Nuclear motion effects on the density matrix of crystals: an ab initio Monte Carlo harmonic approach.

In the frame of the Born-Oppenheimer approximation, nuclear motions in crystals can be simulated rather accurately using a harmonic model. In turn, the electronic first-order density matrix (DM) can be expressed as the statistically weighted average over all its determinations each resulting from an instantaneous nuclear configuration. This model has been implemented in a computational scheme which adopts an ab initio one-electron (Hartree-Fock or Kohn-Sham) Hamiltonian in the CRYSTAL program. After selecting a supercell of reasonable size and solving the corresponding vibrational problem in the harmonic approximation, a Metropolis algorithm is adopted for generating a sample of nuclear configurations which reflects their probability distribution at a given temperature. For each configuration in the sample the "instantaneous" DM is calculated, and its contribution to the observables of interest is extracted. Translational and point symmetry of the crystal as reflected in its average DM are fully exploited. The influence of zero-point and thermal motion of nuclei on such important first-order observables as x-ray structure factors and Compton profiles can thus be estimated.

CRYSCOR: a program for the post-Hartree-Fock treatment of periodic systems.

Cryscor is a periodic post-Hartree-Fock program based on local functions in direct space, i.e., Wannier functions and projected atomic orbitals. It uses atom centered Gaussians as basis functions. The Hartree-Fock reference, as well as symmetry information, is provided by the Crystal program. Cryscor presently features an efficient and parallel implementation of periodic local second order Møller-Plesset perturbation theory (MP2), which allows us to study 1D-, 2D- and 3D-periodic systems beyond 1000 basis functions per unit cell. Apart from the correlation energy also the MP2 density matrix, and from that the Compton profile, are available. Very recently, a new module for calculating excitonic band gaps at the uncorrelated Configuration-Interaction-Singles (CIS) level has been added. Other advancements include new extrapolation techniques for calculating surface adsorption on semi-infinite solids. In this paper the diverse features and recent advances of the present Cryscor version are illustrated by exemplary applications to various systems: the adsorption of an argon monolayer on the MgO (100) surface, the rolling energy of a boron nitride nanoscroll, the relative stability of different aluminosilicates, the inclusion energy of methane in methane-ice-clathrates, and the effect of electron correlation on charge and momentum density of α-quartz. Furthermore, we present some first tentative CIS results for excitonic band gaps of simple 3D-crystals, and their dependence on the diffuseness of the basis set.

Evaluation of the electron momentum density of crystalline systems from Ab initio linear combination of atomic orbitals calculations.

Alternative techniques are presented for the evaluation of the electron momentum density (EMD) of crystalline systems from ab initio linear combination of atomic-orbitals calculations performed in the frame of one-electron self-consistent-field Hamiltonians. Their respective merits and drawbacks are analyzed with reference to two periodic systems with very different electronic features: the fully covalent crystalline silicon and the ionic lithium fluoride. Beyond one-electron Hamiltonians, a post-Hartree-Fock correction to the EMD of crystalline materials is also illustrated in the case of lithium fluoride.

Approaching the theoretical limit in periodic local MP2 calculations with atomic-orbital basis sets: the case of LiH.

The atomic orbital basis set limit is approached in periodic correlated calculations for solid LiH. The valence correlation energy is evaluated at the level of the local periodic second order Møller-Plesset perturbation theory (MP2), using basis sets of progressively increasing size, and also employing "bond"-centered basis functions in addition to the standard atom-centered ones. Extended basis sets, which contain linear dependencies, are processed only at the MP2 stage via a dual basis set scheme. The local approximation (domain) error has been consistently eliminated by expanding the orbital excitation domains. As a final result, it is demonstrated that the complete basis set limit can be reached for both HF and local MP2 periodic calculations, and a general scheme is outlined for the definition of high-quality atomic-orbital basis sets for solids.

Evidence of instantaneous electron correlation from Compton profiles of crystalline silicon.

The combination of new experimental and theoretical techniques provides evidence of instantaneous electron correlation effects in directional Compton profiles of crystalline silicon, which cannot be reproduced when reference is made to a density matrix obtained from a single-determinantal wavefunction. These effects are instead accounted for by a recently implemented post-Hartree-Fock periodic scheme, which gives results in quite good agreement with the high-quality experimental data.

Periodic local-MP2 computational study of crystalline neon.

Face-centered-cubic crystalline Neon is taken as a test system to explore the influence of computational parameters on the quality of the MP2 solution provided by the Cryscor program using a local-correlation approach. The effect of the various approximations adopted is analyzed: basis set limitations, finite size of excitation domains, truncation of the tails of the local functions, approximate evaluation of two-electron integrals, estimate (by extrapolation) of long-range contributions are shown to play roles of different importance. The Ne2 dimer is used as an auxiliary test case in order to allow comparison with recent and accurate literature data.

DFT and local-MP2 periodic study of the structure and stability of two proton-ordered polymorphs of ice.

