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Acke G, Van Hende D, De Vriendt X, Bultinck P. Extending Conceptual Density Functional Theory toward First-Order Reduced Density Matrices: An Open Subsystems Viewpoint on the Fukui Matrix. J Chem Theory Comput 2023; 19:5418-5426. [PMID: 37531218 DOI: 10.1021/acs.jctc.3c00080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/04/2023]
Abstract
As a matrix extension of the Fukui function, a reactivity descriptor grounded within Conceptual Density Functional Theory, the Fukui matrix extends Frontier Molecular Orbital Theory to correlated regimes with its eigendecomposition in Fukui occupations and Fukui naturals. Despite successful applications, the questions remain as to whether replacing a quantity derived from a purely density-based framework by its matrix extension is theoretically well-founded and what chemical information is contained in the corresponding eigendecomposition. In this study, we show that the matrix extension of the Fukui function is only well-defined if one also generalizes the external potential to become nonlocal, leading to the introduction of Conceptual First-Order Reduced Density Matrix Functional Theory. By interpreting the Anderson impurity model from an interacting open subsystem perspective, we show how Fukui occupations and Fukui naturals reflect the influence of an increasing (static) correlation and which characteristic patterns we should expect within a molecular context. This study represents a step in generalizing Conceptual Density Functional Theory beyond its density-based perspective.
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Affiliation(s)
- Guillaume Acke
- Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium
| | - Daria Van Hende
- Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium
| | - Xeno De Vriendt
- Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium
| | - Patrick Bultinck
- Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium
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Senet P. Variational Principle for Eigenmodes of Reactivity in Conceptual Density Functional Theory. ACS OMEGA 2020; 5:25349-25357. [PMID: 33043214 PMCID: PMC7542870 DOI: 10.1021/acsomega.0c03684] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/31/2020] [Accepted: 09/08/2020] [Indexed: 06/11/2023]
Abstract
In conceptual density functional theory, reactivity indexes as the Fukui function, the global hardness/softness, and hardness/softness kernels are fundamental linear responses extensively studied to predict the nucleophilic and electrophilic propensities of atoms in molecules. We demonstrate that the hardness/softness kernels of an isolated system can be expanded in eigenmodes, solutions of a variational principle. These modes are divided into two groups: the polarization modes and the charging modes. The eigenvectors of the polarization modes are orthogonal to the Fukui function and can be interpreted as densities induced at a constant chemical potential. The charging modes of an isolated system are associated with virtual charge transfers weighted by the Fukui function and obey an exact nontrivial sum rule. The exact relation between these charging eigenmodes and those of the polarizability kernel is established. The physical interpretation of the modes is discussed. Applications of the present findings to the Thomas-Fermi and von Weizacker kinetic energy functionals are presented. For a confined free quantum gas, described by the von Weizacker kinetic energy functional, we succeed to derive an approximate analytical solution for the Fukui function and for hardness/softness and polarizability kernels. Finally, we indicate how numerical calculations of the hardness kernel of a molecule could be performed from the Kohn-Sham orbitals.
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Oña OB, De Clercq O, Alcoba DR, Torre A, Lain L, Van Neck D, Bultinck P. Atom and Bond Fukui Functions and Matrices: A Hirshfeld-I Atoms-in-Molecule Approach. Chemphyschem 2016; 17:2881-9. [PMID: 27381271 DOI: 10.1002/cphc.201600433] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2016] [Indexed: 11/09/2022]
Abstract
The Fukui function is often used in its atom-condensed form by isolating it from the molecular Fukui function using a chosen weight function for the atom in the molecule. Recently, Fukui functions and matrices for both atoms and bonds separately were introduced for semiempirical and ab initio levels of theory using Hückel and Mulliken atoms-in-molecule models. In this work, a double partitioning method of the Fukui matrix is proposed within the Hirshfeld-I atoms-in-molecule framework. Diagonalizing the resulting atomic and bond matrices gives eigenvalues and eigenvectors (Fukui orbitals) describing the reactivity of atoms and bonds. The Fukui function is the diagonal element of the Fukui matrix and may be resolved in atom and bond contributions. The extra information contained in the atom and bond resolution of the Fukui matrices and functions is highlighted. The effect of the choice of weight function arising from the Hirshfeld-I approach to obtain atom- and bond-condensed Fukui functions is studied. A comparison of the results with those generated by using the Mulliken atoms-in-molecule approach shows low correlation between the two partitioning schemes.
