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Cárdenas C, Ayers PW, Chakraborty D, Gómez T, Echeverri A, Munoz F, Fuentealba P. On the link between the reaction force constant and conceptual DFT. J Mol Model 2024; 30:332. [PMID: 39276242 DOI: 10.1007/s00894-024-06137-2] [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: 05/24/2024] [Accepted: 09/03/2024] [Indexed: 09/16/2024]
Abstract
CONTEXT The reaction force constant ( κ ), introduced by Professor Alejandro Toro-Labbé, plays a pivotal role in characterizing the reaction pathway by assessing the curvature of the potential energy profile along the intrinsic reaction coordinate. This study establishes a novel link between κ and the reactivity descriptors of conceptual density functional theory (c-DFT). Specifically, we derive expressions that relate the reaction force constant to nuclear softness and variations in chemical potential. Our findings indicate that regions of the reaction pathway where κ is negative match with significant electronic structure rearrangements, while positive κ regions match mostly with geometric rearrangements. This correlation between κ and c-DFT reactivity descriptors enhances our understanding of the underlying forces driving chemical reactions and offers new perspectives for analyzing reaction mechanisms. METHODS The internal reaction path for the proton transfer in SNOH, chemical potential, and nuclear softness were computed using DFT with B3LYP exchange-correlation functional and 6-311++G(d,2p) basis set.
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Affiliation(s)
- Carlos Cárdenas
- Departmento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile.
- Center for the Development of Nanoscience and Nanotechnology (CEDENNA), Santiago, Chile.
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, L8S 4M1, Canada.
| | - Debajit Chakraborty
- Department of Physics, Wake Forest University, Winston-Salem, NC, 27109, USA
| | - Tatiana Gómez
- Theoretical and Computational Chemistry Center, Institute of Applied Chemical Sciences, Faculty of Engineering, Universidad Autonoma de Chile, Avenida Pedro de Valdivia 425, Santiago, Chile
| | - Andrea Echeverri
- Departmento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile
| | - Francisco Munoz
- Departmento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile
- Center for the Development of Nanoscience and Nanotechnology (CEDENNA), Santiago, Chile
| | - Patricio Fuentealba
- Departmento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Casilla 653, Santiago, Chile
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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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Abstract
The chemical space contains all possible compounds that can be imagined. Its size easily equals the number of fundamental particles in the observable universe. Rational design of compounds aims to find those sectors of the chemical space where compounds optimize a set of desired properties. Then, rational design demands tools to efficiently navigate the chemical space. Ab initio alchemical derivatives offer the possibility to navigate, without empiricism, the energy landscape through alchemical transformations. An alchemical transformation is any process, physical or fictitious, that connects to points in the chemical space. In this work, those transformations are constructed as a perturbative expansion of the energy with respect to perturbations in the stoichiometry. The response functions of that expansion are what is called alchemical derivatives. In this work we assess how effective alchemical derivatives are in predicting energy changes associated to changes in the composition. We do this by including in the expansion, for the first time, electrostatic, polarization and electron-transfer effects. The system we chose is one that challenges alchemical derivatives because none of these effects dominates its behavior. The transmutations studied here correspond to substitutional doping of Al13 with up to four atoms of Si, Al13-nSin. Two types of transformations are considered, those in which the number of electrons remains constant and those in which the number of electrons also changes. It is found that contrary to what has been reported before, polarization cannot be neglected. If polarization is not included, alchemical derivatives fail to predict the change of energy and the relative energy between isomers. For isoelectronic substitution of four or more atoms, the perturbative approach collapses because the strength of the perturbation becomes too strong to guarantee convergence of the series. It is shown, however, that if only one atom is mutated at a time, alchemical derivatives rank pretty well the isomers of Al13-nSin according to their energy. In the case of non-isoelectronic transformations, it is observed that the series rapidly diverges with increasing number of electrons. In this situation, it becomes more important to keep the degree of transmutation of the parent system small.
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Affiliation(s)
- Macarena Muñoz
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, 653-Santiago, Chile.
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Alcoba DR, Lain L, Torre A, Oña OB, Chamorro E. Fukui and dual-descriptor matrices within the framework of spin-polarized density functional theory. Phys Chem Chem Phys 2013; 15:9594-604. [DOI: 10.1039/c3cp50736j] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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Cárdenas C, Ayers PW, Cedillo A. Reactivity indicators for degenerate states in the density-functional theoretic chemical reactivity theory. J Chem Phys 2011; 134:174103. [PMID: 21548669 DOI: 10.1063/1.3585610] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Carlos Cárdenas
- Departamento de Fisica, Facultad de Ciencias, Universidad de Chile, Santiago, Chile
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Cuevas-Saavedra R, Rabi N, Ayers PW. The unconstrained local hardness: an intriguing quantity, beset by problems. Phys Chem Chem Phys 2011; 13:19594-600. [DOI: 10.1039/c1cp21646e] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Affiliation(s)
- Rogelio Cuevas-Saavedra
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada L8S 4M1
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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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Chamorro E, Pérez P, Duque M, De Proft F, Geerlings P. Dual descriptors within the framework of spin-polarized density functional theory. J Chem Phys 2008; 129:064117. [DOI: 10.1063/1.2965594] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.7] [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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Guerra D, Andrés J, Chamorro E, Pérez P. Understanding the chemical reactivity of phenylhalocarbene systems: an analysis based on the spin-polarized density functional theory. Theor Chem Acc 2007. [DOI: 10.1007/s00214-007-0263-0] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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