In a recent paper on Hartree-Fock (HF) calculations on solid LiH with large Gaussian-type basis sets, Paier et al. [Phys. Rev. B 80, 174114 (2009)] report a comment that we dispute: that similar calculations appear unlikely to be feasible using the CRYSTAL code. Here we show that using a full HF approach within periodic boundary conditions as implemented in the CRYSTAL code the same total energy is obtained as from the schemes adopted by Paier et al.

The structure and the vibrational spectrum of akdalaite (5Al(2)O(3)center dot H2O, also known as tohdite) have been investigated at the periodic ab-initio quantum-mechanical level by using a high quality Gaussian type basis set and the hybrid B3LYP Hamiltonian with the CRYSTAL06 code. Three space groups proposed in the literature, namely P6(3)mc and its two P31c and Cmc2(1) subgroups, have been considered, obtaining essentially the same energy (the largest total energy difference is 0.2 kJ/mol per cell) and geometry.The harmonic frequencies at the Gamma point have been computed. Isotopic substitution and graphical representation permit a complete classification of normal modes in terms of simple models (octahedra and tetrahedra modes, hydrogen stretching and bending). The Al-O octahedra and tetrahedra modes appear below 880 cm(-1), Al-OH bending modes are located in the range 870-900 cm(-1), and OH stretching modes are at 3330-3400 cm(-1).

An X-ray constrained wavefunction (XCW) is a wavefunction constrained to reproduce the structure factors from X-ray charge density experiment [1].XCW's have primarily been used to obtain accurate images of the electron density in molecular crystals [1].In this talk the XCW method is extended to the calculation of linear and non-linear optical response properties for several molecular crystals [2].The theory used for the calculation of bulk (crystalline) susceptibilities and refractive indices from molecular polarisabilities will be reviewed.Results for several systems will be presented and discussed.I will also outline a method for improved structure determination based on using aspherical atomic densities obtained from quantum mechanical calculations.The new method allows the determination of ADP's for hydrogen atoms from the X-ray data alone [3].. The possibility of using such aspherical densities in everyday structure refinement will be discussed.

A hybrid-exchange DFT hamiltonian and a periodic slab model have been employed to simulate water dissociation at the border of sub-monolayer MgO films deposited on Ag(100). Non-polar and polar borders have been considered, but the reaction energy is higher in the former case. The O-1s core level shifts and the O-H vibrational frequencies have been calculated and shown to be compatible with recent XPS and HREELS data, respectively [Savio et al., J. Chem. Phys., 2003, 119, 12053].

The vibrational spectrum of alpha-AlOOH diaspore has been calculated at the B3LYP level of theory with a double-zeta quality Gaussian-type basis set by using the periodic ab initio CRYSTAL code. Harmonic frequencies at the Gamma point and the corresponding 48 normal modes are analyzed and classified in terms of simple models (octahedra modes, hydrogen stretching, bending, rotations) by direct inspection of eigenvectors, graphical representation, and isotopic substitution. Hydrogen modes are fully separated from the octahedra modes appearing under 800 cm(-1); bending modes are located in the range of 1040-1290 cm(-1), whereas stretching modes appear at 3130-3170 cm(-1). The available experimental IR and Raman spectra are characterized by broad bands, in some cases as large as 800 cm(-1), and individual peaks are obtained by decomposing these bands in terms of Lorentz-Gauss product functions; such a fitting procedure is affected by a relatively large degree of arbitrariness. The comparison of our calculated data with the most complete sets of experimental data shows, nevertheless, a relatively good agreement for all but the H modes; the mean absolute differences for modes not involving H are 10.9 and 7.2 cm(-1) for the IR and the Raman spectra, respectively, the maximum differences being 15.5 and 18.2 cm(-1). For the H bending modes, differences increase to 30 and 37 cm(-1), and for the stretching modes, the calculated frequencies are about 200 cm(-1) higher than the experimental ones; this is not surprising, as anharmonicity is expected to red shift the OH stretching by about 150 cm(-1) in isolated OH groups and even more when the latter is involved in strong hydrogen bonds, as is the case here.

