AbstractFor Abstract see ChemInform Abstract in Full Text.

The vibrational spectrum of Ca3Fe2Si3O12 andradite is calculated at the Gamma point by using the periodic ab initio CRYSTAL program that adopts an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. The full set of frequencies (17 IR active, 25 Raman active, and 55 inactive modes) is calculated. The effect of the basis set on the calculated frequencies is discussed. The modes are characterized by direct inspection of the eigenvectors and isotopic substitution. The present calculations permit us to clarify some of the assignment problems raised by experiments. The mean absolute differences of the various modes with respect to the available experimental IR and Raman data are as small as 9 and 5 cm(-1), respectively.

The OH vibrational frequency of four crystalline compounds ranging from ionic (brucite, Mg(OH)(2), and portlandite, Ca(OH)(2)) to semi-covalent (edingtonite, as representative of free surface OH groups in silica, and acid chabazite, as representative of acid zeolites) has been investigated at quantum mechanical level with the CRYSTAL program using the B3LYP hybrid functional. The OH vibration is calculated in two ways: (i) in the harmonic approximation, by diagonalizing the fully coupled dynamical matrix to yield the harmonic frequency omega(h). (ii) at the anharmonic level, by decoupling the OH stretching mode from the bulk phonons and by numerically solving the one-dimensional Schrodinger equation associated with the OH potential energy to yield the fundamental omega(01) and the first overtone omega(02) frequencies. The harmonic and anharmonic frequencies differ by more than 150 cm(-1). In the cases where direct comparison is possible ( brucite, portlandite and edingtonite), the experimental and calculated frequencies differ by less than 10 cm(-1); the calculated anharmonicity constant, omega(e)x(e) (2 omega(01) - omega(02))/2, is systematically smaller than the experimental value by about 10 cm(-1). The effect of the computational parameters on the computed frequencies is explored, with particular attention to the grid used for the construction of the DFT exchange and correlation contribution to the Hamiltonian and the accuracy in the geometry optimisation.

The central-zone vibrational spectrum of alpha-quartz (SiO2) is calculated by building the Hessian matrix numerically from the analytical gradients of the energy with respect to the atomic coordinates. The nonanalytical part is obtained with a finite field supercell approach for the high-frequency dielectric constant and a Wannier function scheme for the evaluation of Born charges. The results obtained with four different Hamiltonians, namely Hartree-Fock, DFT in its local (LDA) and nonlocal gradient corrected (PBE) approximation, and hybrid B3LYP, are discussed, showing that B3LYP performs far better than LDA and PBE, which in turn provide better results than HF, as the mean absolute difference from experimental frequencies is 6, 18, 21, and 44 cm(-1), respectively, when a split valence basis set containing two sets of polarization functions is used. For the LDA results, comparison is possible with previous calculations based on the Density Functional Perturbation Theory and usage of a plane-wave basis set. The effects associated with the use of basis sets of increasing size are also investigated. It turns out that a split valence plus a single set of d polarization functions provides frequencies that differ from the ones obtained with a double set of d functions and a set of f functions on all atoms by on average less than 5 cm(-1).

The crystalline orbitals of seven oxygen containing compounds with increasing degree of covalent character (MgO, MnO, ZnO, Al2O3, SiO2, AlPO4, and CaSO4) are localized according to a Wannier-Boys mixed scheme recently implemented. The resulting Wannier functions are analyzed in terms of various indices (centroids positions, second-order central moment tensor, its eigenvalues and principal axes, Mulliken population analysis, and atomic localization indices). Systematic trends are observed along the series. (C) 2002 American Institute of Physics.

Results are reported on the geometry optimisation of periodic systems with the Hartree–Fock analytical gradients recently implemented in the Crystal code. Application to the structure optimisation of molecules, polymers, slabs and crystals is presented.

A method for obtaining spatially localized crystalline orbitals starting from delocalized Bloch functions is proposed. The method, that has been implemented in the LCAO CRYSTAL code, is intrinsic and general for nonconducting systems, and provides a set of well localized Wannier functions that can be used for applications that take advantage of their localized character. Examples are given that illustrate the performances and efficiency of the proposed scheme.

