Development of Efficient and Accurate Approximations to Single Reference Correlation Methods using Pair Natural Orbitals

Abstract

Computational chemistry greatly enhances the scientific analysis of experiments and can predict quantities that are experimentally not accessible. However, there is still no approximate method available that is both efficient and accurate enough to serve as general basis for large-scale applications in computational chemistry, at least in the range of 20 to 100 atoms, which covers many challenging problems of present day chemical research. In this dissertation, an accurate and efficient approximation to single reference correlation methods was developed which constitutes a new family of local correlation methods denoted local pair natural orbital (LPNO) methods. The LPNO methods achieve efficiency through localization of the internal space and truncation of the electron pair list together with a tremendous compression of the external space using a truncated pair natural orbitals expansion. Using the LPNO approach, serial and parallel production level implementations for various coupled pair methods, quadratic configuration interaction and coupled cluster with single and double excitations were developed in the framework of the ORCA quantum chemistry program package. Only three cut-off parameters enter the procedure, which control the number of PNOs per electron pair, the size of the significant electron pair list, and the number of contributing auxiliary basis functions per PNO. The rather conservatively chosen default values for the thresholds do not need to be changed or reinvestigated in detail prior to any application study and the LPNO methods can be used in the same way as their untruncated counterparts. The laborious integral transformation associated with the large number of PNOs becomes feasible through the extensive use of local density fitting (RI) techniques. The LPNO approach offers a number of attractive features: a) the smooth and controllable truncation errors; b) the excellent behavior with respect to basis set extension; c) the very compact form of the LPNO wavefunction; d) the absence of any real-space cut-offs or fragmentation schemes. Extended test calculations including thermochemistry, kinetics, weak molecular interactions and potential energy surfaces have consistently shown that the closed-shell LPNO variants together with the default values for the cut-off parameters recover around 99.7 - 99.9 % of the target correlation energy. The open-shell version is slightly less accurate but still more than 99.5 % of the target correlation energy is recovered on average. Although the effective scaling of the computation time with respect to the system size is still about cubic, the LPNO methods are efficient enough for studies on molecules with up to 100 atoms and 2000 basis functions in reasonable wall-clock times, e.g. not more than a few days for a single point energy calculation depending on the number of correlated electrons. The present LPNO methods are already highly suitable and useful for large-scale computational chemistry applications. Thus, due to the high efficiency and accuracy combined with the robustness of the LPNO methods and and their simple black-box use, they have a good chance at becoming a standard tool capable of tackling many interesting problems in contemporary chemical research.