Analytical expressions of exchange and three-center nuclear attraction integrals over 1s and 2s Slater orbitals with different exponents

Compact analytical formulas are given for exchange integrals and three-center nuclear attraction integrals using nonorthogonal Slater orbitals with equal and different exponents which appear in a Hylleraas-CI basis. Since all exponents in the integrals may be different, they are appropriate to optimize exponents and therefore to shorten the wave function expansions.