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Lang L, Cezar HM, Adamowicz L, Pedersen TB. Quantum Definition of Molecular Structure. J Am Chem Soc 2024; 146:1760-1764. [PMID: 38199236 PMCID: PMC10811664 DOI: 10.1021/jacs.3c11467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2023] [Revised: 11/21/2023] [Accepted: 11/22/2023] [Indexed: 01/12/2024]
Abstract
Molecular structure, a key concept of chemistry, has remained elusive from the perspective of all-particle quantum mechanics, despite many efforts. Viewing molecular structure as a manifestation of strong statistical correlation between nuclear positions, we propose a practical method based on Markov chain Monte Carlo sampling and unsupervised machine learning. Application to the D3+ molecule unambiguously shows that it possesses an equilateral triangular structure. These results provide a major step forward in our understanding of the molecular structure from fundamental quantum principles.
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Affiliation(s)
- Lucas Lang
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway
- Technische
Universität Berlin, Institut für Chemie, Theoretische Chemie/Quantenchemie, Sekr. C7, Straße des 17. Juni
135, 10623 Berlin, Germany
| | - Henrique M. Cezar
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway
| | - Ludwik Adamowicz
- Centre
for Advanced Study at the Norwegian Academy of Science and Letters, Drammensveien 78, 0271 Oslo, Norway
- Department
of Chemistry and Biochemistry, University
of Arizona, Tucson, Arizona 85721, United States
| | - Thomas B. Pedersen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, 0315 Oslo, Norway
- Centre
for Advanced Study at the Norwegian Academy of Science and Letters, Drammensveien 78, 0271 Oslo, Norway
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Goli M, Shahbazian S. MC-QTAIM analysis reveals an exotic bond in coherently quantum superposed malonaldehyde. Phys Chem Chem Phys 2023; 25:5718-5730. [PMID: 36744327 DOI: 10.1039/d2cp05499j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton's wavefunction is delocalized between the two wells. Herein we employ a state-of-the-art multi-component quantum theory of atoms in molecules partitioning scheme to obtain the molecular structure, i.e. atoms in molecules and bonding network, from the superposed ab initio wavefunctions of malonaldehyde. In contrast to the familiar clamped-proton portrayal of malonaldehyde, in which the proton forms a hydrogen basin, for the superposed states the hydrogen basin disappears and two novel hybrid oxygen-hydrogen basins appear instead, with an even distribution of the proton population between the two basins. The interaction between the hybrid basins is stabilizing thanks to an unprecedented mechanism. This involves the stabilizing classical Coulomb interaction of the one-proton density in one of the basins with one-electron density in the other basin. This stabilizing mechanism yields a bond foreign to the known bonding modes in chemistry.
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Affiliation(s)
- Mohammad Goli
- School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.
| | - Shant Shahbazian
- Department of Physics, Shahid Beheshti University, Evin, Tehran, Iran.
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Electrons as an environment for nuclei within molecules: a quantitative assessment of their contribution to a classical-like molecular structure. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02857-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Tomeček J, Bouř P. Density Functional Computations of Vibrational Circular Dichroism Spectra beyond the Born-Oppenheimer Approximation. J Chem Theory Comput 2020; 16:2627-2634. [PMID: 32134648 DOI: 10.1021/acs.jctc.0c00081] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Transition-metal complexes provide rich features in vibrational circular dichroism (VCD) spectra, including significant intensity enhancements, and become thus useful in structural and functional studies of molecules. Quite often, however, the vibrational spectral bands are mixed with the electronic ones, and interpretation of such experiments is difficult. In the present study, we elaborate on the theory needed to calculate the VCD intensities beyond the Born-Oppenheimer (BO) approximation. Within a perturbation approach, the coupling between the electronic and vibrational states is estimated using the harmonic approximation and simplified wave functions obtainable from common density functional theory (DFT) computations. Explicit expressions, including Slater determinants and derivatives of molecular orbitals, are given. On a model diamine complex, the implementation is tested and factors affecting spectral intensities and frequencies are investigated. For two larger molecules, the results are in a qualitative agreement with previous experimental data. Typically, the electronic-vibrational interaction Hamiltonian coupling elements are rather small (∼0 to 10 cm-1), which provides negligible contributions to vibrational frequencies and absorption intensities. However, significant changes in VCD spectra are induced due to the large transition magnetic dipole moment associated with the d-d metal transitions. The possibility to model the spectra beyond the BO limit opens the way to further applications of chiral spectroscopy and transition-metal complexes.
