Cluster expansion of the wavefunction. Structure of the closed‐shell orbital theory

A new approach to the closed‐shell orbital theory is presented with the formalism of the cluster expansion of the wavefunction. The four independent excitation operators are used to represent the general determinantal wavefunction and also to discuss the stability of the Hartree–Fock solution. This leads to a new concept called the ’’stability dilemma,’’ which is the key not only in understanding the structure of the orbital theory but also for the extension of the orbital model. Only when the stability dilemma is removed, the correlation effect is taken into account within the framework of the orbital approximation. The closed‐shell orbital theory including the electron correlation is defined as ‖Φ〉=P exp[iF]‖0〉, where the F is the excitation operator to generate the variational space and the P is the projection operator to remove the stability dilemma. The various orbital theories (some are known but some are new) can be obtained by appropriate choices of the F and P. It is shown that the above cluster ...

[1]  C. C. J. Roothaan,et al.  Self-Consistent Field Theory for Open Shells of Electronic Systems , 1960 .

[2]  S. Lunell.  SPIN-PROJECTED HARTREE--FOCK CALCULATIONS ON THE He-LIKE IONS USING GENERAL SPIN ORBITALS. , 1970 .

[3]  K. Hirao,et al.  Cluster expansion of the wavefunction. Pseudo‐orbital theory based on the SAC expansion and its application to the spin density of open‐shell systems , 1978 .

[4]  D. Thouless.  Stability conditions and nuclear rotations in the Hartree-Fock theory , 1960 .

[5]  J. Providência.  CLUSTER EXPANSION OF OPERATOR AVERAGES FOR SYSTEMS OF MANY PARTICLES , 1963 .

[6]  H. Fukutome.  Spin Density Wave and Charge Transfer Wave in Long Conjugated Molecules , 1968 .

[7]  Linked‐Cluster Theorem and Unitarity , 1964 .

[8]  O. Sǐnanoğlu,et al.  Many‐Electron Theory of Atoms and Molecules. III. Effect of Correlation on Orbitals , 1963 .

[9]  P. Löwdin.  THE NORMAL CONSTANTS OF MOTION IN QUANTUM MECHANICS TREATED BY PROJECTION TECHNIQUE , 1962 .

[10]  Kimihiko Hirao,et al.  Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory , 1978 .

[11]  L. C. Snyder,et al.  Unrestricted Hartree—Fock Calculations. I. An Improved Method of Computing Spin Properties , 1964 .

[12]  R. K. Nesbet,et al.  Self‐Consistent Orbitals for Radicals , 1954 .

[13]  K. Hirao,et al.  Cluster expansion of the wavefunction. The open‐shell orbital theory including electron correlation , 1978 .

[14]  Variational localized‐site cluster expansions. I. General theory , 1976 .

[15]  J. Cizek,et al.  Stability Conditions for the Solutions of the Hartree–Fock Equations for Atomic and Molecular Systems. III. Rules for the Singlet Stability of Hartree–Fock Solutions of π‐Electronic Systems , 1970 .

[16]  R. Pauncz.  Alternant Molecular Orbital Method , 1967 .

[17]  William A. Goddard,et al.  Self‐Consistent Procedures for Generalized Valence Bond Wavefunctions. Applications H3, BH, H2O, C2H6, and O2 , 1972 .

[18]  H. Nakatsuji.  On the orbital theories in the spin‐correlation problems. II. Unrestricted and spin‐extended Hartree‐Fock theories , 1973 .

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

[20]  O. Sǐnanoğlu.  A Method for the Analysis of Many-Electron Wave Functions , 1963 .

[21]  R. Nesbet.  Brueckner's Theory and the Method of Superposition of Configurations , 1958 .

[22]  J. Hendeković.  Complex molecular orbital method: Open‐shell theory , 1976 .

[23]  G. W. Pratt,et al.  Discussion on The Hartree-Fock Approximation , 1963 .

[24]  S. Lunell.  On the use of general spin orbitals in the projected Hartree-Fock method , 1972 .

[25]  小谷 正雄.  Tables of molecular integrals , 1955 .

[26]  C. Edmiston.  Relation of Sinanoğlu's Theory of ``Exact Pairs'' to the First Iteration, beyond SCF, in Separated-Pair Theory , 1963 .

[27]  H. Nakatsuji,et al.  On the Unrestricted Hartree–Fock Wavefunction , 1969 .

[28]  John Edward Lennard-Jones,et al.  The molecular orbital theory of chemical valency XVI. A theory of paired-electrons in polyatomic molecules , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[29]  William A. Goddard,et al.  IMPROVED QUANTUM THEORY OF MANY-ELECTRON SYSTEMS. II. THE BASIC METHOD. , 1967 .

[30]  William A. Goddard,et al.  Improved Quantum Theory of Many‐Electron Systems. V. The Spin‐Coupling Optimized GI Method , 1969 .

[31]  K. Sando,et al.  Spin‐Projected and Extended SCF Calculations , 1967 .

[32]  W. Goddard.  Improved Quantum Theory of Many-Electron Systems. III. The GF Method , 1968 .

[33]  U. Kaldor.  Calculation of Extended Hartree‐Fock Wavefunctions , 1968 .

[34]  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 .

[35]  L. Szász.  Pseudopotential Theory of Atoms and Molecules. I. A New Method for the Calculation of Correlated Pair Functions , 1968 .