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We present a fast algorithm to calculate Coulomb/exchange integrals ofprolate spheroidal electronic orbitals, which are the exact solutions of thesingle-electron, two-center Schr\"odinger equation for diatomic molecules. Ourapproach employs Neumann's expansion of the Coulomb repulsion 1/|x-y|, solvesthe resulting integrals symbolically in closed form and subsequently performs anumeric Taylor expansion for efficiency. Thanks to the general form of theintegrals, the obtained coefficients are independent of the particularwavefunctions and can thus be reused later.  Key features of our algorithm include complete avoidance of numericintegration, drafting of the individual steps as fast matrix operations andhigh accuracy due to the exponential convergence of the expansions.  Application to the diatomic molecules O2 and CO exemplifies the developedmethods, which can be relevant for a quantitative understanding of chemicalbonds in general.

Efficient Algorithm for Two-Center Coulomb and Exchange Integrals of Electronic Prolate Spheroidal Orbitals