Unitary Group Approach to Valence Bond and Coupled Cluster Methods

Abstract

It is a great honor to contribute to this volume, dedicated to Professor Larry C. Biedenharn at the occasion of his 70th anniversary. His seminal papers on representation theory of semi-simple Lie groups [1], boson and pattern calculus [2], canonical tensor operators in the unitary group [3], as well as his and J.D. Louck’s authoritative monographs on Racah-Wigner algebras [4,5], represent a fundamental point of departure for any development based on the unitary group symmetry of various physical or chemical systems. Although the standard SU(2) spin angular momentum formalism is in principle adequate when exploring molecular electronic structure, the exploitation of higher unitary group symmetries, that naturally arise when using the molecular orbital (MO) formalism, proved to be very beneficial and useful not only for various methodological advances at various levels of approximation [6–11], but also for the design and development of efficient algorithms and actual computer codes (for references, see [11,12]). In fact, the boson calculus based formalism of unitary group representation theory proved to be a useful source of various new concepts in quant urn-chemical methodology [6–16] that continue to play an important role in diverse approaches to molecular electronic structure, be they of variational or perturbative nature. Moreover, it also provided a unified viewpoint and better insight into various existing schemes, that are based either on the permutation group S N invariance properties of systems involving N indistinguishable particles [17] or the classical spin angular momentum formalism [18].