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Hoffmann G, Guégan F, Labet V, Joubert L, Chermette H, Morell C, Tognetti V. Expanding horizons in conceptual density functional theory: Novel ensembles and descriptors to decipher reactivity patterns. J Comput Chem 2024; 45:1716-1726. [PMID: 38580454 DOI: 10.1002/jcc.27363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Revised: 02/16/2024] [Accepted: 02/22/2024] [Indexed: 04/07/2024]
Abstract
Conceptual density functional theory (CDFT) and the quantum reactivity descriptors stemming from it have proven to be valuable tools for understanding the chemical behavior of molecules. This article is presented as being intrinsically of dual character. In a first part, it briefly reviews, in a deliberately didactical way, the main ensembles in CDFT, while the second half presents two additional ensembles, where the chemical hardness acts as a natural variable, and their respective reactivity descriptors. The evaluation of these reactivity descriptors on common organic chemical reagents are presented and discussed.
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Affiliation(s)
- Guillaume Hoffmann
- Université de Lyon, Institut des Sciences Analytiques, UMR 5280, CNRS, Villeurbanne, France
| | - Frédéric Guégan
- IC2MP UMR 7285, Université de Poitiers - CNRS, Poitiers, France
| | - Vanessa Labet
- Sorbonne Université CNRS, MONARIS, UMR8233, Paris, France
| | - Laurent Joubert
- Univ Rouen Normandie, INSA Rouen Normandie, CNRS, Normandie Univ, COBRA UMR 6014, INC3M FR 3038, Rouen, France
| | - Henry Chermette
- Université de Lyon, Institut des Sciences Analytiques, UMR 5280, CNRS, Villeurbanne, France
| | - Christophe Morell
- Université de Lyon, Institut des Sciences Analytiques, UMR 5280, CNRS, Villeurbanne, France
| | - Vincent Tognetti
- Univ Rouen Normandie, INSA Rouen Normandie, CNRS, Normandie Univ, COBRA UMR 6014, INC3M FR 3038, Rouen, France
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Gómez T, Fuentealba P, Robles-Navarro A, Cárdenas C. Links among the Fukui potential, the alchemical hardness and the local hardness of an atom in a molecule. J Comput Chem 2021; 42:1681-1688. [PMID: 34121207 DOI: 10.1002/jcc.26705] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/14/2021] [Revised: 05/24/2021] [Accepted: 05/31/2021] [Indexed: 02/01/2023]
Abstract
This paper presents a brief summary of the difficulty that resides in the definition of the elusive concept of local chemical hardness. We argue that a definition of local hardness should be useful to a reactivity principle and not just as a mere definition. We then continue with a formal discussion about the benefits and difficulties of using the Fukui potential, which is interpreted as an alchemical derivative (alchemical hardness), as descriptor of local hardness of molecules. Computational evidence shows that the alchemical hardness is at least as good a descriptor as the combination of other two well-stabilized descriptors of local hardness, such as the Fukui function and grand canonical local hardness. Although our results are auspicious for the alchemical hardness as descriptor of local hardness, we finish by calling the attention of the community on the importance of discussing the raison d'être of a local hardness function and its main characteristics. We suggest that an axiomatic construction of local hardness could be they way of constructing a local hardness which is both useful and free of arbitrariness.
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Affiliation(s)
- Tatiana Gómez
- Theoretical and Computational Chemistry Center, Institute of Applied Chemical Sciences, Faculty of Engineering, Universidad Autonoma de Chile, Santiago, Chile
| | - Patricio Fuentealba
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.,Centro para el Desarrollo de la Nanociencia y la Nanotecnología (CEDENNA), Santiago, Chile
| | | | - Carlos Cárdenas
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Santiago, Chile.,Centro para el Desarrollo de la Nanociencia y la Nanotecnología (CEDENNA), Santiago, Chile
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3
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Matrodi A, Noorizadeh S. N-Derivatives of Shannon entropy density as response functions. Phys Chem Chem Phys 2020; 22:21535-21542. [PMID: 32959037 DOI: 10.1039/d0cp03808c] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
The exact first and second order partial derivatives of Shannon entropy density with respect to the number of electrons at constant external potential are introduced as new descriptors for prediction of the active sites of a molecule. The derivatives, which are a measure of the inhomogeneity of electron density, are calculated both exactly (from analytical forms) and approximately (using the finite difference method) for some molecular systems. According to the maximum entropy principle, the extreme value of the first order derivative on the surface of a given molecule should determine the active sites of the molecule in electrophilic and nucleophilic attack. The second order derivative indicates where the Shannon entropy is more concentrated or depleted during the electron exchange. Although these derivatives on the surfaces of helium and neon atoms are uniform, the corresponding values for argon, krypton and xenon atoms are not. This could explain the greater tendency of heavy noble gas atoms to form stable compounds. A dual descriptor is also defined as the difference between the left and right first order derivatives of Shannon entropy density, which allows one to simultaneously predict the preferable sites for electrophilic and nucleophilic attack over the system at point r. Therefore, the reactivity of an atom in a molecule requires the non-uniformity of the first and second order derivatives of Shannon entropy density on the surface of that atom.