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Affiliation(s)
- Josef Tomeček
- Department of Chemistry, Imperial College London, Imperial College Road, London SW7 2AZ, United Kingdom
| | - Petr Bouř
- Institute of Organic Chemistry and Biochemistry, Academy of Sciences, Flemingovo náměstí 2, 16610 Prague, Czech Republic
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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Goli M, Shahbazian S. Hidden aspects of the Structural theory of chemistry: MC-QTAIM analysis reveals "alchemical" transformation from a triatomic to a diatomic structure. Phys Chem Chem Phys 2015; 17:245-55. [PMID: 25388361 DOI: 10.1039/c4cp03722g] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The Structural theory of chemistry introduces chemical/molecular structure as a combination of relative arrangement and bonding patterns of atoms in a molecule. Nowadays, the structure of atoms in molecules is derived from the topological analysis of the quantum theory of atoms in molecules (QTAIM). In this context, a molecular structure is varied by large geometrical variations and concomitant reorganization of electronic structure that usually take place in chemical reactions or under extreme hydrostatic pressure. In this report, a new mode of structural variation is introduced within the context of the newly proposed multi-component QTAIM (MC-QTAIM) that originates from the mass variation of nuclei. Accordingly, XCN and CNX series of species are introduced where X stands for a quantum particle with a unit of positive charge and a variable mass that is varied in discrete steps between the mass of a proton and a positron. Ab initio non-Born-Oppenheimer (non-BO) calculations are done on both series of species and the resulting non-BO wavefunctions are used for the MC-QTAIM analysis, revealing a triatomic structure for the proton mass and a diatomic structure for the positron mass. In both series of species, a critical mass between that of proton and positron mass is discovered where the transition from triatomic to diatomic structure takes place. This abrupt structural transformation has a topological nature resembling the usual phase transitions in thermodynamics. The discovered mass-induced structural transformation is a hidden aspect of the Structural theory which is revealed only beyond the BO paradigm, when nuclei are treated as quantum waves instead of clamped point charges.
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Affiliation(s)
- Mohammad Goli
- Faculty of Chemistry, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, Tehran, Iran19839.
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Simmen B, Mátyus E, Reiher M. Electric transition dipole moment in pre-Born-Oppenheimer molecular structure theory. J Chem Phys 2014; 141:154105. [PMID: 25338879 DOI: 10.1063/1.4897632] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed from explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated through translationally invariant integral expressions. The electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X (1)Σ(g)(+) and B (1)Σ(u)(+) electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.
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Affiliation(s)
- Benjamin Simmen
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Eövtös University, Institute of Chemistry, P.O. Box 32, H-1518, Budapest 112, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Rodríguez C, Urbina A, Torres F, Cazar D, Ludeña E. Non-Born–Oppenheimer nuclear and electronic densities for a three-particle Hooke–Coulomb model. COMPUT THEOR CHEM 2013. [DOI: 10.1016/j.comptc.2013.05.033] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Mátyus E. On the Calculation of Resonances in Pre-Born–Oppenheimer Molecular Structure Theory. J Phys Chem A 2013; 117:7195-206. [DOI: 10.1021/jp4010696] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- Edit Mátyus
- Laboratory of Molecular
Structure and Dynamics, Institute
of Chemistry, Eötvös University, P.O. Box 32, H-1518, Budapest 112, Hungary
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Mátyus E, Reiher M. Molecular structure calculations: A unified quantum mechanical description of electrons and nuclei using explicitly correlated Gaussian functions and the global vector representation. J Chem Phys 2012; 137:024104. [DOI: 10.1063/1.4731696] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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13
