Separation of spin and the fock coordinate wave function method in the N-representability problem

Vaiman, G. E.; Luzanov, A. V.; Mestechkin, M. M.

doi:10.1007/bf01028915

Cited by 23 publications

(15 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…20 However, this formulation is fairly complicated and no implementation or chemical application has been reported so far. A more practical formulation was put forth by Luzanov and co-workers, [21][22][23][24] who provided an explicit expression for the spin density in terms of the one-and two-particle spin-free (charge) density matrices. More recently, an alternative derivation was presented by Gidofalvi and Shepard 25 within the graphically contracted function approach.…”

mentioning

confidence: 99%

Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

Datta

Gauß

2015

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

mentioning

confidence: 99%

Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

Datta

Gauß

2015

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…(5.2) as this is done in Ref. [25] (see also [20]). Now we see that interrelations (5.21)-(5.25) are quite natural.…”

Section: ) Then We Have the Representationsmentioning

confidence: 80%

“…We see that it is advantageous to divide the whole Nelectron system into (n 6 s)-electron subsystems [3,22,23]. On this account, the particles from Q a constitute a fermion subsystem of ''a-electrons'' whereas the particle from Q b do a fermion subsystem of ''b-electrons'' [25]. The whole system is then considered as a fermion composite (bipartite) system.…”

Section: Fock's Construction and Cyclic Symmetry Conditionmentioning

confidence: 99%

“…This favorite preference was also passed to the present author, which was a postgraduate student of Prof. Mestechkin. In the 70s and 80s, the Mestechkin group made some additional progress on the spin-free quantum chemistry within the frame of the Fock theory [25][26][27][28]. Subsequently, practical algorithms and applications based on Waller-Hartree double-determinant expansions appeared in our recent works [29].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Spin‐free quantum chemistry: What one can gain from fock's cyclic symmetry

Luzanov

2010

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

ABSTRACT:The spin-free wave function due to Fock (Zh Eksp Teor Fiz, 1940, 10, 961) is re-examined with a stress on the reduced density matrix (RDM) theory. The key notion of the Fock approach is the cyclic symmetry of wave functions. It is a specific algebraic identity involving transpositions of numbers taken from two different columns of the corresponding Young tableau. We show first how to construct symmetry adapted states by accounting for high-order cyclic symmetry conditions. For Young's projectors, it gives a new expression including nothing but antisymmetrizers. Next, transforming the Fock spin-free state by a duality operator (the star operator in exterior algebra), we arrive at the representation closely related to spin-flip models. In such spin-flip models, a coupling operator is the basic object for which we show that the cyclic symmetry is transformed into a tracelessness of the coupling operator. The main results are related to the spin-free theory of spin properties. In particular, the theorem previously stated (Luzanov and Whyman, Int J Quantum Chem, 1981, 20, 1179) is refined by an explicit general representation of spin density operators through spin-free (charge) RDMs. Some applications implicating high-order RDMs (collectivity numbers, the unpaired electron problem, cumulant spin RDMs, spin correlators, etc.) are also considered. For spin-free RDM components, a new projection procedure without constructing any symmetry adapted state is proposed. An unsolved problem of constructing orthogonal representation matrices within the Fock theory is raised.

show abstract

“…In this case, Â is the two-electron charge density matrix described by McWeeny [22]. For a general case, consider first cyclic permutations of an odd length n ϭ 2 ϩ 1 (25) with a typical element P expressed by the following product of coupled transpositions…”

Section: Weyl Symbols Of Permutation Operatorsmentioning

confidence: 99%

Weyl representation of the permutation operators and exchange interaction

Luzanov

Prezhdo

2003

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

Weyl phase-space representation is derived for the cyclic permutation operators that naturally occur in the quantum theory of exchange interaction. The classical-like phase-space representation of exchange leads to a special type of coupling between the position and momentum variables. With Gaussian electronic structure basis sets in mind, it is shown that the position-momentum coupling seen in the Weyl representation of the exchange interaction is best described by diffuse Gaussians. A classical phase-space analog of exchange is derived for the Heisenberg-Dirac spinHamiltonian. Novel one-electron Wigner functions are introduced for description of the two-electron spin correlations.

show abstract

Separation of spin and the fock coordinate wave function method in the N-representability problem

Cited by 23 publications

References 6 publications

Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

Communication: Spin densities within a unitary group based spin-adapted open-shell coupled-cluster theory: Analytic evaluation of isotropic hyperfine-coupling constants for the combinatoric open-shell coupled-cluster scheme

Spin‐free quantum chemistry: What one can gain from fock's cyclic symmetry

Weyl representation of the permutation operators and exchange interaction

Contact Info

Product

Resources

About