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Affiliation(s)
- Abdolkarim Matrodi
- Chemistry Department, Faculty of Sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
| | - Siamak Noorizadeh
- Chemistry Department, Faculty of Sciences, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
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Guégan F, Lamine W, Chermette H, Morell C. Comment on “Revisiting the definition of local hardness and hardness kernel” by C. A. Polanco-Ramirez, M. Franco-Pérez, J. Carmona-Espíndola, J. L. Gázquez and P. W. Ayers, Phys. Chem. Chem. Phys., 2017, 19, 12355. Phys Chem Chem Phys 2018. [DOI: 10.1039/c7cp04100d] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this comment we show that the derivation proposed Polanco-Ramirez et al. appears naturally in the Taylor expansion of the energy, showing that their whole construction is not artificially built.
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Affiliation(s)
- F. Guégan
- Université de Lyon
- Institut des Sciences Analytiques
- UMR 5280 CNRS
- Université Claude Bernard Lyon 1
- ENS de Lyon
| | - W. Lamine
- Université de Lyon
- Institut des Sciences Analytiques
- UMR 5280 CNRS
- Université Claude Bernard Lyon 1
- ENS de Lyon
| | - H. Chermette
- Université de Lyon
- Institut des Sciences Analytiques
- UMR 5280 CNRS
- Université Claude Bernard Lyon 1
- ENS de Lyon
| | - C. Morell
- Université de Lyon
- Institut des Sciences Analytiques
- UMR 5280 CNRS
- Université Claude Bernard Lyon 1
- ENS de Lyon
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Ordon P, Komorowski L, Jedrzejewski M. Conceptual DFT analysis of the fragility spectra of atoms along the minimum energy reaction coordinate. J Chem Phys 2017; 147:134109. [PMID: 28987090 DOI: 10.1063/1.4995028] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
Theoretical justification has been provided to the method for monitoring the sequence of chemical bonds' rearrangement along a reaction path, by tracing the evolution of the diagonal elements of the Hessian matrix. Relations between the divergences of Hellman-Feynman forces and the energy and electron density derivatives have been demonstrated. By the proof presented on the grounds of the conceptual density functional theory formalism, the spectral amplitude observed on the atomic fragility spectra [L. Komorowski et al., Phys. Chem. Chem. Phys. 18, 32658 (2016)] reflects selectively the electron density modifications in bonds of an atom. In fact the spectral peaks for an atom reveal changes of the electron density occurring with bonds creation, breaking, or varying with the reaction progress.
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Affiliation(s)
- Piotr Ordon
- Department of Physics and Biophysics, Wrocław University of Environmental and Life Sciences, ul. Norwida 25, 50-375 Wrocław, Poland
| | - Ludwik Komorowski
- Department of Physical and Quantum Chemistry, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Mateusz Jedrzejewski
- Department of Physical and Quantum Chemistry, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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Franco-Pérez M, Ayers PW, Gázquez JL, Vela A. Thermodynamic responses of electronic systems. J Chem Phys 2017; 147:094105. [DOI: 10.1063/1.4999761] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Marco Franco-Pérez
- Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - Paul W. Ayers
- Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - José L. Gázquez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
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Franco-Pérez M, Polanco-Ramírez CA, Ayers PW, Gázquez JL, Vela A. New Fukui, dual and hyper-dual kernels as bond reactivity descriptors. Phys Chem Chem Phys 2017; 19:16095-16104. [PMID: 28598466 DOI: 10.1039/c7cp02613g] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We define three new linear response indices with promising applications for bond reactivity using the mathematical framework of τ-CRT (finite temperature chemical reactivity theory). The τ-Fukui kernel is defined as the ratio between the fluctuations of the average electron density at two different points in the space and the fluctuations in the average electron number and is designed to integrate to the finite-temperature definition of the electronic Fukui function. When this kernel is condensed, it can be interpreted as a site-reactivity descriptor of the boundary region between two atoms. The τ-dual kernel corresponds to the first order response of the Fukui kernel and is designed to integrate to the finite temperature definition of the dual descriptor; it indicates the ambiphilic reactivity of a specific bond and enriches the traditional dual descriptor by allowing one to distinguish between the electron-accepting and electron-donating processes. Finally, the τ-hyper dual kernel is defined as the second-order derivative of the Fukui kernel and is proposed as a measure of the strength of ambiphilic bonding interactions. Although these quantities have never been proposed, our results for the τ-Fukui kernel and for τ-dual kernel can be derived in zero-temperature formulation of the chemical reactivity theory with, among other things, the widely-used parabolic interpolation model.
