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.

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.

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.

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.

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.

Calculation of the vibration frequencies of ?-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).

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.