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Richer M, Heidar-Zadeh F, Ríos-Gutiérrez M, Yang XD, Ayers PW. Spin-Polarized Conceptual Density Functional Theory from the Convex Hull. J Chem Theory Comput 2024; 20:4616-4628. [PMID: 38819213 DOI: 10.1021/acs.jctc.4c00213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., {N, S} vs {Nα, Nβ}) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions {P+(r), P-(r)} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.
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Affiliation(s)
- Michelle Richer
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
- Department of Chemistry, McMaster University, 1280 Main St. West, Hamilton, Ontario L8S 4M1, Canada
| | - Farnaz Heidar-Zadeh
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7L 3N6, Canada
| | - Mar Ríos-Gutiérrez
- Department of Organic Chemistry, University of Valencia, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain
| | - Xiaotian Derrick Yang
- Department of Chemistry, McMaster University, 1280 Main St. West, Hamilton, Ontario L8S 4M1, Canada
| | - Paul W Ayers
- Department of Chemistry, McMaster University, 1280 Main St. West, Hamilton, Ontario L8S 4M1, Canada
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2
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Klein J, Pilmé J. Exploring the Reactivity of Donor-Acceptor Systems through a Combined Conceptual and Constrained DFT Approach. J Chem Theory Comput 2024; 20:2010-2021. [PMID: 38353597 DOI: 10.1021/acs.jctc.3c01248] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
In the context of the conceptual density functional theory (cDFT) and based on the computational efficiency of the constrained DFT (CDFT), we demonstrate that chemical reactivity can be governed by the difference between the local interacting chemical potentials of the reactants (referred as Edual), in agreement with Sanderson's equalization principle. In a proof-of-concept study, we investigated illustrative examples involving typical non-covalent donor-acceptor systems and reactive systems are provided. For the selected systems, our approach reveals significant mimicking between Edual and the DFT-computed intermolecular interaction energy profiles. We further evaluate the influence of the Coulomb and exchange-correlation contributions in Edual. These latter results suggest that numerous potential energy surfaces of clusters can be explored using a Sanderson-like model only based on classical interactions between molecular orbitals domains. To conclude, this study achieved a deeper understanding of the principles of cDFT and assessed, in a wider context, its efficiency in predicting the chemical reactivity.
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Affiliation(s)
- Johanna Klein
- Sorbonne Université, CNRS, Laboratoire de Chimie Théorique CC 137, 4 Place Jussieu F., Paris CEDEX 05 75252, France
| | - Julien Pilmé
- Sorbonne Université, CNRS, Laboratoire de Chimie Théorique CC 137, 4 Place Jussieu F., Paris CEDEX 05 75252, France
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3
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Irons TJP, Huynh BC, Teale AM, De Proft F, Geerlings P. Molecular charge distributions in strong magnetic fields: a conceptual and current DFT study. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2145245] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Affiliation(s)
- Tom J. P. Irons
- School of Chemistry, University of Nottingham, Nottingham, UK
| | - Bang C. Huynh
- School of Chemistry, University of Nottingham, Nottingham, UK
| | - Andrew M. Teale
- School of Chemistry, University of Nottingham, Nottingham, UK
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel, Brussels, Belgium
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel, Brussels, Belgium
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4
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Fias S, Ayers PW, De Proft F, Geerlings P. Properties of the density functional response kernels and its implications on chemistry. J Chem Phys 2022; 157:114102. [PMID: 36137804 DOI: 10.1063/5.0094653] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An overview of mathematical properties of the non-local second order derivatives of the canonical, grand canonical, isomorphic, and grand isomorphic ensembles is given. The significance of their positive or negative semidefiniteness and the implications of these properties for atoms and molecules are discussed. Based on this property, many other interesting properties can be derived, such as the expansion in eigenfunctions, bounds on the diagonal and off-diagonal elements, and the eigenvalues of these kernels. We also prove Kato's theorem for the softness kernel and linear response and the dissociation limit of the linear responses as the sum of the linear responses of the individual fragments when dissociating a system into two non-interacting molecular fragments. Finally, strategies for the practical calculation of these kernels, their eigenfunctions, and their eigenvalues are discussed.