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Affiliation(s)
- Marco Franco-Pérez
- Department of Chemistry, McMaster University, Hamilton, Ontario, L8S 4M1, Canada.
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8
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Franco-Pérez M, Ayers PW, Gázquez JL, Vela A. Local chemical potential, local hardness, and dual descriptors in temperature dependent chemical reactivity theory. Phys Chem Chem Phys 2017; 19:13687-13695. [DOI: 10.1039/c7cp00692f] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
From the definition of a local chemical potential, well-behaved expressions for the local hardness and the dual descriptors are derived.
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Affiliation(s)
- Marco Franco-Pérez
- Department of Chemistry
- McMaster University
- Hamilton
- Canada
- Departamento de Química
| | - Paul W. Ayers
- Department of Chemistry
- McMaster University
- Hamilton
- Canada
| | - José L. Gázquez
- Departamento de Química
- Universidad Autónoma Metropolitana-Iztapalapa
- Ciudad de México
- Mexico
| | - Alberto Vela
- Departamento de Química
- Centro de Investigación y de Estudios Avanzados
- Ciudad de México
- Mexico
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9
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Polanco-Ramírez CA, Franco-Pérez M, Carmona-Espíndola J, Gázquez JL, Ayers PW. Revisiting the definition of local hardness and hardness kernel. Phys Chem Chem Phys 2017; 19:12355-12364. [DOI: 10.1039/c7cp00691h] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Local hardness is redefined following similar rules to those of local softness. The new concept describes chemical trends correctly.
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Affiliation(s)
| | - Marco Franco-Pérez
- Departamento de Química
- Universidad Autónoma Metropolitana-Iztapalapa
- México
- Mexico
- Department of Chemistry
| | | | - José L. Gázquez
- Departamento de Química
- Universidad Autónoma Metropolitana-Iztapalapa
- México
- Mexico
| | - Paul W. Ayers
- Department of Chemistry
- McMaster University
- Hamilton
- Canada
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11
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Miranda-Quintana RA, Ayers PW. Fractional electron number, temperature, and perturbations in chemical reactions. Phys Chem Chem Phys 2016; 18:15070-80. [DOI: 10.1039/c6cp00939e] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The mathematical framework of conceptual density functional theory is extended to use the eigenstates and eigenvalues of perturbed subsystems. This unites, justifies, and extends, several previously proposed models.
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Affiliation(s)
| | - Paul W. Ayers
- Department of Chemistry & Chemical Biology
- McMaster University
- Hamilton
- Canada L8S 4M1
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12
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Franco-Pérez M, Ayers PW, Gázquez JL, Vela A. Local and linear chemical reactivity response functions at finite temperature in density functional theory. J Chem Phys 2015; 143:244117. [DOI: 10.1063/1.4938422] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Marco Franco-Pérez
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D.F. 09340, Mexico
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - José L. Gázquez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D.F. 09340, Mexico
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados (Cinvestav), Av. Instituto Politécnico Nacional 2508, México, D.F. 07360, Mexico
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13
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Franco-Pérez M, Gázquez JL, Ayers PW, Vela A. Revisiting the definition of the electronic chemical potential, chemical hardness, and softness at finite temperatures. J Chem Phys 2015; 143:154103. [DOI: 10.1063/1.4932539] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Franco-Pérez M, Gázquez JL, Vela A. Electronic chemical response indexes at finite temperature in the canonical ensemble. J Chem Phys 2015; 143:024112. [DOI: 10.1063/1.4923260] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Marco Franco-Pérez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D. F. 09340, México
- Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México, D. F. 07360, México
| | - José L. Gázquez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, D. F. 09340, México
- Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México, D. F. 07360, México
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, México, D. F. 07360, México
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15
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Theoretical investigation of the selectivity in intramolecular cyclizations of some 2’–aminochalcones to dihydroquinolin–8–ones and indolin–3–ones. J Mol Model 2013; 19:3611-8. [DOI: 10.1007/s00894-013-1893-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2013] [Accepted: 05/15/2013] [Indexed: 11/26/2022]
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16
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Shape entropy’s response to molecular ionization. J Mol Model 2013; 19:1677-83. [DOI: 10.1007/s00894-012-1725-4] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/08/2012] [Accepted: 12/03/2012] [Indexed: 10/27/2022]
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17
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Fuentealba P, Cárdenas C. On the exponential model for energy with respect to number of electrons. J Mol Model 2012; 19:2849-53. [DOI: 10.1007/s00894-012-1708-5] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2012] [Accepted: 11/21/2012] [Indexed: 11/30/2022]
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18
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Matito E, Putz MV. New link between conceptual density functional theory and electron delocalization. J Phys Chem A 2011; 115:12459-62. [PMID: 21561124 DOI: 10.1021/jp200731d] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
In this paper we give a new definition of the softness kernel based on the exchange-correlation density. This new kernel is shown to correspond to the change of electron fluctuation upon external perturbation, thus helping to bridge the gap between conceptual density functional theory and some tools describing electron localization in molecules. With the aid of a few computational calculations on diatomics we illustrate the performance of this new computational tool.
