1
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Chatterjee K, Koczor-Benda Z, Feng X, Krylov AI, Jagau TC. Analytic Evaluation of Nonadiabatic Couplings within the Complex Absorbing Potential Equation-of-Motion Coupled-Cluster Method. J Chem Theory Comput 2023; 19:5821-5834. [PMID: 37647100 DOI: 10.1021/acs.jctc.3c00514] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/01/2023]
Abstract
We present the theory for the evaluation of nonadiabatic couplings (NACs) involving resonance states within the complex absorbing potential equation-of-motion coupled-cluster (CAP-EOM-CC) framework implemented within the singles and doubles approximation. Resonance states are embedded in the continuum and undergo rapid decay through autodetachment. In addition, nuclear motion can facilitate transitions between different resonances and between resonances and bound states. These nonadiabatic transitions affect the chemical fate of resonances and have distinct spectroscopic signatures. The NAC vector is a central quantity needed to model such effects. In the CAP-EOM-CC framework, resonance states are treated on the same footing as bound states. Using the example of fumaronitrile, which supports a bound radical anion and several anionic resonances, we analyze the NAC between bound states and pseudocontinuum states, between bound states and resonances, and between two resonances. We find that the NAC between a bound state and a resonance is nearly independent of the CAP strength and thus straightforward to evaluate, whereas the NAC between two resonance states or between a bound state and a pseudocontinuum state is more difficult to evaluate.
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Affiliation(s)
- Koushik Chatterjee
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium
| | | | - Xintian Feng
- Q-Chem, Inc., 6601 Owens Drive, Suite 240, Pleasanton, California 94588, United States
| | - Anna I Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States
| | - Thomas-C Jagau
- Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium
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2
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Lassmann Y, Curchod BFE. Probing the sensitivity of ab initio multiple spawning to its parameters. Theor Chem Acc 2023; 142:66. [PMID: 37520272 PMCID: PMC10382418 DOI: 10.1007/s00214-023-03004-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Accepted: 07/13/2023] [Indexed: 08/01/2023]
Abstract
Full multiple spawning (FMS) offers a strategy to simulate the nonadiabatic dynamics of molecular systems by describing their nuclear wavefunctions by a linear combination of coupled trajectory basis functions (TBFs). Applying a series of controlled approximations to the full multiple spawning (FMS) equations leads to the ab initio multiple spawning (AIMS), which is compatible with an on-the-fly propagation of the TBFs and an accurate description of nonadiabatic processes. The AIMS strategy and its numerical implementations, however, rely on a series of user-defined parameters. Herein, we investigate the influence of these parameters on the electronic-state population of two molecular systems- trans-azomethane and a two-dimensional model of the butatriene cation. This work highlights the stability of AIMS with respect to most of its parameters, underlines the specific parameters that require particular attention from the user of the method, and offers prescriptions for an informed selection of their value. Supplementary Information The online version contains supplementary material available at 10.1007/s00214-023-03004-w.
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Affiliation(s)
- Yorick Lassmann
- Centre for Computational Chemistry, School of Chemistry, Cantock’s Close, University of Bristol, Bristol, BS8 1TS UK
| | - Basile F. E. Curchod
- Centre for Computational Chemistry, School of Chemistry, Cantock’s Close, University of Bristol, Bristol, BS8 1TS UK
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3
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Lassmann Y, Hollas D, Curchod BFE. Extending the Applicability of the Multiple-Spawning Framework for Nonadiabatic Molecular Dynamics. J Phys Chem Lett 2022; 13:12011-12018. [PMID: 36541684 PMCID: PMC9806853 DOI: 10.1021/acs.jpclett.2c03295] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Accepted: 12/07/2022] [Indexed: 06/17/2023]
Abstract
Ab initio multiple-spawning (AIMS) describes the nonadiabatic dynamics of molecules by expanding nuclear wave functions in a basis of traveling multidimensional Gaussians called trajectory basis functions (TBFs). New TBFs can be spawned whenever nuclear amplitude is transferred between electronic states due to nonadiabatic transitions. While the adaptive size of the TBF basis grants AIMS its characteristic accuracy in describing nonadiabatic processes, it also leads to a fast and uncontrolled growth of the number of TBFs, penalizing computational efficiency. A different flavor of AIMS, called AIMS with informed stochastic selections (AIMSWISS), has recently been proposed to reduce the number of TBFs dramatically. Herein, we test the performance of AIMSWISS for a series of challenging nonadiabatic processes─photodynamics of two-dimensional model systems, 1,2-dithiane and chromium (0) hexacarbonyl─and show that this method is robust and extends the range of molecular systems that can be simulated within the multiple-spawning framework.
