Calculation of One- and Two-Center Overlap Like Quantum Similarity Integrals over ψ^((α)) Exponential Type Functions

One- and two-center overlap like quantum similarity integrals over ψ^((α)) functions are evaluated using the one-center expansion method. These integrals are expressed through expansion coefficients and usual two-center overlap integrals. The expressions derived in this work have no restrictions for the values of orbital parameters, quantum numbers and internuclear distances. Since these integrals of ψ^((α)) functions are calculated for the first time, the comparison is made with literature values obtained from Slater type functions. The computation results are in good agreement with literature values. The algorithm presented in this study could be useful when exponential type functions are employed in quantum similarity measures of atomic and molecular systems.