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Woźniak AP, Adamowicz L, Pedersen TB, Kvaal S. Gaussians for Electronic and Rovibrational Quantum Dynamics. J Phys Chem A 2024; 128:3659-3671. [PMID: 38687971 PMCID: PMC11089519 DOI: 10.1021/acs.jpca.4c00364] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/17/2024] [Revised: 03/23/2024] [Accepted: 04/08/2024] [Indexed: 05/02/2024]
Abstract
The assumptions underpinning the adiabatic Born-Oppenheimer (BO) approximation are broken for molecules interacting with attosecond laser pulses, which generate complicated coupled electronic-nuclear wave packets that generally will have components of electronic and dissociation continua as well as bound-state contributions. The conceptually most straightforward way to overcome this challenge is to treat the electronic and nuclear degrees of freedom on equal quantum-mechanical footing by not invoking the BO approximation at all. Explicitly correlated Gaussian (ECG) basis functions have proved successful for non-BO calculations of stationary molecular states and energies, reproducing rovibrational absorption spectra with very high accuracy. In this Article, we present a proof-of-principle study of the ability of fully flexible ECGs (FFECGs) to capture the intricate electronic and rovibrational dynamics generated by short, high-intensity laser pulses. By fitting linear combinations of FFECGs to accurate wave function histories obtained on a large real-space grid for a regularized 2D model of the hydrogen atom and for the 2D Morse potential, we demonstrate that FFECGs provide a very compact description of laser-driven electronic and rovibrational dynamics.
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Affiliation(s)
| | - Ludwik Adamowicz
- Department
of Chemistry and Biochemistry, University
of Arizona, 1306 E University Blvd, Tucson, Arizona 85721-0041, United States
| | - Thomas Bondo Pedersen
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Simen Kvaal
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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2
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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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3
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Littlejohn R, Rawlinson J, Subotnik J. Representation and conservation of angular momentum in the Born-Oppenheimer theory of polyatomic molecules. J Chem Phys 2023; 158:104302. [PMID: 36922131 DOI: 10.1063/5.0143809] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023] Open
Abstract
This paper concerns the representation of angular momentum operators in the Born-Oppenheimer theory of polyatomic molecules and the various forms of the associated conservation laws. Topics addressed include the question of whether these conservation laws are exactly equivalent or only to some order of the Born-Oppenheimer parameter κ = (m/M)1/4 and what the correlation is between angular momentum quantum numbers in the various representations. These questions are addressed in both problems involving a single potential energy surface and those with multiple, strongly coupled surfaces and in both the electrostatic model and those for which fine structure and electron spin are important. The analysis leads to an examination of the transformation laws under rotations of the electronic Hamiltonian; of the basis states, both adiabatic and diabatic, along with their phase conventions; of the potential energy matrix; and of the derivative couplings. These transformation laws are placed in the geometrical context of the structures in the nuclear configuration space that are induced by rotations, which include the rotational orbits or fibers, the surfaces upon which the orientation of the molecule changes but not its shape, and the section, an initial value surface that cuts transversally through the fibers. Finally, it is suggested that the usual Born-Oppenheimer approximation can be replaced by a dressing transformation, that is, a sequence of unitary transformations that block-diagonalize the Hamiltonian. When the dressing transformation is carried out, we find that the angular momentum operator does not change. This is a part of a system of exact equivalences among various representations of angular momentum operators in Born-Oppenheimer theory. Our analysis accommodates large-amplitude motions and is not dependent on small-amplitude expansions about an equilibrium position. Our analysis applies to noncollinear configurations of a polyatomic molecule; this covers all but a subset of measure zero (the collinear configurations) in the nuclear configuration space.
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Affiliation(s)
- Robert Littlejohn
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Jonathan Rawlinson
- School of Mathematics, University of Manchester, Manchester, United Kingdom
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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4
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Ogilvie JF. Chemistry and quantum mechanics. J CHIN CHEM SOC-TAIP 2021. [DOI: 10.1002/jccs.202100287] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- J. F. Ogilvie
- Centre for Experimental and Constructive Mathematics, Department of Mathematics Simon Fraser University Burnaby British Columbia Canada
- Escuela de Quimica Universidad de Costa Rica, Ciudad Universitaria Rodrigo Facio San Jose Costa Rica
- Institute of Quantum Physics Irkutsk National Research Technical University Irkutsk Russian Federation
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5
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Treating the motion of nuclei and electrons in atomic and molecular quantum mechanical calculations on an equal footing: Non-Born–Oppenheimer quantum chemistry. ADVANCES IN QUANTUM CHEMISTRY 2020. [DOI: 10.1016/bs.aiq.2020.05.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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6
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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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7
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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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8
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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9
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10
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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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11
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Malhado JP, Bearpark MJ, Hynes JT. Non-adiabatic dynamics close to conical intersections and the surface hopping perspective. Front Chem 2014; 2:97. [PMID: 25485263 PMCID: PMC4240175 DOI: 10.3389/fchem.2014.00097] [Citation(s) in RCA: 49] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2014] [Accepted: 10/16/2014] [Indexed: 11/13/2022] Open
Abstract
Conical intersections play a major role in the current understanding of electronic de-excitation in polyatomic molecules, and thus in the description of photochemistry and photophysics of molecular systems. This article reviews aspects of the basic theory underlying the description of non-adiabatic transitions at conical intersections, with particular emphasis on the important case when the dynamics of the nuclei are treated classically. Within this classical nuclear motion framework, the main aspects of the surface hopping methodology in the conical intersection context are presented. The emerging picture from this treatment is that of electronic transitions around conical intersections dominated by the interplay of the nuclear velocity and the derivative non-adiabatic coupling vector field.
