One of the most challenging problems in modern electronic structure theory is the development of affordable ab initio methods that can provide an accurate description of ground- and excited-state molecular potential energy surfaces. Of all approaches to the many-electron correlation problem, the coupled-cluster (CC)(1) methods are regarded as the best methods for high accuracy calculations. Standard single-reference (SR) CC and equation-of-motion CC (EOMCC)(2,3) approaches, such as CCSD(4), CCSD(T)(5), and EOMCCSD(3), provide an excellent description of closed-shell systems and dynamic correlation effects but fail when potential energy surfaces involving bond breaking and biradicals are examined. It has been demonstrated that many of the problems encountered in SRCC or EOMCC calculations can be eliminated by adding non-iterative corrections to CC or EOMCC energies based on the method of moments of CC equations (MMCC)(6). On the other hand, it is well known that the low-order multi-reference many-body perturbation theory (MRMBPT) approaches can provide very good description of electronic quasi-degeneracies with relatively small computer effort. MRMBPT methods also provide straightforward access to ground and excited states. The purpose of this work is to develop a new class of MMCC approaches in which information about the most essential non-dynamic and dynamic correlation effects that are relevant to electronic quasi-degeneracies is extracted from MRMBPT, referred to as MMCC/PT(7,8).

The performance of the basic MMCC/PT approximation, in which inexpensive non-iterative corrections due to triples (MMCC(2,3)/PT) and triples and quadruples (MMCC(2,4)/PT) are added to the ground- and excited state energies obtained with CCSD/EOMCCSD, is illustrated by the results of a few benchmark calculations including bond breaking in HF, F(2), and H(2)0, and excited states of CH+. The test calculations show that at least for single bond breaking and some cases of multiple bond dissociation, the MMCC/PT method eliminates the failures of the conventional CC/EOMCC approaches at large internuclear distances. It also eliminates large errors in EOMCCSD results for excited states dominated by two-electron transition without invoking the expensive steps of high-order iterative EOMCC methods.

In addition to describing the theoretical details behind MMCC/PT and discussing the results from the test calculations, the computational details, specifically the diagram factorization techniques which lead to efficient computer implementation, will be presented in this talk as well.

References:
(1). J. Č