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Affiliation(s)
- Stijn Fias
- McMaster University, 1280 Main St. W, Hamilton, Ontario L8S 4L8, Canada
| | - Paul W Ayers
- McMaster University, 1280 Main St. W, Hamilton, Ontario L8S 4L8, Canada
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
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5
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Geerlings P. From Density Functional Theory to Conceptual Density Functional Theory and Biosystems. Pharmaceuticals (Basel) 2022; 15:ph15091112. [PMID: 36145333 PMCID: PMC9505550 DOI: 10.3390/ph15091112] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/02/2022] [Revised: 08/26/2022] [Accepted: 08/27/2022] [Indexed: 12/03/2022] Open
Abstract
The position of conceptual density functional theory (CDFT) in the history of density functional theory (DFT) is sketched followed by a chronological report on the introduction of the various DFT descriptors such as the electronegativity, hardness, softness, Fukui function, local version of softness and hardness, dual descriptor, linear response function, and softness kernel. Through a perturbational approach they can all be characterized as response functions, reflecting the intrinsic reactivity of an atom or molecule upon perturbation by a different system, including recent extensions by external fields. Derived descriptors such as the electrophilicity or generalized philicity, derived from the nature of the energy vs. N behavior, complete this picture. These descriptors can be used as such or in the context of principles such as Sanderson’s electronegativity equalization principle, Pearson’s hard and soft acids and bases principle, the maximum hardness, and more recently, the minimum electrophilicity principle. CDFT has known an ever-growing use in various subdisciplines of chemistry: from organic to inorganic chemistry, from polymer to materials chemistry, and from catalysis to nanotechnology. The increasing size of the systems under study has been coped with thanks to methodological evolutions but also through the impressive evolution in software and hardware. In this flow, biosystems entered the application portfolio in the past twenty years with studies varying (among others) from enzymatic catalysis to biological activity and/or the toxicity of organic molecules and to computational peptidology. On the basis of this evolution, one can expect that “the best is yet to come”.
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Affiliation(s)
- Paul Geerlings
- Research Group of General Chemistry (ALGC), Faculty of Science and Bio-Engineering Science, Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
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6
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Miranda-Quintana RA, Heidar-Zadeh F, Fias S, Chapman AEA, Liu S, Morell C, Gómez T, Cárdenas C, Ayers PW. Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles. Front Chem 2022; 10:929464. [PMID: 35936089 PMCID: PMC9352952 DOI: 10.3389/fchem.2022.929464] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2022] [Accepted: 06/27/2022] [Indexed: 11/13/2022] Open
Abstract
In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the “|dμ| big is good” rule or the maximum hardness principle. Expressions for the change in chemical potential (μ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign.
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Affiliation(s)
- Ramón Alain Miranda-Quintana
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, FL, United States
- *Correspondence: Ramón Alain Miranda-Quintana, ; Tatiana Gómez, Carlos Cárdenas, ; Paul W. Ayers,
| | | | - Stijn Fias
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
| | - Allison E. A. Chapman
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, NC, United states
| | - Christophe Morell
- Université de Lyon, Universit́e Claude Bernard Lyon 1, Institut des Sciences Analytiques, UMR CNRS 5280, Villeurbanne Cedex, France
| | - Tatiana Gómez
- Theoretical and Computational Chemistry Center, Institute of Applied Chemical Sciences, Faculty of Engineering, Universidad Autonoma de Chile, Santiago, Chile
- *Correspondence: Ramón Alain Miranda-Quintana, ; Tatiana Gómez, Carlos Cárdenas, ; Paul W. Ayers,
| | - Carlos Cárdenas
- Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
- Centro para el desarrollo de la Nanociencias y Nanotecnologia, CEDENNA, Santiago, Chile
- *Correspondence: Ramón Alain Miranda-Quintana, ; Tatiana Gómez, Carlos Cárdenas, ; Paul W. Ayers,
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
- *Correspondence: Ramón Alain Miranda-Quintana, ; Tatiana Gómez, Carlos Cárdenas, ; Paul W. Ayers,
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7
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Miranda-Quintana RA, Heidar-Zadeh F, Fias S, Chapman AEA, Liu S, Morell C, Gómez T, Cárdenas C, Ayers PW. Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents. Front Chem 2022; 10:906674. [PMID: 35769444 PMCID: PMC9234655 DOI: 10.3389/fchem.2022.906674] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2022] [Accepted: 04/19/2022] [Indexed: 12/13/2022] Open
Abstract
Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.