The electronic properties of unsupported and supported NiO films on Ag(100) have been studied theoretically using two methods. Results from density functional theory using the GGA+U approach and plane wave basis sets have been compared with those obtained with a hybrid functional and an atomic orbital basis set. In general the two approaches provide similar answers, with the exception of the NiO band gap which is better reproduced in the hybrid DFT approach. Both unsupported and supported films have an antiferromagnetic ordering, and only the magnetization of the Ni ions at direct contact with the metal substrate is slightly reduced, the rest being basically unperturbed. At variance with MgO/Ag(100) interfaces, NiO films adhere to Ag(100) with a bonding which includes also important covalent contributions. This results in a much smaller work function change than in MgO/Ag(100) and in tails of the NiO states which contribute to the density of states at the Fermi level.

A quantum-mechanical calculation of the zone-centre phonon spectrum of beryl has been performed, by using an hybrid HF/DFT Hamiltonian (B3LYP). An excellent agreement with the experiment has been obtained, being the difference between the calculated and the experimental vibrational frequencies (Raman, IR-TO and IR-LO) less than 5 cm−1 on average. In the few cases where a relatively large disagreement between calculated and experimental data is observed, an explanation can be found which attributes the reason of the discrepancies to the experimental data rather than to the calculated ones. The calculation (i) allows the identification, in the experimental spectra, of the peaks corresponding to fundamental modes, overtones, combination bands and leakage; (ii) solves problems of band assignements due to the presence of LO–TO splitting in the IR spectra; (iii) provides the frequencies of silent modes; (iv) permits a full analysis of the atomic motion corresponding to each normal mode.

MOF-5 is by far the most relevant member of the new class of metal - organic framework materials and has been adopted as a case study to show that reliable ab initio prediction of materials properties of complex systems can be obtained by means of a solid state computational tool like the CRYSTAL code. Structure, electronic properties and vibrational frequencies of MOF-5 computed at the B3LYP level of theory are reported and discussed. Animations representing MOF- 5 vibrations are available at the web site: www. crystal. unito. it/ vibs/ mof5.

It is shown that a local MP2 approach can be conveniently adopted as a first step towards the post-Hartree–Fock description of crystalline solids. The relation of a new periodic MP2 code (CRYSCOR) to a classical Hartree–Fock program (CRYSTAL) is outlined. As an illustration, the case of LiH, a prototypical ionic crystal, is treated in some detail by analyzing the effect of the perturbative correction on equilibrium geometry, lattice energy and electron distribution (X-ray structure factors, directional Compton profiles), with reference to experimental data.

AbstractFor Abstract see ChemInform Abstract in Full Text.

The vibrational spectrum of Mg(3)Al(2)Si(3)O(12) pyrope 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, 55 silent modes) is calculated. The effect of the basis set and of the computational parameters on the calculated frequencies is discussed. It is shown that the mean absolute difference with respect to the experimental IR and RAMAN data is as small as 6 and 8 cm(-1), respectively. The IR and RAMAN modes are fully characterized by various tools such as isotopic substitution, direct inspection of the eigenvectors, and graphical representation. The present calculation permits to clarify some of the assignment and interpretation problems raised by experiment and previous simulations with force fields.

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.

The crystalline orbitals of KNbO3 are localized according to an iterative mixed Wannier-Boys scheme. The transformed orbitals turn out to be extremely localized; their features and degree of localization are described in terms of various indices. The spontaneous polarization and the effective Born charges of the various atoms are evaluated starting from the localized Wannier function (LWF) centroids and from delocalized Bloch functions through the Berry phase (BP) scheme. It turns out that the results provided by both approaches agree very well (for example, the spontaneous polarization is 0.3361 and 0.3347 C/m(2) from the LWF and BP methods, respectively).

The paramagnetic F center in LiF is investigated at a quantum mechanical level with the CRYSTAL98 periodic code by using a supercell scheme. The isotropic and anisotropic components of the hyperfine coupling tensor describing the interaction between the unpaired electron and the nuclear spins up to the seventh nearest neighbors of the defect are computed by using two different Hamiltonians (Hartree-Fock and local density approximation), and turn out to compare reasonably well with electron paramagnetic resonance and electron-nuclear double resonance data. A term of the hyperfine tensor, not yet available experimentally, is presented for future comparison. The defect wave function is analyzed in terms of the charge and spin density maps, band structure, and Mulliken population.

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 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.