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Culpitt T, Peters LDM, Tellgren EI, Helgaker T. Time-dependent nuclear-electronic orbital Hartree-Fock theory in a strong uniform magnetic field. J Chem Phys 2023; 158:114115. [PMID: 36948801 DOI: 10.1063/5.0139675] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023] Open
Abstract
In an ultrastrong magnetic field, with field strength B ≈ B0 = 2.35 × 105 T, molecular structure and dynamics differ strongly from that observed on the Earth. Within the Born-Oppenheimer (BO) approximation, for example, frequent (near) crossings of electronic energy surfaces are induced by the field, suggesting that nonadiabatic phenomena and processes may play a more important role in this mixed-field regime than in the weak-field regime on Earth. To understand the chemistry in the mixed regime, it therefore becomes important to explore non-BO methods. In this work, the nuclear-electronic orbital (NEO) method is employed to study protonic vibrational excitation energies in the presence of a strong magnetic field. The NEO generalized Hartree-Fock theory and time-dependent Hartree-Fock (TDHF) theory are derived and implemented, accounting for all terms that result as a consequence of the nonperturbative treatment of molecular systems in a magnetic field. The NEO results for HCN and FHF- with clamped heavy nuclei are compared against the quadratic eigenvalue problem. Each molecule has three semi-classical modes owing to the hydrogen-two precession modes that are degenerate in the absence of a field and one stretching mode. The NEO-TDHF model is found to perform well; in particular, it automatically captures the screening effects of the electrons on the nuclei, which are quantified through the difference in energy of the precession modes.
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Affiliation(s)
- Tanner Culpitt
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Laurens D M Peters
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Erik I Tellgren
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- 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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Monzel L, Pausch A, Peters L, Tellgren E, Helgaker T, Klopper W. Molecular Dynamics of Linear Molecules in Strong Magnetic Fields. J Chem Phys 2022; 157:054106. [DOI: 10.1063/5.0097800] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born-Oppenheimer potential energy surfaces are calculated at the Hartree-Fock and MP2 levels of theory, using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges.
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Affiliation(s)
- Laurenz Monzel
- Karlsruhe Institute of Technology Institute of Physical Chemistry, Germany
| | - Ansgar Pausch
- Karlsruhe Institute of Technology Faculty of Chemistry and Biosciences, Germany
| | | | | | | | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology Faculty of Chemistry and Biosciences, Germany
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Beutel M, Ahrens A, Huang C, Suzuki Y, Varga K. Deformed explicitly correlated Gaussians. J Chem Phys 2021; 155:214103. [PMID: 34879658 DOI: 10.1063/5.0066427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Deformed explicitly correlated Gaussian (DECG) basis functions are introduced, and their matrix elements are calculated. All matrix elements can be calculated analytically in a closed form, except the Coulomb one, which has to be approximated by a Gaussian expansion. The DECG basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole self-interaction term in the Pauli-Fierz Hamiltonian. Examples are presented showing the accuracy and necessity of deformed Gaussian basis functions to accurately solve light-matter coupled systems in cavity QED.
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Affiliation(s)
- Matthew Beutel
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Alexander Ahrens
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Chenhang Huang
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | | | - Kálmán Varga
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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Stanke M, Palikot E, Sharkey KL, Adamowicz L. Benchmark calculations of the 2D Rydberg spectrum of lithium. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1925765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, Toruń, PL, Poland
| | - Ewa Palikot
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
| | - Keeper L. Sharkey
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
- Interdisciplinary Center for Modern Technologies, Nicolaus Copernicus University, Toruń, PL, Poland
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Adamowicz L, Stanke M, Tellgren E, Helgaker T. A quantum-mechanical non-Born–Oppenheimer model of a molecule in a strong magnetic field. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.138041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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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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Adamowicz L, Stanke M, Tellgren E, Helgaker T. A computational quantum-mechanical model of a molecular magnetic trap. J Chem Phys 2018; 149:244112. [PMID: 30599715 DOI: 10.1063/1.5055767] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A model for describing the states of a molecular system trapped in a cavity created by a fast-rotating strong magnetic field is proposed and implemented. All-particle explicitly correlated Gaussian functions with shifted centers are employed in the model to expand the wave functions of the system. Both "internal" states associated with the system's rovibrational and electronic motions and the "external" states associated with translational motion of the center of mass of the system in the cavity are calculated. The states are visualized by density plots. The model is applied to a trapped HD molecule.
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Affiliation(s)
- Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA and Interdisciplinary Center for Modern Technologies, Nicolaus Copernicus University, ul. Wileńska 4, Toruń, PL 87-100, Poland
| | - Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, ul. Grudzia̧dzka 5, Toruń PL 87-100, Poland
| | - Erik Tellgren
- Hyllerras Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Trygve Helgaker
- Hyllerras Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
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