Flórez, E. Francisco, J. M. Recio, and M. Bermejo, Some important problems of the theoretical analysis of the dd electronic transitions in ionic crystals are presented and discussed. The work is limited to the wavefunctional 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 mainlyd states; (c) electron correlation and quantitative spectral prediction; (d) variation of the electronic transitions with the cluster geometry, and (e) spinorbit 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, 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 Ftype centers in KMgF_{3}, MgO and ZnS. 

114. A. Martín Pendás, and E. Francisco, doi locator: doi:10.1103/PhysRevA.43.3384. 

115. V. Luaña, M. Flórez, J. M. Recio, L. Pueyo, M. Bermejo, and R. M. Pitzer, 

116. E. Francisco, and L. Pueyo, 

117. M. Flórez, V. Luaña, M. Bermejo, and L. Pueyo, The electronic structures of the KMgF_{3} and KZnF_{3} cubic perovskites have been calculated with the ab initio perturbed ion (PI) method, a scheme drived from the theory of electronic separability of multielectron systems and the ab initio model potential approach of Huzinaga. 

118. M. Bermejo, J. M. Recio, V. Luaña, and L. Pueyo, We use the HartreeFockRoothaan method of J. W. Richardson et al. (1971), augmented with coreprojection operators and including renormalization corrections, to compute the $R(MF) distance evolution of the electronic structure of several MF_{6}$ octahedral clusters. 

119. Richard B. Ross, Víctor Luaña, Walter C. Ermler, Russell M. Pitzer, and C. William Kern, 

120. R. B. Ross, W. C. Ermler, V. Luaña, R. M. Pitzer, and C. W. Kern, 

121. J. M. Recio, V. Luaña, L. Pueyo, and M. Bermejo, 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, Download a reprint: PRB421791ovLR90MgO.pdf. doi locator: doi:10.1103/PhysRevB.42.1791. 

123. V. Luaña, and L. Pueyo, Download a reprint: PRB413800ovLP90aiPI.pdf. doi locator: doi:10.1103/PhysRevB.41.3800. 

124. J. M. Recio, V. Luaña, and L. Pueyo, 

125. V. Luaña, and L. Pueyo, Download a reprint: PRB3911093ovLP89clusterlattice.pdf. doi locator: doi:10.1103/PhysRevB.39.11093. 

126. V. Luaña, M. Bermejo, M. Flórez, J. M. Recio, and L. Pueyo, doi locator: doi:10.1063/1.456307. 

127. G. Fernández Rodrigo, and L. Pueyo, 

128. J. M. Recio, and L. Pueyo, doi locator: doi:10.1016/01661280(88)80438X. 

129. J. F. van der Maelen, M. Bermejo, and L. Pueyo, doi locator: doi:10.1016/01661280(88)80441X. 

130. V. Luaña, and L. Pueyo, 

131. E. Francisco, and L. Pueyo, doi locator: doi:10.1103/PhysRevB.37.5278. 

132. E. Francisco, V. Luaña, J. M. Recio, and L. Pueyo, 

133. V. M. García Fernández, G. Fernández Rodrigo, and L. Pueyo, doi locator: doi:10.1016/01661280(88)804433. 

134. M. Bermejo, V. Luaña, J. M. Recio, and L. Pueyo, doi locator: doi:10.1016/01661280(88)804421. 

135. M. T. Barriuso, J. A. Aramburu, M. Moreno, M. Flórez, G. Fernández Rodrigo, and L. Pueyo, doi locator: doi:10.1103/PhysRevB.38.4239. 

136. G. Fernández Rodrigo, and L. Pueyo, 

137. G. Fernández Rodrigo, L. Pueyo, M. Moreno, and M. T. Barriuso, 

138. G. Fernández Rodrigo, M. Flórez, L. Pueyo, M. Moreno, and M. T. Barriuso, 

139. J. F. van der Maelen, C. Pérez Llera, and L. Pueyo, 

140. V. Luaña, G. Fernández Rodrigo, M. Flórez, E. Francisco, J. M. Recio, J. F. van der Maelen, L. Pueyo, and M. Bermejo, 

141. V. Luaña, G. Fernández Rodrigo, E. Francisco, L. Pueyo, and M. Bermejo, 

142. V. Luaña, and L. Pueyo, 

143. V. Luaña, E. Francisco, M. Flórez, J. M. Recio, and L. Pueyo, 

144. M. Flórez, L. Seijo, and L. Pueyo, doi locator: doi:10.1103/PhysRevB.35.2474.2. 

145. E. Francisco, L. Seijo, and L. Pueyo, 

146. E. Francisco, L. Seijo, and L. Pueyo, 

147. E. Francisco, and L. Pueyo, doi locator: doi:10.1103/PhysRevA.36.1978. 

148. E. Francisco, V. Luaña, and L. Pueyo, 

149. E. Francisco, M. Flórez, Z. Barandiarán, G. Fernández Rodrigo, V. Luaña, J. M. Recio, M. Bermejo, L. Seijo, and L. Pueyo, 

