Adaptive multiconfigurational wave functions

A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff $\Lambda$. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than $\Lambda$. The resulting $\Lambda$-CI wave function is adaptive, being able to represent both single-reference and multireference electronic states. We also consider a more compact wave function parameterization ($\Lambda$+SD-CI), which is based on a small $\Lambda$-CI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build $\Lambda$-CI wave functions. The first is based on an approximate prescreening of the full configuration interaction space, while the second consists of a breadth-first search coupled with pruning. The $\Lambda$-CI and $\Lambda$+SD-CI approaches are used to compute the dissociation curve of N$_2$ and the potential energy curves for the first three singlet states of C$_2$. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the $\Lambda$-CI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu$_2$O$_2^{2+}$ core, illustrates an alternative use of the $\Lambda$-CI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent high-level multireference coupled cluster computations.