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Affiliation(s)
- Ramón Alain Miranda-Quintana
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, FL, United States
- *Correspondence: Ramón Alain Miranda-Quintana, ; Carlos Cárdenas, ; Paul W. Ayers, ; Tatiana Gómez,
| | | | - Stijn Fias
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
| | - Allison E. A. Chapman
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, NC, United States
| | - Christophe Morell
- Université de Lyon, Université Claude Bernard Lyon 1, Institut des Sciences Analytiques-UMR CNRS 5280, Villeurbanne, France
| | - Tatiana Gómez
- Theoretical and Computational Chemistry Center, Institute of Applied Chemical Sciences, Faculty of Engineering, Universidad Autonoma de Chile, Santiago, Chile
- *Correspondence: Ramón Alain Miranda-Quintana, ; Carlos Cárdenas, ; Paul W. Ayers, ; Tatiana Gómez,
| | - Carlos Cárdenas
- Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
- Centro para el desarrollo de la Nanociencias y Nanotecnologia, CEDENNA, Santiago, Chile
- *Correspondence: Ramón Alain Miranda-Quintana, ; Carlos Cárdenas, ; Paul W. Ayers, ; Tatiana Gómez,
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON, Canada
- *Correspondence: Ramón Alain Miranda-Quintana, ; Carlos Cárdenas, ; Paul W. Ayers, ; Tatiana Gómez,
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8
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Zaklika J, Hładyszowski J, Ordon P, Komorowski L. From the Electron Density Gradient to the Quantitative Reactivity Indicators: Local Softness and the Fukui Function. ACS OMEGA 2022; 7:7745-7758. [PMID: 35284764 PMCID: PMC8908489 DOI: 10.1021/acsomega.1c06540] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/19/2021] [Accepted: 01/12/2022] [Indexed: 06/14/2023]
Abstract
Important reactivity measures such as the local softness, the Fukui function, and the global hardness have been calculated directly from first principles with the use of the electron density function, beyond the finite difference approximation. Our recently derived density gradient theorem and the principle of nearsightedness of the electronic matter have been instrumental in obtaining the original, albeit approximate, result on the local softness of an atom. By integration of the local softness s(r), we obtain the global softness S and the Fukui function f(r) = s(r)/S. Local and global softness values have also been calculated analytically for the basic hydrogenic orbitals; the general relation to the atomic number S = σZ -2 has been demonstrated, with constants σ characteristic for each orbital type. Global hardness η = 1/S calculated for atoms and ions has been favorably tested against its conventional measure given by the finite difference approximation: (I - A). Calculated test results for atoms and ions in rows 1-4 of the periodic table have been presented.
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Affiliation(s)
- Jarosław Zaklika
- Department of Physical and Quantum Chemistry, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
| | - Jerzy Hładyszowski
- Department of Physical Chemistry and Biophysics, Wrocław Medical University, ul. Borowska 211 A, 50-556 Wrocław, Poland
| | - Piotr Ordon
- Department of Physics and Biophysics, Wrocław University of Environmental and Life Sciences, ul. Norwida 25, 50-373 Wrocław, Poland
| | - Ludwik Komorowski
- Department of Physical and Quantum Chemistry, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
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9
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Francotte R, Irons TJP, Teale AM, de Proft F, Geerlings P. Extending conceptual DFT to include external variables: the influence of magnetic fields. Chem Sci 2022; 13:5311-5324. [PMID: 35655570 PMCID: PMC9093152 DOI: 10.1039/d1sc07263c] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2021] [Accepted: 03/24/2022] [Indexed: 11/21/2022] Open
Abstract
An extension of conceptual DFT to include the influence of an external magnetic field is proposed in the context of a program set up to cope with the ever increasing variability of reaction conditions and concomitant reactivity.
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Affiliation(s)
- Robin Francotte
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Tom J. P. Irons
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
| | - Andrew M. Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Frank de Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
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10
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Carmona-Espíndola J, Gázquez JL. Charge transfer excitations and constrained density functional theory. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02860-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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11
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Well-normalized charge-transfer models: a more general derivation of the hard/soft-acid/base principle. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02840-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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12
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Islas-Vargas C, Guevara-García A, Galván M. Electronic structure behavior of PbO 2, IrO 2, and SnO 2 metal oxide surfaces (110) with dissociatively adsorbed water molecules as a function of the chemical potential. J Chem Phys 2021; 154:074704. [PMID: 33607881 DOI: 10.1063/5.0035208] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A detailed analysis of the electronic structure of three different electrochemical interfaces as a function of the chemical potential (μ) is performed using the grand canonical density functional theory in the joint density functional theory formulation. Changes in the average number of electrons and the density of states are also described. The evaluation of the global softness, which measures the tendency of the system to gain or lose electrons, is straightforward under this formalism. The observed behavior of these quantities depends on the electronic nature of the electrochemical interfaces.
