Clifford algebra realization of Rumer-Weyl basis

Section: Introductionsupporting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

Aromaticity in metallacyclobutadienes from the perspective of the valence bond theory

Rincón

1994

“…This essentially amounts to an efficient scheme for generating Rumer or Weyl [22] basis states as linear combinations of Slater determinants. Using these, one can either transform the Hamiltonian and overlap matrices (if memory permits) or one can select the states of correct S quantum number after diagonalization.…”

Section: Discussionmentioning

confidence: 99%

A graphical approach to configuration interaction studies in molecules using determinants of nonorthogonal orbitals

Rettrup

Thorsteinsson

Sarma

1991

A direct graphical approach is presented for the evaluation of matrix elements of a spin-free Hamiltonian between Slater determinants of nonorthogonal orbitals. The matrix element contributions are obtained by repeated use o f N -2 electron minors of the overlap matrix that are generated by independent looping of reduced N -2 electron graphs for the a-and P-strings of the determinants. Because of the successive generation of the matrix contributions, the method is well suited for direct diagonalization schemes.

“…For spin-independent Hamiltonians, used in molecular electronic structure calculations, we can conveniently employ a spin-free formulation, based either on symmetric group S N or unitary group U(n) formalism, as pioneered by Matsen [18,19]. Recently, the suitability of the CAUGA formalism for the representation of VB functions was noticed [26,27,29] and the use of bonded tableaux [35] within the UGA formalism examined.…”

Section: Caliga Realization Of Vb Statesmentioning

confidence: 99%

“…However, when we employ a much larger group U(2") and its subduction to U(n), n designating the orbital number, we obtain a very general formalism referred to as the Clifford algebra UGA (CAUGA) [26-301. In this approach, any spinadapted many-electron basis can be expressed in terms of a canonical basis of a totally symmetric, two-box representation of U(2"). In fact, this representation is most natural for the canonical VB states [26,27,29], which makes this formalism particularly suitable for the VB theory. It is the main purpose of this paper to outline one possible implementation of this formalism for VB calculations, which has been recently exploited at the semiempirical level [17,31].…”

Section: Introductionmentioning

confidence: 99%

Valence bond approach exploiting Clifford algebra realization of Rumer–Weyl basis

Paldus

1992

A detailed algorithm is described that enables an implementation of a general valence bond (VB) method using the Clifford algebra unitary group approach (CAUGA). In particular, a convenient scheme for the generation and labeling of classical Rumer-Weyl basis (up to a phase) is formulated, and simple rules are given for the evaluation of matrix elements of unitary group generators, and thus of any spin-independent operator, in this basis. The case of both orthogonal and nonorthogonal atomic orbital bases is considered, so that the proposed algorithm can also be exploited in molecular orbital configuration interaction calculations, if desired, enabling a greater flexibility for N-electron basis-set truncation than is possible with the standard Gel'fandTsetlin basis. Finally, an exploitation of this formalism for the VB method, based on semiempirical Pariser-Parr-Pople (ppp)-type Hamiltonian and nonorthogonal overlap-enhanced atomic orbital basis, and its computer implementation, enabling us to carry out arbitrarily truncated or full VB calculations, is described in detail.