1
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Littlejohn R, Rawlinson J, Subotnik J. Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom. J Chem Phys 2024; 160:114103. [PMID: 38501907 DOI: 10.1063/5.0192465] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2023] [Accepted: 02/19/2024] [Indexed: 03/20/2024] Open
Abstract
This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ2, where κ = (m/M)1/4 is the usual Born-Oppenheimer parameter. The lowest order term is the usual Born-Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born-Oppenheimer theory. We show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born-Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.
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Affiliation(s)
- Robert Littlejohn
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - Jonathan Rawlinson
- School of Mathematics, University of Manchester, Manchester, United Kingdom
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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2
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Pieroni C, Sangiogo Gil E, Ibele LM, Persico M, Granucci G, Agostini F. Investigating the Photodynamics of trans-Azobenzene with Coupled Trajectories. J Chem Theory Comput 2024; 20:580-596. [PMID: 38177105 DOI: 10.1021/acs.jctc.3c00978] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2024]
Abstract
In this work, we present the first implementation of coupled-trajectory Tully surface hopping (CT-TSH) suitable for applications to molecular systems. We combine CT-TSH with the semiempirical floating occupation molecular orbital-configuration interaction electronic structure method to investigate the photoisomerization dynamics of trans-azobenzene. Our study shows that CT-TSH can capture correctly decoherence effects in this system, yielding consistent electronic and nuclear dynamics in agreement with (standard) decoherence-corrected TSH. Specifically, CT-TSH is derived from the exact factorization and the electronic coefficients' evolution is directly influenced by the coupling of trajectories, resulting in the improvement of internal consistency if compared to standard TSH.
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Affiliation(s)
- Carlotta Pieroni
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
| | - Eduarda Sangiogo Gil
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France
| | - Lea M Ibele
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France
| | - Maurizio Persico
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
| | - Giovanni Granucci
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
| | - Federica Agostini
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France
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3
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Ibele LM, Sangiogo Gil E, Curchod BFE, Agostini F. On the Nature of Geometric and Topological Phases in the Presence of Conical Intersections. J Phys Chem Lett 2023; 14:11625-11631. [PMID: 38100675 DOI: 10.1021/acs.jpclett.3c02672] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2023]
Abstract
The observable nature of topological phases related to conical intersections in molecules is studied. Topological phases should be ubiquitous in molecular processes, but their elusive character has often made them a topic of discussion. To shed some light on this issue, we simulate the dynamics governed by a Jahn-Teller Hamiltonian and analyze it employing two theoretical representations of the molecular wave function: the adiabatic and the exact factorization. We find fundamental differences between effects related to topological phases arising exclusively in the adiabatic representation, and thus not related to any physical observable, and geometric phases within the exact factorization that can be connected to an observable quantity. We stress that while the topological phase of the adiabatic representation is an intrinsic property of the Hamiltonian, the geometric phase of the exact factorization depends on the dynamics that the system undergoes and is connected to the circulation of the nuclear momentum field.
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Affiliation(s)
- Lea M Ibele
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Eduarda Sangiogo Gil
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Basile F E Curchod
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, U.K
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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4
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Dupuy L, Talotta F, Agostini F, Lauvergnat D, Poirier B, Scribano Y. Adiabatic and Nonadiabatic Dynamics with Interacting Quantum Trajectories. J Chem Theory Comput 2022; 18:6447-6462. [DOI: 10.1021/acs.jctc.2c00744] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Lucien Dupuy
- Laboratoire Univers et Particules de Montpellier, UMR-CNRS 5299, Université de Montpellier, Place Eugène Bataillon, 34095Montpellier, France
| | - Francesco Talotta
- Université Paris-Saclay, CNRS, Institut de Chimie Physique, UMR-CNRS 8000, 91405Orsay, France
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique, UMR-CNRS 8000, 91405Orsay, France
| | - David Lauvergnat
- Université Paris-Saclay, CNRS, Institut de Chimie Physique, UMR-CNRS 8000, 91405Orsay, France
| | - Bill Poirier
- Department of Chemistry and Biochemistry, and Department of Physics, Texas Tech University, Box 41061, 79409-1061Lubbock, Texas, United States
| | - Yohann Scribano
- Laboratoire Univers et Particules de Montpellier, UMR-CNRS 5299, Université de Montpellier, Place Eugène Bataillon, 34095Montpellier, France
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5
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Villaseco Arribas E, Agostini F, Maitra NT. Exact Factorization Adventures: A Promising Approach for Non-Bound States. Molecules 2022; 27:molecules27134002. [PMID: 35807246 PMCID: PMC9267945 DOI: 10.3390/molecules27134002] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2022] [Revised: 06/07/2022] [Accepted: 06/09/2022] [Indexed: 11/29/2022] Open
Abstract
Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.
