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Abstract
AbstractTwo complementary methodologies for extracting useful insights into electronic structure and bonding from contemporary wavefunctions are compared. The first of these, known as the analysis of domain-averaged Fermi holes (DAFH), mostly provides visually appealing descriptions of the role and the extent of electron sharing in chemical bonding. The second one, known as the fragment, atom, localized, delocalized and interatomic (FALDI) charge density decomposition scheme, uses the partitioning of certain localization and delocalization indices to focus on highly visual contributions associated with individual domains and with pairs of domains, respectively. Four variants of a FALDI-like approach are investigated here in some detail, mostly to establish which of them are the most reliable and the most informative. In addition to ‘full’ calculations that use the correlated pair density, the consequences for the DAFH and FALDI-like procedures of using instead a popular one-electron approximation are explored. Additionally, the geometry dependence of the degree of acceptability of the errors that this introduces for delocalization indices is assessed for different formal bond multiplicities. The familiar molecular test systems employed for these various linked investigations are the breaking of the bonds in H2 and in N2, as well as the nature of the bonding in B2H6, as a simple example of multicenter bonding. One of the key outcomes of this study is a clear understanding of how DAFH analysis and a particular variant of FALDI-like analysis could be most profitably deployed to extract complementary insights into more complex and/or controversial bonding situations.
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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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Pendás AM, Francisco E. Quantum Chemical Topology as a Theory of Open Quantum Systems. J Chem Theory Comput 2018; 15:1079-1088. [DOI: 10.1021/acs.jctc.8b01119] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- A. Martín Pendás
- Departamento de Química Física y Analítica, Facultad de Química, Universidad de Oviedo, 33006 Oviedo, Spain
| | - E. Francisco
- Departamento de Química Física y Analítica, Facultad de Química, Universidad de Oviedo, 33006 Oviedo, Spain
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Ponec R, Cooper DL. Theoretical investigations of the chemical bonding in MM'O 2 clusters (M, M' = Be, Mg, Ca). J Mol Model 2018; 24:226. [PMID: 30091072 DOI: 10.1007/s00894-018-3764-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/21/2018] [Accepted: 07/24/2018] [Indexed: 10/28/2022]
Abstract
Motivated by the known stability of the somewhat unusual Be2O2 rhombus, which features a short Be-Be distance but no direct metal-metal bonding, we investigate the nature of the bonding interactions in the analogous clusters MM'O2 (M, M' = Be, Mg, Ca). CCSD/cc-pVTZ and CCSD(T)/cc-pVQZ calculations, amongst others, are used to determine optimized geometries and the dissociation energies for splitting the MM'O2 clusters into metal oxide monomers. The primary tools used to investigate the chemical bonding are the analysis of domain-averaged Fermi holes, including the generation of localized natural orbitals, and the calculation of appropriate two- and three-center bond indices. Insights emerging from these various analyses concur with earlier studies of M2O2 rhombic clusters in that direct metal-metal bonding was not observed in the MM'O2 rings whereas weak three-center (3c) bonding was detected in the MOM' moieties. In general terms, these mixed MM'O2 clusters exhibit features that are intermediate between those of M2O2 and M'2O2, and the differences between the M and M' atoms appear to have little impact on the overall degree of 3c MOM' bonding. Graphical abstract Bonding situation in MM'O2 clusters (M, M' = Be, Mg, Ca).
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Affiliation(s)
- Robert Ponec
- Institute of Chemical Process Fundamentals, Czech Academy of Sciences Prague 6, 165 02, Suchdol 2, Czech Republic.
