Silvia Casassa

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 CO2 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.

Local-MP2 electron correlation method for nonconducting crystals.

Rigorous methods for the post-HF (HF-Hartree-Fock) determination of correlation corrections for crystalline solids are currently being developed following different strategies. The CRYSTAL program developed in Torino and Daresbury provides accurate HF solutions for periodic systems in a basis set of Gaussian type functions; for insulators, the occupied HF manifold can be represented as an antisymmetrized product of well localized Wannier functions. This makes possible the extension to nonconducting crystals of local correlation linear scaling On techniques as successfully and efficiently implemented in Stuttgarts MOLPRO program. These methods exploit the fact that dynamic electron correlation effects between remote parts of a molecule (manifesting as dispersive interactions in intermolecular perturbation theory) decay as an inverse sixth power of the distance R between these fragments, that is, much more quickly than the Coulomb interactions that are treated already at the HF level. Translational symmetry then permits the crystalline problem to be reduced to one concerning a cluster around the reference zero cell. A periodic local correlation program (CRYSCOR) has been prepared along these lines, limited for the moment to the solution of second-order Moller-Plesset equations. Exploitation of point group symmetry is shown to be more important and useful than in the molecular case. The computational strategy adopted and preliminary results concerning five semiconductors with tetrahedral structure (C, Si, SiC, BN, and BeS) are presented and discussed.

Ab initio study of HCl and HF interaction with crystalline ice. I. Physical adsorption

A quantum-mechanical ab initio study is presented concerning the physisorption of HCl and HF on ice surfaces, modeled with periodic, proton-ordered thin films. Three methods are adopted: (1) Periodic two-dimensional calculations concerning ice surfaces, both clean and covered with ordered overlayers; (2) embedded cluster calculations, concerning two-dimensional ordered structures interacting with a single molecule; (3) molecular cluster calculations, simulating a portion of the surface. The combined and interactive use of these techniques has permitted us to recognize some deficiencies of molecular cluster models of ice and to correct for them. The energy of physisorption of HCl on a perfect basal surface of ice is estimated to be about 8 kcal/mol, on prismatic faces about 11 kcal/mol. Adsorption energies of HF are larger by 4 to 5 kcal/mol.

Proton-ordered models of ordinary ice for quantum-mechanical studies

A periodic Hartree-Fock ab initio study is presented concerning two proton-ordered structures of ordinary ice: one ferro-electric (C-ice), the other anti-ferro-electric (P-ice). The calculated energies are practically coincident, and in good agrement with the experimental stability of disordered ice Ih. Slabs are cut out from these crystals in order to formulate a model for studying the surface properties of ordinary ice. The stability of these two-dimensional periodic systems is discussed, and the relaxation of the P-ice slab formed by two bilayers parallel to the (001) face is considered. Finally, an embedded cluster method is adopted to calculate geometric and energetic properties of KOH and NaOH dissolved in C- and P-ice at low concentration. This study permits us to discuss the role of KOH in promoting the transition from disordered Ih to ordered C-ice, which has been observed to occur at 72 K [Leadbetter et al., J. Chem. Phys. 82, 424 (1985)].

Proton-ordered ice structures at zero pressure. A quantum-mechanical investigation

Abstract The results of quantum-mechanical computations are presented concerning the properties of two periodic structures of ice: ice XI (space group Cmc2 1 ), the only experimentally known proton-ordered structures at zero pressure, and the hypothetical structure here denoted as P-ice (space group Pna2 1 ). The latter is selected as a simple model of ordinary disordered ice. The equilibrium geometry and relative stability of the two phases are studied by performing periodic Hartee-Fock calculations. The difference in stability of the two structures is within the estimated computational accuracy, and they may be considered to be essentially iso-energetic. We also present the results of an embedded-cluster Hartree-Fock study of the substitutional KOH impurity in the two structures: the interest in this problem comes from the fact that the disorder-order transition in ice XI is catalyzed by the presence of non-negligible quantities of dissolved potassium hydroxide. The KOH solution in ice XI is favored with respect to that in P-ice by a few kcal/mol. This difference could support the hypothesis that microcrystals of ice XI are formed around individual KOH molecules.

