1
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Jaquet R. A nearly complete treatment of the effect of non-adiabaticity on rovibrational energies of H3+ (Part III). J Chem Phys 2024; 161:054109. [PMID: 39092944 DOI: 10.1063/5.0215051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2024] [Accepted: 07/16/2024] [Indexed: 08/04/2024] Open
Abstract
In this article, significant contributions of non-adiabaticity for the rovibrational bound states up to 25 000 cm-1 and total angular momentum J = 0-20 of H3+ are investigated. A coupled-perturbed full configuration interaction (CP-FCI) treatment is applied to calculate all couplings between electronic states caused by the nuclear motion. These derivative couplings were evaluated up to the second order by means of a perturbation treatment and include all nuclear Cartesian first and second derivatives of the electronic wavefunctions. In particular, the coupling of special derivatives with respect to r and R in the Jacobi coordinate representation is more significant than thought. The perturbation approach is especially optimal for the treatment of weak non-adiabaticity in case of rovibrational energies in H3+ and had not been available before for H3+ or other triatomics. Using exclusively Gaussian basis functions for CP-FCI appears to be sufficient, because explicit correlated wavefunctions are already used for all other potential energy contributions. Our work is an extension of earlier non-adiabatic investigations based on first derivative couplings of electronic states that led to the concept of geometry-dependent effective nuclear masses and which needs only a single potential energy surface for the dynamics. The implementation allows us to include all non-adiabatic effects up to the order of O(μ-2), μ being the reduced nuclear mass. Our treatment works for any isotopologue and for the whole potential energy curve or surface. By this treatment, a further reduction in deviations to experimental data for most rovibrational levels to less than 0.1 cm-1 is possible. For the related transition frequencies, 1366 of 1720 known rovibrational transitions in H3+ have deviations less than 0.1 cm-1 without using any empirically adjustable parameters or optimizing the nuclear mass for a specific transition. For many questionable assignments (deviations >0.3 cm-1) of observed transitions in H3+, a new labeling is proposed.
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Affiliation(s)
- Ralph Jaquet
- Theoretical Chemistry, Department of Chemistry and Biology, Siegen University, 57068 Siegen, Germany
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2
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Nonn Á, Margócsy Á, Mátyus E. Bound-State Relativistic Quantum Electrodynamics: A Perspective for Precision Physics with Atoms and Molecules. J Chem Theory Comput 2024; 20:4385-4395. [PMID: 38789399 DOI: 10.1021/acs.jctc.4c00128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/26/2024]
Abstract
Precision physics aims to use atoms and molecules to test and develop the fundamental theory of matter, possibly beyond the Standard Model. Most of the atomic and molecular phenomena are described by the quantum electrodynamics (QED) sector of the Standard Model. Do we have the computational tools, algorithms, and practical equations for the most possible complete computation of atoms and molecules within the QED sector? What is the fundamental equation to start with? Is it still Schrödinger's wave equation for molecular matter, or is there anything beyond that? This paper provides a concise overview of the relativistic QED framework and recent numerical developments targeting precision physics and spectroscopy applications with common features of the robust and successful relativistic quantum chemistry methodology.
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Affiliation(s)
- Ádám Nonn
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Ádám Margócsy
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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3
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Liu QH, Tan Y, Cheng CF, Hu SM. Precision spectroscopy of molecular hydrogen. Phys Chem Chem Phys 2023; 25:27914-27925. [PMID: 37843424 DOI: 10.1039/d3cp03042c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2023]
Abstract
Precision measurements on the hydrogen molecule are of fundamental importance in understanding molecular theory. Comparison of accurate experimental data and theoretical results are used to test the quantum electrodynamics theory and determine physical constants used in the calculation. We review recent advances and perspectives in the precision spectroscopy of molecular hydrogen, representing state-of-the-art molecular spectroscopy methods and cutting-edge high-precision calculations.
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Affiliation(s)
- Qian-Hao Liu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Yan Tan
- Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Cun-Feng Cheng
- Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
| | - Shui-Ming Hu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, 230026, China.
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4
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Ferenc D, Mátyus E. Evaluation of the Bethe Logarithm: From Atom to Chemical Reaction. J Phys Chem A 2023; 127:627-633. [PMID: 36626594 DOI: 10.1021/acs.jpca.2c05790] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
A general computational scheme for the (nonrelativistic) Bethe logarithm is developed, opening the route to "routine" evaluation of the leading-order quantum electrodynamics correction (QED) relevant for spectroscopic applications for small polyatomic and polyelectronic molecular systems. The implementation relies on the Schwartz method and minimization of a Hylleraas functional. In relation with electronically excited states, a projection technique is considered, which ensures positive definiteness of the functional over the entire parameter (photon momentum) range. Using this implementation, the Bethe logarithm is converged to a relative precision better than 1:103 for selected electronic states of the two-electron H2 and H3+, and the three-electron He2+ and H+H2 molecular systems. The present work focuses on nuclear configurations near the local minimum of the potential energy surface, but the computations can be repeated also for other structures.
