Laplace-transformed multi-reference second-order perturbation theories in the atomic and active molecular orbital basis

摘要

In the present article, we show how to formulate the partially contractedn-electron valence second order perturbation theory (NEVPT2) energies in theatomic and active molecular orbital basis by employing the Laplacetransformation of orbital-energy denominators (OED). As atomic-orbital (AO)basis functions are inherently localized and the number of active orbitals iscomparatively small, our formulation is particularly suited for alinearly-scaling NEVPT2 implementation. Some of the NEVPT2 energy contributionscan be formulated completely in the AO basis as single-reference second-orderM{\o}ller-Plesset perturbation theory and benefit from sparse active-pseudodensity matrices - particularly if the active molecular orbitals are localizedonly in parts of a molecule. Furthermore, we show that for multi-referenceperturbation theories it is particularly challenging to find optimal parametersof the numerical Laplace transformation as the fit range may vary among the 8different OEDs by many orders of magnitude. Selecting the number of quadraturepoints for each OED separately according to an accuracy-based criterion allowsus to control the errors in the NEVPT2 energies reliably.