Orbital Theories of Electronic Structure

We show that in the Hartree—Fock approximation there exists a uniquely defined Hermitian potential which describes the interaction of a model subgroup of electrons with the rest of the system. This potential can be divided into two parts. The first part is the difference between the Hartree—Fock Hamiltonian for the system and the model Hamiltonian. The second part is a nonlocal potential which cancels (screens) some of the first part. The essential point in the derivation is our choice of definition for model orbitals in the system. The only condition that must be satisfied by the occupied orbitals of the system is that they be linearly independent. It is also shown that there exist equations describing the best orbitals to use in a calculation by a linear combination of atomic orbitals method. They are the best orbitals to use because they give the exact answer. As a concrete example of our ideas we have treated numerically the LiH molecule. In order to link our method with others that have been describe...

[1]  J. C. Phillips,et al.  Energy-Band Interpolation Scheme Based on a Pseudopotential , 1958 .

[2]  S. P. Keller,et al.  Interactions of Closed Shell Ions , 1952 .

[3]  G. Koster.  Localized Functions in Molecules and Crystals , 1953 .

[4]  W. Adams,et al.  On the Solution of the Hartree‐Fock Equation in Terms of Localized Orbitals , 1961 .

[5]  R. Nesbet.  Configuration interaction in orbital theories , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[6]  K. Sawada,et al.  On the Stability of the Hartree-Fock Solution in Many-Body Problem , 1961 .

[7]  John Edward Lennard-Jones,et al.  The determination of molecular orbitals , 1949, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

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

[9]  R. Parmenter.  Electronic Energy Bands in Crystals , 1952 .

[10]  P. Löwdin.  Quantum Theory of Many-Particle Systems. III. Extension of the Hartree-Fock Scheme to Include Degenerate Systems and Correlation Effects , 1955 .

[11]  Per-Olov Löwdin,et al.  Quantum Theory of Many-Particle Systems. II. Study of the Ordinary Hartree-Fock Approximation , 1955 .

[12]  B. H. Chirgwin,et al.  The electronic structure of conjugated systems. VI , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[13]  B. Segall.  Fermi Surface and Energy Bands of Copper , 1962 .

[14]  M. De.  Handbuch der Physik , 1957 .

[15]  Conyers Herring,et al.  A New Method for Calculating Wave Functions in Crystals , 1940 .

[16]  G. G. Hall.  Applications of quantum mechanics in theoretical chemistry , 1959 .

[17]  A. Karo.  Configuration Interaction in the Lithium Hydride Molecule. II. An SCF LCAO‐MO Approach , 1959 .

[18]  Clemens C. J. Roothaan,et al.  New Developments in Molecular Orbital Theory , 1951 .

[19]  G. Parzen.  Electronic Energy Bands in Metals , 1953 .

[20]  V. Heine,et al.  Cancellation of kinetic and potential energy in atoms, molecules, and solids , 1961 .

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

[22]  G. Wannier.  The Structure of Electronic Excitation Levels in Insulating Crystals , 1937 .

[23]  P. Löwdin.  Band Theory, Valence Bond, and Tight‐Binding Calculations , 1962 .

[24]  John C. Slater,et al.  Magnetic Effects and the Hartree-Fock Equation , 1951 .

[25]  A. Karo,et al.  Configuration Interaction in the Lithium Hydride Molecule. I. A Determinantal AO Approach , 1959 .

[26]  R. S. Mulliken.  Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .