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Barrena-Espés D, Munárriz J, Martín Pendás Á. How electrons still guard the space: Electron number distribution functions based on QTAIM∩ELF intersections. J Chem Phys 2024; 160:144106. [PMID: 38591678 DOI: 10.1063/5.0199318] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 03/24/2024] [Indexed: 04/10/2024] Open
Abstract
Despite the importance of the one-particle picture provided by the orbital paradigm, a rigorous understanding of the spatial distribution of electrons in molecules is still of paramount importance to chemistry. Considerable progress has been made following the introduction of topological approaches, capable of partitioning space into chemically meaningful regions. They usually provide atomic partitions, for example, through the attraction basins of the electron density in the quantum theory of atoms in molecules (QTAIM) or electron-pair decompositions, as in the case of the electron localization function (ELF). In both cases, the so-called electron distribution functions (EDFs) provide a rich statistical description of the electron distribution in these spatial domains. Here, we take the EDF concept to a new fine-grained limit by calculating EDFs in the QTAIM ∩ ELF intersection domains. As shown in AHn systems based on main group elements, as well as in the CO, NO, and BeO molecules, this approach provides an exquisitely detailed picture of the electron distribution in molecules, allowing for an insightful combination of the distribution of electrons between Lewis entities (such as bonds and lone pairs) and atoms at the same time. Besides mean-field calculations, we also explore the impact of electron correlation through Hartree-Fock (HF), density functional theory (DFT) (B3LYP), and CASSCF calculations.
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Affiliation(s)
- Daniel Barrena-Espés
- Departamento de Química Física y Analítica, Universidad de Oviedo, 33006 Oviedo, Spain
| | - Julen Munárriz
- Departamento de Química Física and Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Universidad de Zaragoza, 50009 Zaragoza, Spain
| | - Ángel Martín Pendás
- Departamento de Química Física y Analítica, Universidad de Oviedo, 33006 Oviedo, Spain
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Martín Pendás Á, Francisco E. The role of references and the elusive nature of the chemical bond. Nat Commun 2022; 13:3327. [PMID: 35680893 PMCID: PMC9184482 DOI: 10.1038/s41467-022-31036-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 05/30/2022] [Indexed: 11/16/2022] Open
Abstract
Chemical bonding theory is of utmost importance to chemistry, and a standard paradigm in which quantum mechanical interference drives the kinetic energy lowering of two approaching fragments has emerged. Here we report that both internal and external reference biases remain in this model, leaving plenty of unexplored territory. We show how the former biases affect the notion of wavefunction interference, which is purportedly recognized as the most basic bonding mechanism. The latter influence how bonding models are chosen. We demonstrate that the use of real space analyses are as reference-less as possible, advocating for their use. Delocalisation emerges as the reference-less equivalent to interference and the ultimate root of bonding. Atoms (or fragments) in molecules should be understood as a statistical mixture of components differing in electron number, spin, etc. The theory of chemical bonding relies on arbitrary references. Here the authors report a fundamental study on the chemical bond showing that considering the binding fragments as objects in real space enables to eliminate inherent biases.
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Affiliation(s)
- Ángel Martín Pendás
- Departamento de Química Física y Analítica, Universidad de Oviedo, 33006, Oviedo, Spain.
| | - Evelio Francisco
- Departamento de Química Física y Analítica, Universidad de Oviedo, 33006, Oviedo, Spain
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Franco-Pérez M. The electronic temperature and the effective chemical potential parameters of an atom in a molecule. A Fermi-Dirac semi-local variational approach. Phys Chem Chem Phys 2022; 24:807-816. [PMID: 34908052 DOI: 10.1039/d1cp04071e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We developed a numerical procedure to compute the electronic temperature and the effective (local) chemical potential undergone by electrons belonging to a particular molecular species. Our strategy relies on consider atomic basins as open quantum (sub)systems within the context of the quantum theory of atoms in molecules. Each basin is represented by the two parameters, the electronic temperature and the effective chemical potential, which are determined by distributing electrons (fermions) imbedded in each atomic region, through a Fermi-Dirac semi-local variational procedure. The results obtained for 40 different chemical species show that the effective chemical potential is a useful tool to reveal the most acidic/basic atoms in a molecule while the electronic temperature is closely related to the concept of chemical hardness at the local level. Our numerical data also indicate that the electronic temperature values undergone by electrons imbedded in atomic basins are way beyond the room temperature condition, allowing to fractionally occupy several of the one-particle quantum states. In this context, we developed two new indexes useful to reveal outstanding orbitals involved in the chemical reactivity of atoms in molecules.
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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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Guerra C, Ayarde-Henríquez L, Duque-Noreña M, Cárdenas C, Pérez P, Chamorro E. On the nature of bonding in the photochemical addition of two ethylenes: C-C bond formation in the excited state? Phys Chem Chem Phys 2021; 23:20598-20606. [PMID: 34505860 DOI: 10.1039/d1cp03554a] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this work, the 2s + 2s (face-to-face) prototypical example of a photochemical reaction has been re-examined to characterize the evolution of chemical bonding. The analysis of the electron localization function (as an indirect measure of the Pauli principle) along the minimum energy path provides strong evidence supporting that CC bond formation occurs not in the excited state but in the ground electronic state after crossing the rhombohedral S1/S0 conical intersection.
