Asymptotic Expansions of Barnett-Coulson-Lowdin Functions of High Order

摘要

The Barnett-Coulson-Lowdin functions (BCLFs) arise as coefficients in series expansions of Slater type orbitals about a displaced center. Following a detailed review of these functions, in this work, we provide full asymptotic expansions for them as the order of the modified Bessel functions that go into their construction tends to infinity. In doing so, we make use of some recent asymptotic expansions of modified Bessel functions that appeared in the paper [Ref. 22]. In molecular computations, BCLFs must be computed very many times. Therefore, it is necessary to design methods by which BCLFs can be computed efficiently. In this work, we also propose an iterative method for computing a whole sequence of BCLFs quickly, and accurately for some range of parameters. This method is implemented using quadruple-precision arithmetic, which is sufficient and present in some high-level programming language compilers used in scientific computing, such as FORTRAN 77 and C. The number of arithmetic operations needed for the proposed method is very small.