Antiferromagnetic vs. non-magnetic ε phase of solid oxygen. Periodic density functional theory studies using a localized atomic basis set and the role of exact exchange.

The question of the non-magnetic (NM) vs. antiferromagnetic (AF) nature of the ε phase of solid oxygen is a matter of great interest and continuing debate. In particular, it has been proposed that the ε phase is actually composed of two phases, a low-pressure AF ε1 phase and a higher pressure NM ε0 phase [Crespo et al., Proc. Natl. Acad. Sci. U. S. A., 2014, 111, 10427]. We address this problem through periodic spin-restricted and spin-polarized Kohn-Sham density functional theory calculations at pressures from 10 to 50 GPa using calibrated GGA and hybrid exchange-correlation functionals with Gaussian atomic basis sets. The two possible configurations for the antiferromagnetic (AF1 and AF2) coupling of the 0 ≤ S ≤ 1 O2 molecules in the (O2)4 unit cell were studied. Full enthalpy-driven geometry optimizations of the (O2)4 unit cells were done to study the pressure evolution of the enthalpy difference between the non-magnetic and both antiferromagnetic structures. We also address the evolution of structural parameters and the spin-per-molecule vs. pressure. We find that the spin-less solution becomes more stable than both AF structures above 50 GPa and, crucially, the spin-less solution yields lattice parameters in much better agreement with experimental data at all pressures than the AF structures. The optimized AF2 broken-symmetry structures lead to large errors of the a and b lattice parameters when compared with experiments. The results for the NM model are in much better agreement with the experimental data than those found for both AF models and are consistent with a completely non-magnetic (O2)4 unit cell for the low-pressure regime of the ε phase.

The V + I defects in diamond: An ab initio investigation of the electronic structure, of the Raman and IR spectra, and of their possible recombination.

The double defect in diamond, vacancy (V) plus 〈100〉 self-split-interstitial (V+I), is investigated at the ab initio quantum mechanical level, by considering the vicinal case VI1 (V is one of the first neighbors of one of the two C atoms constituting the I defect) and the two possible "second neighbors" cases, VI2D, VI2S, in which a carbon atom is a first neighbor of both V and I. The case in which the two defects are at a larger distance is simulated by considering the two isolated defects separately (VI∞). A 6-21G local Gaussian-type basis set and the B3LYP hybrid functional are used for most of the calculations; richer basis sets and other functionals (a global hybrid as PBE0, a range-separated hybrid as HSE06, LDA, PBE, and Hartree-Fock) have also been used for comparison. With this computational approach we evaluate the energy difference between the various spin states, the location of the corresponding bands in the energy gap of pristine diamond, as well as the defect formation energy of the four defects. The path for the recombination of V and I is explored for the vicinal case, by using the distinguished reaction coordinate strategy. A barrier as high as 0.75 eV is found with B3LYP between VI1 and the perfect diamond recombined structure; when other hybrids are used, as PBE0 or HSE06, the barrier increases up to 1.01 eV (pure density functional theory produces lower barriers: 0.62 and 0.67 for PBE and LDA, respectively). Such a barrier is lower than the one estimated in a very indirect way through experimental data, ranging from 1.3 to 1.7 eV. It confirms however the evidence of the extremely low recombination rate also at high temperature. The Raman (and IR) spectra of the various defects are generated, which permit one to unambiguously attribute to these defects (thanks also to the graphical animation of the modes) many of the peaks observed in damaged diamond above the dominant peak of perfect bulk. For the residual non-attributed peaks, more complicated aggregations of defects should be explored.

Understanding the ε and ζ High-Pressure Solid Phases of Oxygen. Systematic Periodic Density Functional Theory Studies Using Localized Atomic Basis.

The experimentally characterized ε and ζ phases of solid oxygen are studied by periodic Hartree-Fock (HF) and Density Functional Theory calculations at pressures from 10 to 160 GPa using different types of exchange-correlation functionals with Gaussian atomic basis sets. Full geometry optimizations of the monoclinic C2/m (O2)4 unit cell were done to study the evolution of the structural and electronic properties with pressure. Vibrational calculations were performed at each pressure. While periodic HF does not predict the ε-ζ phase transition in the considered range, Local Density approximation and Generalized Gradient approximation methods predict too low transition pressures. The performance of hybrid functional methods is dependent on the amount of non-local HF exchange. PBE0, M06, B3PW91, and B3LYP approaches correctly predict the structural and electronic changes associated with the phase transition. GGA and hybrid functionals predict a pressure range where both phases coexist, but only the latter type of methods yield results in agreement with experiment. Using the optimized (O2)4 unit cell at each pressure we show, through CASSCF(8,8) calculations, that the greater accuracy of the optimized geometrical parameters with increasing pressure is due to a decreasing multireference character of the unit cell wave function. The mechanism of the transition from the non-conducting to the conducting ζ phase is explained through the Electron Pair Localization Function, which clearly reveals chemical bonding between O2 molecules in the ab crystal planes belonging to different unit cells due to much shorter intercell O2-O2 distances.