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Affiliation(s)
- Eduard Matito
- Institute of Physics, University of Szczecin, Szczecin, Poland.
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19
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Morell C, Ayers PW, Grand A, Chermette H. Application of the electron density force to chemical reactivity. Phys Chem Chem Phys 2011; 13:9601-8. [PMID: 21503299 DOI: 10.1039/c0cp02083d] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this paper the concept of force experienced by the electron density is applied to chemical reactivity. The force is based upon the gradient of a local chemical potential. Closely related concepts such as force field lines and local electron flux are defined to provide insight in chemical reactivity. The time evolution of a molecular site density is also proposed. From the divergence of the force, the nucleophilic and electrophilic behaviour of atomic sites are characterized. Finally, the relations between the force and local conceptual DFT descriptors are also given.
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Affiliation(s)
- Christophe Morell
- CEA Grenoble -INAC/SCIB/LAN (UMR-E n°3 CEA-UJF), CEA-Grenoble, 17, rue des Martyrs, F-38054 Grenoble Cedex 9, France.
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20
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Cárdenas C, Tiznado W, Ayers PW, Fuentealba P. The Fukui Potential and the Capacity of Charge and the Global Hardness of Atoms. J Phys Chem A 2011; 115:2325-31. [DOI: 10.1021/jp109955q] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Carlos Cárdenas
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, 653-Santiago, Chile
| | - William Tiznado
- Departamento de Ciencias Químicas, Facultad de Ecología y Recursos Naturales, Universidad Andrés Bello, Avenida República 275, Piso 3, Santiago, Chile
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton Ontario, Canada L8S 4M1
| | - Patricio Fuentealba
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, 653-Santiago, Chile
- Centro para el Desarrollo de la Nociencias y Nanotecnologia, CEDENNA, Avenida Ecuador 3493, Santiago, Chile
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21
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Geerlings P, Borgoo A. Information carriers and (reading them through) information theory in quantum chemistry. Phys Chem Chem Phys 2010; 13:911-22. [PMID: 21109896 DOI: 10.1039/c0cp01046d] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This Perspective discusses the reduction of the electronic wave function via the second-order reduced density matrix to the electron density ρ(r), which is the key ingredient in density functional theory (DFT) as a basic carrier of information. Simplifying further, the 1-normalized density function turns out to contain essentially the same information as ρ(r) and is even of preferred use as an information carrier when discussing the periodic properties along Mendeleev's table where essentially the valence electrons are at stake. The Kullback-Leibler information deficiency turns out to be the most interesting choice to obtain information on the differences in ρ(r) or σ(r) between two systems. To put it otherwise: when looking for the construction of a functional F(AB) = F[ζ(A)(r),ζ(B)(r)] for extracting differences in information from an information carrier ζ(r) (i.e. ρ(r), σ(r)) for two systems A and B the Kullback-Leibler information measure ΔS is a particularly adequate choice. Examples are given, varying from atoms, to molecules and molecular interactions. Quantum similarity of atoms indicates that the shape function based KL information deficiency is the most appropriate tool to retrieve periodicity in the Periodic Table. The dissimilarity of enantiomers for which different information measures are presented at global and local (i.e. molecular and atomic) level leads to an extension of Mezey's holographic density theorem and shows numerical evidence that in a chiral molecule the whole molecule is pervaded by chirality. Finally Kullback-Leibler information profiles are discussed for intra- and intermolecular proton transfer reactions and a simple S(N)2 reaction indicating that the theoretical information profile can be used as a companion to the energy based Hammond postulate to discuss the early or late transition state character of a reaction. All in all this Perspective's answer is positive to the question of whether an even simpler carrier of information than the electron density function ρ(r) can be envisaged: the shape function, integrating to 1 by construction fulfils this role. On the other hand obtaining the information (or information difference) contained in one (or two) systems from ρ(r) or σ(r) can be most efficiently done by using information theory, the Kulback-Leibler information deficiency being at the moment (one of) the most advisable functionals.