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Affiliation(s)
| | - Federica Agostini
- Institut de Chimie Physique UMR8000, Université Paris-Saclay, CNRS, 91405 Orsay, France;
| | - Neepa T. Maitra
- Department of Physics, Rutgers University, Newark, NJ 07102, USA;
- Correspondence:
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6
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Axelrod S, Shakhnovich E, Gómez-Bombarelli R. Excited state non-adiabatic dynamics of large photoswitchable molecules using a chemically transferable machine learning potential. Nat Commun 2022; 13:3440. [PMID: 35705543 PMCID: PMC9200747 DOI: 10.1038/s41467-022-30999-w] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Accepted: 05/23/2022] [Indexed: 12/31/2022] Open
Abstract
Light-induced chemical processes are ubiquitous in nature and have widespread technological applications. For example, photoisomerization can allow a drug with a photo-switchable scaffold such as azobenzene to be activated with light. In principle, photoswitches with desired photophysical properties like high isomerization quantum yields can be identified through virtual screening with reactive simulations. In practice, these simulations are rarely used for screening, since they require hundreds of trajectories and expensive quantum chemical methods to account for non-adiabatic excited state effects. Here we introduce a diabatic artificial neural network (DANN), based on diabatic states, to accelerate such simulations for azobenzene derivatives. The network is six orders of magnitude faster than the quantum chemistry method used for training. DANN is transferable to azobenzene molecules outside the training set, predicting quantum yields for unseen species that are correlated with experiment. We use the model to virtually screen 3100 hypothetical molecules, and identify novel species with high predicted quantum yields. The model predictions are confirmed using high-accuracy non-adiabatic dynamics. Our results pave the way for fast and accurate virtual screening of photoactive compounds.
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Affiliation(s)
- Simon Axelrod
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, 02138, USA.,Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
| | - Eugene Shakhnovich
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, 02138, USA
| | - Rafael Gómez-Bombarelli
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
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7
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Talotta F, Lauvergnat D, Agostini F. Describing the photo-isomerization of a retinal chromophore model with coupled and quantum trajectories. J Chem Phys 2022; 156:184104. [DOI: 10.1063/5.0089415] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The exact factorization of the electron-nuclear wavefunction is applied to the study of the photo- isomerization of a retinal chromophore model. We describe such an ultrafast nonadiabatic process by analyzing the time-dependent potentials of the theory and by mimicking nuclear dynamics with quantum and coupled trajectories. The time-dependent vector and scalar potentials are the signature of the exact factorization, as they guide nuclear dynamics by encoding the complete electronic dynamics and including excited-state effects. Analysis of the potentials is, thus, essential - when possible - to predict the time-dependent behavior of the system of interest. In this work, we employ the exact time-dependent potentials, available for the numerically-exactly solvable model used here, to propagate quantum nuclear trajectories representing the isomerization reaction of the retinal chromophore. The quantum trajectories are the best possible trajectory-based description of the reaction when using the exact-factorization formalism, and thus allow us to assess the performance of the coupled-trajectory, fully approximate, schemes derived from the exact-factorization equations.
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Affiliation(s)
| | - David Lauvergnat
- Institut de Chimie Physique, UMR 8000, CNRS Délégation Ile-de-France Sud, France
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8
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Ibele LM, Curchod BFE, Agostini F. A Photochemical Reaction in Different Theoretical Representations. J Phys Chem A 2022; 126:1263-1281. [PMID: 35157450 PMCID: PMC8883471 DOI: 10.1021/acs.jpca.1c09604] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/02/2022]
Abstract
![]()
The Born–Oppenheimer
picture has forged our representation
and interpretation of photochemical processes, from photoexcitation
down to the passage through a conical intersection, a funnel connecting
different electronic states. In this work, we analyze a full in silico
photochemical experiment, from the explicit electronic excitation
by a laser pulse to the formation of photoproducts following a nonradiative
decay through a conical intersection, by contrasting the picture offered
by Born–Oppenheimer and that proposed by the exact factorization.
