New analytical expressions, symmetry relations and numerical solutions for the rotational overlap integrals

摘要

In this article, extremely simple analytical formulas are obtained for rotational overlap integrals which occur in integrals over two reduced rotation matrix elements. The analytical derivations are based on the properties of the Jacobi polynomials and beta functions. Numerical results and special values for rotational overlap integrals are obtained by using symmetry properties and recurrence relationships for reduced rotation matrix elements. The final results are of surprisingly simple structures and very useful for practical applications.