Application of the Expansion Method for Spherical Harmonics for Computation of Two Center Overlap Integrals (Ⅱ)

Two Center Overlap Integrals의 계산을 위한 Spherical Hamonics 전개방법의 응용 (제2보)

A method for calculation of two center overlap integrals for a pair of Slater type orbitals was developed by Mulliken et al. In this method the spherical polar coordinates for a pair of Slater type orbitals located at two different points are required to be transformed into a spheroidal coordinate set for calculation of two center overlap integrals. A new method, the expansion method for spherical harmonics, in which Slater type orbitals, located at two different points, are expressed in a common coordinate system has been applied for computation of two center overlap integrals. The new method for computation of two center overlap integrals is required to translate Slater type orbitals centered at two different points into the reference point for computation of two center overlap integrals. This work has been expanded the expansion method for spherical harmonics for computation of two center overlap integrals to $|3s{\g}$, $|5s{\g}$ and $|5s{\g}$. Master formulas for two center overlap integrals are derived for these orbitals, using the general expansion formulas. The numerical values of the two center overlap integrals evaluated for a hypothetical NO molecule are in agreement with those of the previous works.

한 쌍의 slater type orbitals에 대한 two overlap integrals을 계산하는 방법이 Mulliken등에 의하여 발전되었다. 이 방법으로 two center integrals을 계산하기 위해서는 한쌍의 Slater type orbital,에 대한 극좌표들 타원좌표로 변환해야한다. 두 점에 위치한 Slater type orbital을 공통좌표상에 전개시키는 새로운 방법 즉 spherical harmonics의 전개방법이 two center overlap integrals, 을 계산하는데 응용되었다. 이 새로운 방법에서는 Slater type orbitals, 을 기준점에 대해 전개시키는 것이 필요하다. 본 연구에서는 two center overlap integral을 계산하기 위한 spherical harmonics 전개방법을 $|3s{\g}$, $|5s{\g}$및 $|5s{\g}$에 까지 확장시켰다. 이들 원자궤도함수의 전개식을 사용하여 two center overlap integrals의 기본식을 유도하였으며, 이 기본식을 사용하여 가상적인 NO 분자에 대한 two cunter overlap integrals의 계산값이 이미 보고된 값과 일치하였다.