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Affiliation(s)
- Paul Geerlings
- Eenheid Algemene Chemie (ALGC), Vrije Universiteit Brussel, Pleinlaan, 2, 1050 Brussels, Belgium.
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22
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Pan XY, Sahni V. Particle number and probability density functional theory and A-representability. J Chem Phys 2010; 132:164116. [PMID: 20441267 DOI: 10.1063/1.3357986] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In Hohenberg-Kohn density functional theory, the energy E is expressed as a unique functional of the ground state density rho(r): E = E[rho] with the internal energy component F(HK)[rho] being universal. Knowledge of the functional F(HK)[rho] by itself, however, is insufficient to obtain the energy: the particle number N is primary. By emphasizing this primacy, the energy E is written as a nonuniversal functional of N and probability density p(r): E = E[N,p]. The set of functions p(r) satisfies the constraints of normalization to unity and non-negativity, exists for each N; N = 1, ..., infinity, and defines the probability density or p-space. A particle number N and probability density p(r) functional theory is constructed. Two examples for which the exact energy functionals E[N,p] are known are provided. The concept of A-representability is introduced, by which it is meant the set of functions Psi(p) that leads to probability densities p(r) obtained as the quantum-mechanical expectation of the probability density operator, and which satisfies the above constraints. We show that the set of functions p(r) of p-space is equivalent to the A-representable probability density set. We also show via the Harriman and Gilbert constructions that the A-representable and N-representable probability density p(r) sets are equivalent.
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Affiliation(s)
- Xiao-Yin Pan
- Department of Physics, Ningbo University, Ningbo 315211, China
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23
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Fuentealba P, Florez E, Tiznado W. Topological Analysis of the Fukui Function. J Chem Theory Comput 2010; 6:1470-8. [DOI: 10.1021/ct100022w] [Citation(s) in RCA: 75] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Patricio Fuentealba
- Departamento de Física, Universidad de Chile, Las Palmeras 3425, Santiago-Chile, Instituto de Química, Universidad de Antioquia, A.A. 1226, Medellín, Colombia, and Departamento de Ciencias Químicas, Facultad de Ecología y Recursos Naturales, Universidad Andres Bello, Av. República 275, Santiago-Chile
| | - Elizabeth Florez
- Departamento de Física, Universidad de Chile, Las Palmeras 3425, Santiago-Chile, Instituto de Química, Universidad de Antioquia, A.A. 1226, Medellín, Colombia, and Departamento de Ciencias Químicas, Facultad de Ecología y Recursos Naturales, Universidad Andres Bello, Av. República 275, Santiago-Chile
| | - William Tiznado
- Departamento de Física, Universidad de Chile, Las Palmeras 3425, Santiago-Chile, Instituto de Química, Universidad de Antioquia, A.A. 1226, Medellín, Colombia, and Departamento de Ciencias Químicas, Facultad de Ecología y Recursos Naturales, Universidad Andres Bello, Av. República 275, Santiago-Chile
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Roy RK, Saha S. Studies of regioselectivity of large molecular systems using DFT based reactivity descriptors. ACTA ACUST UNITED AC 2010. [DOI: 10.1039/b811052m] [Citation(s) in RCA: 77] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Cárdenas C, Echegaray E, Chakraborty D, Anderson JSM, Ayers PW. Relationships between the third-order reactivity indicators in chemical density-functional theory. J Chem Phys 2009; 130:244105. [DOI: 10.1063/1.3151599] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pérez P, Chamorro E, Ayers PW. Universal mathematical identities in density functional theory: Results from three different spin-resolved representations. J Chem Phys 2008; 128:204108. [DOI: 10.1063/1.2916714] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
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Geerlings P, De Proft F. Conceptual DFT: the chemical relevance of higher response functions. Phys Chem Chem Phys 2008; 10:3028-42. [PMID: 18688366 DOI: 10.1039/b717671f] [Citation(s) in RCA: 192] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
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.
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Affiliation(s)
- P Geerlings
- Eenheid Algemene Chemie (ALGC), Faculty of Sciences, Vrije Universiteit Brussel (Free University of Brussels - VUB), Pleinlaan 2, 1050, Brussels.
