Theoretical foundations of purely semiempirical quantum chemistry

All the purely semiempirical quantum chemical theories of molecular electronic structure, such as the Pariser‐Parr‐Pople theory and its all valence electron generalizations like MINDO, assume the existence of an abstract true effective Hamiltonian which acts only within the space spanned by a minimum basis set of valence shell orbitals. Instead of following the customary procedure of attempting to determine the properties of this true effective Hamiltonian by fitting its matrix elements to experiment, this effective Hamiltonian is derived from the full N‐electron molecular Schrodinger equation under the condition that a complete configuration interaction calculation within the valence shell using this true effective Hamiltonian reproduces the exact ground and valence state energies. It is shown that this true effective Hamiltonian also exactly reproduces the projection of the exact ground and valence state wavefunctions on the space spanned by the minimum valence shell basis in the fixed core approximatio...

[1]  M. Karplus,et al.  Convergence of valence bond and molecular orbital theories , 1973 .

[2]  Karl F. Freed,et al.  Towards an ab initio determinition of all the parameters which appear in semi-empirical quantum chemical theories , 1972 .

[3]  Karl F. Freed,et al.  A derivation of the exact pi-electron hamiltonian , 1972 .

[4]  S. Huzinaga,et al.  Theory of Separability of Many‐Electron Systems , 1971 .

[5]  W. Nieuwpoort,et al.  On a relation proposed by Linderberg for the resonance integral in semi-empirical theories , 1971 .

[6]  S. Huzinaga,et al.  Virtual Orbitals in Hartree–Fock Theory. II , 1971 .

[7]  R. Nesbet.  Atomic Bethe-Goldstone Calculation of the Hyperfine Structure of Li ( 2 P 2 ) , 1970 .

[8]  P. Visscher,et al.  Exact Solution of the One‐Band π‐Electron Theory of Benzene , 1970 .

[9]  W. Lugt,et al.  Valence bond theory and the neglect of differential overlap , 1970 .

[10]  O. Sǐnanoğlu,et al.  THEORY OF ATOMIC STRUCTURE INCLUDING ELECTRON CORRELATION. I. THREE KINDS OF CORRELATION IN GROUND AND EXCITED CONFIGURATIONS. , 1969 .

[11]  H. Silverstone,et al.  Modified Perturbation Theory for Atoms and Molecules Based on a Hartree–Fock φ0 , 1968 .

[12]  E. Davidson,et al.  Correlation Energy Calculations and Unitary Transformations for LiH , 1968 .

[13]  Robert A. Harris,et al.  Pi-Electron Hamiltonian. II. Inclusion of Self-Consistent Screening , 1968 .

[14]  J. Linderberg.  Consistency requirement in the Pariser-Parr-Pople model , 1967 .

[15]  O. Sǐnanoğlu,et al.  Many‐Electron Theory of Nonclosed‐Shell Atoms and Molecules. I. Orbital Wavefunction and Perturbation Theory , 1966 .

[16]  O. Sǐnanoğlu,et al.  Sigma and Pi Changes in Valence States of Pi‐Electron Theory and One‐Center Coulomb Repulsion Parameters , 1965 .

[17]  M. Dewar,et al.  GROUND STATES OF CONJUGATED MOLECULES. I. SEMIEMPIRICAL SCF MO TREATMENT AND ITS APPLICATION TO AROMATIC HYDROCARBONS. , 1965, The Journal of chemical physics.

[18]  A. C. Wahl.  Analytic Self‐Consistent Field Wavefunctions and Computed Properties for Homonuclear Diatomic Molecules , 1964 .

[19]  Per-Olov Löwdin,et al.  STUDIES IN PERTURBATION THEORY. X. LOWER BOUNDS TO ENERGY EIGENVALUES IN PERTURBATION-THEORY GROUND STATE , 1964 .

[20]  P. Löwdin.  Studies in Perturbation Theory. IV. Solution of Eigenvalue Problem by Projection Operator Formalism , 1962 .

[21]  O. Sǐnanoğlu,et al.  Many‐Electron Theory of Atoms and Molecules. II , 1962 .

[22]  L. Szász.  ATOMIC MANY-BODY PROBLEM. I. GENERAL THEORY OF CORRELATED WAVE FUNCTIONS , 1962 .

[23]  Peter G. Lykos,et al.  On the Pi‐Electron Approximation and Its Possible Refinement , 1956 .

[24]  R. Pariser.  An Improvement in the π‐Electron Approximation in LCAO MO Theory , 1953 .

[25]  P. Löwdin.  On the Non‐Orthogonality Problem Connected with the Use of Atomic Wave Functions in the Theory of Molecules and Crystals , 1950 .

[26]  K. Roby.  On the theory of electron correlation in atoms and molecules. II. General cluster expansion theory and the general correlated wave functions method , 1972 .

[27]  Y. Sakai,et al.  Further Significance of the Pariser Method for Evaluation of the One‐Center Electron Repulsion Integral , 1971 .

[28]  K. Freed.  Many-Body Theories of the Electronic Structure of Atoms and Molecules , 1971 .

[29]  David L. Beveridge,et al.  Approximate molecular orbital theory , 1970 .

[30]  K. Freed.  Force Constants in Hartree–Fock Theory , 1970 .

[31]  Michael J. S. Dewar,et al.  The molecular orbital theory of organic chemistry , 1969 .

[32]  J. Doll,et al.  Direct Calculation of Natural Orbitals by Many‐Body Perturbation Theory: Application to Helium , 1969 .

[33]  Karl Jug,et al.  On the development of semiempirical methods in the MO formalism , 1969 .

[34]  K. Freed.  Many-Body Approach to Electron Correlation in Atoms and Molecules , 1968 .

[35]  Karl F. Freed,et al.  Generalized Perturbation Theory and its Application to the Problem of the Description of Electron Correlation in Atoms and Molecules , 1968 .

[36]  R. Nesbet.  Atomic Bethe-Goldstone Equations. II. The Ne Atom , 1967 .

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

[38]  L. Salem.  The molecular orbital theory of conjugated systems , 1966 .

[39]  J. Koutecký,et al.  Complete configuration interaction calculation of singlet energy levels of benzene in π-electron approximation , 1965 .

[40]  J. Murrell.  The theory of the electronic spectra of organic molecules , 1963 .

[41]  A. Messiah.  Quantum Mechanics , 1961 .

[42]  William F. Meggers,et al.  Quantum Theory of Atomic Structure , 1960 .