Generalized antisymmetric ordered products, generalized normal ordered products, ordered and ordinary cumulants and their use in many electron correlation problem

Similarity transformed equation of motion coupled cluster theory revisited: a benchmark study of valence excited states

“…This is the easiest possibility. More than a decade ago Mukherjee and Kutzelnigg [60,61] defined a generalization of the concept of normal ordering to the multireference situation (see also references [62,63]), and this has led to a very rich set of developments (canonical transformation theory [64][65][66], antihermitian contracted Schrödinger equation [67,68], internally contracted multireference coupled cluster [69,70]). This generalization has also allowed the development of a promising multireference equation of motion coupled cluster theory [71,72], which uses both the many-body transformation concept, and the generalized normal ordering.…”

Ring coupled-cluster doubles correction to geminal wavefunctions

“…In addition, there appears a redundancy among excited functions in the general case that has to be dealt with. [9] Redundancy is avoided here by resorting to double excitations in the cluster amplitudes. Extensivity is always an issue to consider, especially for a CC theory.…”

“…The latter route has been extensively investigated by professor Debashis Mukherjee throughout his career, starting with open-shell CC formulations [2,3], followed by ideas based on the eigenvalue independent partitioning [4,5] or those exploiting the JeziorskiMonkhorst [6] parametrization of the wavefunction [7]. An extremely simple version of multireference (MR) CC theory was put forward by Mukherjee and coworkers [8,9], inspired by the idea of generalizing the concept of normal ordering for a multideterminantal reference function [10,11] It is the internally contracted MR CC formulation of Ref. [8] that provides the starting point of the present work.…”

“…We take an antisymmetrised product of strongly orthogonal geminal (APSG) function [27] as reference and tailor the theory to be as parallel as possible with the existing ERPA-APSG method of Pernal. This is the reason for picking the original rather than the improved version [9] of the underlying CC theory.…”

“…The MR CC method considered here is based on generalized normal ordering (GNO) and applies the corresponding generalized Wick's theorem (GWT) [9,10,11,30,31]. Double excitations entering the cluster operator have a general flavour.…”