Despite its importance, state-of-the-art algorithms for performing complete active space self-consistent field (CASSCF) computations have lagged far behind those for single reference methods. We develop an algorithm for the CASSCF orbital optimization that uses sparsity in the atomic orbital (AO) basis set to increase the applicability of CASSCF. Our implementation of this algorithm uses graphical processing units (GPUs) and has allowed us to perform CASSCF computations on molecular systems containing more than one thousand atoms. Additionally, we have implemented analytic gradients of the CASSCF energy; the gradients also benefit from GPU acceleration as well as sparsity in the AO basis.
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Both the Fock operator and frozen core operators can be viewed as terms in a normal-ordered electronic Hamiltonian. In the former case, the Hamiltonian is normal-ordered with respect to some single, reference determinant containing all electrons; in the latter case, the reference determinant contains only the core electrons.
In practice, the construction of the J matrix can be avoided since the half transformed ERIs, (μν|tu), have already been formed and . The computational savings from this optimization is minimal.
If the number of orbitals contained in the active space is not treated as a constant, the cost of the CI computation itself can be assumed to dominate, since it scales factorially with the number of active orbitals.
