New methods for accelerating the convergence of molecular electronic integrals over exponential type orbitals
Hassan Safouhi, Philip E. Hoggan · Molecular Physics · 2003
This review on molecular integrals for large electronic systems (MILES) places the problem of analytical integration over exponential-type orbitals (ETOs) in a historical context. After reference to the pioneering work, particularly by Barnett, Shavitt and Yoshimine, it focuses on recent progress towards rapid and accurate analytic solutions of MILES over ETOs. Software such as the hydrogenlike wavefunction package Alchemy by Yoshimine and collaborators is described. The review focuses on convergence acceleration of these highly oscillatory integrals and in particular it highlights suitable nonlinear transformations. Work by Levin and Sidi is described and applied to MILES. A step by step description of progress in the use of nonlinear transformation methods to obtain efficient codes is provided. The recent approach S[Dbar] developed by Safouhi is also presented. The current state of the art in this field is summarized to show that ab initio analytical work over ETOs is now a viable option.