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Affiliation(s)
- Dávid Ferenc
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, BudapestH-1117, Hungary
| | - Edit Mátyus
- ELTE, Eötvös Loránd University, Institute of Chemistry, Pázmány Péter sétány 1/A, BudapestH-1117, Hungary
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5
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Saly E, Ferenc D, Mátyus E. Pre-Born–Oppenheimer energies, leading-order relativistic and QED corrections for electronically excited states of molecular hydrogen. Mol Phys 2023. [DOI: 10.1080/00268976.2022.2163714] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Eszter Saly
- Institute of Chemistry, ELTE, Eötvös Loránd University, Budapest, Hungary
| | - Dávid Ferenc
- Institute of Chemistry, ELTE, Eötvös Loránd University, Budapest, Hungary
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Budapest, Hungary
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6
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Chomaz L, Ferrier-Barbut I, Ferlaino F, Laburthe-Tolra B, Lev BL, Pfau T. Dipolar physics: a review of experiments with magnetic quantum gases. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 86:026401. [PMID: 36583342 DOI: 10.1088/1361-6633/aca814] [Citation(s) in RCA: 20] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/02/2022] [Indexed: 06/17/2023]
Abstract
Since the achievement of quantum degeneracy in gases of chromium atoms in 2004, the experimental investigation of ultracold gases made of highly magnetic atoms has blossomed. The field has yielded the observation of many unprecedented phenomena, in particular those in which long-range and anisotropic dipole-dipole interactions (DDIs) play a crucial role. In this review, we aim to present the aspects of the magnetic quantum-gas platform that make it unique for exploring ultracold and quantum physics as well as to give a thorough overview of experimental achievements. Highly magnetic atoms distinguish themselves by the fact that their electronic ground-state configuration possesses a large electronic total angular momentum. This results in a large magnetic moment and a rich electronic transition spectrum. Such transitions are useful for cooling, trapping, and manipulating these atoms. The complex atomic structure and large dipolar moments of these atoms also lead to a dense spectrum of resonances in their two-body scattering behaviour. These resonances can be used to control the interatomic interactions and, in particular, the relative importance of contact over dipolar interactions. These features provide exquisite control knobs for exploring the few- and many-body physics of dipolar quantum gases. The study of dipolar effects in magnetic quantum gases has covered various few-body phenomena that are based on elastic and inelastic anisotropic scattering. Various many-body effects have also been demonstrated. These affect both the shape, stability, dynamics, and excitations of fully polarised repulsive Bose or Fermi gases. Beyond the mean-field instability, strong dipolar interactions competing with slightly weaker contact interactions between magnetic bosons yield new quantum-stabilised states, among which are self-bound droplets, droplet assemblies, and supersolids. Dipolar interactions also deeply affect the physics of atomic gases with an internal degree of freedom as these interactions intrinsically couple spin and atomic motion. Finally, long-range dipolar interactions can stabilise strongly correlated excited states of 1D gases and also impact the physics of lattice-confined systems, both at the spin-polarised level (Hubbard models with off-site interactions) and at the spinful level (XYZ models). In the present manuscript, we aim to provide an extensive overview of the various related experimental achievements up to the present.
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Affiliation(s)
- Lauriane Chomaz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Physikalisches Institut der Universität Heidelberg, Im Neuenheimer Feld 226, 69120 Heidelberg, Germany
| | - Igor Ferrier-Barbut
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
- Université Paris-Saclay, Institut d'Optique Graduate School, CNRS, Laboratoire Charles Fabry, 91127 Palaiseau, France
| | - Francesca Ferlaino
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
| | - Bruno Laburthe-Tolra
- Université Sorbonne Paris Nord, Laboratoire de Physique des Lasers, F-93430 Villetaneuse, France
- CNRS, UMR 7538, LPL, F-93430 Villetaneuse, France
| | - Benjamin L Lev
- Departments of Physics and Applied Physics and Ginzton Laboratory, Stanford University, Stanford, CA 94305, United States of America
| | - Tilman Pfau
- Physikalisches Institut and Center for Integrated Quantum Science and Technology, Universität Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany
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7
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Dahlmann F, Jusko P, Lara-Moreno M, Halvick P, Marimuthu AN, Michaelsen T, Wild R, Geistlinger K, Schlemmer S, Stoecklin T, Wester R, Brünken S. Predissociation spectroscopy of cold CN −H 2 and CN −D 2. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2085204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Franziska Dahlmann
- Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Innsbruck, Austria
| | - Pavol Jusko
- Max Planck Institute for Extraterrestrial Physics, Garching, Germany
| | | | | | - Aravindh N. Marimuthu
- Radboud University, Institute for Molecules and Materials, FELIX Laboratory, Nijmegen, the Netherlands
| | - Tim Michaelsen
- Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Innsbruck, Austria
| | - Robert Wild
- Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Innsbruck, Austria
| | - Katharina Geistlinger
- Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Innsbruck, Austria
| | | | | | - Roland Wester
- Institut für Ionenphysik und Angewandte Physik, Universität Innsbruck, Innsbruck, Austria
| | - Sandra Brünken
- Radboud University, Institute for Molecules and Materials, FELIX Laboratory, Nijmegen, the Netherlands
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8
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Siłkowski M, Pachucki K. Born–Oppenheimer potentials for Π, Δ, and Φ states of the hydrogen molecule. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2062471] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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9
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Zúñiga J, Bastida A, Requena A, Cerezo J. Ab Initio Partition Functions and Thermodynamic Quantities for the Molecular Hydrogen Isotopologues. J Phys Chem A 2021; 125:9226-9241. [PMID: 34613734 PMCID: PMC8543445 DOI: 10.1021/acs.jpca.1c06468] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2021] [Revised: 09/23/2021] [Indexed: 11/29/2022]
Abstract
In this work, we calculate the partition functions and thermodynamic quantities of molecular hydrogen isotopologues using the rovibrational energy levels provided by the highly accurate ab initio adiabatic potential energy functions recently determined by Pachucki and Komasa (Pachucki, K.; Komasa, J. J. Chem. Phys. 2014, 141, 224103). The partition functions are calculated by including all bound energy levels of the isotopologues, up to their dissociation limits, plus the quasi-bound levels lying below the centrifugal potential barriers. For the homonuclear isotopologues, H2, D2, and T2, we also determine the partition functions and thermodynamic quantities of the normal mixtures using the statistical treatment recently proposed by Colonna et al. (Colonna, G.; D'Angola, A.; Capitelli, M. Int. J. Hydrogen Energy 2012, 37, 9656) based on the definition of the partition function of the mixture, which avoids inconsistencies in the values of the thermodynamic quantities depending directly on the internal partition function, in the high-temperature limit.
