Rationale for a new class of double-hybrid approximations in density-functional theory

We provide a rationale for a new class of double-hybrid approximations introduced by Br\'emond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchange-correlation density functional with Hartree-Fock exchange weighted by \l and second-order M{\o}ller-Plesset (MP2) correlation weighted by \l^3. We show that this double-hybrid model can be understood in the context of the density-scaled double-hybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled correlation functional E_c[n_{1/\l}] by a linear function of \l, interpolating between MP2 at \l=0 and a density-functional approximation at \l=1. Numerical results obtained with the Perdew-Burke-Ernzerhof density functional confirms the relevance of this double-hybrid model.Comment: 4 pages, 2 figures, to appear in Journal of Chemical Physic

Analytic Gradients for Complete Active Space Pair-Density Functional Theory

Analytic gradient routines are a desirable feature for quantum mechanical methods, allowing for efficient determination of equilibrium and transition state structures and several other molecular properties. In this work, we present analytical gradients for multiconfiguration pair-density functional theory (MC-PDFT) when used with a state-specific complete active space self-consistent field reference wave function. Our approach constructs a Lagrangian that is variational in all wave function parameters. We find that MC-PDFT locates equilibrium geometries for several small- to medium-sized organic molecules that are similar to those located by complete active space second-order perturbation theory but that are obtained with decreased computational cost

Range-separated double-hybrid density-functional theory applied to periodic systems

International audienceQuantum chemistry methods exploiting density-functional approximations for short-range electron-electron interactions and second-order M{{\o}}ller-Plesset (MP2) perturbation theory for long-range electron-electron interactions have been implemented for periodic systems using Gaussian-type basis functions and the local correlation framework. The performance of these range-separated double hybrids has been benchmarked on a significant set of systems including rare-gas, molecular, ionic, and covalent crystals. The use of spin-component-scaled MP2 for the long-range part has been tested as well. The results show that the value of $\mu$ = 0.5 bohr^{--1} for the range-separation parameter usually used for molecular systems is also a reasonable choice for solids. Overall, these range-separated double hybrids provide a good accuracy for binding energies using basis sets of moderate sizes such as cc-pVDZ and aug-cc-pVDZ

Développement de nouvelles méthodes hybrides en théorie de la fonctionnelle de la densité par séparation linéaire de l'interaction électronique

This thesis draws together methodological contributions to the hybrid methods in density functional theory (DFT). The combination of DFT and several wave function methods has been done by linear separation of the electron-electron interaction in the multideterminantal extension of the Kohn-Sham scheme. Aiming at improving the calculation of (near-)degeneracy correlation effects in molecular systems, we have developed the multiconfigurational hybrids which combine DFT with a multiconfiguration self-consistent field calculation. The coupling between DFT and second-order Møller-Plesset perturbation theory (MP2) has provided the theoretical justification and development of double hybrid approximations which have been tested for molecular and extended systems.Cette thèse rassemble des contributions méthodologiques aux méthodes hybrides en théorie de la fonctionnelle de la densité (DFT). La combinaison de la DFT et de plusieurs méthodes de fonction d'onde a été réalisée par séparation linéaire de l'interaction électronique dans l'extension multidéterminantale de la méthode de Kohn-Sham. Afin d'améliorer le calcul des effets de corrélation de (quasi-)dégénérescence des systèmes moléculaires, nous avons développé les hybrides multiconfigurationnels qui combinent la DFT avec un calcul de champ autocohérent multiconfigurationnel. Le couplage de la DFT avec une théorie de perturbation Møller-Plesset du deuxième ordre (MP2) a donné la justification théorique et le développement d'approximations "double hybrides" qui ont été testées sur des systèmes moléculaires et étendus