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Bochicchio RC, Maulén B. Quantum states of physical domains in molecular systems: A three-state model approach. J Chem Phys 2023; 159:234111. [PMID: 38108479 DOI: 10.1063/5.0182310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 11/22/2023] [Indexed: 12/19/2023] Open
Abstract
The physical regions (domains or basins) within the molecular structure are open systems that exchange charge between them and, consequently, house a fractional number of electrons (net charge). The natural framework describing the quantum states for these domains is the density matrix (DM) in its grand-canonical version, which corresponds to a convex expansion into a set of basis states of an integer number of electrons. In this report, it is shown that the solution for these quantities is supported by the DM expansion into three states of different numbers of particles: the neutral and two (edge) ionic states. The states and the average number of particles in the domains (fractional occupation population) are determined by the coefficients of the expansion in terms of the fundamental transference magnitudes, revealing the donor/acceptor character of the domains by which the quantum accessible states are discussed.
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Affiliation(s)
- Roberto C Bochicchio
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA) Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Boris Maulén
- Departamento de Ciencias Químicas, Facultad de Ciencias Exactas, Universidad Andres Bello, Santiago, Chile
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2
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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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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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Cárdenas C, Heidar-Zadeh F, Ayers PW. Benchmark values of chemical potential and chemical hardness for atoms and atomic ions (including unstable anions) from the energies of isoelectronic series. Phys Chem Chem Phys 2018; 18:25721-25734. [PMID: 27711480 DOI: 10.1039/c6cp04533b] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present benchmark values for the electronic chemical potential and chemical hardness from reference data for ionization potentials and electron affinities. In cases where the energies needed to compute these quantities are not available, we estimate the ionization potential of the metastable (di)anions by extrapolation along the isoelectronic series, taking care to ensure that the extrapolated data satisfy reasonable intuitive rules to the maximum possible extent. We also propose suitable values for the chemical potential and chemical hardness of zero-electron species. Because the values we report are faithful to the trends in accurate data on atomic energies, we believe that our proposed values for the chemical potential and chemical hardness are ideally suited to conceptual studies of chemical trends across the periodic table. The critical nuclear charge (Z critical) of the isoelectronic series with 2 < N < 96 has also been reported for the first time.
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Affiliation(s)
- Carlos Cárdenas
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago 7800024, Chile. and Centro para el Desarrollo de la Nanociencia y la Nanotecnología (CEDENNA), Avda. Ecuador 3493, Santiago 9170124, Chile
| | - Farnaz Heidar-Zadeh
- Department of Chemistry & Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada and Department of Inorganic & Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium and Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Paul W Ayers
- Department of Chemistry & Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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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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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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Conceptual DFT analysis of the regioselectivity of 1,3-dipolar cycloadditions: nitrones as a case of study. J Mol Model 2017; 23:236. [DOI: 10.1007/s00894-017-3382-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2016] [Accepted: 05/30/2017] [Indexed: 10/19/2022]
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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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9
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Miranda-Quintana RA. Comments on “On the non-integer number of particles in molecular system domains: treatment and description”. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1945-2] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Miranda-Quintana RA, Ayers PW. Fractional electron number, temperature, and perturbations in chemical reactions. Phys Chem Chem Phys 2016; 18:15070-80. [DOI: 10.1039/c6cp00939e] [Citation(s) in RCA: 57] [Impact Index Per Article: 7.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The mathematical framework of conceptual density functional theory is extended to use the eigenstates and eigenvalues of perturbed subsystems. This unites, justifies, and extends, several previously proposed models.
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Affiliation(s)
| | - Paul W. Ayers
- Department of Chemistry & Chemical Biology
- McMaster University
- Hamilton
- Canada L8S 4M1
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12
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Bochicchio RC. On the non-integer number of particles in molecular system domains: treatment and description. Theor Chem Acc 2015. [DOI: 10.1007/s00214-015-1743-2] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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13
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Sundholm D. On energetic prerequisites of attracting electrons. J Chem Phys 2014; 140:234111. [DOI: 10.1063/1.4883676] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Energy dependence with the number of particles: Density and reduced density matrices functionals. Chem Phys Lett 2014. [DOI: 10.1016/j.cplett.2013.12.071] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Bochicchio RC, Miranda-Quintana RA, Rial D. Communication: Reduced density matrices in molecular systems: Grand-canonical electron states. J Chem Phys 2013; 139:191101. [DOI: 10.1063/1.4832495] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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