Fock coordinate function method for separation of spin variables in transition density matrices

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Explicit equations for the constants a and b of the energy as the average expectation value for the minimal domain of states giving the Roothaan energy functional are derived in terms of the total spin value and the "seniority" quantum number. The state with off-diagonal long-range order can appear in the framework of the Roothaan scheme for the quasidegenerate system as an alternative to the Hund rule. Admissible many-electron states are established for all configurations of the icosahedral symmetry group systems, and corresponding a and b coefficients are calculated.

Section: Charge Densities Of the Averaged "Quasispin" Multipletsupporting

confidence: 60%

Section: Charge Densities Of the Averaged "Quasispin" Multipletmentioning

confidence: 99%

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Roothaan's open shell theory from the viewpoint of an orthogonal group

Klimko¹,

Mestechkin²

1990

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“…(2) serves by itself as a generating function for producing of states with m # s on the replacement of all la) by [ a ) + 51p), where 5 is a gcnerating parameter [12]. Hence, the RDM-k generating function [16] t+u,r- (83) is RDM-k of the corresponding modification of Iq) in Eq. (2) and can be derived by the procedure resembling the deduction of Eqs.…”

Section: Some Generalizations and Applicationsmentioning

confidence: 99%

“…For this purpose we utilize the Fock generating function method [12] and auxiliary procedures described in detail in Ref. 16. However it should be repeated that the wave function with m = s in the form of Eq.…”

Section: Some Generalizations and Applicationsmentioning

confidence: 99%

Structure and spin‐purity conditions for reduced density matrices of arbitrary order

Luzanov

Whyman²

1981

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For arbitrary k, the separation of spin variables is performed in the reduced density matrix of the kth order (RDM-k) on the basis of the Fock coordinate function method. The independent spatial components of RDM-k are analyzed. For RDM-k of the total spin eigenstate, their number is proved never to exceed its spin multiplicity 2s + 1. Integral and other nontrivial interrelations between spatial components are established which turn out to be the necessary and sufficient conditions of spin purity of a wavefunction corresponding to a given RDM-k. It is shown that the r-rank k-particle spin distribution matrix F;, defined as a spatial coefficient at the spin-tensorial operator of rank r in the RDM-k expansion, can be obtained by reduction of the (k + r)-particle charge density matrix F:+r. In particular, all spatial components of RDM-2 are explicitly expressed in terms of the four-electron charge density matrix only. This allows us to propose some approximative formulas for the McWeeny-Mizuno spin-orbit and spinspin coupling functions in the case of the weak spin contamination.

Collectivity, shell openness indices, and complexity measures of multiconfigurational states: Computations within full CI scheme

Luzanov¹,

Zhikol²

2005

ABSTRACT:It is shown that the multiconfigurational character of the N-electron wave function can be treated by a new quantitative index, N eff , computed as a special matrix invariant of the full wave function. Along with N eff , a simpler index N eff av is given due to the Kutzelnigg and Smith open-shell theory. The indices are compared with an effective number of unpaired electrons introduced by Takatsuki, Fueno, and Yamaguchi. Full configuration interaction (FCI) computations on such quantities realized in the present work for atoms and dissociation reactions lead to the conclusion that all indices give a qualitatively similar picture. It is stressed that N eff as a more complicated quantity reflects a global complexity of the electronic state, while other indices represent the electron structure peculiarities only at the one-electron level.