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Affiliation(s)
- Claudia Islas-Vargas
- Universidad Autónoma Metropolitana Iztapalapa, Departamento de Química, CP 09340 México, Mexico
| | - Alfredo Guevara-García
- CONACYT-Universidad Autónoma Metropolitana Iztapalapa, Departamento de Química, CP 09340 México, Mexico
| | - Marcelo Galván
- Universidad Autónoma Metropolitana Iztapalapa, Departamento de Química, CP 09340 México, Mexico
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13
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Clarys T, Stuyver T, De Proft F, Geerlings P. Extending conceptual DFT to include additional variables: oriented external electric field. Phys Chem Chem Phys 2021; 23:990-1005. [PMID: 33404573 DOI: 10.1039/d0cp05277a] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The extension of the E = E[N, v] functional for exploring chemical reactivity in a conceptual DFT context to include external electric fields is discussed. Concentrating on the case of a homogeneous field the corresponding response functions are identified and integrated, together with the conventional response functions such as permanent dipole moment and polarizability, in an extended response function tree associated with the E = E[N, v, ε] functional. In a case study on the dihalogens F2, Cl2, Br2, I2 the sensitivity of condensed atomic charges (∂q/∂ε) is linked to the polarizability of the halogen atoms. The non-integrated (∂ρ(r)/∂ε) response function, directly related to the field induced density change, is at the basis of these features. It reveals symmetry breaking for a perpendicular field, not detectable in its atom condensed counterpart, and accounts for the induced dipole moment directly related to the molecular polarizability. The much higher sensitivity of the electronic chemical potential/electronegativity as compared to the chemical hardness is highlighted. The response of the condensed Fukui functions to a parallel electric field increases when going down in the periodic table and is interpreted in terms of the extension of the outer contours in the non-condensed Fukui function. In the case of a perpendicular field the (∂f(r)/∂ε) response function hints at stereoselectivity with a preferential side of attack which is not retrieved in its condensed form. In an application the nucleophilic attack on the carbonyl group in H2CO is discussed. Similar to the dihalogens, stereoselectivity is displayed in the Fukui function for nucleophilic attack (f+) in the case of a perpendicular electric field, and opposite to the one that would arise based on the induced density. Disentangling the expression for the evolution of the Fukui function in the presence of an electric field reveals that this difference can be traced back to local differences in the polarization or induced density between the anionic and the neutral system. This difference may be exploited, e.g. for an appropriately substituted H2CO, to generate enantioselectivity.
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Affiliation(s)
- Tom Clarys
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | - Thijs Stuyver
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium. and Institute of Chemistry, The Hebrew University, Jerusalem, 91904, Israel
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium.
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14
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Miranda‐Quintana RA, Ayers PW, Heidar‐Zadeh F. Reactivity and Charge Transfer Beyond the Parabolic Model: the “|Δμ| Big is Good” Principle. ChemistrySelect 2021. [DOI: 10.1002/slct.202004055] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Paul W. Ayers
- Department of Chemistry & Chemical Biology McMaster University Hamilton Ontario Canada
| | - Farnaz Heidar‐Zadeh
- Department of Chemistry Queen's University 90 Bader Lane Kingston Ontario Canada
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15
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Franco-Pérez M, Gázquez JL, Ayers PW, Vela A. Temperature-Dependent Approach to Electronic Charge Transfer. J Phys Chem A 2020; 124:5465-5473. [PMID: 32501006 DOI: 10.1021/acs.jpca.0c02496] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A charge transfer model is developed within the framework of the grand canonical ensemble through the analysis of the behavior of the fractional charge as a function of the chemical potential of the bath when the temperature and the external chemical potential are kept fixed. Departing from the fact that, before the interaction between two species, each one has a zero fractional charge, one can identify two situations after the interaction occurs where the fractional charge of at least one of the species is different from zero, indicating that there has been charge transference. One of them corresponds to the case when one of the species is immersed in a bath conformed by the other one, while the other is related to the case in which both species are present in equal amounts (stoichiometric proportion). Correlations between the fractional charges and average energies, thus obtained with experimental equilibrium constants, kinetic rate constants, hydration constants, and bond enthalpies, indicate that, although at the experimental temperatures, they are very small quantities, they have chemically meaningful information. Additionally, in the stoichiometric case, one also finds a rather good correlation between the equalized chemical potential and the one obtained from experimental information for a test set of diatomic and triatomic molecules.
