Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory

Cárdenas, Carlos; Ayers, Paul W.; Cedillo, Andrés

doi:10.1063/1.3585610

Cited by 79 publications

(71 citation statements)

References 90 publications

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“…This approximation will be used in this work. Additionally, in those cases where the frontier orbitals are degenerate, an average over the set of degenerate orbitals has been used [38][39][40][41] In our proposal, in contrast with the classical condensation schemes [42,43] (i.e., by means of atomic charges), the molecular space is partitioned into Fukui basins, which in turn are characterized by attractors at position k, according to the topological analysis of the gradient field of the Fukui function. Not only does this scheme avoid some ambiguities related with others (such as basis set dependence), [44][45][46] but it also provides regions of chemical interest that are not necessarily nuclear positions, which enrich the regioselectivity analysis.…”

Section: Theoretical Modelsmentioning

confidence: 99%

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Si_n (n = 12–20) clusters

et al. 2017

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Theoretical studies are essential for the structural characterization of clusters, when it comes to rationalize their unique size-dependent properties and composition. However, the rapid growth of local minima on the potential energy surface (PES), with respect to cluster size, makes the candidate identification a challenging undertaking. In this article, we introduce a hybrid strategy to explore the PES of clusters. This proposal involves the use of a biased initial population of a genetic algorithm procedure. Each individual in this population is built by assembling small fragments, according to the best matching of the Fukui function. The performance of a genetic algorithm procedure. The performance of the method is assessed on the PES exploration of medium-sized Si clusters (n = 12-20). The most relevant results are: (a) the method converges at almost half of the time used by the canonical version of the GA and, (b) in all the studied cases, with the exception of Si and Si , the method allowed to identify the global minimum (GM) and other important low-lying structures. Additionally, the apparent deficiency of the proposal to identify the GM was corrected when a Si atom, or other low-lying isomers, were considered to build the clusters. © 2017 Wiley Periodicals, Inc.

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Section: Theoretical Modelsmentioning

confidence: 99%

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Si_n (n = 12–20) clusters

et al. 2017

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“…(15) we assume that none of the reference states used to parameterize the model has spatially degenerate ground states. [38,39] Derivatives of the density with respect to N and  define the local reactivity indicators of conceptual DFT. The first derivative with respect to N is the Fukui function, [40][41][42] …”

Section: Local Reactivity Indicatorsmentioning

confidence: 99%

An explicit approach to conceptual density functional theory descriptors of arbitrary order

Heidar‐Zadeh

Richer

Fias

et al. 2016

Chemical Physics Letters

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We present explicit formulas for arbitrary-order derivatives of the energy, grand potential, electron density, and higher-order response functions with respect to the number of electrons, and the chemical potential for any smooth and differentiable model of the energy versus the number of electrons. The resulting expressions for global reactivity descriptors (hyperhardnesses and hypersoftnesses), local reactivity descriptors (hyperFukui functions and local hypersoftnesses), and nonlocal response functions are easy to evaluate computationally. Specifically, the explicit formulas for global/local/nonlocal hypersoftnesses of arbitrary order are derived using Bell polynomials. Explicit expressions for global and local hypersoftness indicators up to fifth order are presented.

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“…Provided that the system has no degenerate states, δ E δ v(r) N corresponds to ρ (r), the electron density function of the molecule. In case of degenerate states, the density to be used derives from degenerate perturbation theory [7][8][9] . Provided non-degenerate states, some trivial manipulations reveal that the dual descriptor is actually the N-derivative of the Fukui function f (r) [10][11][12] :…”

Section: Introductionmentioning

confidence: 99%

Analysis of molecular and (di)atomic dual-descriptor functions and matrices

et al. 2017

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In this work, the dual descriptor is studied in matrix form f (2) (r, r ) and both coordinates condensed to atoms, resulting in atomic and diatomic (or where applicable, bond) condensed single values. This double partitioning method of the dual descriptor matrix is proposed within the Hirshfeld-I atoms-in-molecule framework although it is easily extended to other atoms-in-molecules methods. Diagonalising the resulting atomic and bond dual descriptor matrices gives eigenvalues and eigenvectors describing the reactivity of atoms and bonds. The dual descriptor function is the diagonal element of the underlying matrix. The extra information contained in the atom and bond resolution is highlighted and the effect of choosing either the fragment of molecular response or response of molecular fragment approach is quantified. IntroductionOne of the essential tasks in chemistry is the analysis of chemical observations and their classification to ultimately be able to rationalise them in a model that even allows predicting the outcome of future experiments. This quite ambitious task has been met to admirable extent by introducing such classifications as acids and bases, hard and soft substances and many more. Over time, a vast toolbox of concepts and quantities was introduced with many of these developed either before the advent of quantum mechanics or without relying on the latter theory. This has resulted in a sort of gap between much of chemical theory and quantum mechanics although clearly quantum mechanics can give rise to much more and deeper insight in the underlying mechanisms of chemical reactivity. Fortunately, some eminent scientists have, over the years, picked up the challenge of closing this gap. One of the leading persons in this, is Robert G. Parr who is among the founding fathers of what is now known as chemical density functional theory (often still referred to as conceptual density functional theory, cDFT) 1-3 , and who was able to link many existing theories to the energy of a chemical system and its derivatives with respect to its basic variables, including the number of electrons and the external potential. This Taylor expansion of the energy has already given rise to numerous new reactivity descriptors or has allowed previously known key quantities like electronegativity to be identified with some of these derivatives.In this work we are interested in the dual descriptor introduced by Morell et al. 4,5 as the difference between the Fukui function for the addition of an electron minus that for the removal of an electron, or alternatively as the functional derivative of the hardness which in itself is the second derivative of the energy with respect to the number of electrons. As such, the dual descriptor is a mixed third order derivative of the energy 6 :In Eq.(1), f (2) (r) is the dual descriptor evaluated at a point r, E is the energy, N the number of electrons and v(r) the external potential. Provided that the system has no degenerate states, δ E δ v(r) N corresponds to ρ (r), the electron ...

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Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory

Cited by 79 publications

References 90 publications

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Si_n (n = 12–20) clusters

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Si_n (n = 12–20) clusters

An explicit approach to conceptual density functional theory descriptors of arbitrary order

Analysis of molecular and (di)atomic dual-descriptor functions and matrices

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Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory

Cited by 79 publications

References 90 publications

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Sin (n = 12–20) clusters

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Sin (n = 12–20) clusters

An explicit approach to conceptual density functional theory descriptors of arbitrary order

Analysis of molecular and (di)atomic dual-descriptor functions and matrices

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Product

Resources

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A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Si_n (n = 12–20) clusters

A Fukui function‐guided genetic algorithm. Assessment on structural prediction of Si_n (n = 12–20) clusters