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Affiliation(s)
| | | | - James T Hynes
- Department of Chemistry and Biochemistry, University of Colorado, Boulder Boulder, CO, USA ; Département de Chimie, École Normale Supérieur, UMR ENS-CNRS-UPMC 8640 Paris, France
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12
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Strasburger K. High angular momentum states of lithium atom, studied with symmetry-projected explicitly correlated Gaussian lobe functions. J Chem Phys 2014; 141:044104. [PMID: 25084878 DOI: 10.1063/1.4890373] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
Method of construction of wave functions approximating eigenfunctions of the [Formula: see text] operator is proposed for high angular momentum states of few-electron atoms. Basis functions are explicitly correlated Gaussian lobes, projected onto irreducible representations of finite point groups. Variational calculations have been carried out for the lowest states of lithium atom, with quantum number L in the range from 1 to 8. Nonrelativistic energies accurate to several dozens of nanohartree have been obtained. For 2(2)P, 3(2)D, and 4(2)F states they agree well with the reference results. Transition frequencies have been computed and compared with available experimental data.
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Affiliation(s)
- Krzysztof Strasburger
- Theoretical Chemistry Group, Institute of Physical and Theoretical Chemistry, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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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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14
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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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15
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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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16
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Cioslowski J, Strasburger K, Matito E. The three-electron harmonium atom: The lowest-energy doublet and quadruplet states. J Chem Phys 2012; 136:194112. [DOI: 10.1063/1.4717461] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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17
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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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18
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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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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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23
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Kato T, Yamanouchi K. Time-dependent multiconfiguration theory for describing molecular dynamics in diatomic-like molecules. J Chem Phys 2009; 131:164118. [DOI: 10.1063/1.3249967] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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24
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Hijikata Y, Nakashima H, Nakatsuji H. Solving non-Born–Oppenheimer Schrödinger equation for hydrogen molecular ion and its isotopomers using the free complement method. J Chem Phys 2009; 130:024102. [DOI: 10.1063/1.3048986] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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25
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Bubin S, Adamowicz L. Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters. J Chem Phys 2006; 124:224317. [PMID: 16784284 DOI: 10.1063/1.2204605] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.
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Affiliation(s)
- Sergiy Bubin
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA.
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26
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Sutcliffe B, Woolley RG. Comment on ‘Molecular structure in non-Born–Oppenheimer quantum mechanics’. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.04.022] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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27
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Császár AG, Czakó G, Furtenbacher T, Tennyson J, Szalay V, Shirin SV, Zobov NF, Polyansky OL. On equilibrium structures of the water molecule. J Chem Phys 2005; 122:214305. [PMID: 15974736 DOI: 10.1063/1.1924506] [Citation(s) in RCA: 105] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3 x 10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e) (BO)=0.957 82 A and theta e (BO)=104.48(5) degrees , respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of H2 (16)O is r(e) (ad)=0.957 85 A and theta e (ad)=104.50(0) degrees , respectively, while those of D2 (16)O are r(e) (ad)=0.957 83 A and theta e (ad)=104.49(0) degrees . Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A0 and B0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of H2 16O, obtained from experimentally determined A'0 and B'0 rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e) (sp)=0.957 77 A and theta e (sp)=104.48 degrees .
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Affiliation(s)
- Attila G Császár
- Department of Theoretical Chemistry, Eötvös University, H-1518 Budapest 112, P.O. Box 32, Hungary.
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Cafiero M, Adamowicz L. Non-Born–Oppenheimer molecular structure and one-particle densities for H2D+. J Chem Phys 2005; 122:184305. [PMID: 15918702 DOI: 10.1063/1.1891707] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We show that the nonadiabatic (non-Born-Oppenheimer) ground state of a three-nuclei system can be effectively calculated with the use of an explicitly correlated Gaussian basis set with floating centers. Sample calculations performed for the H2D+ system with various basis set sizes show good convergence with respect to both the total energy and the expectation values of the internuclear distances (molecular geometry), the distances between the nuclei and the electrons, and between the electrons. We also provide a derivation of the formulas for one-particle density calculations and some density plots showing the spatial distribution of the H2D+ nuclear and electronic densities.
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Affiliation(s)
- Mauricio Cafiero
- Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA
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29
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Bednarz E, Bubin S, Adamowicz L. Non-Born–Oppenheimer variational calculations of HT+ bound states with zero angular momentum. J Chem Phys 2005; 122:164302. [PMID: 15945679 DOI: 10.1063/1.1884602] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report fully nonadiabatic calculations of all rotationless bound states of HT+ molecular ion (t+p+e-) carried out in the framework of the variational method. We show that, in all the states, except the two highest ones, the bond in the system can be described as covalent. In the highest two states the bond becomes essentially ionic and HT+ can be described as a T+H+ complex. The wave function of the system was expanded in terms of spherically symmetric, explicitly correlated Gaussian functions with preexponential multipliers consisting of powers of the internuclear distance. Apart from the total energies of the states, we have calculated the expectation values of the t-p, t-e, and p-e interparticle distances, their squares, and the nucleus-nucleus correlation functions.
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Affiliation(s)
- Eugeniusz Bednarz
- Department of Chemistry, University of Arizona, Tucson, Arizona 85721, USA
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30
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Bednarz * E, Bubin S, Adamowicz L. Integrals for non-Born–Oppenheimer calculations of molecules with three nuclei. Mol Phys 2005. [DOI: 10.1080/00268970512331339314] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Nucleus–nucleus correlation function in non-Born–Oppenheimer molecular calculations: vibrationally excited states of HD+. Chem Phys Lett 2005. [DOI: 10.1016/j.cplett.2005.01.009] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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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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