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Affiliation(s)
- Marco Franco-Pérez
- Facultad de Química, Universidad Nacional Autónoma de México, Cd. Universitaria, Ciudad de México 04510, México
| | - José L Gázquez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México 09340, México
| | - Paul W Ayers
- Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, México
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16
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Study of organic reactions using chemical reactivity descriptors derived through a temperature-dependent approach. Theor Chem Acc 2020. [DOI: 10.1007/s00214-020-2557-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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17
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Geerlings P, Chamorro E, Chattaraj PK, De Proft F, Gázquez JL, Liu S, Morell C, Toro-Labbé A, Vela A, Ayers P. Conceptual density functional theory: status, prospects, issues. Theor Chem Acc 2020. [DOI: 10.1007/s00214-020-2546-7] [Citation(s) in RCA: 77] [Impact Index Per Article: 19.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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18
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Ochoa-Calle A, Guevara-García A, Vazquez-Arenas J, González I, Galván M. Establishing the Relationship between Quantum Capacitance and Softness of N-Doped Graphene/Electrolyte Interfaces within the Density Functional Theory Grand Canonical Kohn-Sham Formalism. J Phys Chem A 2020; 124:573-581. [PMID: 31876420 DOI: 10.1021/acs.jpca.9b10885] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The joint density functional theory (JDFT) is applied in the context of the grand canonical Kohn-Sham theory to calculate the global and local softness of pristine and N-substituted graphene structures. A comparison is established between the different theoretical approaches to evaluate total capacitance, revealing that the JDFT approach presents the closest result of this property with experimental data. A model of series capacitors is used to determine the quantum and nonquantum contributions of total capacitance, which enables us to determine the limitations of the rigid band approximation for the studied systems. It is found that global chemical softness is proportional to the total capacitance measured in the experiments, when the geometry relaxation is neglected. In this context, it is possible to obtain quantum and total capacitance (and consequently softness) from an average number of electrons vs applied potential plots and the model of series capacitors. Likewise, the relation of capacitance and softness gives rise to a new definition of local capacitance within the JDFT formalism. The evaluation of global and local softness paves the way to analyze electrochemical surface reactivity as a function of applied potential for a solid-electrolyte interface.
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Affiliation(s)
- Alvaro Ochoa-Calle
- Departamento de Química , Universidad Autónoma Metropolitana-Iztapalapa , Apartado Postal, 55-534, 09340 Iztapalapa, CDMX , México
| | - Alfredo Guevara-García
- Departamento de Química , CONACYT-Universidad Autónoma Metropolitana-Iztapalapa , Apartado Postal, 55-534, 09340 Iztapalapa, CDMX , México
| | - Jorge Vazquez-Arenas
- Departamento de Química , CONACYT-Universidad Autónoma Metropolitana-Iztapalapa , Apartado Postal, 55-534, 09340 Iztapalapa, CDMX , México
| | - Ignacio González
- Departamento de Química , Universidad Autónoma Metropolitana-Iztapalapa , Apartado Postal, 55-534, 09340 Iztapalapa, CDMX , México
| | - Marcelo Galván
- Departamento de Química , Universidad Autónoma Metropolitana-Iztapalapa , Apartado Postal, 55-534, 09340 Iztapalapa, CDMX , México
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19
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Franco-Pérez M. An electronic temperature definition for the reactive electronic species: Conciliating practical approaches in conceptual chemical reactivity theory with a rigorous ensemble formulation. J Chem Phys 2019; 151:074105. [PMID: 31438714 DOI: 10.1063/1.5096561] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By working under the framework of the Helmholtz potential as a functional of the equilibrium density matrix, in this contribution, we provide theoretical evidence about a particular thermodynamic situation, where electronic species display their highest susceptibility to exchange electrons to or from surroundings. This situation is denominated as the electronic temperature condition. Neutral chemical species display their lowest possible hardness value at the electronic temperature condition, and remarkably, under this circumstance, the exchange of any amount of electronic charge will necessarily be translated into a net increase in the corresponding chemical hardness. Chemical response functions defined as partial derivatives of the Helmholtz potential with respect to the (average) number of electrons and evaluated at the electronic temperature condition provide comparable results than those obtained from the coarse quadratic approximation to the exact dependence of the electronic energy vs the number of electrons, including composite quantities as the electrophilicity index. In this context, we show that the exact Helmholtz potential dependence with respect to the number of electrons can accurately be approximated by "temperature dependent" polynomial fits (up to fourth order), evaluated at the electronic temperature condition.
