Buckingham expansion is important for understanding molecular multipoles and (hyper)polarizabilities. In this study, we give a complete derivation of Buckingham expansion in the traced form using successive Taylor series. Based on such derivation, a general Buckingham expansion in the traced form is proposed, and from which numerical calculations with finite field method of high accuracy can be achieved. The transformations from the traced multipoles and multipole-multipole polarizabilities to the corresponding traceless counterparts are realized with an auxiliary traced electric field gradient. The applications of the finite field method in this study show good agreements with previous theoretical calculations and experimental measurements.

中文翻译：

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白金汉扩展中的分子多极子和（超）极化率：重新审视

白金汉展开式对于理解分子多极子和（超）极化率很重要。在这项研究中，我们使用连续的泰勒级数以跟踪形式给出了白金汉展开的完整推导。在此推导的基础上，提出了一种一般的追迹形式的白金汉展开式，由此可以实现高精度的有限域法数值计算。从追踪的多极和多极-多极极化率到相应的无痕对应物的转换是通过辅助追踪电场梯度实现的。有限域方法在本研究中的应用与先前的理论计算和实验测量结果吻合良好。