The equilibrium geometry and the formation energy of two periodic polymorphs of Ice have been theoretically studied: the former (Ice XI, crystal group Cmc2(1)) is experimentally observed as the most stable structure at low temperature and pressure; the latter (crystal group Pna2(1)) is the simplest proton-ordered model of ordinary ice. With the Crystal code, the problem is solved using Hartree-Fock (HF), pure Kohn-Sham (PW91), or hybrid (B3LYP) one-electron Hamiltonians. The B3LYP results are those in best agreement with the experiment. Using the B3LYP-optimized geometry and starting from the corresponding HF Crystal solution, the energetics of the two polymorphs have been investigated at an ab initio MP2 level using the Cryscor code, based on a local-correlation approach: these calculations have allowed us not only to confirm the excellent B3LYP results as concerns the formation energy and the relative stability of the two structures but also to analyze the role in this respect of the intra- and intermolecular contributions to the correlation energy. Since both Crystal and Cryscor adopt a basis set of localized Gaussian-type functions and since very small energy differences are involved, utter attention has been paid to correcting for the basis set superposition error in the calculation of formation energies.

Periodic density functional theory and local-MP2 study of the librational modes of Ice XI.

Two periodic codes, CRYSTAL and CRYSCOR, are here used to simulate and characterize the librational modes of the nu(R) band of Ice XI: this band has been found experimentally to be the region of the vibrational spectrum of ordinary ice most affected by the transition from the proton-disordered (Ice Ih) to the proton-ordered (Ice XI) phase. With CRYSTAL, the problem is solved using Hartree-Fock (HF), pure Kohn-Sham (PW91) or hybrid (B3LYP) one-electron Hamiltonians: the harmonic approximation is employed to obtain the vibrational spectrum after optimizing the geometry. The B3LYP results are those in best agreement with the experiment. For a given crystalline geometry, CRYSCOR computes the energy per cell in an ab initio HF+MP2 approximation using a local-correlation approach; this technique is employed for recalculating the frequencies of the different modes identified by the B3LYP approach, by fully accounting for long range dispersive interactions. The effect of anharmonicity is evaluated separately for each mode both in the B3LYP and HF+MP2 case. The two approaches accurately reproduce the four-peak structure of the librational band. The harmonic B3LYP nu(R) bandwidth of 70 meV is lowered to 60 meV by anharmonic corrections, and becomes 57 meV in the HF+MP2 anharmonic calculation, in excellent agreement with the experimental IINS data (56-59 meV). The assignment of the librational modes is discussed.

Periodic local MP2 method for the study of electronic correlation in crystals: Theory and preliminary applications.

A computational technique for solving the MP2 equations for periodic systems using a local-correlation approach and implemented in the CRYSCOR code is presented. The Hartree-Fock solution provided by the CRYSTAL program is used as a reference. The motivations for the implementation of the new code are discussed, and the techniques adopted are briefly recalled. With respect to the original formulation (Pisani et al., J Chem Phys 2005, 122, 094113), many new features have been introduced in CRYSCOR to improve its efficiency and robustness. In particular, an adaptation of the density fitting scheme to translationally periodic systems is described, based on Fourier transformation techniques. Three examples of application are provided, concerning the CO(2) crystal, proton transfer in ice XI, and the adsorption of methane on MgO (001). The results obtained with the periodic LMP2 method for these systems appear more reliable than the ones obtained using density functional theory.

Reactivity of the non stoichiometric Ni3O4 phase supported at the Pd(100) surface: interaction with Au and other transition metal atoms.

In this work we have studied, employing ab initio periodic calculations, the interaction between the non-stoichiometric Ni(3)O(4) monolayer (a rhombic distribution of vacancies hereafter referred to as RH-Ni(3)O(4)) supported on the Pd(100) surface and several transition metal atoms (Ni, Cu, Pd, Pt, Ag, Au). The interaction produces a regular array of metal centers uniformly distributed in size and shape. According to the size of the atom and the ionization potential, the nature of the interaction ranges from an essentially electrostatic one to a polar-covalent one. The chemical reactivity versus the CO molecule of the overlayer resulting from the saturation with Au atoms of the Ni vacancies has been investigated.

Cationic and anionic vacancies on the NiO(100) surface: DFT+U and hybrid functional density functional theory calculations.