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Affiliation(s)
- Marco Franco-Pérez
- Facultad de Química, Universidad Nacional Autónoma de México, Cd. Universitaria, 04510 Ciudad de México, Mexico
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20
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Miranda-Quintana RA, Franco-Pérez M, Gázquez JL, Ayers PW, Vela A. Chemical hardness: Temperature dependent definitions and reactivity principles. J Chem Phys 2018; 149:124110. [DOI: 10.1063/1.5040889] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [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, Ave. San Rafael Atlixco 186, Ciudad de México 09340, Mexico
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Ciudad Universitaria, CP 04510 México D.F., Mexico
| | - José L. Gázquez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Ave. San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
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21
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Abstract
In this work some possibilities for deriving a local electrophilicity are studied. First, we consider the original definition proposed by Chattaraj, Maiti, and Sarkar (J Phys Chem A 107:4973, 2003), in which the local electrophilicity is given by the product of the global electrophilicity, and the Fukui function for charge acceptance is derived by two different approaches, making use of the chain rule for functional derivatives. We also modify the proposals based on the electron density so as to have a definition with the same units of the original definition, which also introduces a dependence in the Fukui function for charge donation. Additionally, we also explore other possibilities using the tools of information theory and the temperature dependent reactivity indices of the density functional theory of chemical reactivity. The poor results obtained from the last two approaches lead us to conjecture that this is due to the fact that the global electrophilicity is not a derivative, like most of the other reactivity indices. The conclusion is that Chattaraj's suggestion seems to be the simplest, but at the same time a very reliable approach to this important property.
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22
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Franco-Pérez M, Gázquez JL, Ayers PW, Vela A. Thermodynamic Justification for the Parabolic Model for Reactivity Indicators with Respect to Electron Number and a Rigorous Definition for the Electrophilicity: The Essential Role Played by the Electronic Entropy. J Chem Theory Comput 2018; 14:597-606. [DOI: 10.1021/acs.jctc.7b00940] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Marco Franco-Pérez
- Departamento
de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México, 09340, México
- 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, México
| | - Paul W. Ayers
- Department
of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Alberto Vela
- Departamento
de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, Ciudad de México, 07360, México
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23
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Miranda-Quintana RA, Kim TD, Cárdenas C, Ayers PW. The HSAB principle from a finite-temperature grand-canonical perspective. Theor Chem Acc 2017. [DOI: 10.1007/s00214-017-2167-y] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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24
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Miranda-Quintana RA, Chattaraj PK, Ayers PW. Finite temperature grand canonical ensemble study of the minimum electrophilicity principle. J Chem Phys 2017; 147:124103. [DOI: 10.1063/1.4996443] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
| | - Pratim K. Chattaraj
- Department of Chemistry and Center for Theoretical Studies, Indian Institute of Technology, Kharagpur 721302, India
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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25
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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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26
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Franco-Pérez M, Gázquez JL, Ayers PW, Vela A. Thermodynamic hardness and the maximum hardness principle. J Chem Phys 2017; 147:074113. [DOI: 10.1063/1.4998701] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [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, Ciudad de México 09340, Mexico
- 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
| | - Paul W. Ayers
- Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - 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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27
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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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28
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29
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Affiliation(s)
- Ramón Alain Miranda-Quintana
- Department of Chemical Physics, Faculty of Chemistry, University of Havana, Havana, Cuba and Department of Chemistry & Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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30
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Flores-Gallegos N. A logarithmic informational temperature scale as a criterion to classify molecular systems. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2017. [DOI: 10.1142/s021963361750016x] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this work, we applied a definition of informational energy and informational temperature using 1865 molecules and showed that such definitions can classify molecules with similar chemical properties such as hardness, softness and chemical potential.