The exact factorization offers an alternative understanding of photochemistry
that does not rely on concepts such as electronic states, nonadiabatic
couplings, and conical intersections. On the basis of nonadiabatic
quantum dynamics performed for a two-state 2D model system, this work
allows us to compare Born–Oppenheimer and exact factorization
for (i) an explicit photoexcitation with and without the Condon approximation,
(ii) the passage of a nuclear wavepacket through a conical intersection,
(iii) the formation of excited stationary states in the Franck–Condon
region, and (iv) the use of classical and quantum trajectories in
the exact factorization picture to capture nonadiabatic processes
triggered by a laser pulse.
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Affiliation(s)
- Lea M Ibele
- Department of Chemistry, Durham University, Durham DH1 3LE, United Kingdom
| | - Basile F E Curchod
- Department of Chemistry, Durham University, Durham DH1 3LE, United Kingdom
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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9
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Vindel-Zandbergen P, Matsika S, Maitra NT. Exact-Factorization-Based Surface Hopping for Multistate Dynamics. J Phys Chem Lett 2022; 13:1785-1790. [PMID: 35170972 DOI: 10.1021/acs.jpclett.1c04132] [Citation(s) in RCA: 13] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
A surface-hopping algorithm recently derived from the exact factorization approach, SHXF [Ha et al. J. Phys. Chem. Lett. 2018, 9, 1097], introduces an additional term in the electronic equation of surface hopping that couples electronic states through the quantum momentum. This term not only provides a first-principles description of decoherence, but here we show it is crucial to accurately capture nonadiabatic dynamics when more than two states are occupied at any given time. Using a vibronic coupling model of the uracil cation, we show that the lack of this term in traditional surface-hopping methods, including those with decoherence corrections, leads to failure to predict the dynamics through a three-state intersection, while SHXF performs similarly to the multiconfiguration time-dependent Hartree quantum dynamics benchmark.
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Affiliation(s)
| | - Spiridoula Matsika
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Neepa T Maitra
- Department of Physics, Rutgers University, Newark, New Jersey 07102, United States
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10
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Ibele LM, Curchod BFE. Dynamics near a conical intersection-A diabolical compromise for the approximations of ab initio multiple spawning. J Chem Phys 2021; 155:174119. [PMID: 34742188 DOI: 10.1063/5.0071376] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs-in principle exact in FMS-are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born-Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation.
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Affiliation(s)
- Lea M Ibele
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - Basile F E Curchod
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
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11
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Abstract
In this paper, we discuss coupled-trajectory schemes for molecular-dynamics simulations of excited-state processes. New coupled-trajectory strategies to capture decoherence effects, revival of coherence and nonadiabatic interferences in long-time dynamics are proposed, and compared to independent-trajectory schemes. The working framework is provided by the exact factorization of the electron-nuclear wave function, and it exploits ideas emanating from various surface-hopping schemes. The new coupled-trajectory algorithms are tested on a one-dimensional two-state system using different model parameters which allow one to induce different dynamics. The benchmark is provided by the numerically exact solution of the time-dependent Schrödinger equation.
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Affiliation(s)
- Carlotta Pieroni
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via G. Moruzzi 13, 56124 Pisa, Italy
| | - Federica Agostini
- CNRS, Institut de Chimie Physique UMR8000, Université Paris-Saclay, 91405 Orsay, France
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12
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Schirò M, Eich FG, Agostini F. Quantum-classical nonadiabatic dynamics of Floquet driven systems. J Chem Phys 2021; 154:114101. [PMID: 33752379 DOI: 10.1063/5.0043790] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a trajectory-based approach for excited-state molecular dynamics simulations of systems subject to an external periodic drive. We combine the exact-factorization formalism, allowing us to treat electron-nuclear systems in nonadiabatic regimes, with the Floquet formalism for time-periodic processes. The theory is developed starting with the molecular time-dependent Schrödinger equation with the inclusion of an external periodic drive that couples to the system dipole moment. With the support of the Floquet formalism, quantum dynamics is approximated by combining classical-like, trajectory-based, nuclear evolution with electronic dynamics represented in the Floquet basis. The resulting algorithm, which is an extension of the coupled-trajectory mixed quantum-classical scheme for periodically driven systems, is applied to a model study, exactly solvable, with different field intensities.
