Sanibel Symposium

We explore the All Configuration Mean Energy (ACME) conditions for MCSCF orbital optimization and for nonlinear arc factor optimization within the Graphically Contracted Function (GCF) method. The ACME conditions consist of a state-averaged optimization in which the number of states included in the averaging procedure is the dimension of the basis and all states have equal weights. In the MCSCF optimization case, the state averaging is over the dimension of the configuration state function (CSF) expansion space N_CSF; in the GCF case, it is over the dimension of the nonlinear GCF expansion space N_GCF. When the MCSCF CSF expansion space is represented with the graphical unitary group approach (GUGA), the ACME energy and reduced density matrices (RDM) may be evaluated with an efficient recursive procedure with effort  and does not depend on N_CSF; _orb is the number of active orbitals and the factor ω ranges from 1 to  where N_e( is the number of active electrons) depending on the complexity of the underlying Shavitt graph. This allows orbital optimization to be performed for MCSCF expansions of practically unlimited size. Other MCSCF features considered include the associated orbital optimization equations, the partitioning of the redundant and essential orbital optimization parameters, and the implementation of analytic energy gradients and nonadiabatic coupling for arbitrary highlevel electronic structure methods based on the ACME MCSCF orbitals. In the GCF method the ACME conditions result in energy and RDM computational effort that scales as   a factor of N_GCF less than usual.

 

This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences, U.S. Department of Energy, under contract number DE-AC02-06CH11357