1
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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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2
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Goli M, Bressanini D, Shahbazian S. On the nature of the two-positron bond: evidence for a novel bond type. Phys Chem Chem Phys 2023; 25:29531-29547. [PMID: 37905569 DOI: 10.1039/d3cp03003b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
The nature of the newly proposed two-positron bond in (PsH)2, which is composed of two protons, four electrons and two positrons, is considered in this contribution. The study is done at the multi-component-Hartree-Fock (MC-HF) and the Diffusion Monte Carlo (DMC) levels of theory by comparing ab initio data, analyzing the spatial structure of the DMC wavefunction, and applying the multi-component quantum theory of atoms in molecules and the two-component interacting quantum atoms energy partitioning schemes to the MC-HF wavefunction. The analysis demonstrates that (PsH)2 to a good approximation may be conceived of as two slightly perturbed PsH atoms, bonded through a two-positron bond. In contrast to the usual two-electron bonds, the positron exchange phenomenon is quite marginal in the considered two-positron bond. The dominant stabilizing mechanism of bonding is a novel type of classical electrostatic interaction between the positrons, which are mainly localized between nuclei, and the surrounding electrons. To emphasize its uniqueness, this mechanism of bonding is proposed to be called gluonic which has also been previously identified as the main driving mechanism behind formation of the one-positron bond in [H-,e+,H-]. We conclude that the studied two-positron bond should not be classified as a covalent bond and it must be seen as a brand-new type of bond, foreign to the electronic bonding modes discovered so far in the purely electronic systems.
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Affiliation(s)
- Mohammad Goli
- School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.
| | - Dario Bressanini
- Dipartimento di Scienza e Alta Tecnologia, Università dell'Insubria, Como, Italy.
| | - Shant Shahbazian
- Department of Physics, Shahid Beheshti University, Evin, Tehran 19839-69411, Iran.
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3
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Mátyus E, Martín Santa Daría A, Avila G. Exact quantum dynamics developments for floppy molecular systems and complexes. Chem Commun (Camb) 2023; 59:366-381. [PMID: 36519578 DOI: 10.1039/d2cc05123k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Molecular rotation, vibration, internal rotation, isomerization, tunneling, intermolecular dynamics of weakly and strongly interacting systems, intra-to-inter-molecular energy transfer, hindered rotation and hindered translation over surfaces are important types of molecular motions. Their fundamentally correct and detailed description can be obtained by solving the nuclear Schrödinger equation on a potential energy surface. Many of the chemically interesting processes involve quantum nuclear motions which are 'delocalized' over multiple potential energy wells. These 'large-amplitude' motions in addition to the high dimensionality of the vibrational problem represent challenges to the current (ro)vibrational methodology. A review of the quantum nuclear motion methodology is provided, current bottlenecks of solving the nuclear Schrödinger equation are identified, and solution strategies are reviewed. Technical details, computational results, and analysis of these results in terms of limiting models and spectroscopically relevant concepts are highlighted for selected numerical examples.
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Affiliation(s)
- Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
| | - Alberto Martín Santa Daría
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
| | - Gustavo Avila
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary.
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4
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Affiliation(s)
- Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie Vladimir-Prelog-Weg 2 8093 Zürich Switzerland
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5
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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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6
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Mátyus E, Cassam-Chenaï P. Orientational decoherence within molecules and emergence of the molecular shape. J Chem Phys 2021; 154:024114. [PMID: 33445882 DOI: 10.1063/5.0036568] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The question of classicality is addressed in relation with the shape of the nuclear skeleton of molecular systems. As the most natural environment, the electrons of the molecule are considered as continuously monitoring agents for the nuclei. For this picture, an elementary formalism of decoherence theory is developed and numerical results are presented for few-particle systems. The numerical examples suggest that the electron-nucleus Coulomb interaction is sufficient for inducing a blurred shape with strong quantum coherences in compounds of the lightest elements, H2, D2, T2, and HeH+.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
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7
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Muolo A, Mátyus E, Reiher M. H 3 + as a five-body problem described with explicitly correlated Gaussian basis sets. J Chem Phys 2019; 151:154110. [PMID: 31640358 DOI: 10.1063/1.5121318] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Various explicitly correlated Gaussian (ECG) basis sets are considered for the solution of the molecular Schrödinger equation with particular attention to the simplest polyatomic system, H3 +. Shortcomings and advantages are discussed for plain ECGs, ECGs with the global vector representation, floating ECGs and their numerical projection, and ECGs with complex parameters. The discussion is accompanied with particle density plots to visualize the observations. In order to be able to use large complex ECG basis sets in molecular calculations, a numerically stable algorithm is developed, the efficiency of which is demonstrated for the lowest rotationally and vibrationally excited states of H2 and H3 +.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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8
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Schild A. On the Probability Density of the Nuclei in a Vibrationally Excited Molecule. Front Chem 2019; 7:424. [PMID: 31245359 PMCID: PMC6562893 DOI: 10.3389/fchem.2019.00424] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2019] [Accepted: 05/22/2019] [Indexed: 11/24/2022] Open
Abstract
For localized and oriented vibrationally excited molecules, the qualitative features of the one-body probability density of the nuclei (one-nucleus density) are investigated. Like the familiar and widely used one-electron density that represents the probability of finding an electron at a given location in space, the one-nucleus density represents the probability of finding a nucleus at a given position in space independent of the location of the other nuclei and independent of their type. In contrast to the electrons, however, the nuclei are comparably localized. Due to this localization of the individual nuclei, the one-nucleus density provides a quantum-mechanical representation of the "chemical picture" of the molecule as an object that can largely be understood in a three-dimensional space, even though its full nuclear probability density is defined on the high-dimensional configuration space of all the nuclei. We study how the nodal structure of the wavefunctions of vibrationally excited states translates to the one-nucleus density. It is found that nodes do not necessarily lead to visible changes in the one-nucleus density: Already for relatively small molecules, only certain vibrational excitations change the one-nucleus density qualitatively compared to the ground state. It turns out that there are simple rules for predicting the shape of the one-nucleus density from the normal mode coordinates. A Python module for the computation of the one-nucleus density is provided at https://gitlab.com/axelschild/mQNMc.
