Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Canakkale, Turkey.
J Mol Model. 2011 Apr;17(4):851-6. doi: 10.1007/s00894-010-0777-6. Epub 2010 Jun 25.
By the use of ellipsoidal coordinates, the two-center Coulomb and hybrid integrals over complete orthonormal sets of Ψα-ETO exponential type orbitals arising in ab initio calculations of molecules are evaluated, where α = 1,0, -1, -2, ...,. These integrals are expressed through the auxiliary functions Q(ns)(q) and G(-ns)(q). The comparison is made with some values of integrals for Slater type orbitals the computation results of which are in good agreement with those obtained in the literature. The relationships obtained are valid for the arbitrary quantum numbers, screening constants and location of orbitals. Closed form expressions for two-center Coulomb and hybrid integrals for 1s and 2s orbitals with α = 1 are also presented. As an example of application, the Hartree-Fock-Roothaan calculations for the ground state of H(2) molecule are carried out with α = 1 and α = 0.
利用球坐标，评估了在分子从头算中出现的完整正交归一的 Ψα-ETO 指数型轨道的两中心库仑和混合积分，其中α=1,0,-1,-2，...。这些积分通过辅助函数 Q(ns)(q)和 G(-ns)(q)表示。与 Slater 型轨道积分的一些值进行了比较，其计算结果与文献中的结果吻合良好。所得关系对于任意量子数、屏蔽常数和轨道位置均有效。还给出了α=1 的 1s 和 2s 轨道的两中心库仑和混合积分的闭式表达式。作为应用实例，对 H(2)分子基态的哈特ree-Fock-Roothaan 计算进行了α=1 和α=0 的计算。
