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Morrigan L, Neville SP, Gregory M, Boguslavskiy AE, Forbes R, Wilkinson I, Lausten R, Stolow A, Schuurman MS, Hockett P, Makhija V. Ultrafast Molecular Frame Quantum Tomography. PHYSICAL REVIEW LETTERS 2023; 131:193001. [PMID: 38000424 DOI: 10.1103/physrevlett.131.193001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Revised: 09/05/2023] [Accepted: 10/03/2023] [Indexed: 11/26/2023]
Abstract
We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH_{3}). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH_{3}, we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.
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Affiliation(s)
- Luna Morrigan
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
| | - Simon P Neville
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Margaret Gregory
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
| | - Andrey E Boguslavskiy
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Ruaridh Forbes
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Iain Wilkinson
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Institute for Electronic Structure Dynamics, Helmholtz-Zentrum für Materialien und Energie, Hahn-Meitner-Platz 1, 14109 Berlin, Germany
| | - Rune Lausten
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Albert Stolow
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
- NRC-uOttawa Joint Centre for Extreme and Quantum Photonics (JCEP), Ottawa, Ontario K1A 0R6, Canada
| | - Michael S Schuurman
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada
| | - Paul Hockett
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Varun Makhija
- Department of Chemistry and Physics, University of Mary Washington, Fredericksburg, Virginia 22401, USA
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Gregory M, Neville S, Schuurman M, Makhija V. A laboratory frame density matrix for ultrafast quantum molecular dynamics. J Chem Phys 2022; 157:164301. [DOI: 10.1063/5.0109607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In most cases, the ultrafast dynamics of resonantly excited molecules are considered and almost always computed in the molecular frame, while experiments are carried out in the laboratory frame. Here, we provide a formalism in terms of a lab frame density matrix, which connects quantum dynamics in the molecular frame to those in the laboratory frame, providing a transparent link between computation and measurement. The formalism reveals that in any such experiment, the molecular frame dynamics vary for molecules in different orientations and that certain coherences, which are potentially experimentally accessible, are rejected by the orientation-averaged reduced vibronic density matrix. Instead, molecular angular distribution moments are introduced as a more accurate representation of experimentally accessible information. Furthermore, the formalism provides a clear definition of a molecular frame quantum tomography and specifies the requirements to perform such a measurement enabling the experimental imaging of molecular frame vibronic dynamics. Successful completion of such a measurement fully characterizes the molecular frame quantum dynamics for a molecule at any orientation in the laboratory frame.
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Affiliation(s)
- Margaret Gregory
- Department of Chemistry and Physics, University of Mary Washington, 1301 College Avenue, Fredericksburg, Virginia 22401, USA
| | - Simon Neville
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
| | - Michael Schuurman
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario K1N 6N5, Canada
| | - Varun Makhija
- Department of Chemistry and Physics, University of Mary Washington, 1301 College Avenue, Fredericksburg, Virginia 22401, USA
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Sharma K, Miller TA, Stanton JF. Vibronically coupled states: computational considerations and characterisation of vibronic and rovibronic spectroscopic parameters. INT REV PHYS CHEM 2021. [DOI: 10.1080/0144235x.2021.1874118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Ketan Sharma
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH, USA
| | - Terry A. Miller
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, OH, USA
| | - John F. Stanton
- Department of Chemistry, University of Florida, Gainesville, FL, USA
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Liu J, Miller TA. Jet-Cooled Laser-Induced Fluorescence Spectroscopy of Cyclohexoxy: Rotational and Fine Structure of Molecules in Nearly Degenerate Electronic States. J Phys Chem A 2014; 118:11871-90. [DOI: 10.1021/jp504326p] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jinjun Liu
- Department