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Affiliation(s)
- José Zúñiga
- Departamento
de Química Física, Universidad
de Murcia, 30100 Murcia, Spain
| | - Adolfo Bastida
- Departamento
de Química Física, Universidad
de Murcia, 30100 Murcia, Spain
| | - Alberto Requena
- Departamento
de Química Física, Universidad
de Murcia, 30100 Murcia, Spain
| | - Javier Cerezo
- Departamento
de Química, Universidad Autónoma
de Madrid, 28049 Madrid, Spain
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10
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High-precision Hy-CI and E-Hy-CI studies of atomic and molecular properties. ADVANCES IN QUANTUM CHEMISTRY 2021. [DOI: 10.1016/bs.aiq.2021.05.010] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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11
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Ferenc D, Korobov VI, Mátyus E. Nonadiabatic, Relativistic, and Leading-Order QED Corrections for Rovibrational Intervals of ^{4}He_{2}^{+} (X ^{2}Σ_{u}^{+}). PHYSICAL REVIEW LETTERS 2020; 125:213001. [PMID: 33274993 DOI: 10.1103/physrevlett.125.213001] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2020] [Accepted: 09/23/2020] [Indexed: 06/12/2023]
Abstract
The rovibrational intervals of the ^{4}He_{2}^{+} molecular ion in its X ^{2}Σ_{u}^{+} ground electronic state are computed by including the nonadiabatic, relativistic, and leading-order quantum-electrodynamics corrections. Good agreement of theory and experiment is observed for the rotational excitation series of the vibrational ground state and the fundamental vibration. The lowest-energy rotational interval is computed to be 70.937 69(10) cm^{-1} in agreement with the most recently reported experimental value, 70.937 589(23)(60)_{sys} cm^{-1} [L. Semeria et al., Phys. Rev. Lett. 124, 213001 (2020)PRLTAO0031-900710.1103/PhysRevLett.124.213001].
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Affiliation(s)
- Dávid Ferenc
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
| | - Vladimir I Korobov
- Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest H-1117, Hungary
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12
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Palikot E, Stanke M, Adamowicz L. An algorithm for calculating the Bethe logarithm for small molecules with all-electron explicitly correlated Gaussian functions. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137859] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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13
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Affiliation(s)
- Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Shandong University, Qingdao, Shandong 266237, People’s Republic of China
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14
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Jaquet R, Lesiuk M. Analysis of QED and non-adiabaticity effects on the rovibrational spectrum of H 3 + using geometry-dependent effective nuclear masses. J Chem Phys 2020; 152:104109. [PMID: 32171219 DOI: 10.1063/1.5144293] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The influence of QED effects (including one- and two-electron Lamb-shift, Araki-Sucher term, one-loop self-energy, and finite nuclear size correction) together with non-adiabatic effects on the rovibrational bound states of H3 + has been investigated. Non-adiabaticity is modeled by using geometry-dependent effective nuclear masses together with only one single potential energy surface. In conclusion, for rovibrational states below 20 000 cm-1, QED and relativistic effects do nearly compensate, and a potential energy surface based on Born-Oppenheimer energies and diagonal adiabatic corrections has nearly the same quality as the one including relativity with QED; the deviations between the two approaches for individual rovibrational states are mostly below 0.02 cm-1. The inclusion of non-adiabatic effects is important, and it reduces deviations from experiments mostly below 0.1 cm-1.
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Affiliation(s)
- Ralph Jaquet
- Theoretical Chemistry, Siegen University, Siegen, Germany
| | - Michal Lesiuk
- Faculty of Chemistry, University of Warsaw, Warsaw, Poland
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15
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Trivikram TM, Salumbides EJ, Jungen C, Ubachs W. Excitation of H 2 at large internuclear separation: outer well states and continuum resonances. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1599457] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- T. M. Trivikram
- Department of Physics and Astronomy, and LaserLaB, Vrije Universiteit, Amsterdam, The Netherlands
| | - E. J. Salumbides
- Department of Physics and Astronomy, and LaserLaB, Vrije Universiteit, Amsterdam, The Netherlands
| | - Ch. Jungen
- Department of Physics and Astronomy, University College London, London, United Kingdom
| | - W. Ubachs
- Department of Physics and Astronomy, and LaserLaB, Vrije Universiteit, Amsterdam, The Netherlands
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16
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Mátyus E, Teufel S. Effective non-adiabatic Hamiltonians for the quantum nuclear motion over coupled electronic states. J Chem Phys 2019; 151:014113. [PMID: 31272174 DOI: 10.1063/1.5097899] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The quantum mechanical motion of the atomic nuclei is considered over a single- or a multidimensional subspace of electronic states which is separated by a gap from the rest of the electronic spectrum over the relevant range of nuclear configurations. The electron-nucleus Hamiltonian is block-diagonalized up to O(εn+1) through a unitary transformation of the electronic subspace, and the corresponding nth-order effective Hamiltonian is derived for the quantum nuclear motion. Explicit but general formulas are given for the second- and the third-order corrections. As a special case, the second-order Hamiltonian corresponding to an isolated electronic state is recovered which contains the coordinate-dependent mass-correction terms in the nuclear kinetic energy operator. For a multidimensional, explicitly coupled electronic band, the second-order Hamiltonian contains the usual Born-Oppenheimer terms and nonadiabatic corrections, but generalized mass-correction terms appear as well. These, earlier neglected terms, perturbatively account for the outlying (discrete and continuous) electronic states not included in the explicitly coupled electronic subspace.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Stefan Teufel
- Fachbereich Mathematik, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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17
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Puchalski M, Komasa J, Czachorowski P, Pachucki K. Nonadiabatic QED Correction to the Dissociation Energy of the Hydrogen Molecule. PHYSICAL REVIEW LETTERS 2019; 122:103003. [PMID: 30932623 DOI: 10.1103/physrevlett.122.103003] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Indexed: 06/09/2023]
Abstract
The quantum electrodynamic correction to the energy of the hydrogen molecule has been evaluated without expansion in the electron-proton mass ratio. The obtained results significantly improve the accuracy of theoretical predictions reaching the level of 1 MHz for the dissociation energy, in very good agreement with the parallel measurement [Hölsch et al., Phys. Rev. Lett. 122, 103002 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103002]. Molecular hydrogen has thus become a cornerstone of ultraprecise quantum chemistry, which opens perspectives for determination of fundamental physical constants from its spectra.
