The shape-driven graphical unitary group approach to the electron correlation problem. Application to the ethylene molecule

Abstract

A new method for the approximate solution of Schrödinger’s equation for many electron molecular systems is outlined. The new method is based on the unitary group approach (UGA) and exploits in particular the shape of loops appearing in Shavitt’s graphical representation for the UGA. The method is cast in the form of a direct CI, makes use of Siegbahn’s external space simplifications, and is suitable for very large configuration interaction (CI) wave functions. The ethylene molecule was chosen, as a prototype of unsaturated organic molecules, for the variational study of genuine many (i.e.,≳2) body correlation effects. With a double zeta plus polarization basis set, the largest CI included all valence electron single and double excitations with respect to a 703 configuration natural orbital reference function. This variational calculation, involving 1 046 758 spin- and space-adapted 1Ag configurations, was carried out on a minicomputer. Triple excitations are found to contribute 2.3% of the correlation energy and quadruple excitations 6.4%.

Implementation of a general multireference configuration interaction procedure with analytic gradients in a semiempirical context using the graphical unitary group approach

“…The generation of the total set of loops leads to a tree search problem. Closely related to this algorithm is the shape-driven approach, which was introduced independently by Lischka et al 55 and Saxe et al 56 It differs from the loop-driven algorithm by a division of the active space into internal and external orbitals (see above). Internal partial loop values (precomputed using the loop-driven approach) are combined with external partial loop values (calculated in a direct manner) to obtain the coupling coefficients.…”

“…The active orbitals that are occupied in at least one reference configuration are called internal, in contrast to the active external orbitals that are unoccupied in all reference configurations. Large-scale CI implementations gain much of their efficiency from the latter distinction 11,27,55,56 because a large number of quantities can be precomputed for the relatively small number of internal orbitals. Because at most two electrons are promoted into the external orbitals in a single CSF, the structure of the external part is simple enough to calculate the external contributions as needed.…”

The significance of double substitutions in well-correlated electronic wave functions

“…To provide one more comparison with large-scale CI, we carried out calculations on ethylene to compare with the benchmark CI study of Saxe et al [25]. Their configuration list, although not strictly corresponding to full-cr, did amount to a massive treatment involving over 106 configurations and higher-order configurations constituted the bulk of the configuration list.…”

Perspective on "Group theoretical approach to the configuration interaction and perturbation theory calculations for atomic and molecular systems"

“…(0 1 1) for basis vector 1 or (0 3 1 ) for basis vector 3 ] in Eq. (18) is enough to specify all the information that is required about a CSF and to establish an algorithm for the implicit representation of the basis.…”