Generalized nonorthogonal matrix elements for arbitrary excitations

Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication, H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021), I introduced a generalized nonorthogonal extension to Wick's theorem that allows matrix elements to be derived between excited configurations from different reference determinants. However, that work only provided explicit expressions for one- and two-body matrix elements between singly- or doubly-excited configurations. Here, this framework is extended to compute generalized nonorthogonal matrix elements between arbitrary excitations. Pre-computing and storing intermediate values allows one- and two-body matrix elements to be evaluated with an $\mathcal{O}{(1)}$ scaling relative to the system size, and the LibGNME computational library is introduced to achieve this in practice. These advances make the evaluation of nonorthogonal matrix elements almost as easy as their orthogonal counterparts, facilitating a new phase of development in nonorthogonal electronic structure theory.