Many Center AO Integral Evaluation Using Cartesian Exponential Type Orbitals (CETO'S)

Abstract

Publisher Summary This chapter discusses a general, simple and pedagogical framework based on Cartesian exponential type orbitals (CETO's) functions, to obtain atomic and molecular integrals, which can be potentially used within a LCAO computational system. One and two electron integrals over various operator kinds have been solved and analytical forms found as well, proving in this manner the flexibility and complete possibilities of the proposed methodology. Two center density expansions into separate centers have been employed successfully to overcome the many center integral problem. CETO functions appear in this manner as a plausible alternative to the present Gaussian Type Orbitals (GTO) quantum chemical computational flood, constituting the foundation of another step signaling the path toward Slater type orbital (STO) integral calculation. Many interesting methodological ideas, along the description of CETO's and their alternative forms: spherical exponential type orbitals (SETO's), laplace exponential type orbitals (LETO's), well-oriented CETO's (WO-CETO's), and elementary CETO (E-CETO's), have been also defined: Logical Kronecker delta and nested summation symbols among others. Both concepts permit easily written integrals and related formulae within a compact mathematical formalism, which possess an immediate and intuitive translation to high level programming languages.