| | - David L Cooper
- Department of Chemistry, University of Liverpool, Liverpool, L69 7ZD, UK
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de Lange JH, Cukrowski I. Exact and exclusive electron localization indices within QTAIM atomic basins. J Comput Chem 2018; 39:1517-1530. [DOI: 10.1002/jcc.25223] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2018] [Revised: 03/12/2018] [Accepted: 03/18/2018] [Indexed: 11/06/2022]
Affiliation(s)
- Jurgens H. de Lange
- Department of Chemistry, Faculty of Natural and Agricultural Sciences; University of Pretoria, Lynnwood Road; Hatfield Pretoria 0002 South Africa
| | - Ignacy Cukrowski
- Department of Chemistry, Faculty of Natural and Agricultural Sciences; University of Pretoria, Lynnwood Road; Hatfield Pretoria 0002 South Africa
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Li WL, Lu JB, Zhao L, Ponec R, Cooper DL, Li J, Frenking G. Electronic Structure and Bonding Situation in M2O2 (M = Be, Mg, Ca) Rhombic Clusters. J Phys Chem A 2018; 122:2816-2822. [DOI: 10.1021/acs.jpca.8b01335] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Wan-Lu Li
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jun-Bo Lu
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Lili Zhao
- Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Nanjing 211816, China
| | - Robert Ponec
- Institute of Chemical Process Fundamentals, Czech Academy of Sciences Prague 6, Suchdol 2 165 02 Czech Republic
| | - David L. Cooper
- Department of Chemistry, University of Liverpool, Liverpool L69 7ZD, U.K
| | - Jun Li
- Department of Chemistry and Key Laboratory of Organic Optoelectronics & Molecular Engineering of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Gernot Frenking
- Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Nanjing 211816, China
- Fachbereich Chemie, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, D-35043 Marburg, Germany
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de Lange JH, van Niekerk DME, Cukrowski I. FALDI-based decomposition of an atomic interaction line leads to 3D representation of the multicenter nature of interactions. J Comput Chem 2018; 39:973-985. [DOI: 10.1002/jcc.25175] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2017] [Revised: 12/07/2017] [Accepted: 01/14/2018] [Indexed: 11/09/2022]
Affiliation(s)
- Jurgens H. de Lange
- Department of Chemistry; Faculty of Natural and Agricultural Sciences, University of Pretoria, Lynnwood Road; Hatfield Pretoria 0002 South Africa
| | - Daniel M. E. van Niekerk
- Department of Chemistry; Faculty of Natural and Agricultural Sciences, University of Pretoria, Lynnwood Road; Hatfield Pretoria 0002 South Africa
| | - Ignacy Cukrowski
- Department of Chemistry; Faculty of Natural and Agricultural Sciences, University of Pretoria, Lynnwood Road; Hatfield Pretoria 0002 South Africa
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Golub P, Baranov AI. Domain overlap matrices from plane-wave-based methods of electronic structure calculation. J Chem Phys 2017; 145:154107. [PMID: 27782480 DOI: 10.1063/1.4964760] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Plane waves are one of the most popular and efficient basis sets for electronic structure calculations of solids; however, their delocalized nature makes it difficult to employ for them classical orbital-based methods of chemical bonding analysis. The quantum chemical topology approach, introducing chemical concepts via partitioning of real space into chemically meaningful domains, has no difficulties with plane-wave-based basis sets. Many popular tools employed within this approach, for instance delocalization indices, need overlap integrals over these domains-the elements of the so called domain overlap matrices. This article reports an efficient algorithm for evaluation of domain overlap matrix elements for plane-wave-based calculations as well as evaluation of its implementation for one of the most popular projector augmented wave (PAW) methods on the small set of simple and complex solids. The stability of the obtained results with respect to PAW calculation parameters has been investigated, and the comparison of the results with the results from other calculation methods has also been made.
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Affiliation(s)
- Pavlo Golub
- Department of Chemistry and Food Chemistry, Technical University of Dresden, Bergstrasse 66, 01062 Dresden, Germany
| | - Alexey I Baranov
- Department of Chemistry and Food Chemistry, Technical University of Dresden, Bergstrasse 66, 01062 Dresden, Germany
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Urbina AS, Torres FJ, Rincon L. The electron localization as the information content of the conditional pair density. J Chem Phys 2016; 144:244104. [PMID: 27369494 DOI: 10.1063/1.4954291] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
In the present work, the information gained by an electron for "knowing" about the position of another electron with the same spin is calculated using the Kullback-Leibler divergence (DKL) between the same-spin conditional pair probability density and the marginal probability. DKL is proposed as an electron localization measurement, based on the observation that regions of the space with high information gain can be associated with strong correlated localized electrons. Taking into consideration the scaling of DKL with the number of σ-spin electrons of a system (N(σ)), the quantity χ = (N(σ) - 1) DKLfcut is introduced as a general descriptor that allows the quantification of the electron localization in the space. fcut is defined such that it goes smoothly to zero for negligible densities. χ is computed for a selection of atomic and molecular systems in order to test its capability to determine the region in space where electrons are localized. As a general conclusion, χ is able to explain the electron structure of molecules on the basis of chemical grounds with a high degree of success and to produce a clear differentiation of the localization of electrons that can be traced to the fluctuation in the average number of electrons in these regions.
