Abstract:
For the wave functions of a spin multiplet we carry out, in general form, separation of
the spin variables in the two-particle density matrices, which are constructed from the
three spatial two-particle functions and irreducible tensor spin operators. We find
nontrivial integral relations for these spatial functions, giving necessary conditions of
NN-representability. We show that these spatial components are density matrices of
the Schrödinger wave function for two groups of electrons. The condition of cyclic
symmetry for this function is ensured by one of the obtained integral relations.
Citation:
G. E. Vaiman, A. V. Luzanov, M. M. Mestechkin, “Separation of spin and the fock coordinate wave function method in the NN-representability problem”, TMF, 28:1 (1976), 65–79; Theoret. and Math. Phys., 28:1 (1976), 634–643
\Bibitem{VaiLuzMes76}
\by G.~E.~Vaiman, A.~V.~Luzanov, M.~M.~Mestechkin
\paper Separation of spin and the fock coordinate wave function method in the $N$-representability problem
\jour TMF
\yr 1976
\vol 28
\issue 1
\pages 65--79
\mathnet{http://mi.mathnet.ru/tmf3353}
\transl
\jour Theoret. and Math. Phys.
\yr 1976
\vol 28
\issue 1
\pages 634--643
\crossref{https://doi.org/10.1007/BF01028915}
Linking options:
https://www.mathnet.ru/eng/tmf3353
https://www.mathnet.ru/eng/tmf/v28/i1/p65
This publication is cited in the following 22 articles:
Dipayan Datta, Jürgen Gauss, “Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory”, J. Chem. Theory Comput., 15:3 (2019), 1572
Iakov Polyak, Michael J. Bearpark, Michael A. Robb, “Application of the unitary group approach to evaluate spin density for configuration interaction calculations in a basis of S2 eigenfunctions”, Int J of Quantum Chemistry, 118:12 (2018)
M. M. Mestechkin, “Diagonal N-representability as a method for solving the representability problem”, Russ. J. Phys. Chem. B, 11:2 (2017), 208
Dipayan Datta, Jürgen Gauss, “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”, The Journal of Chemical Physics, 143:1 (2015)
Luzanov A.V., “Rasscheplenie v nulevom pole tripletnykh urovnei sopryazhennykh molekul. sravnenie tochnoi i priblizhennykh p-skhem”, Zhurnal strukturnoi khimii, 53:1 (2013), 7–16
Zero field splitting of triplet levels of conjugated molecules: a comparison of exact and approximate p-schemes
A. V. Luzanov, “Some spin and spin‐free aspects of coulomb correlation in molecules”, Int J of Quantum Chemistry, 112:17 (2012), 2915
Luzanov A.V., “Quantum Fidelity for Analyzing Atoms and Fragments in Molecule: Application to Similarity, Chirality, and Aromaticity”, Int. J. Quantum Chem., 111:10 (2011), 2196–2220
A. V. Luzanov, O. V. Prezhdo, “The spin-polarized extended Brueckner orbitals”, The Journal of Chemical Physics, 135:9 (2011)
Gergely Gidofalvi, Ron Shepard, “The evaluation of spin‐density matrices within the graphically contracted function method”, Int J of Quantum Chemistry, 109:15 (2009), 3552
A. V. Luzanov, O. V. Prezhdo, “Analysis of multiconfigurational wave functions in terms of hole-particle distributions”, The Journal of Chemical Physics, 124:22 (2006)
A. V. Luzanov, O. V. Prezhdo, “Hole-particle characterization of coupled-cluster singles and doubles and related models”, The Journal of Chemical Physics, 125:15 (2006)
A. V. Luzanov, O. V. Prezhdo, “Irreducible charge density matrices for analysis of many‐electron wave functions”, Int J of Quantum Chemistry, 102:5 (2005), 582
A. V. Luzanov, O. A. Zhikol, “Collectivity, shell openness indices, and complexity measures of multiconfigurational states: Computations within full CI scheme”, Int J of Quantum Chemistry, 104:2 (2005), 167
A. V. Luzanov, O. V. Prezhdo, “Weyl representation of the permutation operators and exchange interaction”, Int J of Quantum Chemistry, 96:5 (2004), 474
A. V. Luzanov, Yu. F. Pedash, S. Mokhamad, “Interpretation of multiconfigurational states in the wave-operator method”, Theor Exp Chem, 26:5 (1991), 485
A. V. Luzanov, “The spin-symmetrized Hartree-Fock method”, J Struct Chem, 25:6 (1985), 837
M. M. Mestechkin, G. T. Klimko, V. A. Kuz'mitskii, “The basis of roothaan's method for an open shell”, Theor Exp Chem, 20:6 (1985), 601
John E. Harriman, “Geometry of density matrices. V. Eigenstates”, Phys. Rev. A, 30:1 (1984), 19
A. V. Luzanov, “One-particle approximation in valence-scheme superposition”, Theor Exp Chem, 17:3 (1982), 227
A. V. Luzanov, G. E. Whyman, “Structure and spin‐purity conditions for reduced density matrices of arbitrary order”, Int J of Quantum Chemistry, 20:6 (1981), 1179
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