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4
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Maskri R, Joubert-Doriol L. The moving crude adiabatic alternative to the adiabatic representation in excited state dynamics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20200379. [PMID: 35341311 DOI: 10.1098/rsta.2020.0379] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Accepted: 12/09/2021] [Indexed: 06/14/2023]
Abstract
The choice of the electronic representation in on-the-fly quantum dynamics is crucial. The adiabatic representation is appealing since adiabatic states are readily available from quantum chemistry packages. The nuclear wavepackets are then expanded in a basis of Gaussian functions, which follow trajectories to explore the potential energy surfaces and approximate the potential using a local expansion of the adiabatic quantities. Nevertheless, the adiabatic representation is plagued with severe limitations when conical intersections are involved: the diagonal Born-Oppenheimer corrections (DBOCs) are non-integrable, and the geometric phase effect on the nuclear wavepackets cannot be accounted for unless a model is available. To circumvent these difficulties, the moving crude adiabatic (MCA) representation was proposed and successfully tested in low energy dynamics where the wavepacket skirts the conical intersection. We assess the MCA representation in the case of non-adiabatic transitions through conical intersections. First, we show that using a Gaussian basis in the adiabatic representation indeed exhibits the aforementioned difficulties with a special emphasis on the possibility to regularize the DBOC terms. Then, we show that MCA is indeed able to properly model non-adiabatic transitions. Tests are done on linear vibronic coupling models for the bis(methylene) adamantyl cation and the butatriene cation. This article is part of the theme issue 'Chemistry without the Born-Oppenheimer approximation'.
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Affiliation(s)
- Rosa Maskri
- Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, UMR 8208, MSME, F-77454 Marne-la-Vallée, France
| | - Loïc Joubert-Doriol
- Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, UMR 8208, MSME, F-77454 Marne-la-Vallée, France
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5
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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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6
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Wang Z, Wu C, Liu W. NAC-TDDFT: Time-Dependent Density Functional Theory for Nonadiabatic Couplings. Acc Chem Res 2021; 54:3288-3297. [PMID: 34448566 DOI: 10.1021/acs.accounts.1c00312] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
First-order nonadiabatic coupling (NAC) matrix elements (fo-NACMEs) are the basic quantities in theoretical descriptions of electronically nonadiabatic processes that are ubiquitous in molecular physics and chemistry. Given the large size of systems of chemical interests, time-dependent density functional theory (TDDFT) is usually the first choice of methods. However, the lack of many-electron wave functions in TDDFT renders the formulation of NAC-TDDFT for fo-NACMEs conceptually difficult. Because of this, various variants of NAC-TDDFT have been proposed in the literature from different standing points, including the Hellmann-Feynman-like expression and auxiliary/pseudo-wave function (AWF)-, equation-of-motion (EOM)-, and time-dependent perturbation theory (TDPT)-based formulations. Based on critical analyses, the following conclusions are made here: (1) The Hellmann-Feynman-like expression, which is rooted in exact wave function theory, is hardly useful due to huge demand on basis sets. (2) Although most popular, the AWF variants of NAC-TDDFT are not theoretically founded and become ambiguous particularly for the fo-NACMEs between two excited states, although they do agree with the EOM and TDPT variants under the Tamm-Dancoff approximation. (3) The TDPT variant of NAC-TDDFT is theoretically most rigorous but suffers from numerical instabilities on the one hand and does not differ to a significant extent from the EOM variant on the other hand. (4) As such, the EOM variant of NAC-TDDFT for the fo-NACMEs between the ground and excited states and between two excited states is solely the right choice in practice. These formal analyses are fully supported by numerical experimentations, taking azulene as a showcase. The proper implementation of the EOM variant of NAC-TDDFT is also highlighted, showing that the fo-NACMEs between the ground and excited states and between two excited states are computationally very much the same as the analytic energy gradients of DFT and TDDFT, respectively. Possible future developments of the EOM variant of NAC-TDDFT are also highlighted. Its extensions to spin-adapted open-shell TDDFT and proper treatment of spin-orbit couplings (which are another source of force for electronically nonadiabatic processes) are particularly warranted in the near future.
