New Directions for the Loop-Driven Graphical Unitary Group Approach: Analytic Gradients and an MCSCF Procedure

Abstract

It is becoming increasingly apparent1–10 that the unitary group approach (UGA) provides the theoretical framework for an elegant and exceptionally efficient molecular calculus of quantum mechanical matrix element evaluation. Although this approach was pioneered by physicists primarily concerned with nuclear problems,11 it has more recently been demonstrated to be equally (perhaps more so) applicable to the many-electron problem. In our own research, a direct descendant of that of Paldus2,3 and Shavitt,4 the efficacy of the loop-driven 5,8 graphical UGA (LDGUGA) has been emphasized. In essence, the LDGUGA illuminates vast numbers of previously unrecognized relationships between different Hamiltonian matrix elements. Here we underline the generality of the LDGUGA formalism by establishing its applicability to two longstanding challenges to theoretical chemists. First, the determination of the two-particle density matrix provides a realistic approach to the problem of obtaining analytic energy gradients from correlated wave functions. Secondly, the LDGUGA holds promise for the determination of very large (on the order of 10,000 configurations) multiconfiguration self-consistent-field (MCSCF) wave functions.