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Affiliation(s)
- Axel Schild
- Laboratory for Physical Chemistry, ETH Zürich, Zurich, Switzerland
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9
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Mátyus E. Non-adiabatic mass-correction functions and rovibrational states of 4 He 2 + ( X 2 Σ u + ). J Chem Phys 2018; 149:194112. [PMID: 30466288 DOI: 10.1063/1.5050403] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The mass-correction functions in the second-order non-adiabatic Hamiltonian are computed for the 4 He 2 + molecular ion using the variational method, floating explicitly correlated Gaussian functions, and a general coordinate-transformation formalism. When non-adiabatic rovibrational energy levels are computed using these (coordinate-dependent) mass-correction functions and a highly accurate potential energy and diagonal Born-Oppenheimer correction curve, significantly improved theoretical results are obtained for the nine rotational and two rovibrational intervals known from high-resolution spectroscopy experiments.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter Sétány 1/A, Budapest H-1117, Hungary
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10
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Mátyus E. Non-adiabatic mass correction to the rovibrational states of molecules: Numerical application for the H 2 + molecular ion. J Chem Phys 2018; 149:194111. [PMID: 30466265 DOI: 10.1063/1.5050401] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
General transformation expressions of the second-order non-adiabatic Hamiltonian of the atomic nuclei, including the kinetic-energy correction terms, are derived upon the change from laboratory-fixed Cartesian coordinates to general curvilinear coordinate systems commonly used in rovibrational computations. The kinetic-energy or so-called "mass-correction" tensor elements are computed with the stochastic variational method and floating explicitly correlated Gaussian functions for the H 2 + molecular ion in its ground electronic state. {Further numerical applications for the 4 He 2 + molecular ion are presented in the forthcoming paper, Paper II [E. Mátyus, J. Chem. Phys. 149, 194112 (2018)]}. The general, curvilinear non-adiabatic kinetic energy operator expressions are used in the examples, and non-adiabatic rovibrational energies and corrections are determined by solving the rovibrational Schrödinger equation including the diagonal Born-Oppenheimer as well as the mass-tensor corrections.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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11
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Muolo A, Mátyus E, Reiher M. Explicitly correlated Gaussian functions with shifted-center and projection techniques in pre-Born-Oppenheimer calculations. J Chem Phys 2018; 149:184105. [PMID: 30441913 DOI: 10.1063/1.5050462] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Numerical projection methods are elaborated for the calculation of eigenstates of the non-relativistic many-particle Coulomb Hamiltonian with selected rotational and parity quantum numbers employing shifted explicitly correlated Gaussian functions, which are, in general, not eigenfunctions of the total angular momentum and parity operators. The increased computational cost of numerically projecting the basis functions onto the irreducible representations of the three dimensional rotation-inversion group is the price to pay for the increased flexibility of the basis functions. This increased flexibility allowed us to achieve a substantial improvement for the variational upper bound to the Pauli-allowed ground-state energy of the H 3 + = { p + , p + , p + , e - , e - } molecular ion treated as an explicit five-particle system. We compare our pre-Born-Oppenheimer result obtained for this molecular ion with rotational-vibrational calculations carried out on a potential energy surface.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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12
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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13
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Muolo A, Mátyus E, Reiher M. Generalized elimination of the global translation from explicitly correlated Gaussian functions. J Chem Phys 2018; 148:084112. [PMID: 29495776 DOI: 10.1063/1.5009465] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [B. Simmen et al., Mol. Phys. 111, 2086 (2013)] when the Schrödinger equation is solved variationally with explicitly correlated Gaussian functions. The approach has immediate relevance in many-particle systems which are handled without the Born-Oppenheimer approximation and can be employed also for Dirac-type Hamiltonians. The practical realization and numerical properties of solving the Schrödinger equation in laboratory-frame Cartesian coordinates are demonstrated for the ground rovibronic state of the H2+={p+,p+,e-} ion and the H2 = {p+, p+, e-, e-} molecule.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Institute of Chemistry, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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14
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Cox H, Baskerville AL. The Series Solution Method in Quantum Chemistry for Three-Particle Systems. ADVANCES IN QUANTUM CHEMISTRY 2018. [DOI: 10.1016/bs.aiq.2018.02.003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/15/2023]
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15
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Arias E, Florez E, Pérez–Torres JF. Algorithm based on the Thomson problem for determination of equilibrium structures of metal nanoclusters. J Chem Phys 2017; 146:244107. [DOI: 10.1063/1.4984049] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Affiliation(s)
- E. Arias
- Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
| | - E. Florez
- Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
| | - J. F. Pérez–Torres
- Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
- Escuela de Qumica, Universidad Industrial de Santander, Bucaramanga, Colombia
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16
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Cassam-Chenaï P, Suo B, Liu W. A quantum chemical definition of electron–nucleus correlation. Theor Chem Acc 2017. [DOI: 10.1007/s00214-017-2081-3] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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17
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Joyce T, Varga K. Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum. J Chem Phys 2016; 144:184106. [PMID: 27179470 DOI: 10.1063/1.4948708] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules.
