Generalized Antisymmetric Geminal Powers

Patrick Cassam‐Chenaï

Brian Weiner, Osvaldo Goscinski

The generalized antisymmetrized geminal-power (GAGP) function, shown to be the ground state for the oneparticle-hole propagator, can be computed using the rather simple properties of its reduced density matrices and the properties of unitary transformations. The practical procedure involves limited storage notwithstanding the rather large number of configurations with which the GAGP function can be associated. Using the stability properties previously derived for this function, we construct the self-consistent one-particle-hole propagator.

Valentina Bianchi

Thomas M. Henderson, Gustavo E. Scuseria

Strong pairing correlations are responsible for superconductivity and off-diagonal long-range order in the two-particle density matrix. The antisymmetrized geminal power wave function was championed many years ago as the simplest model that can provide a reasonable qualitative description for these correlations without breaking number symmetry. The fact remains, however, that the antisymmetrized geminal power is not generally quantitatively accurate in all correlation regimes. In this work, we discuss how we might use this wave function as a reference state for a more sophisticated correlation technique such as configuration interaction, coupled cluster theory, or the random phase approximation.

Paweł Tecmer, Katharina Bogusławski

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.