of Chemistry and Conn Center for Renewable Energy Research, University of Louisville, 2320 South Brook Street, Louisville, Kentucky 40292, United States, and
| | - Terry A. Miller
- Laser
Spectroscopy Facility, Department of Chemistry and Biochemistry, The Ohio State University, 120 West 18th Avenue, Columbus Ohio 43210, United States
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Affiliation(s)
- Beth Anne McClure
- Department of Chemistry and Biochemistry, Nanoscale and Quantum Phenomena Institute, Clippinger Laboratories, Ohio University Athens, OH 45701, USA, Fax: +1‐740‐593‐0148
| | - Jeffrey J. Rack
- Department of Chemistry and Biochemistry, Nanoscale and Quantum Phenomena Institute, Clippinger Laboratories, Ohio University Athens, OH 45701, USA, Fax: +1‐740‐593‐0148
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McClure BA, Abrams ER, Rack JJ. Excited State Distortion in Photochromic Ruthenium Sulfoxide Complexes. J Am Chem Soc 2010; 132:5428-36. [DOI: 10.1021/ja9099399] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Affiliation(s)
- Beth Anne McClure
- Department of Chemistry and Biochemistry, Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio 45701
| | - Eric R. Abrams
- Department of Chemistry and Biochemistry, Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio 45701
| | - Jeffrey J. Rack
- Department of Chemistry and Biochemistry, Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio 45701
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Nagesh J, Sibert EL. Vibrational dynamics around the conical intersection: a study of methoxy vibrations on the X̃2E surface. Phys Chem Chem Phys 2010; 12:8250-9. [DOI: 10.1039/c002593c] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Wörner HJ, Qian X, Merkt F. Jahn-Teller effect in tetrahedral symmetry: Large-amplitude tunneling motion and rovibronic structure of CH4+ and CD4+. J Chem Phys 2007; 126:144305. [PMID: 17444710 DOI: 10.1063/1.2712840] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The energy level structures of the ground vibronic states of 12CH4+, 13CH4+, and 12CD4+ have been measured by pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopy. The nuclear spin symmetries of the tunneling-rotational levels have been determined in double-resonance experiments via selected rotational levels of the v3=1 and v3=2 vibrational levels of the X 1A1 ground state of CH4. The energy level structures of 12CH4+, 13CH4+, and 12CD4+ have been analyzed with an effective tunneling-rotational Hamiltonian. The analysis together with a group theoretical treatment of the Tx(e+t2) Jahn-Teller effect in the Td(M) group prove that the equilibrium geometry of 12CH4+, 13CH4+, and 12CD4+ has C2v symmetry and characterize the pseudorotational dynamics in these fluxional cations. The tunneling behavior is discussed in terms of the relevant properties of the potential energy surface, some of which have been recalculated at the CCSD(T)/cc-pVTZ level of ab initio theory.
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Affiliation(s)
- H J Wörner
- Laboratorium für Physikalische Chemie, ETH-Zürich, 8093 Zürich, Switzerland
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Babikov D, Kendrick BK, Zhang P, Morokuma K. Cyclic-N3. II. Significant geometric phase effects in the vibrational spectra. J Chem Phys 2005; 122:44315. [PMID: 15740256 DOI: 10.1063/1.1824905] [Citation(s) in RCA: 61] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An accurate theoretical prediction of the vibrational spectra for a pure nitrogen ring (cyclic-N(3)) molecule is obtained up to the energy of the (2)A(2)/(2)B(1) conical intersection. A coupled-channel approach using the hyperspherical coordinates and the recently published ab initio potential energy surface [D. Babikov, P. Zhang, and K. Morokuma, J. Chem. Phys. 121, 6743 (2004)] is employed. Two independent sets of calculations are reported: In the first set, the standard Born-Oppenheimer approximation is used and the geometric phase effects are totally neglected. In the second set, the generalized Born-Oppenhimer approximation is used and the geometric phase effects due to the D(3h) conical intersection are accurately treated. All vibrational states are analyzed and assigned in terms of the normal vibration mode quantum numbers. The magnitude of the geometric phase effect is determined for each state. One important finding is an unusually large magnitude of the geometric phase effects in the cyclic-N(3): it is approximately 100 cm(-1) for the low-lying vibrational states and exceeds 600 cm(-1) for several upper states. On average, this is almost two orders of magnitude larger than in the previously reported studies. This unique example suggests a favorable path to experimental validation.