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Affiliation(s)
- Marco Schirò
- JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321 Paris Cedex 05, France
| | - Florian G Eich
- HQS Quantum Simulations GmbH, Haid-und-Neu-Straße 7, D-76131 Karlsruhe, Germany
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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13
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Pieroni C, Marsili E, Lauvergnat D, Agostini F. Relaxation dynamics through a conical intersection: Quantum and quantum-classical studies. J Chem Phys 2021; 154:034104. [PMID: 33499611 DOI: 10.1063/5.0036726] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
Abstract
We study the relaxation process through a conical intersection of a photo-excited retinal chromophore model. The analysis is based on a two-electronic-state two-dimensional Hamiltonian developed by Hahn and Stock [J. Phys. Chem. B 104 1146 (2000)] to reproduce, with a minimal model, the main features of the 11-cis to all-trans isomerization of the retinal of rhodopsin. In particular, we focus on the performance of various trajectory-based schemes to nonadiabatic dynamics, and we compare quantum-classical results to the numerically exact quantum vibronic wavepacket dynamics. The purpose of this work is to investigate, by analyzing electronic and nuclear observables, how the sampling of initial conditions for the trajectories affects the subsequent dynamics.
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Affiliation(s)
- Carlotta Pieroni
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Emanuele Marsili
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - David Lauvergnat
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405 Orsay, France
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14
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Temen S, Akimov AV. A Simple Solution to Trivial Crossings: A Stochastic State Tracking Approach. J Phys Chem Lett 2021; 12:850-860. [PMID: 33427475 DOI: 10.1021/acs.jpclett.0c03428] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
We present a new state tracking algorithm based on a stochastic state reassignment that reflects the quantum mechanical interpretation of the state time-overlaps. We assess the new method with a range of model Hamiltonians and demonstrate that it yields the results generally consistent with the deterministic min-cost algorithm. However, the stochastic state tracking algorithm reduces magnitudes of the state population fluctuations as the quantum system evolves toward its equilibrium. The new algorithm facilitates the thermalization of quantum state populations and suppresses the population revivals and oscillations near the equilibrium in many-state systems. The new stochastic algorithm has a favorable computational scaling, is easy to implement due to its conceptual transparency, and treats various types of state identity changes (trivial or avoided crossings and any intermediate cases) on equal footing.
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Affiliation(s)
- Story Temen
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States
| | - Alexey V Akimov
- Department of Chemistry, University at Buffalo, The State University of New York, Buffalo, New York 14260, United States
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15
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Mandal A, Hunt KLC. Quantum transition probabilities due to overlapping electromagnetic pulses: Persistent differences between Dirac's form and nonadiabatic perturbation theory. J Chem Phys 2021; 154:024116. [PMID: 33445917 DOI: 10.1063/5.0020169] [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
The probability of transition to an excited state of a quantum system in a time-dependent electromagnetic field determines the energy uptake from the field. The standard expression for the transition probability has been given by Dirac. Landau and Lifshitz suggested, instead, that the adiabatic effects of a perturbation should be excluded from the transition probability, leaving an expression in terms of the nonadiabatic response. In our previous work, we have found that these two approaches yield different results while a perturbing field is acting on the system. Here, we prove, for the first time, that differences between the two approaches may persist after the perturbing fields have been completely turned off. We have designed a pair of overlapping pulses in order to establish the possibility of lasting differences, in a case with dephasing. Our work goes beyond the analysis presented by Landau and Lifshitz, since they considered only linear response and required that a constant perturbation must remain as t → ∞. First, a "plateau" pulse populates an excited rotational state and produces coherences between the ground and excited states. Then, an infrared pulse acts while the electric field of the first pulse is constant, but after dephasing has occurred. The nonadiabatic perturbation theory permits dephasing, but dephasing of the perturbed part of the wave function cannot occur within Dirac's method. When the frequencies in both pulses are on resonance, the lasting differences in the calculated transition probabilities may exceed 35%. The predicted differences are larger for off-resonant perturbations.