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Affiliation(s)
- Mariusz Puchalski
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Jacek Komasa
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Paweł Czachorowski
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
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18
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Hölsch N, Beyer M, Salumbides EJ, Eikema KSE, Ubachs W, Jungen C, Merkt F. Benchmarking Theory with an Improved Measurement of the Ionization and Dissociation Energies of H_{2}. PHYSICAL REVIEW LETTERS 2019; 122:103002. [PMID: 30932670 DOI: 10.1103/physrevlett.122.103002] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/07/2018] [Revised: 01/29/2019] [Indexed: 06/09/2023]
Abstract
The dissociation energy of H_{2} represents a benchmark quantity to test the accuracy of first-principles calculations. We present a new measurement of the energy interval between the EF ^{1}Σ_{g}^{+}(v=0,N=1) state and the 54p1_{1} Rydberg state of H_{2}. When combined with previously determined intervals, this new measurement leads to an improved value of the dissociation energy D_{0}^{N=1} of ortho-H_{2} that has, for the first time, reached a level of uncertainty that is 3 times smaller than the contribution of about 1 MHz resulting from the finite size of the proton. The new result of 35 999.582 834(11) cm^{-1} is in remarkable agreement with the theoretical result of 35 999.582 820(26) cm^{-1} obtained in calculations including high-order relativistic and quantum-electrodynamics corrections, as reported in the following Letter [M. Puchalski, J. Komasa, P. Czachorowski, and K. Pachucki, Phys. Rev. Lett. 122, 103003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.103003]. This agreement resolves a recent discrepancy between experiment and theory that had hindered a possible use of the dissociation energy of H_{2} in the context of the current controversy on the charge radius of the proton.
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Affiliation(s)
- Nicolas Hölsch
- Laboratorium für Physikalische Chemie, ETH-Zürich, 8093 Zürich, Switzerland
| | - Maximilian Beyer
- Laboratorium für Physikalische Chemie, ETH-Zürich, 8093 Zürich, Switzerland
| | - Edcel J Salumbides
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Kjeld S E Eikema
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Wim Ubachs
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - Christian Jungen
- Department of Physics and Astronomy, University College London, London, WC1E 6BT United Kingdom
| | - Frédéric Merkt
- Laboratorium für Physikalische Chemie, ETH-Zürich, 8093 Zürich, Switzerland
- LaserLaB, Department of Physics and Astronomy, Vrije Universiteit, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
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19
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Lesiuk M, Przybytek M, Balcerzak JG, Musiał M, Moszynski R. Ab initio Potential Energy Curve for the Ground State of Beryllium Dimer. J Chem Theory Comput 2019; 15:2470-2480. [DOI: 10.1021/acs.jctc.8b00845] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michał Lesiuk
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Michał Przybytek
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | | | - Monika Musiał
- Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, Poland
| | - Robert Moszynski
- Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
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20
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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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21
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Jansen P, Semeria L, Merkt F. Fundamental vibration frequency and rotational structure of the first excited vibrational level of the molecular helium ion ( He 2 + ). J Chem Phys 2018; 149:154302. [PMID: 30342452 DOI: 10.1063/1.5051089] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The term values of the rotational levels of the first excited vibrational state of the electronic ground state of He 2 + with a rotational quantum number N + ≤ 13 have been determined with an accuracy of 1.2 × 10-3 cm-1 (∼35 MHz) by multichannel-quantum-defect-theory-assisted Rydberg spectroscopy of metastable He2. Comparison of the experimental term values with the most accurate ab initio results for He 2 + available in the literature [W.-C. Tung, M. Pavanello, and L. Adamowicz, J. Chem. Phys. 136, 104309 (2012)] reveals inconsistencies between the theoretical and experimental results that increase with increasing rotational quantum numbers. The fundamental vibrational wavenumber of He 2 + was determined to be 1628.3832(12) cm-1 by fitting effective molecular constants to the obtained term values.