The present chapter discusses the Hartree-Fock (HF) method for periodic systems with reference to its implementation in the CRYSTAL program. The HF theory is shortly recalled in its Closed Shell (CS), Unrestricted (UHF) and Restricted open shell (RHF) variants; its extension to periodic systems is illustrated. The general features of CRYSTAL, the periodic ab initio linear combination of atomic orbitals (LCAO) program, able to solve the CS, RHF and UHF, as well as Kohn-Sham equations, are presented. Three examples illustrate the capabilities of the CRYSTAL code and the quality of the HF results in comparison with those obtained with the Local Density Approximation using the same code and basis set: NiO in its ferro-magnetic and anti-ferromagnetic structure, trapped electron holes in doped alkaline earth oxides, and F-centres in LiF.

CRYSTAL [1] computes the electronic structure and properties of periodic systems (crystals, surfaces, polymers) within Hartree-Fock [2], Density Functional and various hybrid approximations.CRYSTAL was developed during nearly 30 years (since 1976) [3] by researchers of the Theoretical Chemistry Group in Torino (Italy), and the Computational Materials Science group in CLRC (Daresbury, UK), with important contributions from visiting researchers, as documented by the main authors list and the bibliography.The basic features of the program CRYSTAL are presented, with two examples of application in the field of crystallography [4, 5].

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the groundstate structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M = Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2, and CoF2 is also discussed.

The energetics of the Cl,/MgO(OOl) interface were investigated using the ab initio periodic Hartree-Fock (PHF) method and local density functional correlation corrections to PHF theory, as implemented in the program CRYSTAL92. Estimates of the correlation corrected PHF energies are made by post-SCF evaluations of three gradient corrected functionals. The correlation energy is calculated from the fully converged ground state PHF charge density and added to the PHF total energy. This is the first study of interfacial energetics using the correlation corrected PHF theory. PHF and correlation corrected molecule/surface binding energies are reported for seven orientations of the adsorbate with respect to the surface plane. Three of the configurations align the intramolecular axes along the surface normal and the remaining geometries arrange the molecules heat-to-tail, parallel to the surface plane. The most favorable interaction occurs when chlorine approaches a surface oxygen along the normal direction. This site preference is consistent with a classical electrostatic description of the physisorption process. The binding energy increases with decreasing surface coverage. At the most dilute coverage studied (1:8) the PHF binding energy was 4.1 kcal/mol and the correlation corrected binding energies ranged from 9.2 to 10.3 kcal/mol. All three functionals tended to increase the molecule/surface attractions, shorten the molecule/surface equilibrium distance, increase the curvature of the molecule/surface potential energy surface near equilibrium, and reduce the molecule/molecule repulsions.

Noncubic Mn3O4 spinel (Hausmannite) has been investigated by using the periodic Hartree-Fock CRYSTAL95 program. The structure has been fully optimized, and the computed geometry compares well with the experimental data. The analysis of the wave function in terms of Mulliken charges shows that the net charge of the tetrahedral cation (Mn-A) is very close to the formal one (+1.86 electrons to be compared to +2); for the octahedral site (Mn-B) the net charge is far from the ideal ionic model (+2.3 electrons instead of +3), and the Mn-B-O bonds show some covalent character. The same analysis performed on the spin density gives magnetic moments very close to the ones corresponding to the ideal d(4) and d(5) configurations (4.90 and 3.97 electrons for Mn-A and Mn-B, respectively). The total energy of seven different spin configurations has been evaluated and the corresponding wave function analyzed. Superexchange coupling constants are evaluated by mapping the ab initio energy data to the Ising hamiltonian. It turns out that the intertetrahedral and tetrahedral-octahedral magnetic interactions are small and antiferromagnetic, in agreement with experimental evidence. The Mn-B-Mn-B alone the octahedra chains is ten times larger, whereas the interchain interaction is small and ferromagnetic. [S0163-1829(99)03843-6].

