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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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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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3
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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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Cerón ML, Gomez T, Calatayud M, Cárdenas C. Computing the Fukui Function in Solid-State Chemistry: Application to Alkaline Earth Oxides Bulk and Surfaces. J Phys Chem A 2020; 124:2826-2833. [DOI: 10.1021/acs.jpca.0c00950] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. L. Cerón
- Facultad de Ingenierı́a, Universidad Finis Terrae, Av. Pedro de Valdivia 1509, Providencia, Santiago, Chile
| | - T. Gomez
- Theoretical and Computational Chemistry Center, Institute of Applied Chemical Sciences, Faculty of Engineering, Universidad Autonoma de Chile, El Llano Subercaseaux 2801, Santiago, Chile
| | - M. Calatayud
- Sorbonne Université, CNRS, Laboratoire de Chimie Théorique, LCT, F. 75005 Paris, France
| | - C. Cárdenas
- Departamento de Fı́sica, Facultad de Ciencias, Universidad de Chile, Casilla 635, Santiago, Chile
- Centro para el Desarrollo de la Nanociencia y la Nanotecnologı́a (CEDENNA), Avda. Ecuador 3493, Santiago 9170124, Chile
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Sánchez-Márquez J. New advances in conceptual-DFT: an alternative way to calculate the Fukui function and dual descriptor. J Mol Model 2019; 25:123. [PMID: 31020412 DOI: 10.1007/s00894-019-4000-0] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2018] [Accepted: 03/21/2019] [Indexed: 10/26/2022]
Abstract
An alternative way of calculating the Fukui function and the partial derivative of second order of the electronic density with respect to the number of electrons N is presented, the new formulas agree with the usual ones but only in cases without degeneracy. The new operative formulas are more general than the previous ones and are the right ones for those problematic cases where one or both of the frontier molecular orbitals are degenerate. Finally, we present a new way of applying the finite difference approximation that leads to more realistic results than the usual formulas. Graphical abstract A new way of calculating the Fukui function is presented that results in a new operative formula of the function. It has also been obtained the partial derivative of second order of the electronic density with respect to the number of electrons N, and it agree with the usual formula of the dual descriptor function but only in cases without degeneration.
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Affiliation(s)
- Jesús Sánchez-Márquez
- Departamento de Química-Física, Facultad de Ciencias, Campus Universitario Río San Pedro, Universidad de Cádiz, 11510, Puerto Real, Cádiz, Spain.
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Roos G, Miranda-Quintana RA, Martínez González M. How Biochemical Environments Fine-Tune a Redox Process: From Theoretical Models to Practical Applications. J Phys Chem B 2018; 122:8157-8165. [PMID: 30040409 DOI: 10.1021/acs.jpcb.8b04736] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
In this study, we give a new physical insight into how enzymatic environments influence a redox process. This is particularly important in a biochemical context, in which oxidoreductase enzymes and low-molecular-weight cofactors create a microenvironment, fine-tuning their specific redox potential. We present a new theoretical model, quantitatively backed up by quantum chemically calculated data obtained for key biological sulfur-based model reactions involved in preserving the cellular redox homeostasis during oxidative stress. We show that environmental effects can be quantitatively predicted from the thermodynamic cycle linking ΔΔ G(OX/RED)ref-ligand values to the differential interaction energy ΔΔ Gint of the reduced and oxidized species with the environment. Our obtained data can be linked to hydrogen-bond patterns found in protein active sites. The thermodynamic model is further understood in the framework of molecular orbital theory. The key insight of this work is that the intrinsic properties of neither a redox couple nor the interacting environment (e.g., ligand) are enough by themselves to uniquely predict reduction potentials. Instead, system-environment interactions need to be considered. This study is of general interest as redox processes are pivotal to empower, protect, or damage organisms. Our presented thermodynamic model allows a pragmatically evaluation on the expected influence of a particular environment on a redox process, necessary to fully understand how redox processes take place in living organisms.
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Affiliation(s)
- Goedele Roos
- CNRS UMR 8576, Unité de Glycobiologie Structurale et Fonctionnelle (UGSF) , Université de Lille , 1 Sciences et Technologies 50 Avenue de Halley BP 70478, 59658 Villeneuve d'Ascq Cedex, France
| | | | - Marco Martínez González
- Laboratory of Computational and Theoretical Chemistry, Faculty of Chemistry , University of Havana , 10400 Havana , Cuba.,Departamento de Química, y Centro de Química , Universidade de Coimbra , 3004-535 Coimbra , Portugal
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Fias S, Heidar-Zadeh F, Anderson JSM, Ayers PW, Parr RG. A reference-free stockholder partitioning method based on the force on electrons. J Comput Chem 2017; 39:1044-1050. [DOI: 10.1002/jcc.25114] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2017] [Revised: 09/14/2017] [Accepted: 10/06/2017] [Indexed: 11/08/2022]
Affiliation(s)
- Stijn Fias
- Department of Chemistry & Chemical Biology; McMaster University; Hamilton Ontario Canada L8S 4M1
| | - Farnaz Heidar-Zadeh
- Department of Chemistry & Chemical Biology; McMaster University; Hamilton Ontario Canada L8S 4M1
- Center for Molecular Modeling; Ghent University, Technologiepark 903; 9052 Zwijnaarde Belgium
- 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 Ontario Canada L8S 4M1
| | - Robert G. Parr
- Department of Chemistry; University of North Carolina; Chapel Hill NC USA 27599
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Heidar-Zadeh F, Ayers PW, Verstraelen T, Vinogradov I, Vöhringer-Martinez E, Bultinck P. Information-Theoretic Approaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes. J Phys Chem A 2017; 122:4219-4245. [DOI: 10.1021/acs.jpca.7b08966] [Citation(s) in RCA: 68] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Farnaz Heidar-Zadeh
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
- Department of Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Toon Verstraelen
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Ivan Vinogradov
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Esteban Vöhringer-Martinez
- Departamento de Físico-Química, Facultad de Ciencias Químicas, Universidad de Concepción, Concepción, Chile
| | - Patrick Bultinck
- Department of Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
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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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10
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Analysis of the topology of the electron density and the reactivity descriptors of biomolecules with insecticide activity. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1969-7] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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11
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Heidar-Zadeh F, Ayers PW, Bultinck P. Deriving the Hirshfeld partitioning using distance metrics. J Chem Phys 2014; 141:094103. [DOI: 10.1063/1.4894228] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Farnaz Heidar-Zadeh
- 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
| | - Patrick Bultinck
- Department of Physical and Inorganic Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
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