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Cardosa-Gutierrez M, Levine RD, Remacle F. Electronic Coherences Excited by an Ultra Short Pulse Are Robust with Respect to Averaging over Randomly Oriented Molecules as Shown by Singular Value Decomposition. J Phys Chem A 2024; 128:2937-2947. [PMID: 38568803 DOI: 10.1021/acs.jpca.3c07856] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/05/2024]
Abstract
We report a methodology for averaging quantum photoexcitation vibronic dynamics over the initial orientations of the molecules with respect to an ultrashort light pulse. We use singular value decomposition of the ensemble density matrix of the excited molecules, which allows the identification of the few dominant principal molecular orientations with respect to the polarization direction of the electric field. The principal orientations provide insights into the specific stereodynamics of the corresponding principal molecular vibronic states. The massive compaction of the vibronic density matrix of the ensemble of randomly oriented pumped molecules enables a most efficient fully quantum mechanical time propagation scheme. Two examples are discussed for the quantum dynamics of the LiH molecule in the manifolds of its electronically excited Σ and Π states. Our results show that electronic and vibrational coherences between excited states of the same symmetry are resilient to averaging over an ensemble of molecular orientations and can be selectively excited at the ensemble level by tuning the pulse parameters.
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Affiliation(s)
| | - Raphael D Levine
- Fritz Haber Center, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
- Department of Molecular and Medical Pharmacology, David Geffen School of Medicine, Los Angeles, California 90095, United States
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095, United States
| | - Francoise Remacle
- Theoretical Physical Chemistry, UR MOLSYS, University of Liege, Liege B-4000, Belgium
- Fritz Haber Center, Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Gelfand N, Remacle F, Levine RD. Ultrafast charge migration in the laser induced dynamics of LiH validated by a computation-free isotope effect. Chem Phys Lett 2023. [DOI: 10.1016/j.cplett.2023.140318] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
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Flórez-Angarita MF, Pérez-Torres JF. Photoionization of Oriented HD( 1Σ +) Yields Vibrating HD +( 2Σ +) with Charge Breathing and Small Charge Transfer. J Phys Chem A 2022; 126:8918-8929. [DOI: 10.1021/acs.jpca.2c05050] [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]
Affiliation(s)
| | - J. F. Pérez-Torres
- Universidad Industrial de Santander, carrera 27 calle 9, 680002Bucaramanga, Colombia
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Blavier M, Gelfand N, Levine R, Remacle F. Entanglement of electrons and nuclei: A most compact representation of the molecular wave function. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.139885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Blavier M, Levine RD, Remacle F. Time evolution of entanglement of electrons and nuclei and partial traces in ultrafast photochemistry. Phys Chem Chem Phys 2022; 24:17516-17525. [PMID: 35838986 DOI: 10.1039/d2cp01440h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Broad in energy optical pulses induce ultrafast molecular dynamics where nuclear degrees of freedom are entangled with electronic ones. We discuss a matrix representation of wave functions of such entangled systems. Singular Value Decomposition (SVD) of this matrix provides a representation as a sum of separable terms. Their weights can be arranged in decreasing order. The representation provided by the SVD is equivalent to a Schmidt decomposition. If there is only one term or if one term is already a good approximation, the system is not entangled. The SVD also provides either an exact or a few term approximation for the partial traces. A simple example, the dynamics of LiH upon ultrafast excitation to several non-adiabatically coupled electronic states, is provided. The major contribution to the entanglement is created during the exit from the Franck Condon region. An additional contribution is the entanglement due to the nuclear motion induced non-adiabatic transitions.
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Affiliation(s)
- Martin Blavier
- Theoretical Physical Chemistry, University of Liège, 4000 Liège, Belgium. .,The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - R D Levine
- The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel.,Department of Chemistry and Biochemistry and Department of Molecular and Medical Pharmacology, David Geffen School of Medicine, University of California, Los Angeles, CA 90095, USA
| | - F Remacle
- Theoretical Physical Chemistry, University of Liège, 4000 Liège, Belgium. .,The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
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Blavier M, Komarova K, Gonçalves CEM, Levine RD, Remacle F. Electronic Coherences Steer the Strong Isotope Effect in the Ultrafast Jahn-Teller Structural Rearrangement of Methane Cation upon Tunnel Ionization. J Phys Chem A 2021; 125:9495-9507. [PMID: 34677060 DOI: 10.1021/acs.jpca.1c06431] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We report on fully quantum electronic-nuclear dynamics following sudden ionization from the neutral in the three lowest electronic states of the CH4+ and CD4+ cations. There is a strong Jahn-Teller effect in the Franck-Condon region, and we employ two nuclear degrees of freedom that span the internal coordinates involved in the Jahn-Teller coupling. The initial state results from tunneling ionization by a strong IR field which coherently pumps the three lowest states of the cation, D0, D1, and D2. The quantum dynamical simulations show that a strong isotope effect occurs when the ionization significantly accesses the D2 state of the cation in the Franck-Condon region. The computed isotope effect is larger than expected on the basis of the effective mass ratio. The strong effect is due to fast oscillations of the electronic coherences between the D2 and the D1 and D0 electronic states and their modulation by the nonadiabatic couplings before a significant onset of nuclear motion. The magnitude of the effect is similar to the one that we previously reported for a sudden photoionization process. A strong isotope effect has been observed in high harmonic spectroscopy studies of the very short time dynamics Jahn-Teller structural rearrangement of the methane cation upon sudden ionization.