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Affiliation(s)
- Andres S Urbina
- Universidad San Francisco de Quito (USFQ), Grupo de Química Computacional y Teórica (QCT-USFQ), Departamento de Química e Ingeniería Química, Diego de Robles y Via Interoceanica, Quito 17-1200-841, Ecuador
| | - F Javier Torres
- Universidad San Francisco de Quito (USFQ), Grupo de Química Computacional y Teórica (QCT-USFQ), Departamento de Química e Ingeniería Química, Diego de Robles y Via Interoceanica, Quito 17-1200-841, Ecuador
| | - Luis Rincon
- Universidad San Francisco de Quito (USFQ), Grupo de Química Computacional y Teórica (QCT-USFQ), Departamento de Química e Ingeniería Química, Diego de Robles y Via Interoceanica, Quito 17-1200-841, Ecuador
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Pinto de Magalhães H, Lüthi HP, Bultinck P. Exploring the role of the 3-center–4-electron bond in hypervalent λ3-iodanes using the methodology of domain averaged Fermi holes. Phys Chem Chem Phys 2016; 18:846-56. [DOI: 10.1039/c5cp05343a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
λ3-Iodanes are shown to express pronounced 3-center–4-electron bonds whose strength strongly correlates with the kind of ligands, thereby allowing to modulate the reactivity of these reagents.
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Affiliation(s)
| | - Hans Peter Lüthi
- Department of Chemistry and Applied Biosciences
- ETH Zürich
- CH-8093 Zürich
- Switzerland
| | - Patrick Bultinck
- Department of Inorganic and Physical Chemistry
- Ghent University
- B-9000 Gent
- Belgium
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Francisco E, Martín Pendás A, Costales A. On the interpretation of domain averaged Fermi hole analyses of correlated wavefunctions. Phys Chem Chem Phys 2014; 16:4586-97. [DOI: 10.1039/c3cp54513j] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
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Baranov AI, Ponec R, Kohout M. Domain-averaged Fermi-hole analysis for solids. J Chem Phys 2013; 137:214109. [PMID: 23231219 DOI: 10.1063/1.4768920] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023] Open
Abstract
The domain-averaged Fermi hole (DAFH) orbitals provide highly visual representation of bonding in terms of orbital-like functions with attributed occupation numbers. It was successfully applied on many molecular systems including those with non-trivial bonding patterns. This article reports for the first time the extension of the DAFH analysis to the realm of extended periodic systems. Simple analytical model of DAFH orbital for single-band solids is introduced which allows to rationalize typical features that DAFH orbitals for extended systems may possess. In particular, a connection between Wannier and DAFH orbitals has been analyzed. The analysis of DAFH orbitals on the basis of DFT calculations is applied to hydrogen lattices of different dimensions as well as to the solids diamond, graphite, Na, Cu and NaCl. In case of hydrogen lattices, remarkable similarity is found between the DAFH orbitals evaluated with both the analytical approach and DFT. In case of the selected ionic and covalent solids the DAFH orbitals deliver bonding descriptions, which are compatible with classical orbital interpretation. For metals the DAFH analysis shows essential multicenter nature of bonding.
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Affiliation(s)
- Alexey I Baranov
- Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40, 01187 Dresden, Germany.
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Francisco E, Martín Pendás A, García-Revilla M, Álvarez Boto R. A hierarchy of chemical bonding indices in real space from reduced density matrices and cumulants. COMPUT THEOR CHEM 2013. [DOI: 10.1016/j.comptc.2012.09.009] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Quijano-Quiñones RF, Quesadas-Rojas M, Cuevas G, Mena-Rejón GJ. The rotational barrier in ethane: a molecular orbital study. Molecules 2012; 17:4661-71. [PMID: 22522396 PMCID: PMC6268250 DOI: 10.3390/molecules17044661] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/27/2012] [Revised: 04/12/2012] [Accepted: 04/12/2012] [Indexed: 11/23/2022] Open
Abstract
The energy change on each Occupied Molecular Orbital as a function of rotation about the C-C bond in ethane was studied using the B3LYP, mPWB95 functional and MP2 methods with different basis sets. Also, the effect of the ZPE on rotational barrier was analyzed. We have found that σ and π energies contribution stabilize a staggered conformation. The σ(s) molecular orbital stabilizes the staggered conformation while the stabilizes the eclipsed conformation and destabilize the staggered conformation. The π(z) and molecular orbitals stabilize both the eclipsed and staggered conformations, which are destabilized by the π(v) and molecular orbitals. The results show that the method of calculation has the effect of changing the behavior of the energy change in each Occupied Molecular Orbital energy as a function of the angle of rotation about the C-C bond in ethane. Finally, we found that if the molecular orbital energy contribution is deleted from the rotational energy, an inversion in conformational preference occurs.