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Affiliation(s)
- Cristian Guerra
- Universidad Andres Bello, Facultad de Ciencias Exactas, Departamento de Ciencias Químicas, Avenida República 275, 8370146, Santiago, Chile.
| | - Leandro Ayarde-Henríquez
- Universidad Andres Bello, Facultad de Ciencias Exactas, Departamento de Ciencias Químicas, Avenida República 275, 8370146, Santiago, Chile.
| | - Mario Duque-Noreña
- Universidad Andres Bello, Facultad de Ciencias Exactas, Departamento de Ciencias Químicas, Avenida República 275, 8370146, Santiago, Chile.
| | - Carlos Cárdenas
- Universidad de Chile, Facultad de Ciencias, Departamento de Física, Avenida Las Palmeras 3425, Santiago, Chile. .,Centro para el Desarrollo de la Nanociencia y la Nanotecnología (CEDENNA), 9170124 Santiago, Chile
| | - Patricia Pérez
- Universidad Andres Bello, Facultad de Ciencias Exactas, Departamento de Ciencias Químicas, Avenida República 275, 8370146, Santiago, Chile.
| | - Eduardo Chamorro
- Universidad Andres Bello, Facultad de Ciencias Exactas, Departamento de Ciencias Químicas, Avenida República 275, 8370146, Santiago, Chile.
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Fernández-Alarcón A, Guevara-Vela JM, Casals-Sainz JL, Costales A, Francisco E, Martín Pendás Á, Rocha Rinza T. Photochemistry in Real Space: Batho- and Hypsochromism in the Water Dimer. Chemistry 2020; 26:17035-17045. [PMID: 32822523 DOI: 10.1002/chem.202002854] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2020] [Indexed: 11/09/2022]
Abstract
The development of chemical intuition in photochemistry faces several difficulties that result from the inadequacy of the one-particle picture, the Born-Oppenheimer approximation, and other basic ideas used to build models. It is shown herein how real-space approaches can be efficiently used to gain valuable insights in photochemistry through a simple example of red and blue shift effects: the double hypso- and bathochromic shifts in the low-lying valence excited states of (H2 O)2 . It is demonstrated that 1) the use of these techniques allows the perturbative language used in the theory of intermolecular interactions, even in the strongly interacting short-range regime, to be maintained; 2) one and only one molecule is photoexcited in each of the addressed excited states and 3) the electrostatic interaction between the in-the-cluster molecular dipoles provides a fairly intuitive rationalisation of the observed batho- and hypsochromism. The methods exploited and illustrated herein are able to maintain the individuality and properties of the interacting entities in a molecular aggregate, and thereby they allow chemical intuition in general states, at any geometry and using a broad variety of electronic structure methods to be kept and built.
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Affiliation(s)
- Alberto Fernández-Alarcón
- Institute of Chemistry, National Autonomous University of Mexico, 04510, Mexico City, Mexico.,Department of Analytical and Physical Chemistry, University of Oviedo, 33006, Oviedo, Spain
| | | | - José Luis Casals-Sainz
- Department of Analytical and Physical Chemistry, University of Oviedo, 33006, Oviedo, Spain
| | - Aurora Costales
- Department of Analytical and Physical Chemistry, University of Oviedo, 33006, Oviedo, Spain
| | - Evelio Francisco
- Department of Analytical and Physical Chemistry, University of Oviedo, 33006, Oviedo, Spain
| | - Ángel Martín Pendás
- Department of Analytical and Physical Chemistry, University of Oviedo, 33006, Oviedo, Spain
| | - Tomás Rocha Rinza
- Institute of Chemistry, National Autonomous University of Mexico, 04510, Mexico City, Mexico
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Acke G, De Baerdemacker S, Martín Pendás Á, Bultinck P. Hierarchies of quantum chemical descriptors induced by statistical analyses of domain occupation number operators. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1456] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
| | - Stijn De Baerdemacker
- Department of Chemistry University of New Brunswick Fredericton New Brunswick Canada
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Casals-Sainz JL, Fernández-Alarcón A, Francisco E, Costales A, Martín Pendás Á. Bond Order Densities in Real Space. J Phys Chem A 2020; 124:339-352. [PMID: 31873015 DOI: 10.1021/acs.jpca.9b10113] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this contribution we introduce the concept of bond order density (BOD) on the basis of a previous work on natural adaptive orbitals. We show that BODs may be used to visualize both the global spatial distribution of the covalent bond order and its eigencomponents, which we call bond(ing) channels. BODs can be equally computed at correlated and noncorrelated levels of theory and in ground or excited states, thus offering an appealing description of bond-forming, bond-breaking, and bond-evolution processes. We show the power of the approach by examining a number of homo- and heterodiatomics, including the controversial existence of a fourth bonding component in dicarbon, by analyzing a few interesting bonding situations in polyatomics and chemical transformations, and by exemplifying exotic bonding behaviors in simple excited electronic states.
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Affiliation(s)
- José Luis Casals-Sainz
- Departamento de Química Física y Analítica , Universidad de Oviedo , 33006 Oviedo , Spain
| | - A Fernández-Alarcón
- Departamento de Química Física y Analítica , Universidad de Oviedo , 33006 Oviedo , Spain
| | - Evelio Francisco
- Departamento de Química Física y Analítica , Universidad de Oviedo , 33006 Oviedo , Spain
| | - Aurora Costales
- Departamento de Química Física y Analítica , Universidad de Oviedo , 33006 Oviedo , Spain
| | - Ángel Martín Pendás
- Departamento de Química Física y Analítica , Universidad de Oviedo , 33006 Oviedo , Spain
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