Clifford algebra unitary group approach to many-electron correlation problem

Abstract

Articles you may be interested inA comparison between the Mo/ller-Plesset and Green's function perturbative approaches to the calculation of the correlation energy in the manyelectron problem J. Chem. Phys. 93, 5826 (1990); 10.1063/1.459578 Unitarygroup approach (UGA) to the configuration interaction (CI) problems of the manyelectron systems. II. Weyl graphical method of twobody operator matrix elements J. Chem. Phys. 89, 3079 (1988); 10.1063/1.454964 Parastatistics and the Clifford algebra unitary group approach to the manyelectron correlation problem Unitarygroup approach (UGA) to the configuration interaction (CI) problems of the manyelectron systems: A graphical formula in terms of Young tableausUnitary. group ap~roach (UGA) to the many-electron correlation problem is generalized by eI?beddmg the unttary group l!(n) in a .much larger group U(2n) via the rotation groups SO(m) wIth m = 2n or 2n + 1 and thelr covenng group Spin (m). Exploiting the spinorial Clifford algebra basis associated with Spin (m), it is shown that an arbitrary N-electron configuration state can be repr~sented as a linear combination of two-box Weyl tableaux ofU(2 n ), and the explicit representatlOn for Urn) generators as simple linear combinations ofU(2n) generators is given. The problem ofU(n) generator matrix element evaluation for two-column irreducible representations then red~ces to an elementary p.roblem of evaluation of generator matrix elements for the totally symmetnc two-box representatlOn ofU(2n). Thus a general N-electron problem is effectively reduced to a number of t\~o-boso~ problems. The proposed formalism also enables us to exploit other than Gelfand-Tsethn couphng schemes and particle nonconserving operators.

Bond length alternation in cyclic polyenes. VII. Valence bond theory approach

“…A very nice and convincing demonstration of the importance of this concept, as well as its historical origins, may be found in a paper by Professor McWeeny [29], to whom we dedicate this study. Following this idea and exploiting CAUGA formalism [44,45], we have formulated the so-called PPP-VB method [25,26] and tested it on a number…”

“…Being stimulated by recent advances in VB methodology and its successes at the ab initio level [21-241, we have decided to explore similar ideas at the semiempirical level, relying on the unitary group approach (UGA) [34,35], particularly in its Clifford algebra version (CAUGA) [44,45], and the PPP-type Hamiltonians [7,35]. One of the key ingredients of modern VB-type approaches, be they of the so-called generalized VB (GVB) [21] or spin-coupled VB [22-241 variety, is the utilization of the so-called OEAOs [29] rather than of the strictly localized AOs of the original VB method.…”

Spin-free approach for evaluation of electronic matrix elements using character operators of ?N

“…A CSF is now expressed as an antisymmetrized product of Q, and one of the spin eigenfunctions qi = A(@@,), (9) where d denotes the usual antisymmetrizer defined by A = c E p @ . (10) From the fact that a permutation and its inverse have the same parity and identical character we get…”

An explicit basis of lowering operators for irreducible representations of unitary groups

“…(See Fig. 1 of [40] for an illustration of this in the case of benzene.) Another is that the lowering operators involved are complicated.…”

“…One disadvantage is that the physical significance of the states is somewhat obscure. For instance, in the context of quantum chemistry, Paldus and Sarma have remarked on "the unphysical nature" of the GelfandZetlin basis and have observed that this is a crucial flaw in the valence bond scheme [40]. (See Fig.…”