Separability Problem in General Many Electron Systems

Since few problems of interest admit of solutions in closed form in quantum mechanics, we are obliged to use approximate methods based on expansion schemes of one form or another. Such expansions, when truncated at some finite order, often do not reflect some of the inherent properties of the systems under study. A typical example of this type of failure is the well known “symmetry dilemma” encountered in the Hartree — Fock calculation. The broken- symmetric solutions, occasionally faced, stem from the use of a restricted variation of the function in the subspace of single determinants. A full CI calculation will obviously restore the symmetry, but since that is neither practicable nor desirable, additional conditions are imposed to ensure that the resultant functions are symmetry-adapted even at the trial function level.

[1]  R. Offermann Degenerate many fermion theory in expS form: (II). Comparison with perturbation theory☆ , 1976 .

[2]  M. Durga Prasad,et al.  Development of a size-consistent energy functional for open shell states , 1984 .

[3]  K. Freed,et al.  First principles test of transferability hypothesis of semi-empirical theories using correlated ab initio effective valence shell hamiltonian methods , 1981 .

[4]  D. W. Davies,et al.  Many-body perturbation theory calculations on the electronic states of Li2, LiNa and Na2 , 1981 .

[5]  R. Bartlett,et al.  Multireference coupled-cluster methods using an incomplete model space: Application to ionization potentials and excitation energies of formaldehyde , 1987 .

[6]  R. Bartlett Many-Body Perturbation Theory and Coupled Cluster Theory for Electron Correlation in Molecules , 1981 .

[7]  W. Ey Degenerate many fermion theory in exp S form: (III). Linked valence expansions☆ , 1976 .

[8]  D. Mukherjee Linked-cluster theorem in open shell coupled-cluster theory for mp-mh model space determinants , 1986 .

[9]  H. Monkhorst,et al.  Coupled-cluster method for multideterminantal reference states , 1981 .

[10]  M. Robb,et al.  The method of minimized iterations in multi-reference (effective hamiltonian) perturbation theory , 1981 .

[11]  M. Robb,et al.  Calculation of effective hamiltonians using quasi-degenerate Rayleigh-Schrödinger perturbation theory (QD-RSPT) , 1979 .

[12]  D. Mukherjee The linked-cluster theorem in the open-shell coupled-cluster theory for incomplete model spaces , 1986 .

[13]  W. Kutzelnigg,et al.  Connected‐diagram expansions of effective Hamiltonians in incomplete model spaces. I. Quasicomplete and isolated incomplete model spaces , 1987 .

[14]  H. Weidenmüller,et al.  The effective interaction in nuclei and its perturbation expansion: An algebraic approach , 1972 .

[15]  A. Szabo,et al.  Modern quantum chemistry , 1982 .

[16]  I. Lindgren,et al.  On the connectivity criteria in the open-shell coupled-cluster theory for general model spaces , 1987 .

[17]  N. M. Hugenholtz Perturbation theory of large quantum systems , 1957 .

[18]  Werner Kutzelnigg,et al.  Quantum chemistry in Fock space. I. The universal wave and energy operators , 1982 .

[19]  W. Kutzelnigg,et al.  Connected‐diagram expansions of effective Hamiltonians in incomplete model spaces. II. The general incomplete model space , 1987 .

[20]  Ingvar Lindgren,et al.  Atomic Many-Body Theory , 1982 .

[21]  Coupled-cluster approach for open-shell systems , 1981 .

[22]  Jeffrey Goldstone,et al.  Derivation of the Brueckner many-body theory , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  J. G. Zabolitzky,et al.  Many-fermion theory in expS- (or coupled cluster) form , 1978 .

[24]  H. Weidenmüller,et al.  Perturbation theory for the effective interaction in nuclei , 1973 .

[25]  C. Bloch,et al.  Sur la détermination des premiers états d'un système de fermions dans le cas dégénéré , 1958 .

[26]  Rodney J. Bartlett,et al.  Many‐body perturbation theory, coupled‐pair many‐electron theory, and the importance of quadruple excitations for the correlation problem , 1978 .

[27]  U. Kaldor,et al.  Diagrammatic many-body perturbation theory for general model spaces , 1979 .

[28]  藤田 純一,et al.  A.L. Fetter and J.D. Walecka: Quantum Theory of Many-Particle Systems, McGraw-Hill Book Co., New York, 1971, 601頁, 15×23cm, 7,800円. , 1971 .

[29]  J. Cizek On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell-Type Expansion Using Quantum-Field Theoretical Methods , 1966 .

[30]  A non-perturbative open-shell theory for ionisation potential and excitation energies using HF ground state as the vacuum , 1979 .

[31]  Rajiv K. Kalia,et al.  Condensed Matter Theories: Volume 2 , 1988 .

[32]  A. Fetter,et al.  Quantum Theory of Many-Particle Systems , 1971 .

[33]  F. Coester,et al.  Bound states of a many-particle system , 1958 .

[34]  D. Mukherjee,et al.  A note on the direct calculation of excitation energies by quasi-degenerate MBPT and coupled-cluster theory , 1986 .

[35]  H. Kümmel,et al.  Degenerate many fermion theory in expS form: (I). General formalism , 1976 .

[36]  B. Brandow Linked-Cluster Expansions for the Nuclear Many-Body Problem , 1967 .

[37]  D. Mukherjee,et al.  Correlation problem in open-shell atoms and molecules. A non-perturbative linked cluster formulation , 1975 .

[38]  W. Kutzelnigg,et al.  Quantum chemistry in Fock space. II. Effective Hamiltonians in Fock space , 1983 .

[39]  K. Brueckner,et al.  TWO-BODY FORCES AND NUCLEAR SATURATION. III. DETAILS OF THE STRUCTURE OF THE NUCLEUS , 1955 .

[40]  I. Lindgren Linked-Diagram and Coupled-Cluster Expansions for Multi-Configurational, Complete and Incomplete Model Spaces , 1985 .

[41]  D. Mukherjee,et al.  Application of cluster expansion techniques to open shells: Calculation of difference energies , 1984 .

[42]  D. Mukherjee Aspects of linked cluster expansion in general model space many-body perturbation and coupled-cluster theory , 1986 .

[43]  D. Mukherjee,et al.  Atomic and molecular applications of open-shell cluster expansion techniques with incomplete model spaces , 1988 .

[44]  F. Coester,et al.  Short-range correlations in nuclear wave functions , 1960 .

[45]  Josef Paldus,et al.  Correlation Problems in Atomic and Molecular Systems. IV. Extended Coupled-Pair Many-Electron Theory and Its Application to the B H 3 Molecule , 1972 .