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Affiliation(s)
- Anirban Mandal
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Katharine L C Hunt
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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16
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Dutta J, Mukherjee S, Naskar K, Ghosh S, Mukherjee B, Ravi S, Adhikari S. The role of electron-nuclear coupling on multi-state photoelectron spectra, scattering processes and phase transitions. Phys Chem Chem Phys 2020; 22:27496-27524. [PMID: 33283826 DOI: 10.1039/d0cp04052e] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present first principle based beyond Born-Oppenheimer (BBO) theory and its applications on various models as well as realistic spectroscopic and scattering processes, where the Jahn-Teller (JT) theory is brought in conjunction with the BBO approach on the phase transition of lanthanide complexes. Over one and half decades, our development of BBO theory is demonstrated with ab initio calculations on representative molecules of spectroscopic interest (NO2 radical, Na3 and K3 clusters, NO3 radical, C6H6+ and 1,3,5-C6H3F3+ radical cations) as well as triatomic reactive scattering processes (H+ + H2 and F + H2). Such an approach exhibits the effect of JT, Renner-Teller (RT) and pseudo Jahn-Teller (PJT) type of interactions. While implementing the BBO theory, we generate highly accurate diabatic potential energy surfaces (PESs) to carry out quantum dynamics calculation and find excellent agreement with experimental photoelectron spectra of spectroscopic systems and cross-sections/rate constants of scattering processes. On the other hand, such electron-nuclear couplings incorporated through JT theory play a crucial role in dictating higher energy satellite transitions in the dielectric function spectra of the LaMnO3 complex. Overall, this article thoroughly sketches the current perspective of the BBO approach and its connection with JT theory with various applications on physical and chemical processes.
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Affiliation(s)
- Joy Dutta
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India.
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17
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Farfan CA, Turner DB. A systematic model study quantifying how conical intersection topography modulates photochemical reactions. Phys Chem Chem Phys 2020; 22:20265-20283. [PMID: 32966428 DOI: 10.1039/d0cp03464a] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.
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Affiliation(s)
- Camille A Farfan
- Department of Chemistry, New York University, New York, NY 10003, USA
| | - Daniel B Turner
- Department of Chemistry, New York University, New York, NY 10003, USA
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18
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Talotta F, Agostini F, Ciccotti G. Quantum Trajectories for the Dynamics in the Exact Factorization Framework: A Proof-of-Principle Test. J Phys Chem A 2020; 124:6764-6777. [PMID: 32786992 DOI: 10.1021/acs.jpca.0c03969] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.
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Affiliation(s)
- Francesco Talotta
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France.,Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay, France
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France.,Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay, France
| | - Giovanni Ciccotti
- CNR, Institute for Applied Computing "Mauro Picone" (IAC), Via dei Taurini 19, 00185 Rome, Italy.,School of Physics, University College of Dublin UCD - Belfield, Dublin 4, Ireland.,Dipartimento di Fisica, Università di Roma La Sapienza, P. le A. Moro 5, 00185 Roma, Italy
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19
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Talotta F, Morisset S, Rougeau N, Lauvergnat D, Agostini F. Internal Conversion and Intersystem Crossing with the Exact Factorization. J Chem Theory Comput 2020; 16:4833-4848. [PMID: 32633509 DOI: 10.1021/acs.jctc.0c00493] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a detailed derivation of the generalized coupled-trajectory mixed quantum-classical (G-CT-MQC) algorithm based on the exact-factorization equations. The ultimate goal is to propose an algorithm that can be employed for molecular dynamics simulations of nonradiative phenomena, as the spin-allowed internal conversions and the spin-forbidden intersystem crossings. Internal conversions are nonadiabatic processes driven by the kinetic coupling between electronic states, whereas intersystem crossings are mediated by the spin-orbit coupling. In this paper, we discuss computational issues related to the suitable representation for electronic dynamics and the different natures of kinetic and spin-orbit coupling. Numerical studies on model systems allow us to test the performance of the G-CT-MQC algorithm in different situations.
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Affiliation(s)
- Francesco Talotta
- Institut de Chimie Physique, UMR8000, CNRS, Université Paris-Saclay, 91405 Orsay, France.,Institut des Sciences Moléculaires d'Orsay, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - Sabine Morisset
- Institut des Sciences Moléculaires d'Orsay, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - Nathalie Rougeau
- Institut des Sciences Moléculaires d'Orsay, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - David Lauvergnat
- Institut de Chimie Physique, UMR8000, CNRS, Université Paris-Saclay, 91405 Orsay, France
| | - Federica Agostini
- Institut de Chimie Physique, UMR8000, CNRS, Université Paris-Saclay, 91405 Orsay, France
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20
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Talotta F, Morisset S, Rougeau N, Lauvergnat D, Agostini F. Spin-Orbit Interactions in Ultrafast Molecular Processes. PHYSICAL REVIEW LETTERS 2020; 124:033001. [PMID: 32031839 DOI: 10.1103/physrevlett.124.033001] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2019] [Indexed: 06/10/2023]
Abstract
We investigate spin-orbit interactions in ultrafast molecular processes employing the exact factorization of the electron-nuclear wave function. We revisit the original derivation by including spin-orbit coupling, and show how the dynamics driven by the time-dependent potential energy surface alleviates inconsistencies arising from different electronic representations. We propose a novel trajectory-based scheme to simulate spin-forbidden non-radiative processes, and we show its performance in the treatment of excited-state dynamics where spin-orbit effects couple different spin multiplets.