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Affiliation(s)
- Dmitri Babikov
- Chemistry Department, Marquette University, Wehr Chemistry Building, Milwaukee, WI 53201, USA
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Babikov D, Zhang P, Morokuma K. Cyclic-N3. I. An accurate potential energy surface for the ground doublet electronic state up to the energy of the 2A2/2B1 conical intersection. J Chem Phys 2004; 121:6743-9. [PMID: 15473730 DOI: 10.1063/1.1780158] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
A sophisticated adiabatic ground electronic state potential energy surface for a pure nitrogen ring (cyclic-N3) molecule is constructed based on extensive high-level ab initio calculations and accurate three-dimensional spline representation. Most of the important features of the potential energy surface are presented using various reduced dimensionality slices in internal hyperspherical coordinates as well as full dimensional isoenergy surfaces. Very significant geometric phase effects are predicted in the spectra of rotational-vibrational states of cyclic-N3.
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Affiliation(s)
- Dmitri Babikov
- Chemistry Department, Marquette University, Wehr Chemistry Building, Milwaukee, Wisconsin 53201-1881, USA
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Narevicius E, Moiseyev N, Sadeghpour HR, Cederbaum LS. Extremely narrow peaks in predissociation of sodium dimer due to rovibronic coupling. J Chem Phys 2004; 121:3527-32. [PMID: 15303917 DOI: 10.1063/1.1773171] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
In sodium dimer the 2 (3)Pi(g), 3 (3)Pi(g), and 4 (3)Sigma(g) (+) electronic states are coupled; the coupling of the two (3)Pi(g) states is due to vibrational motion while the nonadiabatic interaction between the (3)Sigma(g) (+) and the (3)Pi(g) states-in particular, the 3 (3)Pi(g) state-is mediated by rotational interaction. The resulting vibronic problem is studied in some detail. The bound vibrational states of the 3 (3)Pi(g) and 4 (3)Pi(g) (+) states lie in the dissociation continuum of the 2 (3)Pi(g) state and become resonances due to the prevailing nonadiabatic coupling. The resonances are calculated using the complex scaling method and the available ab initio adiabatic potential energy curves. It is demonstrated that the resonances associated with rotational nonadiabatic coupling are narrower by several orders of magnitude than those that emerge from the vibrational nonadiabatic coupling. The predissociation cross section is computed and compared with experiment.
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Affiliation(s)
- Edvardas Narevicius
- Institute of Theoretical Atomic, Molecular, and Optical Physics, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
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Abstract
Nonadiabatic effects play an important role in many areas of physics and chemistry. The coupling between electrons and nuclei may, for example, lead to the formation of a conical intersection between potential energy surfaces, which provides an efficient pathway for radiationless decay between electronic states. At such intersections the Born-Oppenheimer approximation breaks down, and unexpected dynamical processes result, which can be observed spectroscopically. We review the basic theory required to understand and describe conical, and related, intersections. A simple model is presented, which can be used to classify the different types of intersections known. An example is also given using wavepacket dynamics simulations to demonstrate the prototypical features of how a molecular system passes through a conical intersection.
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Affiliation(s)
- Graham A Worth
- Department of Chemistry, King's College London, The Strand, London, WC2R 2LS, United Kingdom.
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Keil M, Krämer HG, Kudell A, Baig M, Zhu J, Demtröder W, Meyer W. Rovibrational structures of the pseudorotating lithium trimer 21Li3: Rotationally resolved spectroscopy and ab initio calculations of the A 2E″←X 2E′ system. J Chem Phys 2000. [DOI: 10.1063/1.1308091] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Varandas AJC, Xu ZR. Nuclear dynamics in the vicinity of the crossing seam: Theory and application to vibrational spectrum of H3. J Chem Phys 2000. [DOI: 10.1063/1.480823] [Citation(s) in RCA: 43] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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15
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VARANDAS AJC, YU HG, XU ZR. Vibrational spectrum of ground state Li3and statistical analysis of the energy levels. Mol Phys 1999. [DOI: 10.1080/00268979909483064] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Wang J, Krämer HG, Keil M, von Busch H, Demtröder W. Photodepletion spectroscopy and predissociation of the Na3 A′(′) state. Chem Phys Lett 1999. [DOI: 10.1016/s0009-2614(99)00002-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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