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Affiliation(s)
- Zikuan Wang
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Chenyu Wu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
| | - Wenjian Liu
- Qingdao Institute for Theoretical and Computational Sciences, Institute of Frontier and Interdisciplinary Science, Shandong University, Qingdao, Shandong 266237, China
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7
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Weight BM, Mandal A, Huo P. Ab initio symmetric quasi-classical approach to investigate molecular Tully models. J Chem Phys 2021; 155:084106. [PMID: 34470343 DOI: 10.1063/5.0061934] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We perform on-the-fly non-adiabatic molecular dynamics simulations using the symmetrical quasi-classical (SQC) approach with the recently suggested molecular Tully models: ethylene and fulvene. We attempt to provide benchmarks of the SQC methods using both the square and triangle windowing schemes as well as the recently proposed electronic zero-point-energy correction scheme (the so-called γ correction). We use the quasi-diabatic propagation scheme to directly interface the diabatic SQC methods with adiabatic electronic structure calculations. Our results showcase the drastic improvement of the accuracy by using the trajectory-adjusted γ-corrections, which outperform the widely used trajectory surface hopping method with decoherence corrections. These calculations provide useful and non-trivial tests to systematically investigate the numerical performance of various diabatic quantum dynamics approaches, going beyond simple diabatic model systems that have been used as the major workhorse in the quantum dynamics field. At the same time, these available benchmark studies will also likely foster the development of new quantum dynamics approaches based on these techniques.
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Affiliation(s)
- Braden M Weight
- Department of Physics and Astronomy, University of Rochester, Rochester, New York 14627, USA
| | - Arkajit Mandal
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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8
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Matsika S. Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections. Chem Rev 2021; 121:9407-9449. [PMID: 34156838 DOI: 10.1021/acs.chemrev.1c00074] [Citation(s) in RCA: 50] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.
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Affiliation(s)
- Spiridoula Matsika
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
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9
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Fedorov DA, Seritan S, Fales BS, Martínez TJ, Levine BG. PySpawn: Software for Nonadiabatic Quantum Molecular Dynamics. J Chem Theory Comput 2020; 16:5485-5498. [PMID: 32687710 DOI: 10.1021/acs.jctc.0c00575] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
Abstract
The ab initio multiple spawning (AIMS) method enables nonadiabatic quantum molecular dynamics simulations in an arbitrary number of dimensions, with potential energy surfaces provided by electronic structure calculations performed on-the-fly. However, the intricacy of the AIMS algorithm complicates software development, deployment on modern shared computer resources, and postsimulation data analysis. PySpawn is a nonadiabatic molecular dynamics software package that addresses these issues. The program is designed to be easily interfaced with electronic structure software, and an interface to the TeraChem software package is described here. PySpawn introduces a task-based reorganization of the AIMS algorithm, allowing fine-grained restart capability and setting the stage for efficient parallelization in a future release. PySpawn includes a user-friendly and interactive Python analysis module that will enable novice users to painlessly adopt AIMS. As a demonstration of PySpawn's simulation capability and analysis module, we report complete active space self-consistent field-based AIMS simulations of the 1,2-dithienyl-1,2-dicyanoethene molecule, a promising molecular photoswitch.