CRYSTAL and EMBED, two computational tools for the ab initio study of electronic properties of crystals

The present study discusses the main features of the two programs CRYSTAL and EMBED developed for the ab initio study of the electronic properties of perfect periodic structures and of crystals with local defects, respectively. After a brief historical introduction, the structure of CRYSTAL is outlined and some specific aspects are discussed in detail: the use of local basis functions, the way of dealing with the Coulomb and the exchange series, the exploitation of point symmetry, the possibility to adopt either the Hartree–Fock approach or one among a variety of Kohn–Sham Hamiltonians. The present capabilities of the program are illustrated by a survey of selected applications from existing literature. Information is provided concerning work in progress aimed at removing some of the limitations of the code and improving its performance. The characteristics of EMBED are analyzed with emphasis given to the critical aspects of the method: limits of validity of the fundamental approximation on which the embedding technique relies, problems of convergence of the self-consistent procedure; and the delicate issue of the estimate of the defect formation energy. Again, a critical survey of applications clarifies the capabilities of the code. The envisaged improvements to be introduced in a forthcoming release of EMBED are presented. The present and prospective role of the two programs in the field of computational studies of condensed matter problems is outlined.

Periodic quantum mechanical simulation of the He-MgO(100) interaction potential

He-atom scattering is a well established and valuable tool for investigating surface structure. The correct interpretation of the experimental data requires an accurate description of the He-surface interaction potential. A quantum-mechanical treatment of the interaction potential is presented using the current dominant methodologies for computing ground state energies (Hartree-Fock, local and hybrid-exchange density functional theory) and also a novel post-Hartree-Fock ab initio technique for periodic systems (a local implementation of Mo̸ller-Plesset perturbation theory at second order). The predicted adsorption well depth and long range behavior of the interaction are compared with that deduced from experimental data in order to assess the accuracy of the interaction potential.

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.

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.

Quantum‐mechanical condensed matter simulations with CRYSTAL

The latest release of the Crystal program for solid‐state quantum‐mechanical ab initio simulations is presented. The program adopts atom‐centered Gaussian‐type functions as a basis set, which makes it possible to perform all‐electron as well as pseudopotential calculations. Systems of any periodicity can be treated at the same level of accuracy (from 0D molecules, clusters and nanocrystals, to 1D polymers, helices, nanorods, and nanotubes, to 2D monolayers and slab models for surfaces, to actual 3D bulk crystals), without any artificial repetition along nonperiodic directions for 0–2D systems. Density functional theory calculations can be performed with a variety of functionals belonging to several classes: local‐density (LDA), generalized‐gradient (GGA), meta‐GGA, global hybrid, range‐separated hybrid, and self‐consistent system‐specific hybrid. In particular, hybrid functionals can be used at a modest computational cost, comparable to that of pure LDA and GGA formulations, because of the efficient implementation of exact nonlocal Fock exchange. Both translational and point‐symmetry features are fully exploited at all steps of the calculation, thus drastically reducing the corresponding computational cost. The various properties computed encompass electronic structure (including magnetic spin‐polarized open‐shell systems, electron density analysis), geometry (including full or constrained optimization, transition‐state search), vibrational properties (frequencies, infrared and Raman intensities, phonon density of states), thermal properties (quasi‐harmonic approximation), linear and nonlinear optical properties (static and dynamic [hyper]polarizabilities), strain properties (elasticity, piezoelectricity, photoelasticity), electron transport properties (Boltzmann, transport across nanojunctions), as well as X‐ray and inelastic neutron spectra. The program is distributed in serial, parallel, and massively parallel versions. In this paper, the original developments that have been devised and implemented in the last 4 years (since the distribution of the previous public version, Crystal14, occurred in December 2013) are described.