A unified scheme for the calculation of differentiated and undifferentiated molecular integrals over solid-harmonic Gaussians.
A unified scheme for the calculation of differentiated and undifferentiated molecular integrals over solid-harmonic Gaussians.
复制标题
用于计算固体调和高斯上的微分和无微分分子积分的统一方案。
DOI：
10.1039/b705594c
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
T. Helgaker
中科院分区：
文献类型：
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作者：
Simen Reine;E. Tellgren;T. Helgaker
利用笛卡尔和埃尔米特高斯原子轨道的固体调和组合是相同的这一事实，提出了一种计算固体调和原子轨道上分子积分的新方案，即在埃尔米特原子轨道上而不是在笛卡尔原子轨道上进行积分。由于赫米高斯函数被定义为球面高斯函数的导数，相应的分子积分就变成了球面高斯函数上的积分的导数，其到固体调和基的转换与笛卡尔高斯函数上的积分的转换方式相同，使用相同的展开系数。所提出的固体调和Hermite格式简化了导数分子积分的计算，因为核坐标的微分仅仅增加了Hermite量子数，从而为未微分和微分四中心分子积分提供了统一的格式。对于二中心和三中心双电子积分，固体调和埃尔米特格式特别有效，相对于笛卡尔格式显著降低了成本。
Utilizing the fact that solid-harmonic combinations of Cartesian and Hermite Gaussian atomic orbitals are identical, a new scheme for the evaluation of molecular integrals over solid-harmonic atomic orbitals is presented, where the integration is carried out over Hermite rather than Cartesian atomic orbitals. Since Hermite Gaussians are defined as derivatives of spherical Gaussians, the corresponding molecular integrals become the derivatives of integrals over spherical Gaussians, whose transformation to the solid-harmonic basis is performed in the same manner as for integrals over Cartesian Gaussians, using the same expansion coefficients. The presented solid-harmonic Hermite scheme simplifies the evaluation of derivative molecular integrals, since differentiation by nuclear coordinates merely increments the Hermite quantum numbers, thereby providing a unified scheme for undifferentiated and differentiated four-center molecular integrals. For two- and three-center two-electron integrals, the solid-harmonic Hermite scheme is particularly efficient, significantly reducing the cost relative to the Cartesian scheme.
K. L. Ngai：“过冷液体中的热力学脆性和动力学脆性：分子液体中缺失的边界”J。
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