Kurokawa Yusaku I, Nakashima Hiroyuki, Nakatsuji Hiroshi
Quantum Chemistry Research Institute, Kyodai Katsura Venture Plaza 107, Goryo Oohara 1-36, Nishikyo-ku, Kyoto 615-8245, Japan.
J Chem Phys. 2014 Jun 7;140(21):214103. doi: 10.1063/1.4879266.
We derived the necessary conditions that must be satisfied by the non-relativistic time-independent exact wave functions for many-particle systems at a two-particle coalescence (or cusp) point. Some simple conditions are known to be Kato's cusp condition (CC) and Rassolov and Chipman's CC. In a previous study, we derived an infinite number of necessary conditions that two-particle wave functions must satisfy at a coalescence point. In the present study, we extend these conditions to many-particle systems. They are called general coalescence conditions (GCCs), and Kato's CC and Rassolov and Chipman's CC are included as special conditions. GCCs can be applied not only to Coulombic systems but also to any system in which the interaction between two particles is represented in a power series of inter-particle distances. We confirmed the correctness of our derivation of the GCCs by applying the exact wave function of a harmonium in electron-electron and electron-nucleus coalescence situations. In addition, we applied the free complement (FC) wave functions of a helium atom to the GCCs to examine the accuracy of the FC wave function in the context of a coalescence situation.
我们推导了多粒子系统在双粒子合并（或尖点）处非相对论性与时间无关的精确波函数必须满足的必要条件。已知一些简单条件，如加藤尖点条件（CC）以及拉索洛夫和奇普曼的CC。在之前的一项研究中，我们推导了双粒子波函数在合并点必须满足的无穷多个必要条件。在本研究中，我们将这些条件扩展到多粒子系统。它们被称为一般合并条件（GCCs），加藤的CC以及拉索洛夫和奇普曼的CC作为特殊条件包含在内。GCCs不仅可以应用于库仑系统，还可以应用于任何两粒子间相互作用以粒子间距离的幂级数表示的系统。我们通过在电子 - 电子和电子 - 原子核合并情形中应用谐振子的精确波函数，证实了我们对GCCs推导方法的正确性。此外，我们将氦原子的自由互补（FC）波函数应用于GCCs，以在合并情形的背景下检验FC波函数的准确性。