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Affiliation(s)
- Paul Jansen
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Luca Semeria
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Frédéric Merkt
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
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22
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, ELTE Eötvös Loránd University, Budapest, Hungary
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23
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Puchalski M, Spyszkiewicz A, Komasa J, Pachucki K. Nonadiabatic Relativistic Correction to the Dissociation Energy of H_{2}, D_{2}, and HD. PHYSICAL REVIEW LETTERS 2018; 121:073001. [PMID: 30169069 DOI: 10.1103/physrevlett.121.073001] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2018] [Indexed: 06/08/2023]
Abstract
The relativistic correction to the dissociation energy of H_{2}, D_{2}, and HD molecules has been accurately calculated without expansion in the small electron-nucleus mass ratio. The obtained results indicate the significance of nonadiabatic effects and resolve the discrepancy of theoretical predictions with recent experimental values for H_{2} and D_{2}. While the theoretical accuracy is now significantly improved and is higher than the experimental one, we observe about 3σ discrepancy for the dissociation energy of HD, which requires further investigation.
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Affiliation(s)
- Mariusz Puchalski
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Anna Spyszkiewicz
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Jacek Komasa
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
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24
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Cheng CF, Hussels J, Niu M, Bethlem HL, Eikema KSE, Salumbides EJ, Ubachs W, Beyer M, Hölsch N, Agner JA, Merkt F, Tao LG, Hu SM, Jungen C. Dissociation Energy of the Hydrogen Molecule at 10^{-9} Accuracy. PHYSICAL REVIEW LETTERS 2018; 121:013001. [PMID: 30028156 DOI: 10.1103/physrevlett.121.013001] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2018] [Indexed: 06/08/2023]
Abstract
The ionization energy of ortho-H_{2} has been determined to be E_{I}^{o}(H_{2})/(hc)=124 357.238 062(25) cm^{-1} from measurements of the GK(1,1)-X(0,1) interval by Doppler-free, two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave, near-infrared laser spectroscopy. E_{I}^{o}(H_{2}) was used to derive the dissociation energy of H_{2}, D_{0}^{N=1}(H_{2}), at 35 999.582 894(25) cm^{-1} with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.
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Affiliation(s)
- C-F Cheng
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - J Hussels
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - M Niu
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - H L Bethlem
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - K S E Eikema
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - E J Salumbides
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - W Ubachs
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - M Beyer
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - N Hölsch
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - J A Agner
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - F Merkt
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - L-G Tao
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology China, Hefei, 230026 China
| | - S-M Hu
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology China, Hefei, 230026 China
| | - Ch Jungen
- Laboratoire Aimé Cotton du CNRS, Bâtiment 505, Université de Paris-Sud, F-91405 Orsay, France and Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
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25
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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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26
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Trivikram TM, Schlösser M, Ubachs W, Salumbides EJ. Relativistic and QED Effects in the Fundamental Vibration of T_{2}. PHYSICAL REVIEW LETTERS 2018; 120:163002. [PMID: 29756935 DOI: 10.1103/physrevlett.120.163002] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Indexed: 06/08/2023]
Abstract
The hydrogen molecule has become a test ground for quantum electrodynamical calculations in molecules. Expanding beyond studies on stable hydrogenic species to the heavier radioactive tritium-bearing molecules, we report on a measurement of the fundamental T_{2} vibrational splitting (v=0→1) for J=0-5 rotational levels. Precision frequency metrology is performed with high-resolution coherent anti-Stokes Raman spectroscopy at an experimental uncertainty of 10-12 MHz, where sub-Doppler saturation features are exploited for the strongest transition. The achieved accuracy corresponds to a 50-fold improvement over a previous measurement, and it allows for the extraction of relativistic and QED contributions to T_{2} transition energies.
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Affiliation(s)
- T Madhu Trivikram
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - M Schlösser
- Tritium Laboratory Karlsruhe, Institute of Technical Physics, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
| | - W Ubachs
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - E J Salumbides
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
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27
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Tao LG, Liu AW, Pachucki K, Komasa J, Sun YR, Wang J, Hu SM. Toward a Determination of the Proton-Electron Mass Ratio from the Lamb-Dip Measurement of HD. PHYSICAL REVIEW LETTERS 2018; 120:153001. [PMID: 29756862 DOI: 10.1103/physrevlett.120.153001] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Indexed: 06/08/2023]
Abstract
Precision spectroscopy of the hydrogen molecule is a test ground of quantum electrodynamics (QED), and it may serve for the determination of fundamental constants. Using a comb-locked cavity ring-down spectrometer, for the first time, we observed the Lamb-dip spectrum of the R(1) line in the overtone of hydrogen deuteride (HD). The line position was determined to be 217 105 182.79±0.03_{stat}±0.08_{syst} MHz (δν/ν=4×10^{-10}), which is the most accurate rovibrational transition ever measured in the ground electronic state of molecular hydrogen. Moreover, from calculations including QED effects up to the order m_{e}α^{6}, we obtained predictions for this R(1) line as well as for the HD dissociation energy, which are less accurate but signaling the importance of the complete treatment of nonadiabatic effects. Provided that the theoretical calculation reaches the same accuracy, the present measurement will lead to a determination of the proton-to-electron mass ratio with a precision of 1.3 parts per billion.
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Affiliation(s)
- L-G Tao
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology of China, Hefei, 230026 China
| | - A-W Liu
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology of China, Hefei, 230026 China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026 China
| | - K Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093, Warsaw, Poland
| | - J Komasa
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Y R Sun
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology of China, Hefei, 230026 China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026 China
| | - J Wang
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology of China, Hefei, 230026 China
| | - S-M Hu
- Hefei National Laboratory for Physical Sciences at Microscale, iChem center, University of Science and Technology of China, Hefei, 230026 China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026 China
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28
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Cozijn FMJ, Dupré P, Salumbides EJ, Eikema KSE, Ubachs W. Sub-Doppler Frequency Metrology in HD for Tests of Fundamental Physics. PHYSICAL REVIEW LETTERS 2018; 120:153002. [PMID: 29756874 DOI: 10.1103/physrevlett.120.153002] [Citation(s) in RCA: 39] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2017] [Indexed: 06/08/2023]
Abstract
Weak transitions in the (2,0) overtone band of the hydrogen deuteride molecule at λ=1.38 μm were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1)=217105181895(20) kHz; R(2)=219042856621(28) kHz; R(3)=220704304951(28) kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and they open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.