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Affiliation(s)
- Dmitry A Fedorov
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
| | - Stefan Seritan
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, Menlo Park, California 94305, United States
| | - B Scott Fales
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, Menlo Park, California 94305, United States
| | - Todd J Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, Menlo Park, California 94305, United States
| | - Benjamin G Levine
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, United States
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10
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Curchod BFE, Glover WJ, Martínez TJ. SSAIMS-Stochastic-Selection Ab Initio Multiple Spawning for Efficient Nonadiabatic Molecular Dynamics. J Phys Chem A 2020; 124:6133-6143. [PMID: 32580552 DOI: 10.1021/acs.jpca.0c04113] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Ab initio multiple spawning provides a powerful and accurate way of describing the excited-state dynamics of molecular systems, whose strength resides in the proper description of coherence effects during nonadiabatic processes thanks to the coupling of trajectory basis functions. However, the simultaneous propagation of a large number of trajectory basis functions can be numerically inconvenient. We propose here an elegant and simple solution to this issue, which consists of (i) detecting uncoupled groups of coupled trajectory basis functions and (ii) selecting stochastically one of these groups to continue the ab initio multiple spawning dynamics. We show that this procedure can reproduce the results of full ab initio multiple spawning dynamics in cases where the uncoupled groups of trajectory basis functions stay uncoupled throughout the dynamics (which is often the case in high-dimensional problems). We present and discuss the aforementioned idea in detail and provide simple numerical applications on indole, ethylene, and protonated formaldimine, highlighting the potential of stochastic-selection ab initio multiple spawning.
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Affiliation(s)
- Basile F E Curchod
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - William J Glover
- NYU Shanghai, 1555 Century Ave., Shanghai 200122, China.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China.,Department of Chemistry, New York University, New York, New York 10003, United States
| | - Todd J Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States.,SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
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11
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Zhou W, Mandal A, Huo P. Quasi-Diabatic Scheme for Nonadiabatic On-the-Fly Simulations. J Phys Chem Lett 2019; 10:7062-7070. [PMID: 31665889 DOI: 10.1021/acs.jpclett.9b02747] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We use the quasi-diabatic (QD) propagation scheme to perform on-the-fly nonadiabatic simulations of the photodynamics of ethylene. The QD scheme enables a seamless interface between accurate diabatic-based quantum dynamics approaches and adiabatic electronic structure calculations, explicitly avoiding any efforts to construct global diabatic states or reformulate the diabatic dynamics approach to the adiabatic representation. Using the partial linearized path-integral approach and the symmetrical quasi-classical approach as the diabatic dynamics methods, the QD propagation scheme enables direct nonadiabatic simulation with complete active space self-consistent field on-the-fly electronic structure calculations. The population dynamics obtained from both approaches are in a close agreement with the quantum wavepacket-based method and outperform the widely used trajectory surface-hopping approach. Further analysis of the ethylene photodeactivation pathways demonstrates the correct predictions of competing processes of nonradiative relaxation mechanism through various conical intersections. This work provides the foundation of using accurate diabatic dynamics approaches and on-the-fly adiabatic electronic structure information to perform ab initio nonadiabatic simulation.
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Affiliation(s)
- Wanghuai Zhou
- Advanced Functional Material and Photoelectric Technology Research Institution, School of Science , Hubei University of Automotive Technology , Shiyan , Hubei 442002 , People's Republic of China
- Department of Chemistry , University of Rochester , 120 Trustee Road , Rochester , New York 14627 , United States
| | - Arkajit Mandal
- Department of Chemistry , University of Rochester , 120 Trustee Road , Rochester , New York 14627 , United States
| | - Pengfei Huo
- Department of Chemistry , University of Rochester , 120 Trustee Road , Rochester , New York 14627 , United States
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12
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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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13
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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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14
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Miao G, Bellonzi N, Subotnik J. An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry curvature and “magnetic” forces. J Chem Phys 2019; 150:124101. [DOI: 10.1063/1.5088770] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Nicole Bellonzi
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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15
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Mandal A, Sandoval C. JS, Shakib FA, Huo P. Quasi-Diabatic Propagation Scheme for Direct Simulation of Proton-Coupled Electron Transfer Reaction. J Phys Chem A 2019; 123:2470-2482. [DOI: 10.1021/acs.jpca.9b00077] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Juan S. Sandoval C.