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Affiliation(s)
- Tennesse Joyce
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Kálmán Varga
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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18
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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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19
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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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20
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Abstract
Chemical reactivity of a set of reactants is determined by its potential (electronic) energy (hyper)surface. The high dimensionality of this surface renders it difficult to efficiently explore reactivity in a large reactive system. Exhaustive sampling techniques and search algorithms are not straightforward to employ as it is not clear which explored path will eventually produce the minimum energy path of a reaction passing through a transition structure. Here, the chemist's intuition would be of invaluable help, but it cannot be easily exploited because (1) no intuitive and direct tool for the scientist to manipulate molecular structures is currently available and because (2) quantum chemical calculations are inherently expensive in terms of computational effort. In this work, we elaborate on how the chemist can be reintroduced into the exploratory process within a virtual environment that provides immediate feedback and intuitive tools to manipulate a reactive system. We work out in detail how this immersion should take place. We provide an analysis of modern semi-empirical methods which already today are candidates for the interactive study of chemical reactivity. Implications of manual structure manipulations for their physical meaning and chemical relevance are carefully analysed in order to provide sound theoretical foundations for the interpretation of the interactive reactivity exploration.
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Affiliation(s)
- Moritz P. Haag
- Laboratorium für Physikalische Chemie
- ETH Zürich
- CH-8093 Zürich, Switzerland
| | - Markus Reiher
- Laboratorium für Physikalische Chemie
- ETH Zürich
- CH-8093 Zürich, Switzerland
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21
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Kirnosov N, Sharkey KL, Adamowicz L. Charge asymmetry in rovibrationally excited HD+ determined using explicitly correlated all-particle Gaussian functions. J Chem Phys 2013; 139:204105. [PMID: 24289342 DOI: 10.1063/1.4834596] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023] Open
Abstract
Very accurate non-Born-Oppenheimer quantum-mechanical calculations are performed to determine the average values of the interparticle distances and the proton-deuteron density function for the rovibrationally excited HD(+) ion. The states corresponding to excitations to all bound vibrational states (v = 0, ..., 22) and simultaneously excited to the first excited rotational state (N = 1) are considered. To describe each state up to 8000 explicitly correlated all-particle Gaussian functions are used. The nonlinear parameters of the Gaussians are variationally optimized using a procedure that employs the analytical energy gradient determined with respect to these parameters. The results show an increasing asymmetry in the electron distribution with the vibrational excitation as the electron density shifts towards deuteron and away from the proton.
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Affiliation(s)
- Nikita Kirnosov
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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22
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The two-component quantum theory of atoms in molecules (TC-QTAIM): the unified theory of localization/delocalization of electrons, nuclei, and exotic elementary particles. Theor Chem Acc 2013. [DOI: 10.1007/s00214-013-1410-4] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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23
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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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24
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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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25
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Goli M, Shahbazian S. Toward the multi-component quantum theory of atoms in molecules: a variational derivation. Theor Chem Acc 2013. [DOI: 10.1007/s00214-013-1365-5] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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26
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Simmen B, Mátyus E, Reiher M. Elimination of the translational kinetic energy contamination in pre-Born–Oppenheimer calculations. Mol Phys 2013. [DOI: 10.1080/00268976.2013.783938] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Benjamin Simmen
- ETH Zurich, Laboratorium für Physikalische Chemie, , Zurich, Switzerland
| | - Edit Mátyus
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, Pázmány Péter sétány , Budapest, Hungary
| | - Markus Reiher
- ETH Zurich, Laboratorium für Physikalische Chemie, , Zurich, Switzerland
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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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