José R. Mohallem

A further study on the discretisation of the Griffin-Hill-Wheeler equation

It is shown that the discretisation of the Griffin-Hill-Wheeler equation is independent of the character of the weight functionf(α). The possibility of obtaining accurate weight functions through discretisation is discussed and the methods proposed are compared with an existing variational technique. The applications include the classical variational problem of representing hydrogen orbitals in terms of Gaussians as an optimal case.

A universal Gaussian basis set for atoms Li through Ne based on a generator coordinate version of the Hartree–Fock equations

A recently formulated generator coordinate version of the Hartree–Fock equations is applied to atoms Li through Ne. The Griffin–Hill–Wheeler–Hartree–Fock equations are integrated numerically generating a universal Gaussian basis set for these atoms. The results for the total energy are compared with Hartree–Fock–Roothaan (both with Slater‐type and Gaussian orbitals) calculations from the literature.

Universal gaussian and Slater-type basis sets for atoms He to Ar based on an integral version of the Hartree-Fock equations

The Griffin-Hill-Wheeler-Hartree-Fock equations are applied to generate universal gaussian and Slater-type basis sets for the title atoms. The results for the energies compare competitively with atom-optimized calculations at a very low computational cost.

The generator coordinate Hartree-Fock method for molecular systems. Formalism and first applications to H2, LiH and Li2

Abstract The generator coordinate Hartree-Fock method is extended to molecular systems. The resulting equations are integrated numerically through discretization. The method is then implemented with the use of the GAUSSIAN 86 program and applied to the H 2 , LiH and Li 2 diatomic species. The ground state Hartree-Fock energies (and dipole moment in the case of LiH) are calculated and compared with numerical Hartree-Fock values. The role of the molecular weight functions is discussed.

A new algorithm to handle finite nuclear mass effects in electronic calculations: The ISOTOPE program

We report the development of a simple algorithm to modify quantum chemistry codes based on the LCAO procedure, to account for the isotope problem in electronic structure calculations. No extra computations are required compared to standard Born–Oppenheimer calculations. An upgrade of the Gamess package called ISOTOPE is presented, and its applicability is demonstrated in some examples.

Fast Hartree-Fock calculations by simulated dynamics

A molecular-dynamical formulation of the Hartree-Fock (HF) method is presented. The simulated-annealing and simulated-quenching (steepest-descent) techniques are applied to the minimization of the HF energy functional and to the solution of the HF equations. In a test application to the helium atom with Gaussian basis sets both techniques show good performances but have two drawbacks: an excessive number of Fock-matrix calculations and a slowing-down behaviour close to convergence. We propose a new multistep algorithm for the simulated-quenching technique in which both drawbacks are removed: the Fock-matrix calculations are reduced to a minimum and the slowing down does not occur. The resulting program is several times faster than standard self-consistent-field HF programs.

A molecular model for positron complexes: long-range effects on 2γ pair-annihilation rates

A molecular model for positron complexes is developed and used to study the effects of the nucleus–positron distance long-range regime on the 2γ annihilation rates (Γ) of atomic complexes. The available data for Γ of some systems are then rationalized on its basis and some predictions are made. The model is shown to be capable of generating information on positron positioning and of making predictions of values of Γ in molecular complexes as well.

Unified description of chemical bonding in H2 isotopomers, including Ps2, μ2 and bi-excitons

Abstract We developed an unified treatment of the low-lying states of the general A + A + e − e − systems based on the concepts of chemical bonding, using an intuitive valence bond electronic wavefunction. A reduced mass correction accounts for the effects of the finite masses of nuclei A. The potential energy curves, the electronic densities and the ionic contribution show similar behaviour for all systems. The number of vibrational states versus the mass relation λ is obtained and compared to theoretical predictions. We verified that the use of atomic masses instead of nuclear masses is fundamental in order to obtain the only bound state in the cases λ ≃1.

Effective three-body Born-Oppenheimer Hamiltonian including adiabatic corrections

The concept of effective, position-dependent reduced mass is introduced for three-body molecules. It varies continuously between the asymptotic limits and generates a scaled Born-Oppenheimer-type Hamiltonian that contains a substantial amount of the adiabatic correction. A close analytical expression for this correction is obtained, without the explicit calculation of the nuclear kinetic energy matrix element. The approach accounts for the isotope effect and allows the first successful Born-Oppenheimer-type calculation on e-e+e-.

The modified electronic mass approach for the adiabatic corrections in H2

A theory of the modified (distance dependent) electronic mass effect for two-electron diatomic molecules is presented. The modified electronic mass correction is compared with the diagonal Born-Oppenheimer correction to the potential energy curves of H2, suggesting that the adiabatic correction is almost exactly accounted for by this effect.