Abstract
A new algorithm is presented for the calculation of two-center overlap integrals over Slater type orbitals, based on sets of recurrence relations and analytical formulas. The recurrence relations enable us to calculate some of overlap integrals by the use of which other overlap integrals are calculated analytically. The recurrence relations obtained in this work for these `basic overlap integrals' are especially useful for the calculation of any overlap integral for large quantum numbers. An accuracy of the computer results is satisfactory for the values of principal quantum numbers of Slater functions up to 50, and for the arbitrary values of screening constants of atomic orbitals and internuclear distances.
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