Dwayne C. Joseph

Poisson's equation solution of Coulomb integrals in atoms and molecules

The integral bottleneck in evaluating molecular energies arises from the two-electron contributions. These are difficult and time-consuming to evaluate, especially over exponential type orbitals, used here to ensure the correct behaviour of atomic orbitals. In this work, it is shown that the two-centre Coulomb integrals involved can be expressed as one-electron kinetic-energy-like integrals. This is accomplished using the fact that the Coulomb operator is a Greens function of the Laplacian. The ensuing integrals may be further simplified by defining Coulomb forms for the one-electron potential satisfying Poissons equation therein. A sum of overlap integrals with the atomic orbital energy eigenvalue as a factor is then obtained to give the Coulomb energy. The remaining questions of translating orbitals involved in three and four centre integrals and the evaluation of exchange energy are also briefly discussed. The summation coefficients in Coulomb forms are evaluated using the LU decomposition. This algorithm is highly parallel. The Poisson method may be used to calculate Coulomb energy integrals efficiently. For a single processor, gains of CPU time for a given chemical accuracy exceed a factor of 40. This method lends itself to evaluation on a parallel computer. †Dedicated to Professor Nicholas Handy.

State-selective charge exchange in slow collisions of Si3+ ions with H atoms: A molecular state close coupling treatment*)

Charge transfer cross sections are calculated by employing both the quantal and semiclassical e(R) molecular orbital close coupling (MOCC) approximations in the adiabatic representation and compared with other theoretical and experimental results

Electron capture cross sections by O+ from atomic He

The adiabatic representation is used in both the quantal and semi classical molecular orbital close coupling methods (MOCC) to evaluate charge exchange cross sections. Our results show good agreement with experimental cross sections