Franco-Pérez Marco, Ayers Paul W, Gázquez José L, Vela Alberto
Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
Phys Chem Chem Phys. 2017 May 31;19(21):13687-13695. doi: 10.1039/c7cp00692f.
In this work we establish a new temperature dependent procedure within the grand canonical ensemble, to avoid the Dirac delta function exhibited by some of the second order chemical reactivity descriptors based on density functional theory, at a temperature of 0 K. Through the definition of a local chemical potential designed to integrate to the global temperature dependent electronic chemical potential, the local chemical hardness is expressed in terms of the derivative of this local chemical potential with respect to the average number of electrons. For the three-ground-states ensemble model, this local hardness contains a term that is equal to the one intuitively proposed by Meneses, Tiznado, Contreras and Fuentealba, which integrates to the global hardness given by the difference in the first ionization potential, I, and the electron affinity, A, at any temperature. However, in the present approach one finds an additional temperature-dependent term that introduces changes at the local level and integrates to zero. Additionally, a τ-hard dual descriptor and a τ-soft dual descriptor given in terms of the product of the global hardness and the global softness multiplied by the dual descriptor, respectively, are derived. Since all these reactivity indices are given by expressions composed of terms that correspond to products of the global properties multiplied by the electrophilic or nucleophilic Fukui functions, they may be useful for studying and comparing equivalent sites in different chemical environments.
在这项工作中，我们在巨正则系综中建立了一种新的温度相关程序，以避免某些基于密度泛函理论的二阶化学反应性描述符在0 K温度下出现狄拉克δ函数。通过定义一个旨在积分到全局温度相关电子化学势的局部化学势，局部化学硬度用该局部化学势相对于平均电子数的导数来表示。对于三基态系综模型，这种局部硬度包含一个与梅内塞斯、蒂兹纳多、孔特雷拉斯和富恩特阿尔巴直观提出的项相等的项，该项在任何温度下积分到由第一电离势I和电子亲和势A之差给出的全局硬度。然而，在本方法中发现了一个额外的温度相关项，该项在局部层面引入变化且积分结果为零。此外，还分别推导了一个由全局硬度与全局软度的乘积乘以对偶描述符给出的τ - 硬对偶描述符和一个τ - 软对偶描述符。由于所有这些反应性指数都由对应于全局性质乘积乘以亲电或亲核福井函数的项组成的表达式给出，它们可能有助于研究和比较不同化学环境中的等效位点。
