Analogies between Density Functional Theory Response Kernels and Derivatives of Thermodynamic State Functions

In view of its use as reactivity theory,Conceptual Density Functional Theory(DFT),introduced by Parr et al.,has mainly concentrated up to now on the E = E[N,v] functional.However,different ensemble representations can be used involving other variables also,such as ρ and μ.In this study,these different ensemble representations(E,?,F,and R) are briefly reviewed.Particular attention is then given to the corresponding second-order(functional) derivatives,and their analogieswith the second-order derivatives of thermodynamic state functions U,F,H,and G,which are related to each other via Legendre transformations,just as the DFT functionals(Nalewajski and Parr,1982).Starting from an analysis of the convexity/concavity of the DFT functionals,for which explicit proofs are discussed for some cases,the positive/negative definiteness of the associated kernels is derived and a detailed comparison is made with the thermodynamic derivatives.The stability conditions in thermodynamics are similar in structure to the convexity/concavity conditions for the DFT functionals.Thus,the DFT functionals are scrutinized based on the convexity/concavity of their two variables,to yield the possibility of establishing a relationship between the three second-order reactivity descriptors derived from the considered functional.Considering two ensemble representations,F and ?,F is eliminated as it has two dependent(extensive)variables,N and ρ.For ?,on the other hand,which is concave for both of its intensive variables(μ and υ),an inequality is derived from its three second-order(functional) derivatives:the global softness,the local softness,and the softness kernel.Combined with the negative value of the diagonal element of the linear response function,this inequality is shown to be compatible with the Berkowitz-Parr relationship,which relates the functional derivatives of ρ with υ,at constant N and μ.This was recently at stake upon quantifying Kohn's Nearsightedness of Electronic Matter.The analogy of the resulting inequality and the thermodynamic inequality for the G derivatives is highlighted.Potential research paths for this study are briefly addressed;the analogies between finite-temperature DFT response functions and their thermodynamic counterparts and the quest for analogous relationships,as derived in this paper,for DFT functionals that are analogues of entropy-dimensioned thermodynamic functions such as the Massieu function.

运用密度泛函活性理论的信息论方法研究苯并富烯衍生物的芳香性（英文）

文献中已有越来越多的芳香性体系被发现,同时也有越来越多的芳香性指标被提出来,但是如何解释芳香化合物稳定性的起源以及理解芳香性的本质仍然是当今理论化学中一个悬而未决的难题。运用我们新近提出的密度泛函活性理论信息论方法,不久前我们曾对一系列富烯衍生物进行了系统研究并得到了一个全新的认识。本文进一步探讨苯并富烯衍生物的芳香性行为,目的在于考察一个或多个苯环与富烯连接之后其芳香性发生变化的情况。运用香农熵,费舍尔信息,Ghosh-Berkowitz-Parr熵,Onicescu信息能,信息增益,以及相对Rényi熵六个信息量,和四种芳香指标,ASE,HOMA,FLU和NICS,我们系统地研究了信息量和芳香性指标在单、双、三苯并富烯衍生物中的相关性。我们发现,不管是否有苯环与富烯相连,芳香指标和信息量的交叉相关性都是一样的。这表明,虽然苯环本身具有芳香性,但苯环与富烯相连并不能改变富烯的芳香性与反芳香性本质。苯并富烯衍生物与富烯衍生物的芳香性和反芳香性一致。苯并富烯衍生物的芳香性和反芳香性完全取决于富烯本身的芳香性和反芳香性。这些结果为认识和理解复杂体系芳香性和反芳香性起源和本质将提供有益的启示。