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Affiliation(s)
- Francesco Talotta
- Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-Sud, University Paris-Saclay, 91405 Orsay, France
- Institut de Sciences Moléculaires d'Orsay, UMR 8214 CNRS/University Paris-Sud, University Paris-Saclay, 91405 Orsay, France
| | - Sabine Morisset
- Institut de Sciences Moléculaires d'Orsay, UMR 8214 CNRS/University Paris-Sud, University Paris-Saclay, 91405 Orsay, France
| | - Nathalie Rougeau
- Institut de Sciences Moléculaires d'Orsay, UMR 8214 CNRS/University Paris-Sud, University Paris-Saclay, 91405 Orsay, France
| | - David Lauvergnat
- Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-Sud, University Paris-Saclay, 91405 Orsay, France
| | - Federica Agostini
- Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-Sud, University Paris-Saclay, 91405 Orsay, France
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21
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Mukherjee B, Naskar K, Mukherjee S, Ghosh S, Sahoo T, Adhikari S. Beyond Born–Oppenheimer theory for spectroscopic and scattering processes. INT REV PHYS CHEM 2019. [DOI: 10.1080/0144235x.2019.1672987] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Bijit Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | - Koushik Naskar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | - Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | - Sandip Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
| | - Tapas Sahoo
- Department of Chemistry, University of Waterloo, Waterloo, Ontario, Canada
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India
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22
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Ibele LM, Nicolson A, Curchod BFE. Excited-state dynamics of molecules with classically driven trajectories and Gaussians. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1665199] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Affiliation(s)
- Lea M. Ibele
- Department of Chemistry, Durham University, Durham, UK
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23
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Agostini F, Curchod BFE. Different flavors of nonadiabatic molecular dynamics. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1417] [Citation(s) in RCA: 42] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Affiliation(s)
- Federica Agostini
- Laboratoire de Chimie Physique UMR 8000 CNRS/University Paris‐Sud Orsay France
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24
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Gossel GH, Lacombe L, Maitra NT. On the numerical solution of the exact factorization equations. J Chem Phys 2019; 150:154112. [PMID: 31005081 DOI: 10.1063/1.5090802] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The exact factorization (EF) approach to coupled electron-ion dynamics recasts the time-dependent molecular Schrödinger equation as two coupled equations, one for the nuclear wavefunction and one for the conditional electronic wavefunction. The potentials appearing in these equations have provided insight into non-adiabatic processes, and new practical non-adiabatic dynamics methods have been formulated starting from these equations. Here, we provide a first demonstration of a self-consistent solution of the exact equations, with a preliminary analysis of their stability and convergence properties. The equations have an unprecedented mathematical form, involving a Hamiltonian outside the class of Hermitian Hamiltonians usually encountered in time-propagation, and so the usual numerical methods for time-dependent Schrödinger fail when applied in a straightforward way to the EF equations. We find an approach that enables stable propagation long enough to witness non-adiabatic behavior in a model system before non-trivial instabilities take over. Implications for the development and analysis of EF-based methods are discussed.
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Affiliation(s)
- Graeme H Gossel
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Lionel Lacombe
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA
| | - Neepa T Maitra
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, USA
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25
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Marsili E, Farag MH, Yang X, De Vico L, Olivucci M. Two-State, Three-Mode Parametrization of the Force Field of a Retinal Chromophore Model. J Phys Chem A 2019; 123:1710-1719. [PMID: 30753077 DOI: 10.1021/acs.jpca.8b10010] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In recent years, the potential energy surfaces of the penta-2,4-dieniminium cation have been investigated using several electronic structure methods. The resulting pool of geometrical, electronic, and energy data provides a suitable basis for the construction of a topographically correct analytical model of the molecule force field and, therefore, for a better understanding of this class of molecules, which includes the chromophore of visual pigments. In the present contribution, we report the construction of such a model for regions of the force field that drive the photochemical and thermal isomerization of the central double bound of the cation. While previous models included only two modes, it is here shown that the proposed three-mode model and corresponding set of parameters are able to reproduce the complex topographical and electronic structure features seen in electronically correlated data obtained at the XMCQDPT2//CASSCF/6-31G* level of theory.