The electronic structure of oxygen and nickel vacancies at the surface of NiO(100) has been investigated theoretically by means of density functional theory (DFT) comparing plane wave density functional theory with the Hubbard correction DFT+U with atomic-orbital-hybrid-functional (20% exact-exchange) calculations. The two approaches provide a similar description of the nature of the oxygen vacancy. At variance with the same defect center in MgO, where two electrons are trapped in the vacancy, on NiO the charge is more delocalized, partly over the Ni ions around the vacancy, the rest either trapped in the vacancy or delocalized over other Ni ions. Concerning the nickel vacancy, both methods clearly show that the removal of a neutral Ni atom does not result in the oxidation of other nickel ions from Ni2+ to Ni3+ but rather in the formation of two holes in the O 2p valence band. However, the description is slightly different with the approaches, the hybrid functional indicates that the holes are essentially localized on the oxygen ions nearest to the vacancy, while they result much more delocalized from the DFT+U calculation. Comparison with the corresponding results, obtained with the two methods for the case of the Mg vacancy in MgO, suggests that the DFT+U approach does not adequately correct for the self-interaction of the unpaired electrons in this case. However, the overall picture that emerges clearly from the present calculations is that both defects affect the electronic structure in a much wider region in NiO than in MgO.

Normal vibrational analysis of a trans-planar syndiotactic polystyrene chain.

The full vibrational spectra of alpha and beta crystalline phases of syndiotactic polystyrene (sPS), that is, phases presenting the trans-planar conformation, have been experimentally determined and compared with that calculated at the B3LYP/6-31G(d,p) level of theory for an infinite trans-planar chain. The normal vibrational analysis of most representative modes of the periodic model allowed us to give a general description of each one, which was further confirmed by the direct inspection of mode animations. An assignment of the different modes was performed in terms of frequency, relative intensity, and direction of the transition-moment vector of the observed IR peaks as well as Raman vibrational frequencies.

Water dissociation at MgO sub-monolayers on silver: a periodic model study.

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].

An ab initio periodic study of NiO supported at the Pd(100) surface. Part 1: The perfect epitaxial monolayer.

The epitaxial monolayer of NiO on Pd(100) has been theoretically simulated using a hybrid-exchange GGA-DFT Hamiltonian and a slab model, periodic in two dimensions. This "perfect" system is an essential reference for the simulation of nonstoichiometric two-dimensional phases which are formed during the deposition of nickel on palladium in the presence of oxygen. The adequacy of the computational procedure is discussed, especially as concerns the use of a thermal smearing technique which has been adopted to improve the convergence properties of the SCF procedure and to prevent the onset of nonphysical spin-polarized solutions. The equilibrium configuration corresponds to antiferromagnetic order in the overlayer, with oxygens on top of the surface Pd atoms; the ad-film is slightly corrugated with Ni closer to the surface by 0.1 A with respect to O. The interaction energy is quite small, 0.20 eV/NiO unit (about 5 kcal mol(-1)); correspondingly, the electronic and magnetic properties of the Pd slab and the isolated NiO monolayer are only marginally affected by the interaction.

An ab initio periodic study of NiO supported at the Pd(100) surface. Part 2: The nonstoichiometric Ni3O4 phase.

The present computational study describes the structure and properties of a substoichiometric 2D monatomic in the height phase of nickel oxide, c(4 x 2)-Ni(3)O(4), which has been newly found to epitaxially grow under special deposition conditions on the (100) face of palladium. A slab model is adopted where palladium is simulated by a thin film covered on both sides by epilayers, in combination with a DFT hybrid-exchange Hamiltonian; to make convergence of the SCF procedure easier, a thermal smearing technique is used, whose consequences on the results are critically analyzed. Three adsorbed systems are considered and characterized: (i) RH, that is, the c(4 x 2)-Ni(3)O(4) phase with a rhombic distribution of Ni vacancies, as is experimentally observed; SQ, or p(2 x 2)-Ni(3)O(4), which differs from the previous one for a square, instead of a rhombic distribution of vacancies; (iii) OX, or p(2 x 2)-O, that is, a surface oxidized phase of Pd(100) which is believed to be the precursor for the formation of RH. For a better understanding of the interaction of the metal with the adlayers, the isolated substoichiometric oxides, i-RH and i-SQ, have also been studied. It is shown that RH is more stable than SQ by a few tenths of electronvolts per Ni(3)O(4) unit, which justifies its preferential formation and that the surface reaction, OX + 3NiO(ads) --> RH, is thermodynamically possible. Special attention has been devoted to characterize RH from an energetic, geometric, electronic, and magnetic viewpoint. The strong bond which is formed between surface Pd and O ions in the adlayer is responsible for some peculiar aspects of the electronic and magnetic structures of that phase.

Oxide/metal interface distance and epitaxial strain in the NiO/Ag(001) system.

Geometric parameters of NiO films epitaxially grown on Ag(001) were determined using two independent experimental techniques and ab initio simulations. Primary beam diffraction modulated electron emission experiments determined that the NiO films grow with O on top of Ag and that the oxide/metal interface distance is d=2.3+/-0.1 A. Polarization-dependent x-ray absorption, at the Ni-K edge, determined the tetragonal strain (r( parallel )=2.046+/-0.009 A, r( perpendicular )=2.12+/-0.02 A) and d=2.37+/-0.05 A. Periodic slab model results agree with the experiments (d=2.40, r( parallel )=2.07, r( perpendicular )=2.10 A; the O-on-top configuration is the most stable).