Core Hamiltonian Research Articles

Pariser-parr-pople-theory: Linderberg's relation and empirical β-values

Linderberg's formula for the off-diagonal elements of the effective core hamiltonian in Pariser-Parr-Pople-theory is reconsidered. It is shown that, in principle, β-values should be calculated from a modified version of Linderberg's relation. One version of this modification gives good parameters for CI-calculations.

Transition-element hexafluoride systems in ionic lattices. A Suhf molecular orbital study

An unrestricted Hartree-Fock SCFMO method, based on the MCZDO method of Brown and Roby, suitable for computing spin densities in transition-element compounds, is described. The method is used to study spin densities on fluorine in Cs2MnF6, K2NaCrF6, K2MnF6, K2NaFeF6, KMnF3, RbMnF3 and KNiF3 using a “cluster” approximation in which a MF 6 n− unit is explicitly considered. Excellent agreement is obtained between calculated and experimental spin parameters. The effect of the lattice is incorporated by using the electrostatic approximation of Brown, O'Dwyer and Roby. The lattice potential for these highly symmetric systems is found to have little effect on spin densities and charge distributions, but it effects substantial stabilization of the anion molecular orbitals. A general feature of the results is that central-atom 4p orbitals are scarcely involved in bonding, this being confined to the 3d and to some extent the 4s orbitals. Comments are offered on the lack of spin symmetry in the unrestricted Hartree-Fock wavefunctions of these systems, and the need to evaluate the core hamiltonian as accurately as possible.

Soluble Model of Condensation

A soluble model of gas-liquid condensation is constructed by a quantum-mechanical extension of van Kampen's classical analysis. The Hamiltonian of a system of identical particles is separated into a ``core'' and a ``tail'' Hamiltonian. Following van Kampen, we simulate the actual core Hamiltonian by an effective Hamiltonian with the same free energy. The tail Hamiltonian is replaced by its diagonal part in a single-particle basis chosen self-consistently so that the thermodynamics is exactly soluble. The resultant free energy agrees with that of Lieb's quantum-mechanical extension of the van der Waals-Maxwell theory, without the necessity of taking the van der Waals limit of a suitably infinite-ranged and infinitely-weak attractive tail. However, the exchange contributions omitted from the model become negligible only in that limit.

Triplet-State Zero-Field Splittings in Some Aromatic Hydrocarbons and Nitrogen Heterocycles

The SCF-AO's expanded by Löwdin have been used for the calculation of the electron spin dipolar interactions in the triplet-state zero-field splittings of some aromatic molecules. Within a framework of two-center approximation for the spin–spin interaction integrals over atomic orbitals, and adopting the Sklar-type approximation for the exchange-type integrals, excellent agreement with experiments has been obtained for benzene and naphthalene without invoking σ–π interactions. The wavefunctions used were obtained by means of the Pariser–Parr–Pople method, within a full single excitation configuration treatment. This approach has been extended to some aromatic nitrogen heterocycles, but the results, although promising, are poorer, possibly due to the neglect of spin–orbit coupling. Uncertainty in the choice of the C–N resonance integral and the neglect of penetration integrals in the core Hamiltonian may also be factors. Eleven molecules have been treated in all. For comparison, the single-determinant unrestricted Hartree–Fock wavefunctions also have been employed, but these give extremely poor agreement with experiment.

Numerical studies for a theoretical analysis of semiempirical LCAO–CI methods

AbstractA numerical investigation of Del Re and Parr's formulas [1] for the treatment of π systems has been preformed in the case of five‐membered rings, using two different expressions for the core Hamiltonian and different values for the effective charges. The results obtained are discussed by analysing the three stages of the calculation: (a) a non‐iterative LCAO–MO calculation; (b) the same calculation with corrections for exchange and repulsion terms arising from fluctuations of the orbital populations; (c) configuration interaction. The calculations are interesting also because they do not involve the zero differential overlap approximation; a calculation without inclusion of overlap hse been carried out for pyrrole and the results have been compared with those including S.The main conclusions hold also for σ electrons, and can serve to assess better the validity of simple σ calculations.

Consistency requirement in the Pariser-Parr-Pople model

Equivalence between dipole length and dipole velocity forms of oscillator strengths places a condition on the parameters used in the Pariser-Parr-Pople model and suggests a new procedure for the determination of off-diagonal elements of the effective core Hamiltonian.

A Semi-Empirical Theory of the Electronic Spectra and Electronic Structure of Complex Unsaturated Molecules. I.

A semi-empirical theory is outlined which is designed for the correlation and prediction of the wavelengths and intensities of the first main visible or ultraviolet absorption bands and other properties of complex unsaturated molecules, and preliminary application of the theory is made to ethylene and benzene. The theory is formulated in the language of the purely theoretical method of antisymmetrized products of molecular orbitals (in LCAO approximation), including configuration interaction, but departs from this theory in several essential respects. First, atomic orbital integrals involving the core Hamiltonian are expressed in terms of quantities which may be regarded as semi-empirical. Second, an approximation of zero differential overlap is employed, and an optional uniformly charged sphere representation of atomic π-orbitals is introduced, which greatly simplify the evaluation of electronic repulsion integrals and make applications to complex molecules containing heteroatoms relatively simple. Finally, although the theory starts from the π-electron approximation, in which the unsaturation electrons are treated apart from the rest, provision is included for the adjustment of the σ-electrons to the π-electron distribution in a way which does not complicate the mathematics. Electronic energy levels in the theory are expressed in terms of ionization potentials of atoms, resonance integrals of bonds, Coulomb repulsion integrals between two π-electrons on the same atom and between two π-electrons on different atoms, and penetration integrals between π-electrons and neutral atoms. Preliminary applications to ethylene and benzene in which only the carbon-carbon resonance integral is treated as an empirical quantity show that the theory can reproduce the results of the purely theoretical method with very little labor. The reasonableness of considering all of the above quantities as semi-empirical is pointed out, however, and it is through a detailed examination and exploitation of this in the second paper of this series that correction for the inadequacies of the π-electron approximation is made and improved agreement with experiment is attained.