Bacskay George B
School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia.
J Chem Phys. 2022 May 28;156(20):204122. doi: 10.1063/5.0090196.
According to Ruedenberg's classic treatise on the theory of chemical bonding [K. Ruedenberg, Rev. Mod. Phys. 34, 326-376 (1962)], orbital contraction is an integral consequence of covalent bonding. While the concept is clear, its quantification by quantum chemical calculations is not straightforward, except for the simplest of molecules, such as H and H. This paper proposes a new, yet simple, approach to the problem, utilizing the modified atomic orbital (MAO) method of Ehrhardt and Ahlrichs [Theor. Chim. Acta 68, 231 (1985)]. Through the use of MAOs, which are an atom-centered minimal basis formed from the molecular and atomic density operators, the wave functions of the species of interest are re-expanded, allowing the computation of the kinetic energy (and any other expectation value) of free and bonded fragments. Thus, it is possible to quantify the intra- and interfragment changes in kinetic energy, i.e., the effects of contraction. Computations are reported for a number of diatomic molecules H, Li, B, C, N, O, F, CO, P, and Cl and the polyatomics CH-CH, CH-SiH, CH-OH, and CH-CH (where the single bonds between the heavy atoms are studied) as well as dimers of He, Ne, Ar, and the archetypal ionic molecule NaCl. In all cases, it is found that the formation of a covalent bond is accompanied by an increase in the intra-fragment kinetic energy, an indication of orbital contraction and/or deformation.
根据鲁登贝格关于化学键理论的经典论文[K. 鲁登贝格，《现代物理评论》34, 326 - 376 (1962)]，轨道收缩是共价键形成的一个必然结果。虽然这个概念很清晰，但除了像H₂和H₂⁺这样最简单的分子外，通过量子化学计算对其进行量化并非易事。本文提出了一种新的、但很简单的方法来解决这个问题，该方法利用了埃尔哈特和阿尔里希斯的改进原子轨道（MAO）方法[《理论化学学报》68, 231 (1985)]。通过使用MAO（它是由分子和原子密度算符形成的以原子为中心的最小基组），对感兴趣的物种的波函数进行重新展开，从而能够计算自由片段和键合片段的动能（以及任何其他期望值）。因此，可以量化动能在片段内部和片段之间的变化，即收缩效应。本文报道了对多个双原子分子H₂、Li₂、B₂、C₂、N₂、O₂、F₂、CO、P₂和Cl₂，以及多原子分子CH₃ - CH₃、CH₃ - SiH₃、CH₃ - OH和CH₂ = CH₂（其中研究了重原子之间的单键），还有He、Ne、Ar的二聚体以及典型离子分子NaCl的计算结果。在所有情况下，都发现共价键的形成伴随着片段内部动能的增加，这表明存在轨道收缩和/或变形。