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Cherkasov AR, Galkin VI, Zueva EM, Cherkasov RA. The concept of electronegativity. The current state of the problem. RUSSIAN CHEMICAL REVIEWS 2007. [DOI: 10.1070/rc1998v067n05abeh000383] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Chamorro E, Pérez P. Condensed-to-atoms electronic Fukui functions within the framework of spin-polarized density-functional theory. J Chem Phys 2007; 123:114107. [PMID: 16392551 DOI: 10.1063/1.2033689] [Citation(s) in RCA: 75] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A simple formalism devised to calculate the condensed-to-atoms Fukui function [R. R. Contreras, P. Fuentealba, M. Galván, and P. Pérez, Chem. Phys. Lett. 304, 405 (1999)] has been further analyzed within a spin-polarized density-functional theory framework. The model is based on a frozen-core approximation to these local reactivity indices [M. Galván, A. Vela, and J. L. Gázquez, J. Phys. Chem. 92, 6470 (1988)], giving us an extended local reactivity description of systems based on the frontier spin-up and spin-down molecular orbitals. Degenerate molecular spin orbitals have been explicitly included in our model equations. Computational results for the nitric oxide (NO) and some simple carbene systems are presented in order to test the model. These quantities have been discussed in the context of changes both in charge density and spin density within the context of electron charge transfer or spin-polarization processes.
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Affiliation(s)
- Eduardo Chamorro
- Departamento de Ciencias Químicas, Facultad de Ecología y Recursos Naturales, Universidad Nacional Andrés Bello, Santiago, Chile.
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Ayers PW. The physical basis of the hard/soft acid/base principle. Faraday Discuss 2007; 135:161-90; discussion 237-59, 503-6. [PMID: 17328428 DOI: 10.1039/b606877d] [Citation(s) in RCA: 237] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The dependence of molecular properties on the chemical hardness is explored. As the chemical hardness of a molecule increases, its size and polarizability typically decrease and its charge and electronegativity typically increase. On the basis of these properties, the interaction energy between hard and soft acids and bases is quantified, and the physical basis of the global and local hard/soft acid/base (HSAB) principles is elucidated.
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Affiliation(s)
- Paul W Ayers
- Department of Chemistry, McMaster University, Hamilton ON, Canada L8S 4M1
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Geerlings P, Proft FD, Ayers P. Chapter 1 Chemical reactivity and the shape function. THEORETICAL AND COMPUTATIONAL CHEMISTRY 2007. [DOI: 10.1016/s1380-7323(07)80002-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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Chamorro E, De Proft F, Geerlings P. Generalized nuclear Fukui functions in the framework of spin-polarized density-functional theory. J Chem Phys 2005; 123:084104. [PMID: 16164279 DOI: 10.1063/1.1996576] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
An extension of Cohen's nuclear Fukui function is presented in the spin-polarized framework of density-functional theory (SP-DFT). The resulting new nuclear Fukui function indices PhiNalpha and PhiSalpha are intended to be the natural descriptors for the responses of the nuclei to changes involving charge transfer at constant multiplicity and also the spin polarization at constant number of electrons. These generalized quantities allow us to gain new insights within a perturbative scheme based on DFT. Calculations of the electronic and nuclear SP-DFT quantities are presented within a Kohn-Sham framework of chemical reactivity for a sample of molecules, including H2O, H2CO, and some simple nitrenes (NX) and phosphinidenes (PX), with X=H, Li, F, Cl, OH, SH, NH2, and PH2. Results have been interpreted in terms of chemical bonding in the context of Berlin's theorem, which provides a separation of the molecular space into binding and antibinding regions.
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Affiliation(s)
- E Chamorro
- Departamento de Ciencias Químicas, Facultad de Ecología y Recursos Naturales, Universidad Nacional Andrés Bello (UNAB), Avenida República 275, Santiago, Chile.
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Ordon P, Tachibana A. Nuclear reactivity indices within regional density functional theory. J Mol Model 2005; 11:312-6. [PMID: 16047174 DOI: 10.1007/s00894-005-0248-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2004] [Accepted: 01/27/2005] [Indexed: 10/25/2022]
Abstract
Regional chemical potential values-mu(R) have been obtained with the use of nuclear reactivity indices. Perturbational formulae use values of reactivity indices of isolated molecular fragments. The changes of the parameters (DeltaN(R),{ DeltaQ(i)}i epsilonR) within each fragment determine the value of the regional chemical potential after a chemical reaction. The computational scheme has been tested numerically along the chemical reaction path. We have studied a set of chemical reactions to obtain regional chemical potentials (mu(ts)R) and regional transfer potentials (T(ts)R) for transition states of the following chemical reactions: HF+CO=HFCO, HCl+CO=HClCO, HF+SiO=HFSiO and HF+GeO=HFGeO. The results are reasonable and encouraging. Values of these indices show the possible reactivity directions of the transition states examined.
