Highly accurate treatment of dynamical electron correlation through R12 methods and extrapolation techniques

Abstract

The accurate description of short-range electron correlation represents a fundamental challenge for quantum chemical calculations. The hindrance that one has to face originates from an exceedingly slow convergence of dynamical correlation energy with increasing number of Gaussian basis functions. In this perspective, explicitly correlated wave functions and extrapolation techniques are two systematic ways to accelerate the basis-set convergence of molecular-orbital-based standard models. In this thesis, these two approaches are applied and refined to determine highly accurate ground-state properties for closed-shell molecular systems. The two correlation methods mainly used are second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster theory including single and double excitations with a noniterative perturbative correction for connected triple excitations (CCSD(T)). The general theory is described in chapter 1 and chapter 2 reviews the leading concepts, fundamental approximations and main working equations of the family of explicitly correlated wave functions that employs a linear correlation factor, namely the R12 methods. Chapters 3 and 4 present two basis-set convergence studies. First, chapter 3 contains the determination of the equilibrium inversion barrier of ammonia computed at the CCSD(T) level with a two-point extrapolation scheme. Second, chapter 4 is a study of the low proton barrier and of the binding energy of the (H2 O)OH- complex. Data are obtained at the basis-set limit of CCSD(T) by virtue of the R12 correction.

The new developments on the R12 methods aim to extend their application range to larger molecules than the ones computable today. In chapter 5, a new methodology is presented to ease the computation of the R12 correction at the MP2 level. It consists of the introduction of a large (nearly complete) one-electron basis set which adequately solves the resolution of the identity, while the remaining of the calculation can be done with smaller available basis sets. Chapter 6 presents the development in the MP2-R12 framework of a new hybrid correlation factor which is a compromise between the linear correlation factor and the exponential correlation factor, namely r 12 exp(-γr ²12), with γ a positive real parameter. The goal of this correlation factor is to provide a vanishing behavior at large interelectronic distances through the Gaussian geminal, while keeping the linear behavior at short electronic distances. This advanced correlation factor has inspired a modified correlation function to speed up the convergence of the standard CI expansion of the wave function via similarity-transformation of the Hamiltonian. The methodology and results for two-electron systems are given in chapter 7. Finally, chapter 8 gives a series of benchmark calculations for MP2-R12 pair energies of both ethylene and ethane, obtained with localized orbitals following the Boys localization criteria. The concluding chapter (chapter 9) presents the possible impact of these developments when combined with local correlation techniques and gives an outlook for future studies in this direction.