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Affiliation(s)
- Emanuele Marsili
- Dipartimento di Biotecnologie, Chimica e Farmacia , Università di Siena , via A. Moro 2 , I-53100 Siena , Italy
| | - Marwa H Farag
- Department of Chemistry , University of Southern California , Los Angeles , California 90089-0482 , United States
| | - Xuchun Yang
- Department of Chemistry , Bowling Green State University , Bowling Green , Ohio 43403 , United States and
| | - Luca De Vico
- Dipartimento di Biotecnologie, Chimica e Farmacia , Università di Siena , via A. Moro 2 , I-53100 Siena , Italy
| | - Massimo Olivucci
- Dipartimento di Biotecnologie, Chimica e Farmacia , Università di Siena , via A. Moro 2 , I-53100 Siena , Italy.,Department of Chemistry , Bowling Green State University , Bowling Green , Ohio 43403 , United States and.,Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 , Université de Strasbourg-CNRS , F-67034 Strasbourg , France
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26
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Agostini F, Gross E, Curchod BF. Electron-nuclear entanglement in the time-dependent molecular wavefunction. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2019.01.021] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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27
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Gossel GH, Agostini F, Maitra NT. Coupled-Trajectory Mixed Quantum-Classical Algorithm: A Deconstruction. J Chem Theory Comput 2018; 14:4513-4529. [DOI: 10.1021/acs.jctc.8b00449] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Affiliation(s)
- Graeme H. Gossel
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, United States
| | - Federica Agostini
- Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-Sud, 91405 Orsay, France
| | - Neepa T. Maitra
- Department of Physics and Astronomy, Hunter College and the City University of New York, 695 Park Avenue, New York, New York 10065, United States
- The Physics Program and the Chemistry Program of the Graduate Center, City University of New York, 365 Fifth Avenue, New York, United States
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28
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Crespo-Otero R, Barbatti M. Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–Classical Dynamics. Chem Rev 2018; 118:7026-7068. [DOI: 10.1021/acs.chemrev.7b00577] [Citation(s) in RCA: 301] [Impact Index Per Article: 50.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Rachel Crespo-Otero
- School of Biological and Chemical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, United Kingdom
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29
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Affiliation(s)
- Basile F. E. Curchod
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - Todd J. Martínez
- Department of Chemistry and PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
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30
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Halász GJ, Badankó P, Vibók Á. Geometric phase of light-induced conical intersections: adiabatic time-dependent approach. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1431410] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Gábor J. Halász
- Department of Information Technology, University of Debrecen , Debrecen, Hungary
| | - Péter Badankó
- Department of Theoretical Physics, University of Debrecen , Debrecen, Hungary
| | - Ágnes Vibók
- Department of Theoretical Physics, University of Debrecen , Debrecen, Hungary
- ELI-ALPS, ELI-HU Non-Profit Ltd , Szeged, Hungary
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31
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Csehi A, Halász GJ, Cederbaum LS, Vibók Á. Intrinsic and light-induced nonadiabatic phenomena in the NaI molecule. Phys Chem Chem Phys 2017; 19:19656-19664. [PMID: 28489085 DOI: 10.1039/c7cp02164j] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Nonadiabatic effects play a very important role in controlling chemical dynamical processes. They are strongly related to avoided crossings (AC) or conical intersections (CIs) which can either be present naturally or induced by classical laser light in a molecular system. The latter are named as "light-induced avoided crossings" (LIACs) and "light-induced conical intersections" (LICIs). By performing one or two dimensional quantum dynamical calculations LIAC and LICI situations can easily be created even in diatomic molecules. Applying such calculations for the NaI molecule, which is a strongly coupled diatomic in field free case, significant differences between the impact of the LIAC and LICI on the ground state population dynamics were observed. Moreover, obtained results undoubtedly demonstrate that the effect of the LIAC and LICI on the dynamics strongly depends on the intensity and the frequency of the applied laser field as well as the permanent dipole moments of the molecule.
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Affiliation(s)
- András Csehi
- Department of Theoretical Physics, University of Debrecen, PO Box 400, H-4002 Debrecen, Hungary.