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Affiliation(s)
- Ofelia B Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de la Plata, CCT La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (s/n), Sucursal 4, CC 16, 1900, La Plata, Argentina
| | - Olivier De Clercq
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000, Gent, Belgium
| | - Diego R Alcoba
- Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires (Argentina), Instituto de Física de Buenos Aires, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, 1428 Buenos, Aires, Argentina
| | - Alicia Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080, Bilbao, Spain
| | - Luis Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080, Bilbao, Spain
| | - Dimitri Van Neck
- Center for Molecular Modeling, Ghent University, Technologiepark 903, B-9052, Zwijnaarde, Belgium
| | - Patrick Bultinck
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000, Gent, Belgium.
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Morales-Bayuelo A, Caballero J. New insights into steric and electronic effects in a series of phosphine ligands from the perspective of local quantum similarity using the Fukui function. J Mol Model 2015; 21:45. [DOI: 10.1007/s00894-015-2600-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2014] [Accepted: 01/26/2015] [Indexed: 11/24/2022]
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In pursuit of negative Fukui functions: molecules with very small band gaps. J Mol Model 2014; 20:2162. [DOI: 10.1007/s00894-014-2162-3] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2014] [Accepted: 01/27/2014] [Indexed: 10/25/2022]
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Cuevas-Saavedra R, Chakraborty D, Rabi S, Cárdenas C, Ayers PW. Symmetric Nonlocal Weighted Density Approximations from the Exchange-Correlation Hole of the Uniform Electron Gas. J Chem Theory Comput 2012; 8:4081-93. [DOI: 10.1021/ct300325t] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Rogelio Cuevas-Saavedra
- Department
of Chemistry and
Chemical Biology, McMaster University,
Hamilton, Ontario, Canada
| | - Debajit Chakraborty
- Department
of Chemistry and
Chemical Biology, McMaster University,
Hamilton, Ontario, Canada
| | - Sandra Rabi
- Department
of Chemistry and
Chemical Biology, McMaster University,
Hamilton, Ontario, Canada
| | - Carlos Cárdenas
- Departamento de Física,
Facultad de Ciencias, Universidad de Chile, 653-Santiago, Chile
| | - Paul W. Ayers
- Department
of Chemistry and
Chemical Biology, McMaster University,
Hamilton, Ontario, Canada
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Bultinck P, Van Neck D, Acke G, Ayers PW. Influence of electron correlation and degeneracy on the Fukui matrix and extension of frontier molecular orbital theory to correlated quantum chemical methods. Phys Chem Chem Phys 2012; 14:2408-16. [PMID: 22249745 DOI: 10.1039/c2cp22543c] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
The Fukui function is considered as the diagonal element of the Fukui matrix in position space, where the Fukui matrix is the derivative of the one particle density matrix (1DM) with respect to the number of electrons. Diagonalization of the Fukui matrix, expressed in an orthogonal orbital basis, explains why regions in space with negative Fukui functions exist. Using a test set of molecules, electron correlation is found to have a remarkable effect on the eigenvalues of the Fukui matrix. The Fukui matrices at the independent electron model level are mathematically proven to always have an eigenvalue equal to exactly unity while the rest of the eigenvalues possibly differ from zero but sum to zero. The loss of idempotency of the 1DM at correlated levels of theory causes the loss of these properties. The influence of electron correlation is examined in detail and the frontier molecular orbital concept is extended to correlated levels of theory by defining it as the eigenvector of the Fukui matrix with the largest eigenvalue. The effect of degeneracy on the Fukui matrix is examined in detail, revealing that this is another way by which the unity eigenvalue and perfect pairing of eigenvalues can disappear.
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Affiliation(s)
- Patrick Bultinck
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium.