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Goli M, Shahbazian S. The two-component quantum theory of atoms in molecules (TC-QTAIM): foundations. Theor Chem Acc 2012. [DOI: 10.1007/s00214-012-1208-9] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Ludeña EV, Echevarría L, Lopez X, Ugalde JM. Non-Born-Oppenheimer electronic and nuclear densities for a Hooke-Calogero three-particle model: non-uniqueness of density-derived molecular structure. J Chem Phys 2012; 136:084103. [PMID: 22380028 DOI: 10.1063/1.3682244] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider the calculation of non-Born-Oppenheimer, nBO, one-particle densities for both electrons and nuclei. We show that the nBO one-particle densities evaluated in terms of translationally invariant coordinates are independent of the wavefunction describing the motion of center of mass of the whole system. We show that they depend, however, on an arbitrary reference point from which the positions of the vectors labeling the particles are determined. We examine the effect that this arbitrary choice has on the topology of the one-particle density by selecting the Hooke-Calogero model of a three-body system for which expressions for the one-particle densities can be readily obtained in analytic form. We extend this analysis to the one-particle densities obtained from full Coulomb interaction wavefunctions for three-body systems. We conclude, in view of the fact that there is a close link between the choice of the reference point and the topology of one-particle densities that the molecular structure inferred from the topology of these densities is not unique. We analyze the behavior of one-particle densities for the Hooke-Calogero Born-Oppenheimer, BO, wavefunction and show that topological transitions are also present in this case for a particular mass value of the light particles even though in the BO regime the nuclear masses are infinite. In this vein, we argue that the change in topology caused by variation of the mass ratio between light and heavy particles does not constitute a true indication in the nBO regime of the emergence of molecular structure.
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Affiliation(s)
- E V Ludeña
- Centro de Química, Instituto Venezolano de Investigaciones Científicas, IVIC, Apartado 21827, Caracas 1020-A, Venezuela.
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Arapiraca AFC, Jonsson D, Mohallem JR. Vibrationally averaged post Born-Oppenheimer isotopic dipole moment calculations approaching spectroscopic accuracy. J Chem Phys 2011; 135:244313. [DOI: 10.1063/1.3671940] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Mátyus E, Hutter J, Müller-Herold U, Reiher M. Extracting elements of molecular structure from the all-particle wave function. J Chem Phys 2011; 135:204302. [DOI: 10.1063/1.3662487] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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Carbó-Dorca R, Gallegos Saliner A. Notes on quantitative structure-properties relationships (QSPR) part 2: the role of the number of atoms as a molecular descriptor. J Comput Chem 2009; 30:2099-104. [PMID: 19242962 DOI: 10.1002/jcc.21208] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
A previous analysis performed in our laboratory about the polynomial dependency of the atomic quantum self-similarity measures on the atomic number, together with recent publications on quantitative structure-properties relationships (QSPR), based on the number of molecular atoms, published by various authors, have driven us to show here that a simplified form of the fundamental quantum QSPR (QQSPR) equation, permits to theoretically demonstrate the important, but obvious, role of the number of atoms in a molecule, as a possible molecular descriptor. A discussion of the practical use of the number of atoms in QSPR is also given at the end, which also contains a discussion on the role of Ockham's razor in descriptor simplification choices.
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Affiliation(s)
- Ramon Carbó-Dorca
- Institut de Química Computacional, Universitat de Girona, Girona 17071, Catalonia, Spain
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Kapitán J, Hecht L, Bouř P. Raman spectral evidence of methyl rotation in liquid toluene. Phys Chem Chem Phys 2008; 10:1003-8. [DOI: 10.1039/b713965a] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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Sutcliffe BT, Woolley RG. Molecular structure calculations without clamping the nuclei. Phys Chem Chem Phys 2005; 7:3664-76. [PMID: 16358012 DOI: 10.1039/b509723c] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A number of recent papers have considered ways in which molecular structure may be calculated when both the electrons and the nuclei are treated from the outset as quantum particles. This is in contrast to the conventional approach in which the nuclei initially have their positions fixed and so merely provide a potential for electronic motion. The usual approach is generally assumed to be justified by the 1927 work of Born and Oppenheimer. In this paper we discuss what precisely might be anticipated in the way of molecular structure from a mathematical consideration of the spectral properties of the full Coulomb Hamiltonian, to what extent the very idea of molecular structure might be dependent upon treating the nuclei simply as providing a potential and the extent to which the work of Born and Oppenheimer can be used to support this position.
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Affiliation(s)
- Brian T Sutcliffe
- Department of Theoretical Chemistry, Eötvös Loránd University, 112 PO Box 32, H-1518 Budapest, Hungary.
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