On the convergence properties of the Rayleigh–Schrödinger and the Hirschfelder–Silbey perturbation expansions for molecular interaction energies
On the convergence properties of the Rayleigh–Schrödinger and the Hirschfelder–Silbey perturbation expansions for molecular interaction energies
复制标题
分子相互作用能的 Rayleigh-Schrödinger 和 Hirschfelder-Silbey 微扰展开式的收敛性质
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
K. Szalewicz
中科院分区：
文献类型：
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作者：
G. Chałasiński;B. Jeziorski;K. Szalewicz
本文应用瑞利-薛定谔极化理论和赫希菲尔德-西尔贝微扰理论，研究了基态氢原子与质子的相互作用。使用共焦椭圆坐标中表示的大基组轨道进行了高精度的计算。结果表明，对于小的核间距R，极化级数以振荡方式缓慢地收敛到H分子基态1 s σg的能量。然而，在大R时，极化展开仅有效地再现了相互作用能的库仑部分。当库仑能的值达到时，收敛速度急剧恶化，使得交换能实际上不能再现。HS方法在1 s σg和2 p σu两种状态下都能快速收敛，收敛速度与核间距基本无关。如果有限的基组用于解决扰动方程是稳定的对称操作下，HS展开收敛到能量通过最小化的Rayleigh-Ritz功能的空间内所跨越的功能在微扰理论计算。
The Rayleigh–Schrodinger polarization and the Hirschfelder–Silbey (HS) perturbation theories are applied, through the 38th order, to the interaction of a ground-state hydrogen atom with a proton. The calculations were made with high precision using a large basis set of orbitals expressed in the confocal elliptic coordinates. The results obtained show that for small internuclear separations R the polarization series converges slowly in an oscillatory way to the energy of the ground 1sσg state of the H molecule. At large R, however, the polarization expansion reproduces only the Coulomb part of the interaction energy effectively. When the value of the Coulomb energy is reached, the rate of convergence deteriorates drastically so that the exchange energy is not reproduced practically. The HS method converges fast when applied to both the 1sσg and the 2pσu states, the rate of convergence being roughly independent of the internuclear distance. If the finite basis set employed to solve the perturbation equations is stable under the symmetry operations, the HS expansion is shown to converge to the energy obtained by minimizing the Rayleigh–Ritz functional within the space spanned by the functions used in the perturbation theory calculations.