Efficient Novel Approaches for the Calculation of Molecular Response Properties

Abstract

This thesis reports on an efficient implementation of first- and second-order derivatives for non-variational wave functions used for the calculation of molecular properties in a linear response framework. Since, the accurate quantum chemical description of second-order molecular properties is strongly limited by the size of the system, a reliable method, which can be routinely applied from medium-sized to large molecular compounds is desirable.<br /> Inspired by the excellent performance of the recently developed double-hybrid density functionals for energetics, thermodynamics and electron spin resonance hyperfine coupling tensors, this work focused on the efficient implementation of second derivatives for these 'fifth rung' functionals. Density functionals of the 'fifth rung' include non-local correlation by involving virtual Kohn-Sham molecular orbitals.<br /> In double-hybrid functionals part of the semi-local correlation introduced by a gradient corrected exchange correlation functional is replaced by nonlocal, orbital-dependent dynamic correlation by second-order Moller-Plesset (MP2) perturbation theory. Therefore, the theory of second derivatives with respect to imaginary (magnetic) and real (electric) perturbations for non-variational wave functions has been rederived and extended to the use of the popular 'Resolution of the Identity' approximation. The first derivation of second double-hybrid functional derivatives within the 'density fitting' approach is presented. <br /> Besides numerical results for static polarizabilities, chemical shifts and electronic g-tensors, a benchmark study on a fairly large system with an extended basis set (~1400 basis functions) employing the recently developed RIJCOSX approximation is presented in this thesis. Such a calculation is performed within a few days of computer time. We are not aware of any other method beyond self-consistent field theory (Hartree-Fock, density functional theory) that can routinely applied to molecules of dimension. <br /> MP2 is well known as the simplest ab initio method, that accounts for dynamic correlation effects. Besides its plenty advantages MP2 often fails for complicated electronic structures. The reason could be attributed to the poor reference wave function, which is usually of Hartree-Fock quality. A new Ansatz has been derived based on the well-known Hylleraas functional, which minimizes the total energy with respect to the molecular orbital coefficients and the double excitation amplitudes. Consequently, the molecular orbitals can relax in the presence of the dynamic correlation field. This orbital-optimized MP2 method has shown to provide drastically improved energetics compared to the canonical MP2 method. Furthermore, the calculated electron spin resonance hyperfine coupling tensors have almost been of the same quality as what can be achieved with the more rigorous Coupled-Cluster Singles Doubles (CCSD) method, but with substantially less computational effort. The orbital-optimized MP2 method is characterized as an iterative O(N5) procedure, whereas CCSD scales with O(N6) per iteration. The formalism of the orbital-optimized MP2 method has, also for the first time, been extended for the calculation of first- and second-order properties.