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Affiliation(s)
- N. Flores-Gallegos
- Benemérita Universidad de Guadalajara, Centro Universitario de los Valles, Carretera, Guadalajara - Ameca Km. 45.5, C.P. 46600, Ameca, Jalisco, México
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31
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Franco-Pérez M, Heidar-Zadeh F, Ayers PW, Gázquez JL, Vela A. Going beyond the three-state ensemble model: the electronic chemical potential and Fukui function for the general case. Phys Chem Chem Phys 2017; 19:11588-11602. [DOI: 10.1039/c7cp00224f] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The analytical working equations for the chemical potential and the Fukui function for the case of any number of ground and excited states is presented.
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Affiliation(s)
- Marco Franco-Pérez
- Department of Chemistry
- McMaster University
- Hamilton
- Canada
- Departamento de Química
| | - Farnaz Heidar-Zadeh
- Department of Chemistry
- McMaster University
- Hamilton
- Canada
- Department of Inorganic and Physical Chemistry
| | - Paul W. Ayers
- Department of Chemistry
- McMaster University
- Hamilton
- Canada
| | - José L. Gázquez
- Departamento de Química
- División de Ciencias Básicas e Ingeniería
- Universidad Autónoma
- Metropolitana-Iztapalapa
- México
| | - Alberto Vela
- Centro de Investigación y de Estudios Avanzados
- Mexico
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32
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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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33
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Heidar-Zadeh F, Miranda-Quintana RA, Verstraelen T, Bultinck P, Ayers PW. When is the Fukui Function Not Normalized? The Danger of Inconsistent Energy Interpolation Models in Density Functional Theory. J Chem Theory Comput 2016; 12:5777-5787. [DOI: 10.1021/acs.jctc.6b00494] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Farnaz Heidar-Zadeh
- Department of Chemistry & Chemical Biology, McMaster University, Hamilton, L8S 4M1 Ontario, Canada
- Department
of Inorganic and Physical Chemistry, Ghent University, Krijgslaan
281 (S3), 9000 Gent, Belgium
- Center
for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Ramón Alain Miranda-Quintana
- Department of Chemistry & Chemical Biology, McMaster University, Hamilton, L8S 4M1 Ontario, Canada
- Laboratory
of Computational and Theoretical Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba
| | - Toon Verstraelen
- Center
for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Patrick Bultinck
- Department
of Inorganic and Physical Chemistry, Ghent University, Krijgslaan
281 (S3), 9000 Gent, Belgium
| | - Paul W. Ayers
- Department of Chemistry & Chemical Biology, McMaster University, Hamilton, L8S 4M1 Ontario, Canada
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34
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Optimized effective potentials at a glance: the effective exchange potential of Becke–Johnson applied to molecules. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-2004-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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35
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Piedras A, Gómez B, Carmona-Espíndola J, Arroyo R, Gázquez JL. Intramolecular charge transfer model in fluorescence processes. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1997-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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36
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Miranda-Quintana RA, Ayers PW. Systematic treatment of spin-reactivity indicators in conceptual density functional theory. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1995-5] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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37
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38
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Franco-Pérez M, Ayers PW, Gázquez JL. Average electronic energy is the central quantity in conceptual chemical reactivity theory. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1961-2] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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39
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Miranda-Quintana RA, Ayers PW. Interpolation of property-values between electron numbers is inconsistent with ensemble averaging. J Chem Phys 2016; 144:244112. [DOI: 10.1063/1.4953557] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ramón Alain Miranda-Quintana
- Laboratory of Computational and Theoretical Chemistry, Faculty of Chemistry, University of Havana, Havana, Cuba
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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40
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Miranda-Quintana RA, Martínez González M, Ayers PW. Electronegativity and redox reactions. Phys Chem Chem Phys 2016; 18:22235-43. [DOI: 10.1039/c6cp03213c] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Using the maximum hardness principle, we show that the oxidation potential of a molecule increases as its electronegativity increases and also increases as its electronegativity in its oxidized state increases.
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Affiliation(s)
| | - Marco Martínez González
- Laboratory of Computational and Theoretical Chemistry
- Faculty of Chemistry
- University of Havana
- Havana
- Cuba
| | - Paul W. Ayers
- Department of Chemistry & Chemical Biology
- McMaster University
- Hamilton
- Canada
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41
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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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