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32
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Ryabinkin IG, Joubert-Doriol L, Izmaylov AF. Geometric Phase Effects in Nonadiabatic Dynamics near Conical Intersections. Acc Chem Res 2017; 50:1785-1793. [PMID: 28665584 DOI: 10.1021/acs.accounts.7b00220] [Citation(s) in RCA: 69] [Impact Index Per Article: 9.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Dynamical consideration that goes beyond the common Born-Oppenheimer approximation (BOA) becomes necessary when energy differences between electronic potential energy surfaces become small or vanish. One of the typical scenarios of the BOA breakdown in molecules beyond diatomics is a conical intersection (CI) of electronic potential energy surfaces. CIs provide an efficient mechanism for radiationless electronic transitions: acting as "funnels" for the nuclear wave function, they enable rapid conversion of the excessive electronic energy into the nuclear motion. In addition, CIs introduce nontrivial geometric phases (GPs) for both electronic and nuclear wave functions. These phases manifest themselves in change of the wave function signs if one considers an evolution of the system around the CI. This sign change is independent of the shape of the encircling contour and thus has a topological character. How these extra phases affect nonadiabatic dynamics is the main question that is addressed in this Account. We start by considering the simplest model providing the CI topology: two-dimensional two-state linear vibronic coupling model. Selecting this model instead of a real molecule has the advantage that various dynamical regimes can be easily modeled in the model by varying parameters, whereas any fixed molecule provides the system specific behavior that may not be very illustrative. After demonstrating when GP effects are important and how they modify the dynamics for two sets of initial conditions (starting from the ground and excited electronic states), we give examples of molecular systems where the described GP effects are crucial for adequate description of nonadiabatic dynamics. Interestingly, although the GP has a topological character, the extent to which accounting for GPs affect nuclear dynamics profoundly depends on topography of potential energy surfaces. Understanding an extent of changes introduced by the GP in chemical dynamics poses a problem of capturing GP effects by approximate methods of simulating nonadiabatic dynamics that can go beyond simple models. We assess the performance of both fully quantum (wave packet dynamics) and quantum-classical (surface-hopping, Ehrenfest, and quantum-classical Liouville equation) approaches in various cases where GP effects are important. It has been identified that the key to success in approximate methods is a method organization that prevents the quantum nuclear kinetic energy operator to act directly on adiabatic electronic wave functions.
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Affiliation(s)
- Ilya G. Ryabinkin
- Department
of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical
Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Loïc Joubert-Doriol
- Department
of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical
Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Artur F. Izmaylov
- Department
of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
- Chemical
Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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33
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Min SK, Agostini F, Tavernelli I, Gross EKU. Ab Initio Nonadiabatic Dynamics with Coupled Trajectories: A Rigorous Approach to Quantum (De)Coherence. J Phys Chem Lett 2017; 8:3048-3055. [PMID: 28618782 DOI: 10.1021/acs.jpclett.7b01249] [Citation(s) in RCA: 93] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We report the first nonadiabatic molecular dynamics study based on the exact factorization of the electron-nuclear wave function. Our approach (a coupled-trajectory mixed quantum-classical, CT-MQC, scheme) is based on the quantum-classical limit derived from systematic and controlled approximations to the full quantum-mechanical problem formulated in the exact-factorization framework. Its strength is the ability to correctly capture quantum (de)coherence effects in a trajectory-based approach to excited-state dynamics. We show this by benchmarking CT-MQC dynamics against a revised version of the popular fewest-switches surface-hopping scheme that is able to fix its well-documented overcoherence issue. The CT-MQC approach is successfully applied to investigation of the photochemistry (ring-opening) of oxirane in the gas phase, analyzing in detail the role of decoherence. This work represents a significant step forward in the establishment of the exact factorization as a powerful tool to study excited-state dynamics, not only for interpretation purposes but mainly for nonadiabatic ab initio molecular dynamics simulations.
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Affiliation(s)
- Seung Kyu Min
- Department of Chemistry, School of Natural Science, Ulsan National Institute of Science and Technology (UNIST) , Ulsan 44919, Korea
| | - Federica Agostini
- Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-Sud, University Paris-Saclay , 91405 Orsay, France
| | - Ivano Tavernelli
- IBM Research GmbH, Zürich Research Laboratory , 8803 Rüschlikon, Switzerland
| | - E K U Gross
- Max-Planck Institut für Mikrostrukturphysik , Weinberg 2, D-06120 Halle, Germany
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