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Bultinck P, Clarisse D, Ayers PW, Carbo-Dorca R. The Fukui matrix: a simple approach to the analysis of the Fukui function and its positive character. Phys Chem Chem Phys 2011; 13:6110-5. [DOI: 10.1039/c0cp02268c] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
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Kuklin RN, Emets VV. Partial charge transfer during the specific adsorption of halide anions on a metal electrode. RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B 2009. [DOI: 10.1134/s1990793109050182] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Krishtal A, Senet P, Van Alsenoy C. Local softness, softness dipole, and polarizabilities of functional groups: Application to the side chains of the 20 amino acids. J Chem Phys 2009; 131:044312. [DOI: 10.1063/1.3185349] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Melin J, Ayers PW, Ortiz JV. Removing Electrons Can Increase the Electron Density: A Computational Study of Negative Fukui Functions. J Phys Chem A 2007; 111:10017-9. [PMID: 17880054 DOI: 10.1021/jp075573d] [Citation(s) in RCA: 93] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Ab initio and density-functional theory calculations for a family of substituted acetylenes show that removing electrons from these molecules causes the electron density along the C-C bond to increase. This result contradicts the predictions of simple frontier molecular orbital theory, but it is easily explained using the nucleophilic Fukui function-provided that one is willing to allow for the Fukui function to be negative. Negative Fukui functions emerge as key indicators of redox-induced electron rearrangements, where oxidation of an entire molecule (acetylene) leads to reduction of a specific region of the molecule (along the bond axis, between the carbon atoms). Remarkably, further oxidization of these substituted acetylenes (one can remove as many as four electrons!) causes the electron density along the C-C bond to increase even more. This work provides substantial evidence that the molecular Fukui function is sometimes negative and reveals that this is due to orbital relaxation.
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Bultinck P, Fias S, Van Alsenoy C, Ayers PW, Carbó-Dorca R. Critical thoughts on computing atom condensed Fukui functions. J Chem Phys 2007; 127:034102. [PMID: 17655426 DOI: 10.1063/1.2749518] [Citation(s) in RCA: 114] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory.
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Affiliation(s)
- Patrick Bultinck
- Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium.
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Senet P, Aparicio F. Density functional theory fragment descriptors to quantify the reactivity of a molecular family: Application to amino acids. J Chem Phys 2007; 126:145105. [PMID: 17444754 DOI: 10.1063/1.2715570] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
By using the exact density functional theory, one demonstrates that the value of the local electronic softness of a molecular fragment is directly related to the polarization charge (Coulomb hole) induced by a test electron removed (or added) from (at) the fragment. Our finding generalizes to a chemical group a formal relation between these molecular descriptors recently obtained for an atom in a molecule using an approximate atomistic model [P. Senet and M. Yang, J. Chem. Sci. 117, 411 (2005)]. In addition, a practical ab initio computational scheme of the Coulomb hole and related local descriptors of reactivity of a molecular family having in common a similar fragment is presented. As a blind test, the method is applied to the lateral chains of the 20 isolated amino acids. One demonstrates that the local softness of the lateral chain is a quantitative measure of the similarity of the amino acids. It predicts the separation of amino acids in different biochemical groups (aliphatic, basic, acidic, sulfur contained, and aromatic). The present approach may find applications in quantitative structure activity relationship methodology.
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Affiliation(s)
- P Senet
- Institut Carnot de Bourgogne, UMR 5209 CNRS, Université de Bourgogne, 9 Avenue Alain Savary, F-21078 Dijon Cedex, France.
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Abstract
Negative values for the condensed Fukui function are identified as the key to designing molecules in which reduction of the molecule is associated with oxidation of one of the atomic centers, or vice versa. Sufficient conditions for negative condensed Fukui functions are derived, and metal complexes are identified as likely candidates for this exotic redox chemistry. Based on our theoretical understanding of where negative values of the Fukui function occur [P. W. Ayers, R. C. Morrison and R. K. Roy. J. Chem. Phys., 2002, 116, 8731], molecular-orbital diagrams for molecules where molecular oxidation is coupled to atomic reduction (or vice versa) are sketched. Whether one could design a metal complex with these properties is an open question but, if one could, then that compound would have fascinating redox chemistry and interesting magnetic properties. Candidate molecules for this property include metal complexes with small metal-to-ligand and/or ligand-to-metal charge transfer excitation energies.
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Affiliation(s)
- Paul W Ayers
- Department of Chemistry, McMaster University, Hamilton, Ontario, Canada L8S 4M1
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