Crittenden Deborah L, Bernard Yves A
Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia.
J Chem Phys. 2009 Aug 7;131(5):054110. doi: 10.1063/1.3204011.
Compact expressions for spherically averaged position and momentum density integrals are given in terms of spherical Bessel functions (j(n)) and modified spherical Bessel functions (i(n)), respectively. All integrals required for ab initio calculations involving s, p, d, and f-type Gaussian functions are tabulated, highlighting a neat isomorphism between position and momentum space formulae. Spherically averaged position and momentum densities are calculated for a set of molecules comprising the ten-electron isoelectronic series (Ne-CH(4)) and the eighteen-electron series (Ar-SiH(4), F(2)-C(2)H(6)).
球平均位置和动量密度积分的紧凑表达式分别根据球贝塞尔函数（j(n)）和修正球贝塞尔函数（i(n)）给出。列出了涉及s、p、d和f型高斯函数的从头算所需的所有积分，突出了位置和动量空间公式之间的一种简洁同构关系。针对一组包含十电子等电子系列（Ne-CH₄）和十八电子系列（Ar-SiH₄、F₂-C₂H₆）的分子计算了球平均位置和动量密度。