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Affiliation(s)
- F M J Cozijn
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - P Dupré
- Laboratoire de Physico-Chimie de l'Atmosphère, Université du Littoral Côte d'Opale, 189A Avenue Maurice Schumann, 59140 Dunkerque, France
| | - E J Salumbides
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - K S E Eikema
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - W Ubachs
- Department of Physics and Astronomy, LaserLaB, Vrije Universiteit Amsterdam, de Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
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29
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Fichet S. Quantum Forces from Dark Matter and Where to Find Them. PHYSICAL REVIEW LETTERS 2018; 120:131801. [PMID: 29694222 DOI: 10.1103/physrevlett.120.131801] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Revised: 01/05/2018] [Indexed: 06/08/2023]
Abstract
We observe that sub-GeV dark matter (DM) induces Casimir-Polder forces between nucleons that can be accessed by experiments from nuclear to molecular scales. We calculate the nucleon-nucleon potentials arising in the DM effective theory and note that their main features are fixed by dimensional analysis and the optical theorem. Molecular spectroscopy and neutron scattering turn out be DM search experiments and are found to be complementary to nucleon-based DM direct detection. Existing data set limits on DM with mass up to ∼3-50 MeV and with effective interaction up to the O(10-100) MeV scale, constraining a region typically difficult to reach for other experiments.
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Affiliation(s)
- Sylvain Fichet
- ICTP-SAIFR and IFT-UNESP, Rua Dr. Bento Teobaldo Ferraz 271, São Paulo, Brazil
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30
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Altmann RK, Dreissen LS, Salumbides EJ, Ubachs W, Eikema KSE. Deep-Ultraviolet Frequency Metrology of H_{2} for Tests of Molecular Quantum Theory. PHYSICAL REVIEW LETTERS 2018; 120:043204. [PMID: 29437464 DOI: 10.1103/physrevlett.120.043204] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2017] [Indexed: 06/08/2023]
Abstract
Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73) kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.
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Affiliation(s)
- R K Altmann
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - L S Dreissen
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - E J Salumbides
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - W Ubachs
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
| | - K S E Eikema
- LaserLaB, Department of Physics and Astronomy, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, Netherlands
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31
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Jansen P, Semeria L, Merkt F. Determination of the Spin-Rotation Fine Structure of He_{2}^{+}. PHYSICAL REVIEW LETTERS 2018; 120:043001. [PMID: 29437449 DOI: 10.1103/physrevlett.120.043001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2017] [Indexed: 06/08/2023]
Abstract
Measuring spin-rotation intervals in molecular cations is challenging, particularly so when the ions do not have electric-dipole-allowed rovibrational transitions. We present a method, based on an angular-momentum basis transformation, to determine the spin-rotational fine structure of molecular ions from the fine structure of high Rydberg states. The method is illustrated by the determination of the so far unknown spin-rotation fine structure of the fundamentally important He_{2}^{+} ion in the X ^{2}Σ_{u}^{+} state. The fine-structure splittings of the v^{+}=0, N^{+}=1, 3, and 5 levels of He_{2}^{+} are 7.96(14), 17.91(32), and 28.0(6) MHz, respectively. The experiment relies on the use of single-mode cw radiation to record spectra of high Rydberg states of He_{2} from the a ^{3}Σ_{u}^{+} metastable state.
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Affiliation(s)
- Paul Jansen
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Luca Semeria
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Frédéric Merkt
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
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32
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Garbacz P, Łach G. Isotope Effects on Nuclear Magnetic Shielding in Molecular Hydrogen. J Phys Chem A 2018; 122:590-593. [DOI: 10.1021/acs.jpca.7b11342] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Piotr Garbacz
- Faculty
of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
| | - Grzegorz Łach
- Faculty
of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
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33
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Non-Born-Oppenheimer calculations of the rovibrational spectrum of H2 excited to the second rotational level. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2016.12.049] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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34
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Puchalski M, Komasa J, Czachorowski P, Pachucki K. Complete α^{6} m Corrections to the Ground State of H_{2}. PHYSICAL REVIEW LETTERS 2016; 117:263002. [PMID: 28059550 DOI: 10.1103/physrevlett.117.263002] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2016] [Indexed: 06/06/2023]
Abstract
We perform the calculation of all relativistic and quantum electrodynamic corrections of the order of α^{6} m to the ground electronic state of a hydrogen molecule and present improved results for the dissociation and the fundamental transition energies. These results open the window for the high-precision spectroscopy of H_{2} and related low-energy tests of fundamental interactions.
