On the optimization of Gaussian basis sets
On the optimization of Gaussian basis sets
复制标题
高斯基组的优化
DOI：
10.1063/1.1516801
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发表时间：
2003
影响因子：
4.4
通讯作者：
M. Frisch
中科院分区：
文献类型：
--
作者：
G. A. Petersson;Shijun Zhong;J. Montgomery;M. Frisch
提出了高斯基函数Ylm(φ,φ)rle - αjr2的指数αj优化的新方法，并对其进行了评价。这些非线性变分参数之间的强耦合阻碍了指数的直接优化。然而，对指数j: ln αj=∑k=0kmaxAkPk(（2j−2)/(Nprim−1)−1）的正交Legendre多项式Pk中指数的对数展开，得到了一组新的良条件参数Ak，以及从偶调和基集（kmax=1）到完全优化基集（kmax=Nprim−1）的完整良条件指数优化序列。相对于六项展开的精确数值自洽域极限的误差始终不超过完全优化基集的误差的25%。因此，即使对于最大的高斯原语集，也不需要优化超过6个条件良好的变分参数。
A new procedure for the optimization of the exponents, αj, of Gaussian basis functions, Ylm(ϑ,φ)rle−αjr2, is proposed and evaluated. The direct optimization of the exponents is hindered by the very strong coupling between these nonlinear variational parameters. However, expansion of the logarithms of the exponents in the orthonormal Legendre polynomials, Pk, of the index, j: ln αj=∑k=0kmaxAkPk((2j−2)/(Nprim−1)−1), yields a new set of well-conditioned parameters, Ak, and a complete sequence of well-conditioned exponent optimizations proceeding from the even-tempered basis set (kmax=1) to a fully optimized basis set (kmax=Nprim−1). The error relative to the exact numerical self-consistent field limit for a six-term expansion is consistently no more than 25% larger than the error for the completely optimized basis set. Thus, there is no need to optimize more than six well-conditioned variational parameters, even for the largest sets of Gaussian primitives.