Doubly Occupied Pair Coupled Cluster F12 Approach

Excited states with pair coupled cluster doubles tailored coupled cluster theory

It is known that some non-dynamic effects of electron correlation can be included in coupled cluster theory using a tailoring technique that separates the effects of non-dynamic and dynamic correlations. Recently, the simple pCCD (pair coupled cluster doubles) wavefunction was shown to provide good results for some non-dynamic correlation problems, such as bond-breaking, in a spin-adapted way with no active space selection. In this paper, we report a study of excited states using "tailored coupled cluster singles and doubles," to attempt to use pCCD as a kernel for more complete coupled-cluster singles and doubles (CCSD) results for excited states. Several excited states are explored from those primarily due to single excitations to those dominated by doubly excited states and from singlet-triplet splittings for some diradical states. For the first two situations, tailored pCCD-TCCSD offers no improvement over equation of motion-CCSD. However, when we explore the singlet-triplet gap of diradical molecules that are manifestly multi-reference, a pCCD kernel provides improved results, particularly with generalized valence bond orbitals.

Geminal-based electronic structure methods in quantum chemistry. Toward a geminal model chemistry

In this review, we discuss the recent progress in developing geminal-based theories for challenging problems in quantum chemistry. Specifically, we focus on the antisymmetrized geminal power, generalized valence bond, antisymmetrized product of strongly orthogonal geminals, singlet-type orthogonal geminals, the antisymmetric product of 1-reference orbital geminal, also known as the pair coupled cluster doubles ansatz, and geminals constructed from Richardson-Gaudin states. Furthermore, we review various corrections to account for the missing dynamical correlation effects in geminal models and possible extensions to target electronically excited states and open-shell species. Finally, we discuss some numerical examples and present-day challenges for geminal-based models, including a quantitative and qualitative analysis of wave functions, and software availability.