The linear response kernel of conceptual DFT as a measure of electron delocalisation

Sablon, Nick; Proft, Frank De; Geerlings, Pau̧l

doi:10.1016/j.cplett.2010.08.031

Cited by 52 publications

(65 citation statements)

References 45 publications

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“…47 Some of the present authors recently presented a purely numerical, finite difference-type approach on one hand and a simple perturbational approach based on the Kohn-Sham non-interacting system 10 on the other hand leading to the first extensive numerical studies of the linear response function. [48][49][50][51] Note that similar type of problems arise in the case of first-order functional derivatives of the electronic chemical potential and the chemical hardness with respect to v(r). They appear in a mixed second-or higher order energy derivatives in which, using a Maxwell relation, the d/dN type problems were circumvented by writing the Fukui function as the functional derivative of the electronic chemical potential and the dual descriptor as the functional derivative of the hardness.…”

Section: Introductionmentioning

confidence: 92%

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Analytical evaluation of Fukui functions and real-space linear response function

Yang

Cohen

Proft

et al. 2012

The Journal of Chemical Physics

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Many useful concepts developed within density functional theory provide much insight for the understanding and prediction of chemical reactivity, one of the main aims in the field of conceptual density functional theory. While approximate evaluations of such concepts exist, the analytical and efficient evaluation is, however, challenging, because such concepts are usually expressed in terms of functional derivatives with respect to the electron density, or partial derivatives with respect to the number of electrons, complicating the connection to the computational variables of the Kohn-Sham one-electron orbitals. Only recently, the analytical expressions for the chemical potential, one of the key concepts, have been derived by Cohen, Mori-Sánchez, and Yang, based on the potential functional theory formalism. In the present work, we obtain the analytical expressions for the real-space linear response function using the coupled perturbed Kohn-Sham and generalized Kohn-Sham equations, and the Fukui functions using the previous analytical expressions for chemical potentials of Cohen, Mori-Sánchez, and Yang. The analytical expressions are exact within the given exchange-correlation functional. They are applicable to all commonly used approximate functionals, such as local density approximation (LDA), generalized gradient approximation (GGA), and hybrid functionals. The analytical expressions obtained here for Fukui function and linear response functions, along with that for the chemical potential by Cohen, Mori-Sánchez, and Yang, provide the rigorous and efficient evaluation of the key quantities in conceptual density functional theory within the computational framework of the Kohn-Sham and generalized Kohn-Sham approaches. Furthermore, the obtained analytical expressions for Fukui functions, in conjunction with the linearity condition of the ground state energy as a function of the fractional charges, also lead to new local conditions on the exact functionals, expressed in terms of the second-order functional derivatives. We implemented the expressions and demonstrate the efficacy with some atomic and molecular calculations, highlighting the importance of relaxation effects.

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Section: Introductionmentioning

confidence: 92%

“…The more elaborate evaluation of the linear response function, needing also condensation [48][49][50][51] for chemical interpretation will be the subject of a follow-up paper. All calculations for the Fukui function were done using Eq.…”

Section: Implementation and Numerical Examplesmentioning

confidence: 99%

Analytical evaluation of Fukui functions and real-space linear response function

Yang

Cohen

Proft

et al. 2012

The Journal of Chemical Physics

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“…[24] Recent researchh as also revealed the interpretive and predictives ignificance of other reactivity descriptors, such as the duald escriptor [25] and the linear response function. [26] While the HSAB principle is being challenged nowadays for the treatment of ambident reactivity,c onceptual DFT descriptors offer insight into this special type of reactivity.…”

Section: Introductionmentioning

confidence: 99%

Ambident Nucleophilic Substitution: Understanding Non‐HSAB Behavior through Activation Strain and Conceptual DFT Analyses

Bettens

Alonso

Proft

et al. 2020

Chemistry A European J

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The ability to understand and predict ambident reactivity is key to the rational design of organic syntheses. An approach to understand trends in ambident reactivity is the hard and soft acids and bases (HSAB) principle. The recent controversy over the general validity of this principle prompted us to investigate the competing gas‐phase SN2 reaction channels of archetypal ambident nucleophiles CN−, OCN−, and SCN− with CH3Cl (SN2@C) and SiH3Cl (SN2@Si), using DFT calculations. Our combined analyses highlight the inability of the HSAB principle to correctly predict the reactivity trends of these simple, model reactions. Instead, we have successfully traced reactivity trends to the canonical orbital‐interaction mechanism and the resulting nucleophile–substrate interaction energy. The HOMO–LUMO orbital interactions set the trend in both SN2@C and SN2@Si reactions. We provide simple rules for predicting the ambident reactivity of nucleophiles based on our Kohn–Sham molecular orbital analysis.

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“…In recent years, some of the present authors have used the linear response function to investigate inductive, mesomeric and hyperconjugative effects, aromaticity and antiaromaticity, opting for an atom condensation scheme in order to reduce the computational effort required [16][17][18][19][20][21][22]. Specifically, the object under study was given by…”

Section: Introductionmentioning

confidence: 99%

The polarisability of atoms and molecules: a comparison between a conceptual density functional theory approach and time-dependent density functional theory

et al. 2015

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We investigate the local polarisability or polarisability density using both a conceptual density functional theory approach based on the linear response function and time-dependent density functional theory. Using a zero frequency in the latter, we can immediately compare both approaches. Using an analytical expression for the linear response kernel, we are able to systematically analyse α(r) throughout the periodic table. An extension to molecules is also made with a study of the CO molecule retrieving the connection between local softness and local polarisability. IntroductionConceptual density functional theory (conceptual DFT [1,2]) provides us with a strong formal basis for various well-known chemical concepts. Since chemical reactions can be thought of as perturbations of a system in its number of electrons N and/or its external potential v(r), conceptual DFT, also known as chemical reactivity theory, can therefore be thought of as the study of the electronic energy functional E[N ; v(r)]. Rather than studying the energy in its entirety, one can study the response of the energy with respect to variations in the number of electrons and/or the external potential by looking at the Taylor expansion of the energy (see Equation (3) in Section 2.1).One can then identify the (mixed) derivatives of E with respect to N and v(r), (δ n + m E/∂N n δv m ), with response functions or reactivity indices [2,3]. The two derivatives with n + m = 1 -being the electronic density, corresponding to (n = 0, m = 1), and the electronic chemical potential, corresponding to (n = 1, m = 0) -have been studied intensively before. The same holds for two of those with n + m = 2, specifically the chemical hardness, (n = 2, m = 0), and the Fukui function, (n = 1, m = 1), as well as for some of those with n + m = 3, specifically the hyperhardness, (n = 2, m = 0), and the dual descriptor, (n = 2, m = 1). For a review, see Geerlings and De Proft [3]. In contrast to these derivatives, the final one with n + m = 2, corresponding to (n = 0, m = 2), has received less attention. This index is known as the linear response kernel χ (r, r ). Note that although there has not been much focus on the chemistry

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The linear response kernel of conceptual DFT as a measure of electron delocalisation

Cited by 52 publications

References 45 publications

Analytical evaluation of Fukui functions and real-space linear response function

Analytical evaluation of Fukui functions and real-space linear response function

Ambident Nucleophilic Substitution: Understanding Non‐HSAB Behavior through Activation Strain and Conceptual DFT Analyses

The polarisability of atoms and molecules: a comparison between a conceptual density functional theory approach and time-dependent density functional theory

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