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Affiliation(s)
- Mariusz Puchalski
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Jacek Komasa
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
| | - Paweł Czachorowski
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
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35
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Shan W, Liu Q, Li J, Cai N, Saidi WA, Zhou G. Hydrogen-induced atomic structure evolution of the oxygen-chemisorbed Cu(110) surface. J Chem Phys 2016; 145:234704. [DOI: 10.1063/1.4972070] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Weitao Shan
- Department of Mechanical Engineering and Materials Science and Engineering Program, State University of New York, Binghamton, New York 13902, USA
| | - Qianqian Liu
- Department of Mechanical Engineering and Materials Science and Engineering Program, State University of New York, Binghamton, New York 13902, USA
| | - Jonathan Li
- Department of Physics, Applied Physics and Astronomy and Materials Science and Engineering Program, State University of New York, Binghamton, New York 13902, USA
| | - Na Cai
- Department of Mechanical Engineering and Materials Science and Engineering Program, State University of New York, Binghamton, New York 13902, USA
| | - Wissam A. Saidi
- Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Guangwen Zhou
- Department of Mechanical Engineering and Materials Science and Engineering Program, State University of New York, Binghamton, New York 13902, USA
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36
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Semeria L, Jansen P, Merkt F. Precision measurement of the rotational energy-level structure of the three-electron molecule He 2. J Chem Phys 2016; 145:204301. [PMID: 27908106 DOI: 10.1063/1.4967256] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The term values of all rotational levels of the 4He2+ X+ 2Σu+ (ν+=0) ground vibronic state with rotational quantum number N+ ≤ 19 have been determined with an accuracy of 8 × 10-4 cm-1 (∼25 MHz) by multichannel-quantum-defect-theory-assisted Rydberg spectroscopy of metastable He2∗. Comparison of these term values with term values recently calculated ab initio by Tung et al. [J. Chem. Phys. 136, 104309 (2012)] reveals discrepancies that rapidly increase with increasing rotational quantum number and reach values of 0.07 cm-1 (∼2.1 GHz) at N+ = 19.
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Affiliation(s)
- Luca Semeria
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Paul Jansen
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Frédéric Merkt
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
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37
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Mustroph H. Potential-Energy Surfaces, the Born-Oppenheimer Approximations, and the Franck-Condon Principle: Back to the Roots. Chemphyschem 2016; 17:2616-29. [DOI: 10.1002/cphc.201600243] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2016] [Revised: 05/12/2016] [Indexed: 11/11/2022]
Affiliation(s)
- Heinz Mustroph
- FEW Chemicals GmbH; Technikumstraße 1 06756 Bitterfeld-Wolfen Germany
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38
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Pachucki K, Komasa J. Schrödinger equation solved for the hydrogen molecule with unprecedented accuracy. J Chem Phys 2016; 144:164306. [DOI: 10.1063/1.4948309] [Citation(s) in RCA: 34] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Jacek Komasa
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
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39
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Burgess DR. An Evaluation of Gas Phase Enthalpies of Formation for Hydrogen-Oxygen (H xO y) Species. JOURNAL OF RESEARCH OF THE NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY 2016; 121:108-138. [PMID: 34434616 PMCID: PMC7339710 DOI: 10.6028/jres.121.005] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 03/11/2016] [Indexed: 06/13/2023]
Abstract
We have compiled gas phase enthalpies of formation for nine hydrogen-oxygen species (HxOy) and selected recommended values for H, O, OH, H2O, HO2, H2O2, O3, HO3, and H2O3. The compilation consists of values derived from experimental measurements, quantum chemical calculations, and prior evaluations. This work updates the recommended values in the NIST-JANAF (1985) and Gurvich et al. (1989) thermochemical tables for seven species. For two species, HO3 and H2O3 (important in atmospheric chemistry) and not found in prior thermochemical evaluations, we also provide supplementary data consisting of molecular geometries, vibrational frequencies, and torsional potentials which can be used to compute thermochemical functions. For all species, we also provide supplementary data consisting of zero point energies, vibrational frequencies, and ion reaction energetics.
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Affiliation(s)
- Donald R Burgess
- National Institute of Standards and Technology, Gaithersburg, MD 20899
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40
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Beyer M, Merkt F. Observation and Calculation of the Quasibound Rovibrational Levels of the Electronic Ground State of H2+. PHYSICAL REVIEW LETTERS 2016; 116:093001. [PMID: 26991172 DOI: 10.1103/physrevlett.116.093001] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2015] [Indexed: 06/05/2023]
Abstract
Although the existence of quasibound rotational levels of the X^{+} ^{2}Σ_{g}^{+} ground state of H_{2}^{+} was predicted a long time ago, these states have never been observed. Calculated positions and widths of quasibound rotational levels located close to the top of the centrifugal barriers have not been reported either. Given the role that such states play in the recombination of H(1s) and H^{+} to form H_{2}^{+}, this lack of data may be regarded as one of the largest unknown aspects of this otherwise accurately known fundamental molecular cation. We present measurements of the positions and widths of the lowest-lying quasibound rotational levels of H_{2}^{+} and compare the experimental results with the positions and widths we calculate using a potential model for the X^{+} state of H_{2}^{+} which includes adiabatic, nonadiabatic, relativistic, and radiative corrections to the Born-Oppenheimer approximation.
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Affiliation(s)
- Maximilian Beyer
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - Frédéric Merkt
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
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Jansen P, Semeria L, Hofer LE, Scheidegger S, Agner JA, Schmutz H, Merkt F. Precision Spectroscopy in Cold Molecules: The Lowest Rotational Interval of He_{2}^{+} and Metastable He_{2}. PHYSICAL REVIEW LETTERS 2015; 115:133202. [PMID: 26451553 DOI: 10.1103/physrevlett.115.133202] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2015] [Indexed: 06/05/2023]
Abstract
Multistage Zeeman deceleration was used to generate a slow, dense beam of translationally cold He_{2} molecules in the metastable a ^{3}Σ_{u}^{+} state. Precision measurements of the Rydberg spectrum of these molecules at high values of the principal quantum number n have been carried out. The spin-rotational state selectivity of the Zeeman-deceleration process was exploited to reduce the spectral congestion, minimize residual Doppler shifts, resolve the Rydberg series around n=200 and assign their fine structure. The ionization energy of metastable He_{2} and the lowest rotational interval of the X^{+} ^{2}Σ_{u}^{+} (ν^{+}=0) ground state of ^{4}He_{2}^{+} have been determined with unprecedented precision and accuracy by Rydberg-series extrapolation. Comparison with ab initio predictions of the rotational energy level structure of ^{4}He_{2}^{+} [W.-C. Tung, M. Pavanello, and L. Adamowicz, J. Chem. Phys. 136, 104309 (2012)] enabled us to quantify the magnitude of relativistic and quantum-electrodynamics contributions to the fundamental rotational interval of He_{2}^{+}.