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Affiliation(s)
- Martin Blavier
- Theoretical Physical Chemistry, University of Liège, 4000 Liège, Belgium
| | - Ksenia Komarova
- The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
| | - Cayo E M Gonçalves
- Theoretical Physical Chemistry, University of Liège, 4000 Liège, Belgium
| | - R D Levine
- The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel.,Department of Chemistry and Biochemistry and Department of Molecular and Medical Pharmacology, David Geffen School of Medicine, University of California, Los Angeles, California 90095, United States
| | - F Remacle
- Theoretical Physical Chemistry, University of Liège, 4000 Liège, Belgium.,The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel
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Armstrong GSJ, Khokhlova MA, Labeye M, Maxwell AS, Pisanty E, Ruberti M. Dialogue on analytical and ab initio methods in attoscience. THE EUROPEAN PHYSICAL JOURNAL. D, ATOMIC, MOLECULAR, AND OPTICAL PHYSICS 2021; 75:209. [PMID: 34720730 PMCID: PMC8550504 DOI: 10.1140/epjd/s10053-021-00207-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 06/18/2021] [Indexed: 06/13/2023]
Abstract
The perceived dichotomy between analytical and ab initio approaches to theory in attosecond science is often seen as a source of tension and misconceptions. This Topical Review compiles the discussions held during a round-table panel at the 'Quantum Battles in Attoscience' cecam virtual workshop, to explore the sources of tension and attempt to dispel them. We survey the main theoretical tools of attoscience-covering both analytical and numerical methods-and we examine common misconceptions, including the relationship between ab initio approaches and the broader numerical methods, as well as the role of numerical methods in 'analytical' techniques. We also evaluate the relative advantages and disadvantages of analytical as well as numerical and ab initio methods, together with their role in scientific discovery, told through the case studies of two representative attosecond processes: non-sequential double ionisation and resonant high-harmonic generation. We present the discussion in the form of a dialogue between two hypothetical theoreticians, a numericist and an analytician, who introduce and challenge the broader opinions expressed in the attoscience community.
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Affiliation(s)
- Gregory S. J. Armstrong
- Centre for Theoretical Atomic, Molecular, and Optical Physics, Queen’s University Belfast, Belfast, BT7 1NN UK
| | - Margarita A. Khokhlova
- Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Straße 2A, 12489 Berlin, Germany
- Department of Physics, Imperial College London, South Kensington Campus, London, SW7 2AZ UK
| | - Marie Labeye
- CNRS, PASTEUR, Département de chimie, Ecole Normale Supérieure, PSL University, Sorbonne Université, 75005 Paris, France
| | - Andrew S. Maxwell
- Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
- Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT UK
| | - Emilio Pisanty
- Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Straße 2A, 12489 Berlin, Germany
- Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
| | - Marco Ruberti
- Department of Physics, Imperial College London, South Kensington Campus, London, SW7 2AZ UK
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Komarova K, Remacle F, Levine RD. The density matrix via few dominant observables: The quantum interference in the isotope effect for atto-pumped N 2. J Chem Phys 2021; 155:024109. [PMID: 34266251 DOI: 10.1063/5.0053784] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023] Open
Abstract
Atto- and sub-femto-photochemistry enables preparation of molecules in a coherent superposition of several electronic states. Recently [Ajay et al., Proc. Natl. Acad. Sci. U. S. A. 115, 5890-5895 (2018)], we examined an effect of the nuclear mass during the non-adiabatic transfer between strongly coupled Rydberg and valence electronic states in N2 excited by an ultrafast pulse. Here, we develop and analyze an algebraic description for the density matrix and its logarithm, the surprisal, in such a superposition of states with a focus on the essentially quantum effect of mass. This allows for the identification of a few observables that accurately characterize the density matrix of the system with several coupled electron-nuclear states. We compact the time evolution in terms of time-dependent coefficients of these observables. Using the few observables, we derive an analytical expression for the time-dependent surprisal. This provides a mass-dependent phase factor only in the observables off-diagonal in the electronic index. The isotope effect is shown to be explicitly driven by the shift in the equilibrium position of the valence state potential. It is analytically given as a time-dependent phase factor describing the interference in the overlap of the two wave packets on the coupled electronic states. This phase factorizes as a product of classical and quantal contributions.
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Affiliation(s)
- K Komarova
- The Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - F Remacle
- The Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
| | - R D Levine
- The Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
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Khalil M, Mukamel S. Ultrafast spectroscopy and diffraction from XUV to x-ray. J Chem Phys 2020; 153:100401. [DOI: 10.1063/5.0026054] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Munira Khalil
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Shaul Mukamel
- Department of Chemistry and Physics and Astronomy, University of California, Irvine, California 92697, USA
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Valentini A, van den Wildenberg S, Remacle F. Selective bond formation triggered by short optical pulses: quantum dynamics of a four-center ring closure. Phys Chem Chem Phys 2020; 22:22302-22313. [DOI: 10.1039/d0cp03435e] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Making bonds with attopulses: quantum dynamics of the ring closure of norbornadiene to quadricyclane.
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Affiliation(s)
- Alessio Valentini
- Theoretical Physical Chemistry
- RU MOLSYS
- University of Liege
- B4000 Liege
- Belgium
| | | | - F. Remacle
- Theoretical Physical Chemistry
- RU MOLSYS
- University of Liege
- B4000 Liege
- Belgium
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