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, 

151. M. Flórez, M. Bermejo, V. Luaña, E. Francisco, J. M. Recio, and L. Pueyo, 

152. L. Seijo, M. Flórez, and L. Pueyo, doi locator: doi:10.1016/00104655(86)902377. 

153. L. Seijo, Z. Barandiarán, V. Luaña, and L. Pueyo, 

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, 

155. V. Luaña, Z. Barandiarán, and L. Pueyo, Model potentials appropriate for molecular calculations with Slatertype (ST) basis sets have been generated for the firstrow transitionmetal 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 allelectron 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 transitionmetal compounds with STO 2 zeta quality. 58 references, 3 figures, 12 tables. 

156. M. Flórez, L. Seijo, and L. Pueyo, doi locator: doi:10.1103/PhysRevB.34.1200. The pure electronic dd spectrum of the MnF_{6}^{4} complex ion has been computed at different values of the Mn^{2+}F^{} distance R along the a_{1g}$ vibration mode, following an openshell selfconsistentfieldmolecularorbital (SCFMO) methodology. Both clusterinvacuo and clusterinthelattice (RbMnF_{3}) calculations have been performed in terms of rigidlattice and partiallyrelaxedlattice models. Theoretical spectral parameters have been obtained from the SCF results, and the evolution of the 3d splitting and the dd 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 doubleexcitation 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 (4244) kK to double excitations. The energy splitting of the ^{4}A_{1g}, ^{4}E^{a}_{g} states and its relationship with the electronic delocalization of the 3d MO's have been analyzed. The present calculation predicts, for MnF_{6}^{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 RbMnF_{3} 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, 

158. J. A. Sordo, and L. Pueyo, doi locator: doi:10.1016/01661280(85)850867. A set of HartreeFockRoothaan (HFR) wave functions $\alpha_{i}$_{i=16}$ for the nickel atom (3d^{8}4s^{2}:^{3}F) has been constructed by simply adding one STO (Slater Type Orbital) to the $2\zeta$, ClementiRoetti basis set. The application of several quality tests and the calculation of some atomic properties show that some of the wave functions obtained, $\alpha_{i}$_{i=2,4,5,6}$, are comparable with the highquality multiterm HFR basis sets. The intermediate size of the $\alpha_{i}$_{i=2,4,5,6}$ wave functions makes them specially appropriate for molecular calculations. 

159. Z. Barandiarán, L. Seijo, and L. Pueyo, 

160. Z. Barandiarán, and L. Pueyo, doi locator: doi:10.1063/1.446858. 

161. Z. Barandiarán, and L. Pueyo, doi locator: doi:10.1063/1.445971. 

162. Z. Barandiarán, L. Pueyo, and F. GómezBeltrán, doi locator: doi:10.1063/1.445303. The clusterlattice interaction involving the CrF^{3}_{6} in K_{2}NaCrF_{6} 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 selfconsistency. 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 corelattice and valencelattice portions reveals that the earlier procedure of centering the lattice potential function on the ligand site is inappropriate for improving the cluster invacuo calculation of the equilibrium metalligand 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 $\bar\nu(a_{1g})$, the horizontal displacement of the ^{4}T_{2g} with respect to the ^{4}A_{2g}, the vertical Stokes shift associated with these two states and the ligandtometal charge transfer originated in the SCF process. 

163. L. Pueyo, and J. W. Richardson, doi locator: doi:10.1063/1.441768. 

164. L. Pueyo, and J. W. Richardson, doi locator: doi:10.1063/1.435334. Correlation energy as an empirical correction is introduced into otherwise ab initiotype calculations of the electronic structure of trnasition metal complexes. The strong field MO electronic states are expanded in a series of freeion 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 NiF_{6}^{4} and CrF_{6}^{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 NiF_{6}^{4} and from 2980 to 450 in CrF_{6}^{3}. An analysis of the influence of the electronic delocalization on the calculated spectra suggests that the chargetransfer 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, 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 openshell SCF MO methodology. An initial, isolatedcluster description is presented and compared with a more elaborate representation which includes the external lattice potential, a cluster correlation energy correction, and spinorbit and configuration interactions. When these refinements are included, the six transition energies observed in K_{2}NaCrF_{6} 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 t^{3} doublets; the calculation places t^{3}^{2}T_{1g} above t^{3}^{2}E_{g} and below t^{2}e$^{4}T_{2g}. Due to the variation of spinorbit interaction with distance, these levels change in character so rapidly that a more realistic procedure than the usual FranckCondon approximation has been employed in the calculation of the transition intensity pattern via the magnetic dipole mechanism. Surprisingly, the equilibrium distance of $1\Gamma_{7}^{4}T_{2g}$ 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 doubletquartet mixing, the structure of the ^{4}A_{2g}  ^{2}T_{2g} broad band, and the Stokes shift observed in the emission spectra of those crystals. 