Periodic density functional theory calculations for 3-dimensional polyacetylene with empirical dispersion terms.

We report periodic B3LYP density functional theory calculations for three-dimensional (3D) trans-polyacetylene (t-PA) fibers. Empirical dispersion terms, as proposed by Grimme, are included with an appropriate re-scaling to yield the B3LYP+D* method implemented in CRYSTAL06. The dispersion corrections are critical for obtaining correct unit cell parameters. In our calculations the out-of-phase P2(1)/n structure turns out to be a transition state for the interchain relative translational motion, which lies about 0.35 kcal mol(-1) above the two symmetrically located in-phase P2(1)/a minima. These results provide a possible new explanation for the observed XRD intensities. Our calculations should also be useful for comparison with more costly non-empirical treatments of 3D PA and other pi-conjugated polymers.

Periodic density functional theory studies of Li-doped polythiophene: dependence of electronic and structural properties on dopant concentration.

We report periodic B3LYP6-31G(**) density functional theory calculations on Li-doped polythiophene at various dopant concentrations using (SC(4)H(2))(m)Li(2) unit cells for m=2, 6, and 10. Uniform doping by Li atoms and by pairs of Li atoms on adjacent thiophene rings are considered with the primary aim of comparing polaron versus bipolaron properties. Properties examined include geometries, charge distributions, polaron/bipolaron formation energies, dopant binding energies, band structures, and densities of states.

Ab initio simulation of the IR spectra of pyrope, grossular, and andradite.

IR spectra of pyrope Mg(3)Al(2)Si(3)O(12), grossular Ca(3)Al(2)Si(3)O(12) and andradite Ca(3)Fe(2)Si(3)O(12) garnets were simulated with the periodic ab initio CRYSTAL code by adopting an all-electron Gaussian-type basis set and the B3LYP Hamiltonian. Two sets of 17 F(1u) Transverse Optical (TO) and Longitudinal Optical (LO) frequencies were generated, together with their intensities. Because the generation of LO modes requires knowledge of the high frequency dielectric constant epsilon(infinity) and Born effective charges, they were preliminary evaluated by using a finite field saw-tooth model and well localized Wannier functions, respectively. As a by-product, the static dielectric constant epsilon(0) was also obtained. The agreement of the present calculated wavenumbers (i.e. peak positions) with the available experimental data is excellent, in that the mean absolute difference for the full set of data smaller than 8 cm(-1). Missing peaks in experimental spectra were found to correspond to modes with low calculated intensities. Correspondence between TO and LO modes was established on the basis of the overlap between the eigenvectors of the two sets and similarity of isotopic shifts; as result, the so called LO-TO splitting could be determined. Animation of the normal modes was employed to support the proposed pairing.

Ab initio investigation of structure and cohesive energy of crystalline urea.

The structure and cohesive energy of crystalline urea have been investigated at the ab initio level of calculation. The performance of different Hamiltonians in dealing with a hydrogen-bonded molecular crystal as crystalline urea is assessed. Detailed calculations carried out by adopting both HF and some of the most popular DFT methods in solid-state chemistry are reported. Local, gradient-corrected, and hybrid functionals have been adopted: SVWN, PW91, PBE, B3LYP, and PBE0. First, a 6-31G(d,p) basis set has been adopted, and then the basis set dependence of computed results has been investigated at the B3LYP level. All calculations were carried out by using a development version of the periodic ab initio code CRYSTAL06, which allows full optimization of lattice parameters and atomic coordinates. With the 6-31G(d,p) basis set, structural features are well reproduced by hybrid methods and GGA. LDA gives lattice parameters and hydrogen-bond distances that are too small relative to experiment, while at the HF level the opposite trend is observed. Results show that hybrid methods are more accurate than HF and both LDA and GGA functionals, with a trend in the computed properties similar to that of hydrogen-bonded molecular complexes. When BSSE and ZPE are taken into account, all methods, except LDA, give computed cohesive energies that are underestimated with respect to the experimental sublimation enthalpy. Dispersion energy, not properly taken into account by DFT methods, plays a crucial role. Such a deficiency also affects dramatically the computed crystalline structure, especially when large basis sets are adopted. We show that this is an artifact due to the BSSE. Indeed, with small basis sets the BSSE gives an extra-binding that compensates for the missing dispersion forces, thus yielding structures in fortuitous agreement with experiment.

Periodic Hartree-Fock and density functional theory calculations for Li-doped polyacetylene chains.

We have performed periodic restricted Hartree-Fock/6-31G** and B3LYP6-31G** density functional theory calculations on Li-doped trans-polyacetylene at various dopant concentrations, using C(2m)H(2m)Li2 unit cells (m = 7-14). Except for maintaining P1 rod symmetry the geometry was completely optimized for both uniform and nonuniform doping structures. In addition to geometry we obtain atomic charges, along with soliton formation and dopant binding energies, as well as band structures and densities of states. A thorough analysis of the band structure and density of states, as a function of dopant concentration, is presented. We also characterize the complex nature of the binding interaction between Li and the polyacetylene chain.

