Geerlings P, De Proft F
Eenheid Algemene Chemie (ALGC), Faculty of Sciences, Vrije Universiteit Brussel (Free University of Brussels - VUB), Pleinlaan 2, 1050, Brussels.
Phys Chem Chem Phys. 2008 Jun 7;10(21):3028-42. doi: 10.1039/b717671f. Epub 2008 Mar 13.
In recent years conceptual density functional theory offered a perspective for the interpretation/prediction of experimental/theoretical reactivity data on the basis of a series of response functions to perturbations in the number of electrons and/or external potential. This approach has enabled the sharp definition and computation, from first principles, of a series of well-known but sometimes vaguely defined chemical concepts such as electronegativity and hardness. In this contribution, a short overview of the shortcomings of the simplest, first order response functions is illustrated leading to a description of chemical bonding in a covalent interaction in terms of interacting atoms or groups, governed by electrostatics with the tendency to polarize bonds on the basis of electronegativity differences. The second order approach, well known until now, introduces the hardness/softness and Fukui function concepts related to polarizability and frontier MO theory, respectively. The introduction of polarizability/softness is also considered in a historical perspective in which polarizability was, with some exceptions, mainly put forward in non covalent interactions. A particular series of response functions, arising when the changes in the external potential are solely provoked by changes in nuclear configurations (the "R-analogues") are also systematically considered. The main part of the contribution is devoted to third order response functions which, at first sight, may be expected not to yield chemically significant information, as turns out to be for the hyperhardness. A counterexample is the dual descriptor and its R analogue, the initial hardness response, which turns out to yield a firm basis to regain the Woodward-Hoffmann rules for pericyclic reactions based on a density-only basis, i.e. without involving the phase, sign, symmetry of the wavefunction. Even the second order nonlinear response functions are shown possibly to bear interesting information, e.g. on the local and global polarizability. Its derivatives may govern the influence of charge on the polarizability, the R-analogues being the nuclear Fukui function and the quadratic and cubic force constants. Although some of the higher order derivatives may be difficult to evaluate a comparison with the energy expansion used in spectroscopy in terms of nuclear displacements, nuclear magnetic moments, electric and magnetic fields leads to the conjecture that, certainly cross terms may contain new, intricate information for understanding chemical reactivity.
近年来，概念密度泛函理论基于一系列对电子数和/或外部势扰动的响应函数，为解释/预测实验/理论反应性数据提供了一个视角。这种方法使得从第一原理出发，能够清晰地定义和计算一系列著名但有时定义模糊的化学概念，如电负性和硬度。在本论文中，阐述了最简单的一阶响应函数的缺点，并简要概述了共价相互作用中化学键的描述，即相互作用的原子或基团之间的静电作用，这种作用基于电负性差异有使键极化的趋势。直到现在广为人知的二阶方法分别引入了与极化率和前线分子轨道理论相关的硬度/软度和福井函数概念。极化率/软度的引入也从历史角度进行了考量，其中极化率除了一些例外情况，主要是在非共价相互作用中提出的。还系统地考虑了一类特殊的响应函数，当外部势的变化仅由核构型的变化引起时（“R类似物”）。论文的主要部分致力于三阶响应函数，乍一看，人们可能认为它不会产生具有化学意义的信息，超硬度就是如此。一个反例是双描述符及其R类似物，即初始硬度响应，结果表明它为仅基于密度（即不涉及波函数的相位、符号、对称性）重新获得周环反应的伍德沃德 - 霍夫曼规则提供了坚实的基础。甚至二阶非线性响应函数也可能承载有趣的信息，例如关于局部和全局极化率的信息。它的导数可能控制电荷对极化率的影响，R类似物是核福井函数以及二次和三次力常数。尽管一些高阶导数可能难以评估，但与光谱学中用于描述核位移、核磁矩、电场和磁场的能量展开式进行比较后推测，交叉项肯定可能包含用于理解化学反应性的新的复杂信息。
