Evaluation of full valence correlation energies and gradients

Complete-active-space self-consistent field (CASSCF) wave functions are central to understanding strongly correlated molecules as they capture the entirety of electronic interactions within a subset of the orbital space. The most interesting case for CASSCF is the full valence limit, where all bonding and an equal number of virtual orbitals are included in the active space, and no approximation is made in selecting the important valence orbitals or electrons. While conventional algorithms require exponential computational time to evaluate full valence CASSCF, this article shows that the method of increments can do the same with polynomial effort, in a new method denoted iCASSCF. The method of increments can also provide density matrices and other necessary ingredients for the construction of the nuclear gradient. These goals are met through a many-body expansion that breaks the problem into smaller pieces that are subsequently reassembled to form close approximations of conventional CAS results. Practical demonstrations on a number of medium-sized molecules, with up to 116 valence electrons correlated in 116 orbitals, show the power of this methodology.