Efficient and accurate local approximations to coupled-electron pairapproaches: An attempt to revive the pair natural orbital method

摘要

Coupled-electron pair approximations (CEPAs) and coupled-pair functionals (CPFs) have beenpopular in the 1970s and 1980s and have yielded excellent results for small molecules. Recently,interest in CEPA and CPF methods has been renewed. It has been shown that these methods lead tocompetitive thermochemical, kinetic, and structural predictions. They greatly surpass second orderMoller-Plesset and popular density functional theory based approaches in accuracy and areintermediate in quality between CCSD and CCSD(T) in extended benchmark studies. In this workan efficient production level implementation of the closed shell CEPA and CPF methods is reportedthat can be applied to medium sized molecules in the range of 50-100 atoms and up to about 2000basis functions. The internal space is spanned by localized internal orbitals. The external space isgreatly compressed through the method of pair natural orbitals (PNOs) that was also introduced bythe pioneers of the CEPA approaches. Our implementation also makes extended use of densityfitting (or resolution of the identity) techniques in order to speed up the laborious integraltransformations. The method is called local pair natural orbital CEPA (LPNO-CEPA) (LPNO-CPF).The implementation is centered around the concepts of electron pairs and matrix operations.Altogether three cutoff parameters are introduced that control the size of the significant pair list, theaverage number of PNOs per electron pair, and the number of contributing basis functions per PNO.With the conservatively chosen default values of these thresholds, the method recovers about 99.8%of the canonical correlation energy. This translates to absolute deviations from the canonical resultof only a few kcal mol-1 . Extended numerical test calculations demonstrate that LPNO-CEPA(LPNO-CPF) has essentially the same accuracy as parent CEPA (CPF) methods forthermochemistry, kinetics, weak interactions, and potential energy surfaces but is up to 500 timesfaster. The method performs best in conjunction with large and flexible basis sets. These results openthe way for large-scale chemical applications.