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Affiliation(s)
- Paul Jansen
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Luca Semeria
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | | | - Simon Scheidegger
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Josef A Agner
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Hansjürg Schmutz
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | - Frédéric Merkt
- Laboratory of Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
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Niu ML, Salumbides EJ, Ubachs W. Communication: Test of quantum chemistry in vibrationally hot hydrogen molecules. J Chem Phys 2015; 143:081102. [PMID: 26328810 DOI: 10.1063/1.4929568] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Precision measurements are performed on highly excited vibrational quantum states of molecular hydrogen. The v = 12, J = 0 - 3 rovibrational levels of H2 (X(1)Σg (+)), lying only 2000 cm(-1) below the first dissociation limit, were populated by photodissociation of H2S and their level energies were accurately determined by two-photon Doppler-free spectroscopy. A comparison between the experimental results on v = 12 level energies with the best ab initio calculations shows a good agreement, where the present experimental accuracy of 3.5 × 10(-3) cm(-1) is more precise than theory, hence providing a gateway to further test theoretical advances in this benchmark quantum system.
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Affiliation(s)
- M L Niu
- Department of Physics and Astronomy and LaserLaB, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - E J Salumbides
- Department of Physics and Astronomy and LaserLaB, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | - W Ubachs
- Department of Physics and Astronomy and LaserLaB, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
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Pachucki K, Komasa J. Leading order nonadiabatic corrections to rovibrational levels of H2, D2, and T2. J Chem Phys 2015. [DOI: 10.1063/1.4927079] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Jacek Komasa
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
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Gato-Rivera B. Constraining extra space dimensions using precision molecular spectroscopy. ACTA ACUST UNITED AC 2015. [DOI: 10.1088/1742-6596/626/1/012052] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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45
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Mátyus E, Szidarovszky T, Császár AG. Modelling non-adiabatic effects in H₃⁺: solution of the rovibrational Schrödinger equation with motion-dependent masses and mass surfaces. J Chem Phys 2015; 141:154111. [PMID: 25338885 DOI: 10.1063/1.4897566] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H3(+), for which a global adiabatic potential energy surface accurate to better than 0.1 cm(-1) exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D(3h) point-group symmetry is employed. The vibrational mass of the proton in H3(+) is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m(opt,p)((v))=m(nuc,p)+0.31224m(e). This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary
| | - Tamás Szidarovszky
- MTA-ELTE Research Group on Complex Chemical Systems, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Attila G Császár
- Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518, Budapest 112, Hungary and MTA-ELTE Research Group on Complex Chemical Systems, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
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Pachucki K, Komasa J. Accurate adiabatic correction in the hydrogen molecule. J Chem Phys 2014; 141:224103. [DOI: 10.1063/1.4902981] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Krzysztof Pachucki
- Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
| | - Jacek Komasa
- Faculty of Chemistry, Adam Mickiewicz University, Umultowska 89b, 61-614 Poznań, Poland
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Salam A. Quantum electrodynamics effects in atoms and molecules. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2014. [DOI: 10.1002/wcms.1211] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- A. Salam
- Department of Chemistry; Wake Forest University; Winston-Salem NC USA
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Stanke M, Adamowicz L. Non-Born-Oppenheimer calculations of the pure vibrational spectrum of T₂ including relativistic corrections. J Chem Phys 2014; 141:154302. [PMID: 25338891 DOI: 10.1063/1.4897631] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
We report very accurate calculations of the complete pure vibrational spectrum of the T2 molecule with an approach where the Born-Oppenheimer (BO) approximation is not assumed. As the considered states correspond to the zero total angular momentum, their non-BO wave functions are spherically symmetric and are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even nonnegative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α(2) (where α is the fine structure constant) calculated as expectation values of the operators representing these effects.
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Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzia̧dzka 5, 87-100 Toruń, Poland
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
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Garberoglio G, Jankowski P, Szalewicz K, Harvey AH. Path-integral calculation of the second virial coefficient including intramolecular flexibility effects. J Chem Phys 2014; 141:044119. [DOI: 10.1063/1.4890440] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Giovanni Garberoglio
- Interdisciplinary Laboratory for Computational Science (LISC), FBK-CMM and University of Trento, via Sommarive 18, I-38123 Povo (TN), Italy
| | - Piotr Jankowski
- Department of Quantum Chemistry, Faculty of Chemistry, Nicolaus Copernicus University, Gagarina 7, PL-87-100 Toruń, Poland
| | - Krzysztof Szalewicz
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - Allan H. Harvey
- Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305-3337, USA
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Sprecher D, Jungen C, Merkt F. Determination of the binding energies of the np Rydberg states of H2, HD, and D2 from high-resolution spectroscopic data by multichannel quantum-defect theory. J Chem Phys 2014; 140:104303. [DOI: 10.1063/1.4866809] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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