Interaction of molecular hydrogen with open transition metal centers for enhanced binding in metal-organic frameworks: a computational study.

Molecular hydrogen is known to form stable, "nonclassical" sigma complexes with transition metal centers that are stabilized by donor-acceptor interactions and electrostatics. In this computational study, we establish that strong H2 sorption sites can be obtained in metal-organic frameworks by incorporating open transition metal sites on the organic linkers. Using density functional theory and energy decomposition analysis, we investigate the nature and characteristics of the H2 interaction with models of exposed open metal binding sites {half-sandwich piano-stool shaped complexes of the form (Arene)ML(3- n)(H2)n [M=Cr, Mo, V(-), Mn(+); Arene = C6H5X (X=H, F, Cl, OCH3, NH2, CH3, CF3) or C6H3Y2X (Y=COOH, X=CF3, Cl; L=CO; n=1-3]}. The metal-H2 bond dissociation energy of the studied complexes is calculated to be between 48 and 84 kJ/mol, based on the introduction of arene substituents, changes to the metal core, and of charge-balancing ligands. Thus, design of the binding site controls the H2 binding affinity and could be potentially used to control the magnitude of the H2 interaction energy to achieve reversible sorption characteristics at ambient conditions. Energy decomposition analysis illuminates both the possibilities and present challenges associated with rational materials design.

Semiempirical double-hybrid density functional with improved description of long-range correlation.

The recently proposed new family of "double-hybrid" density functionals [Grimme, S. J. Chem. Phys. 2006, 124, 34108] replaces a fraction of the semi-local correlation energy by a non-local correlation energy expression that employs the Kohn-Sham orbitals in second-order many-body perturbation theory. These functionals have provided results of high accuracy over a wide range of properties but fail to accurately describe long-range van der Waals interactions. In this work, a distance-dependent scaling factor for the non-local correlation energy is introduced to address this problem, and two new double-hybrid density functionals are proposed. The new functionals are optimized with the finite cc-pVTZ basis on training sets of atomization energies and intermolecular interaction energies. They are compared against (scaled) second-order Møller-Plesset perturbation theories and popular density functionals including the hybrid-GGA functional B3-LYP and the first double-hybrid functional (B2-PLYP). Tests are performed on an extensive set including reaction energies, barrier heights, weakly interacting complexes, transition-metal systems, molecular geometries, and harmonic vibrational frequencies. Within the cc-pVTZ atomic orbital basis, we have demonstrated the ability to find a parametrization scheme which is simultaneously able to describe thermochemistry and weakly bound systems with a satisfactory degree of accuracy.

Unravelling the origin of intermolecular interactions using absolutely localized molecular orbitals.

An energy decomposition analysis (EDA) method is proposed to isolate physically relevant components of the total intermolecular interaction energies such as the contribution from interacting frozen monomer densities, the energy lowering due to polarization of the densities, and the further energy lowering due to charge-transfer effects. This method is conceptually similar to existing EDA methods such as Morokuma analysis but includes several important new features. The first is a fully self-consistent treatment of the energy lowering due to polarization, which is evaluated by a self-consistent field calculation in which the molecular orbital coefficients are constrained to be block-diagonal (absolutely localized) in the interacting molecules to prohibit charge transfer. The second new feature is the ability to separate forward and back-donation in the charge-transfer energy term using a perturbative approximation starting from the optimized block-diagonal reference. The newly proposed EDA method is used to understand the fundamental aspects of intermolecular interactions such as the degree of covalency in the hydrogen bonding in water and the contributions of forward and back-donation in synergic bonding in metal complexes. Additionally, it is demonstrated that this method can be used to identify the factors controlling the interaction of the molecular hydrogen with open metal centers in potential hydrogen storage materials and the interaction of methane with rhenium complexes.

Orbital-optimized opposite-spin scaled second-order correlation: an economical method to improve the description of open-shell molecules.

Coupled-cluster methods based on Brueckner orbitals are well known to resolve the problems of symmetry breaking and spin contamination that are often associated with Hartree-Fock orbitals. However, their computational cost is large enough to prevent application to large molecules. Here the authors present a simple approximation where the orbitals are optimized with the mean-field energy plus a correlation energy taken as the opposite-spin component of the second-order many-body correlation energy, scaled by an empirically chosen parameter (recommended as 1.2 for general applications). This "optimized second-order opposite-spin" (abbreviated as O2) method requires fourth-order computation on each orbital iteration. O2 is shown to yield predictions of structure and frequencies for closed-shell molecules that are very similar to scaled second-order Moller-Plesset methods. However, it yields substantial improvements for open-shell molecules, where problems with spin contamination and symmetry breaking are shown to be greatly reduced.

Quartic-Scaling Analytical Energy Gradient of Scaled Opposite-Spin Second-Order Møller-Plesset Perturbation Theory.

The analytical gradient of the "scaled opposite spin" (SOS-) and "modified opposite spin" (MOS-) second-order Møller-Plesset perturbation theory (MP2) methods is derived and implemented. Both energy and the first derivative can be evaluated efficiently with a fourth-order scaling algorithm by using a combination of auxiliary basis expansions and Laplace transformation techniques as opposed to the traditional fifth-order approach of MP2. A statistical analysis of 178 small molecules suggests that the new gradient scheme provides geometries of MP2 quality, indicating the reliability of the method in general chemical applications. A more specific study of the group VI transition metal carbonyl complexes indicates that the new scheme improves the MP2 description relative to available experimental data and higher-order theories. The proposed gradient scheme thus endeavors to obtain improved structural features at reduced computational cost.

Advances in methods and algorithms in a modern quantum chemistry program package.

Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.

Computational studies of molecular hydrogen binding affinities: the role of dispersion forces, electrostatics, and orbital interactions.

Intermolecular interactions between H2 and ligands, metals, and metal-ligand complexes determine the binding affinities of potential hydrogen storage materials (HSM), and thus their extent of potential for practical use. A brief survey of current activity on HSM is given. The key issue of binding strengths is examined from a basic perspective by surveying the distinct classes of interactions (dispersion, electrostatics, orbital interactions) in first a general way, and then in the context of calculated binding affinities for a range of model systems.

Scaled opposite spin second order Møller-Plesset theory with improved physical description of long-range dispersion interactions.

Separate scaling of the same-spin and opposite spin contributions to the second-order Møller-Plesset energy can yield statistically improved performance for a variety of chemical problems. If only the opposite spin contribution is scaled, it is also possible to reduce the computational complexity from fifth order to fourth order in system size, with very little degradation of the results. However neither of these scaled MP2 energies recovers the full MP2 result for the dispersion energy of nonoverlapping systems. This deficiency is addressed in this work by using a distance-dependent scaling of the opposite spin correlation energy. The resulting method is compared against the previously proposed scaled MP2 methods on a range of problems involving both short and long-range interactions.

Scaled opposite-spin second order Møller-Plesset correlation energy: an economical electronic structure method.

A simplified approach to treating the electron correlation energy is suggested in which only the alpha-beta component of the second order Møller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite-spin second order energy (SOS-MP2), where MP2 is Møller-Plesset theory, yields results for relative energies and derivative properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the fifth order computational steps associated with MP2 theory, even without exploiting any spatial locality. A fourth order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.