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Affiliation(s)
- Piotr Ordon
- Department of Microengineering, Kyoto University, Kyoto, 606-8501, Japan.
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De Proft F, Ayers PW, Sen KD, Geerlings P. On the importance of the “density per particle” (shape function) in the density functional theory. J Chem Phys 2004; 120:9969-73. [PMID: 15268015 DOI: 10.1063/1.1729856] [Citation(s) in RCA: 87] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The central role of the shape function sigma(r) from the density functional theory (DFT), the ratio of the electron density rho(r) and the number of electrons N of the system (density per particle), is investigated. Moreover, its relationship with DFT based reactivity indices is established. In the first part, it is shown that an estimate for the chemical hardness can be obtained from the long range behavior of the shape function and its derivative with respect to the number of electrons at a fixed external potential. Next, the energy of the system is minimized with the constraint that the shape function should integrate to unity; the associated Lagrange multiplier is shown to be related to the electronic chemical potential micro of the system. Finally, the importance of the shape function for both molecular structure, reactivity, and similarity is outlined.
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Affiliation(s)
- F De Proft
- Eenheid Algemene Chemie, Vrije Universiteit Brussel, Faculteit Wetenschappen, Pleinlaan 2, 1050 Brussels, Belgium
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Torrent-Sucarrat M, Luis JM, Duran M, Toro-Labbé A, Solà M. Relations among several nuclear and electronic density functional reactivity indexes. J Chem Phys 2003. [DOI: 10.1063/1.1615763] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Affiliation(s)
- P Geerlings
- Eenheid Algemene Chemie, Faculteit Wetenschappen, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium.
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Soleilhavoup M, Saccavini C, Lepetit C, Lavigne G, Maurette L, Donnadieu B, Chauvin R. Parallel Approaches to Mono- and Bis-Propargylic Activation via Co2(CO)8 and [Ru3(μ-Cl)(CO)10]-. Organometallics 2002. [DOI: 10.1021/om010568w] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michèle Soleilhavoup
- Laboratoire de Chimie de Coordination du CNRS, 205 Route de Narbonne, 31077 Toulouse Cedex 4, France
| | - Catherine Saccavini
- Laboratoire de Chimie de Coordination du CNRS, 205 Route de Narbonne, 31077 Toulouse Cedex 4, France
| | - Christine Lepetit
- Laboratoire de Chimie de Coordination du CNRS, 205 Route de Narbonne, 31077 Toulouse Cedex 4, France
| | - Guy Lavigne
- Laboratoire de Chimie de Coordination du CNRS, 205 Route de Narbonne, 31077 Toulouse Cedex 4, France
| | - Luc Maurette
- Laboratoire de Chimie de Coordination du CNRS, 205 Route de Narbonne, 31077 Toulouse Cedex 4, France
| | - Bruno Donnadieu
- Laboratoire de Chimie de Coordination du CNRS, 205 Route de Narbonne, 31077 Toulouse Cedex 4, France
| | - Remi Chauvin
- Laboratoire de Chimie de Coordination du CNRS, 205 Route de Narbonne, 31077 Toulouse Cedex 4, France
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Chamorro E, Fuentealba P, Contreras R. Higher order derivatives for nuclear indexes in the framework of density functional theory. J Chem Phys 2001. [DOI: 10.1063/1.1394755] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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De Proft F, Geerlings P. Conceptual and computational DFT in the study of aromaticity. Chem Rev 2001; 101:1451-64. [PMID: 11710228 DOI: 10.1021/cr9903205] [Citation(s) in RCA: 424] [Impact Index Per Article: 18.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- F De Proft
- Eenheid Algemene Chemie, Vrije Universiteit Brussel, Faculteit Wetenschappen, Pleinlaan 2, 1050 Brussels, Belgium
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Ayers PW, Parr RG. Variational principles for describing chemical reactions. Reactivity indices based on the external potential. J Am Chem Soc 2001; 123:2007-17. [PMID: 11456823 DOI: 10.1021/ja002966g] [Citation(s) in RCA: 153] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In a recent paper [J. Am. Chem. Soc. 2000, 122, 2010], the authors explored variational principles that help one understand chemical reactivity on the basis of the changes in electron density associated with a chemical reaction. Here, similar methods are used to explore the effect changing the external potential has on chemical reactivity. Four new indices are defined: (1) a potential energy surface that results from the second-order truncation of the Taylor series in the external potential about some reference, Upsilon(R(1),R(2),.,R(M)()); (2) the stabilization energy for the equilibrium nuclear geometry (relative to some reference), Xi; (3) the flexibility, or "lability", of the molecule at equilibrium, Lambda; and (4) the proton hardness, Pi, which performs a role in the theory of Brönsted-Lowry acids and bases that is similar to the role of the chemical hardness in the theory of Lewis acids and bases. Applications considered include the orientation of a molecule in an external electric field, molecular association reactions, and reactions between Brönsted-Lowry acids and bases.