Vibrational spectrum of katoite Ca3Al2[(OH)4]3: a periodic ab initio study.

The vibrational spectrum of the Si-free katoite hydrogarnet (116 atoms in the unit cell) has been calculated at the periodic ab initio quantum mechanical level with the CRYSTAL program, by using a Gaussian type basis set and the hybrid B3LYP Hamiltonian. The harmonic frequencies at the Gamma point have been obtained by diagonalizing the mass-weighted Hessian matrix, that is evaluated by numerical differentiation of the analytical first derivatives of the energy with respect to the atomic Cartesian coordinates. The parameters controlling the numerical differentiation, as well as the numerical integration of the exchange-correlation functional for the self-consistent field (SCF) calculation, are shown to affect the obtained frequencies by less than 3 cm-1. Before diagonalization, the dynamical matrix is transformed to a block diagonal form according to the irreducible representations of the point group, so that the 345 vibrational modes are automatically classified by symmetry. Various tools are adopted (graphical representation, isotopic substitution, "freezing" part of the unit cell) that permit a complete classification of normal modes and, in particular, an analysis of the modes in terms of simple models (octahedra modes, Ca modes, H stretching, bending, rotations). The harmonic OH stretching band (48 modes) is quite narrow (20 cm-1), indicating that the interaction among OH groups is very weak. As the OH stretching modes are known to be totally separable from the other modes and strongly anharmonic, the one-dimensional Schroedinger equation for the anharmonic oscillator is solved numerically for the two extreme situations, corresponding to the vibration of one decoupled OH and of all 48 OH groups moving in phase. The anharmonic frequencies are 3682 and 3673 cm-1, respectively, in good agreement with IR experiments (a single band at 3661 cm-1 with a width at half band height of 33 cm-1) and confirming that the interaction between OH groups is extremely weak.

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 Stuttgart's 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.

The isobutylene-isobutane alkylation process in liquid HF revisited.

Details on the mechanism of HF catalyzed isobutylene-isobutane alkylation were investigated. On the basis of available experimental data and high-level quantum chemical calculations, a detailed reaction mechanism is proposed taking into account solvation effects of the medium. On the basis of our computational results, we explain why the density of the liquid media and stirring rates are the most important parameters to achieve maximum yield of alkylate, in agreement with experimental findings. The ab initio Car-Parrinello molecular dynamics calculations show that isobutylene is irreversibly protonated in the liquid HF medium at higher densities, leading to the ion pair formation, which is shown to be a minimum on the potential energy surface after optimization using periodic boundary conditions. The HF medium solvates preferentially the fluoride anion, which is found as solvated [FHF](-) or solvated F(-.)(HF)(3). On the other hand, the tert-butyl cation is weakly solvated, where the closest HF molecules appear at a distance of about 2.9 Angstrom with the fluorine termination of an HF chain.

Calculation of the vibration frequencies of alpha-quartz: the effect of Hamiltonian and basis set.

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 calculation of the vibrational frequencies of crystalline compounds and its implementation in the CRYSTAL code.

The problem of numerical accuracy in the calculation of vibrational frequencies of crystalline compounds from the hessian matrix is discussed with reference to alpha-quartz (SiO(2)) as a case study and to the specific implementation in the CRYSTAL code. The Hessian matrix is obtained by numerical differentiation of the analytical gradient of the energy with respect to the atomic positions. The process of calculating vibrational frequencies involves two steps: the determination of the equilibrium geometry, and the calculation of the frequencies themselves. The parameters controlling the truncation of the Coulomb and exchange series in Hartree-Fock, the quality of the grid used for the numerical integration of the Exchange-correlation potential in Density Functional Theory, the SCF convergence criteria, the parameters controlling the convergence of the optimization process as well as those controlling the accuracy of the numerical calculation of the Hessian matrix can influence the obtained vibrational frequencies to some extent. The effect of all these parameters is discussed and documented. It is concluded that with relatively economical computational conditions the uncertainty related to these parameters is smaller than 2-4 cm(-1). In the case of the Local Density Approximation scheme, comparison is possible with recent calculations performed with a Density Functional Perturbation Theory method and a plane-wave basis set.

Cluster and periodic calculations of the ethene protonation reaction catalyzed by theta-1 zeolite: influence of method, model size, and structural constraints.

The protonation of ethene by three different acid sites of theta-1 zeolite was theoretically studied to analyze the extent and relevance of the following aspects of heterogeneous catalysis: the local geometry of the Brønsted acid site in a particular zeolite, the size of the cluster used to model the catalyst, the degree of geometry relaxation around the active site, and the effects related to medium- and long-range interactions between the reaction site and its environment. It has been found that while the reaction energy is very sensitive to the local geometry of the site, the activation energy is mainly affected by the methodology used and by electrostatic effects on account of the carbocationic nature of the transition state.