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Affiliation(s)
- Ramiro F. Quijano-Quiñones
- Laboratory of Pharmaceutical Chemistry, Faculty of Chemistry, Autonomous University of Yucatan, 41 No. 421 Col. Industrial, C.P. 97150, Merida, Yucatan, Mexico; (M.Q.-R.); (G.J.M.-R.)
| | - Mariana Quesadas-Rojas
- Laboratory of Pharmaceutical Chemistry, Faculty of Chemistry, Autonomous University of Yucatan, 41 No. 421 Col. Industrial, C.P. 97150, Merida, Yucatan, Mexico; (M.Q.-R.); (G.J.M.-R.)
| | - Gabriel Cuevas
- Institute of Chemistry, National Autonomous University of Mexico, Circuito Exterior, Ciudad Universitaria, C.P. 04510 Mexico D.F., Mexico;
| | - Gonzalo J. Mena-Rejón
- Laboratory of Pharmaceutical Chemistry, Faculty of Chemistry, Autonomous University of Yucatan, 41 No. 421 Col. Industrial, C.P. 97150, Merida, Yucatan, Mexico; (M.Q.-R.); (G.J.M.-R.)
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Francisco E, Martín Pendás A, Blanco MA. A connection between domain-averaged Fermi hole orbitals and electron number distribution functions in real space. J Chem Phys 2009; 131:124125. [DOI: 10.1063/1.3239467] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Liu S, Govind N, Pedersen LG. Exploring the origin of the internal rotational barrier for molecules with one rotatable dihedral angle. J Chem Phys 2009; 129:094104. [PMID: 19044862 DOI: 10.1063/1.2976767] [Citation(s) in RCA: 52] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Continuing our recent endeavor, we systematically investigate in this work the origin of internal rotational barriers for small molecules using the new energy partition scheme proposed recently by one of the authors [S. B. Liu, J. Chem. Phys. 126, 244103 (2007)], where the total electronic energy is decomposed into three independent components, steric, electrostatic, and fermionic quantum. Specifically, we focus in this work on six carbon, nitrogen, and oxygen containing hydrides, CH(3)CH(3), CH(3)NH(2), CH(3)OH, NH(2)NH(2), NH(2)OH, and H(2)O(2), with only one rotatable dihedral angle [angle]H-X-Y-H (X,Y=C,N,O). The relative contributions of the different energy components to the total energy difference as a function of the internal dihedral rotation will be considered. Both optimized-geometry (adiabatic) and fixed-geometry (vertical) differences are examined, as are the results from the conventional energy partition and natural bond orbital analysis. A wealth of strong linear relationships among the total energy difference and energy component differences for different systems have been observed but no universal relationship applicable to all systems for both cases has been discovered, indicating that even for simple systems such as these, there exists no omnipresent, unique interpretation on the nature and origin of the internal rotation barrier. Different energy components can be employed for different systems in the rationalization of the barrier height. Confirming that the two differences, adiabatic and vertical, are disparate in nature, we find that for the vertical case there is a unique linear relationship applicable to all the six molecules between the total energy difference and the sum of the kinetic and electrostatic energy differences. For the adiabatic case, it is the total potential energy difference that has been found to correlate well with the total energy difference except for ethane whose rotation barrier is dominated by the quantum effect.
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Affiliation(s)
- Shubin Liu
- Renaissance Computing Institute, University of North Carolina, Chapel Hill, North Carolina 27599-3455, USA
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Ponec R, Lendvay G, Sundberg MR. Structure and Bonding in Binuclear Metal Carbonyls from the Analysis of Domain Averaged Fermi Holes. 2. Fe2(CO)82− and Fe2(CO)8. J Phys Chem A 2008; 112:9936-45. [DOI: 10.1021/jp804390a] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Robert Ponec
- Institute of Chemical Process Fundamentals of the ASCR, v.v.i., Prague 6, Suchdol 2, 165 02, Czech Republic
| | - György Lendvay
- Institute of Structural Chemistry, Chemical Research Center, Hungarian Academy of Sciences, H-1525 Budapest, P.O. Box 17, Hungary
| | - Markku R. Sundberg
- Laboratory of Inorganic Chemistry, Department of Chemistry, P.O. Box 55, 00014 University of Helsinki, Finland
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