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Affiliation(s)
- P W Ayers
- Department of Chemistry, The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
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42
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The response of atomic electron densities to point perturbations in the external potential. ACTA ACUST UNITED AC 2001. [DOI: 10.1016/s0166-1280(00)00579-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Chamorro E, Contreras R, Fuentealba P. Some relationships within the nonlocal (pair–site) chemical reactivity formalism of density functional theory. J Chem Phys 2000. [DOI: 10.1063/1.1327265] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gilardoni F, Bell AT, Chakraborty A, Boulet P. Density Functional Theory Calculations of the Oxidative Dehydrogenation of Propane on the (010) Surface of V2O5†. J Phys Chem B 2000. [DOI: 10.1021/jp001746m] [Citation(s) in RCA: 65] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- François Gilardoni
- Chemical and Materials Sciences Divisions, Lawrence Berkeley National Laboratory, Departments of Chemistry and Chemical Engineering, University of California, Berkeley, California 94720-1462, and Department of Physical Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, CH-1211 Geneve 4, Switzerland
| | - Alexis T. Bell
- Chemical and Materials Sciences Divisions, Lawrence Berkeley National Laboratory, Departments of Chemistry and Chemical Engineering, University of California, Berkeley, California 94720-1462, and Department of Physical Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, CH-1211 Geneve 4, Switzerland
| | - Arup Chakraborty
- Chemical and Materials Sciences Divisions, Lawrence Berkeley National Laboratory, Departments of Chemistry and Chemical Engineering, University of California, Berkeley, California 94720-1462, and Department of Physical Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, CH-1211 Geneve 4, Switzerland
| | - Pascal Boulet
- Chemical and Materials Sciences Divisions, Lawrence Berkeley National Laboratory, Departments of Chemistry and Chemical Engineering, University of California, Berkeley, California 94720-1462, and Department of Physical Chemistry, University of Geneva, 30 Quai Ernest-Ansermet, CH-1211 Geneve 4, Switzerland
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Gutiérrez J, Paz-Sandoval M, Robles J. Synthesis, characterization and a theoretical investigation of the formation of silicon, germanium and tin azapentadiene compounds from lithium azapentadienyls. J Organomet Chem 2000. [DOI: 10.1016/s0022-328x(99)00752-4] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Fuentealba P, Cedillo A. The variations of the hardness and the Kohn–Sham Fukui function under an external perturbation. J Chem Phys 1999. [DOI: 10.1063/1.478033] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Contreras R, Domingo LR, Andrés J, Pérez P, Tapia O. Nonlocal (Pair Site) Reactivity from Second-Order Static Density Response Function: Gas- and Solution-Phase Reactivity of the Acetaldehyde Enolate as a Test Case. J Phys Chem A 1999. [DOI: 10.1021/jp982801i] [Citation(s) in RCA: 44] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Renato Contreras
- Departament de Ciènces Experimentals, Universitat Jaume I, Box 242, 12080, Castelló, Spain, Departament de Química Orgànica, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain, and Department of Physical Chemistry, Uppsala University, Box 532, S-751 21, Uppsala, Sweden
| | - Luis R. Domingo
- Departament de Ciènces Experimentals, Universitat Jaume I, Box 242, 12080, Castelló, Spain, Departament de Química Orgànica, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain, and Department of Physical Chemistry, Uppsala University, Box 532, S-751 21, Uppsala, Sweden
| | - Juan Andrés
- Departament de Ciènces Experimentals, Universitat Jaume I, Box 242, 12080, Castelló, Spain, Departament de Química Orgànica, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain, and Department of Physical Chemistry, Uppsala University, Box 532, S-751 21, Uppsala, Sweden
| | - Patricia Pérez
- Departament de Ciènces Experimentals, Universitat Jaume I, Box 242, 12080, Castelló, Spain, Departament de Química Orgànica, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain, and Department of Physical Chemistry, Uppsala University, Box 532, S-751 21, Uppsala, Sweden
| | - Orlando Tapia
- Departament de Ciènces Experimentals, Universitat Jaume I, Box 242, 12080, Castelló, Spain, Departament de Química Orgànica, Universitat de València, Dr. Moliner 50, 46100 Burjassot, València, Spain, and Department of Physical Chemistry, Uppsala University, Box 532, S-751 21, Uppsala, Sweden
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