We report the bulk and surface properties of lithium computed within a full potential LCGTO formalism using both density functional theory and the Hartree-Fock approximation. We examine the convergence of computed properties with respect to numerical approximations and also explore the use of finite temperature density functional theory. We demonstrate that fully converged calculations reproduce cohesive properties, elastic constants, band structure, and surface energies in full agreement with experimental data and, where available, previous calculations.

The capabilities of the present version of the CRYSTAL program (CRYSTAL98) in the description of the structural, electronic and magnetic properties of perfect and defective crystalline systems will be illustrated with reference to three examples: (i) The relative stability of the ferromagnetic and anti-ferromagnetic structures of a transition metal insulator; we will illustrate how different magnetic states can be obtained and evaluate the corresponding superexchange coupling constant J. (ii) The relative stability of the different acidic sites obtained by inserting an Al atom at (and by linking the accompanying H atom to) non-equivalent zeolite framework positions has been evaluated; the geometry of the various Si(OH)Al groups and the frequency of the OH stretching are compared. (iii) The physico-chemical features of a trapped hole formed when a monovalent alkali metal ion is substituted for a divalent cation in bulk alkaline earth oxides; the properties computed and compared with available experimental data are: the degree of localization of the hole, the relaxation of the defect ion and its neighbours, the electric field gradient, the Fermi contact term and the anisotropic hyperfine coupling constant.

The equilibrium geometry and total energy of four all-silica zeolite frameworks, sodalite, chabazite, faujasite and edingtonite, have been obtained at a periodic ab initio all-electron level (CRYSTAL code) and compared with the corresponding quantities for α- and β-quartz. The dependence of the results on the adopted basis set and hamiltonian (Hartree–Fock, or with an a posteriori correlation correction; various local and gradient-corrected density functional methods and Becke's hybrid scheme) is discussed. The various methods provide a similar order in the relative stabilities; large quantitative differences are however observed, Hartree–Fock and LDA results being at the extremes. The combined use of force-field and ab initio schemes in the geometry optimization is discussed.

The structural, electronic and magnetic properties of the perovskite systems KMF3 (M=Mn, Fe, Co, Ni) have been investigated with CRYSTAL95, a periodic abinitio Hartree–Fock program. An all-electron Gaussian basis set has been used. The equation of state has been determined first for the cubic structure; then deviations from cubic symmetry have been explored, with the result that the Mn, Fe and Co systems are found to be slightly more stable in a tetragonal geometry. The systems are almost fully ionic, with net charges for K and M of +1, ca. -0.9 and ca. +1.8 ∣e∣, respectively. The antiferromagnetic (AFM) is always more stable than the ferromagnetic (FM) phase; the energy difference ΔE=E(FM)-E(AFM) is shown: (a) to be additive with respect to the number of M–M first neighbours; (b) to increase with decreasing lattice parameter according to an inverse power law; and (c) to become zero when the M–F–M angle approaches 90°. The super-exchange coupling constants, evaluated from ΔE by using an Ising model hamiltonian, are in qualitative agreement with the experimental data (from 30% to 45% of the latter). Mulliken population data, charge and spin density maps and density of states are used to illustrate the electronic structure.

First-principles periodic Hartree-Fock calculations of the ground state electron distribution and empty oxygen p states in Li0.125Ni0.875O and Li0.25Ni0.75O are reported which provide direct evidence of oxygen p holes in Li-doped NiO. Calculated changes in the densities of empty oxygen p states are in good agreement with oxygen K-edge spectra. The empty states of the Li-doped materials provide a theoretical value of the band gap in NiO which, unlike previous estimates, is reasonably close to the observed value of 3.7 eV.

Ab initio Hartree-Fock (I-IF) theory has been applied to galena (PbS). Pseudopotentials are used to describe the Pb core states and Gaussian basis sets have been developed for S (all electron) and Pb (valence only). The effect of the approximations made (HF theory, the basis set and the pseudopotential) on the structural energetics have been examined in detail. The computed lattice constant and elastic constants are in fair agreement with experiment. The effect of basis set on these properties is minor whereas different choices of pseudopotential and correlation corrections significantly affect the results. The density of states is insensitive to these approximations and in good agreement with spectroscopic data.