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Farnaz A. Shakib
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
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16
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Fedorov DA, Levine BG. A discontinuous basis enables numerically exact solution of the Schrödinger equation around conical intersections in the adiabatic representation. J Chem Phys 2019; 150:054102. [PMID: 30736673 DOI: 10.1063/1.5058268] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Solving the vibrational Schrödinger equation in the neighborhood of conical intersections in the adiabatic representation is a challenge. At the intersection point, first- and second-derivative nonadiabatic coupling matrix elements become singular, with the singularity in the second-derivative coupling (diagonal Born-Oppenheimer correction) being non-integrable. These singularities result from discontinuities in the vibronic functions associated with the individual adiabatic states, and our group has recently argued that these divergent matrix elements cancel when discontinuous adiabatic vibronic functions sum to a continuous total nonadiabatic wave function. Here we describe the realization of this concept: a novel scheme for the numerically exact solution of the Schrödinger equation in the adiabatic representation. Our approach is based on a basis containing functions that are discontinuous at the intersection point. We demonstrate that the individual adiabatic nuclear wave functions are themselves discontinuous at the intersection point. This proves that discontinuous basis functions are essential to any tractable method that solves the Schrödinger equation around conical intersections in the adiabatic representation with high numerical precision. We establish that our method provides numerically exact results by comparison to reference calculations performed in the diabatic representation. In addition, we quantify the energetic error associated with constraining the density to be zero at the intersection point, a natural approximation. Prospects for extending the present treatment of a two-dimensional model to systems of higher dimensionality are discussed.
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Affiliation(s)
- Dmitry A Fedorov
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Benjamin G Levine
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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17
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Baskov R, White AJ, Mozyrsky D. Improved Ehrenfest Approach to Model Correlated Electron-Nuclear Dynamics. J Phys Chem Lett 2019; 10:433-440. [PMID: 30621396 DOI: 10.1021/acs.jpclett.8b03061] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Mixed quantum-classical mechanical descriptions are critical to modeling coupled electron-nuclear dynamics, i.e., nonadiabatic molecular dynamics, relevant to photochemical and photophysical processes. We introduce an efficient description of such dynamics in terms of an effective Hamiltonian that not only properly captures electron-nuclear correlation effects but also helps develop an efficient computational method. In particular, we introduce a coupled Gaussian wavepacket parametrization of the nuclear wave function, which generalizes the Ehrenfest approach to account for electron-nuclei correlations. We test this new approach, Ehrenfest-Plus, on a suite of model problems that probe electron-nuclear correlation in nonadiabatic transitions. The high accuracy of our approach, combined with mixed quantum-classical efficiency, opens a path for improved simulation of nonadiabatic molecular dynamics in realistic molecular systems.
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Affiliation(s)
- Roman Baskov
- Institute of Physics of the National Academy of Sciences of Ukraine , Pr. Nauky 46 , Kyiv-28 MSP 03028 , Ukraine
| | - Alexander J White
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
| | - Dmitry Mozyrsky
- Theoretical Division , Los Alamos National Laboratory , Los Alamos , New Mexico 87545 , United States
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18
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Torres A, Prado LR, Bortolini G, Rego LGC. Charge Transfer Driven Structural Relaxation in a Push-Pull Azobenzene Dye-Semiconductor Complex. J Phys Chem Lett 2018; 9:5926-5933. [PMID: 30257563 DOI: 10.1021/acs.jpclett.8b02490] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Photoexcited structural dynamics in azo-compounds may differ fundamentally whether the push-pull photochromic azo-compound is isolated or forms a heterogeneous charge transfer complex, due to a sudden oxidation of the chromophore. Herein, we use a quantum-classical self-consistent approach that incorporates nonadiabatic excited-state electronic quantum dynamics into molecular mechanics to study the photoexcited dynamics of the push-pull azo-compound para-Methyl Red in the gas phase and sensitizing the (101) anatase surface of TiO2. We find that the photoinduced S2/S0 trans-to- cis isomerization of para-Methyl Red in the gas phase occurs through a pedal-like torsion around the ϕCNNC dihedral angle, without evidence to support the inversion mechanism, likewise in the parent azobenzene molecule. However, the photoexcited structural relaxation of the charge transfer complex para-Methyl Red/TiO2 contrasts essentially with the isolated azo-compounds. Immediately after photoexcitation, the excited electron flows into the TiO2 conduction band, with an injection time constant of ≃5 fs, and no indication of isomerization is observed during the 1.5 ps simulations. Instead, a strong vibronic relaxation occurs that excites the NN stretching mode of the azo-group, which is ultimately ascribed to the NA relaxation, and delocalization, of the hole wavepacket.
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Affiliation(s)
- Alberto Torres
- Department of Physics , Universidade Federal de Santa Catarina , Florianópolis , SC 88040-900 , Brazil
| | - Luciano R Prado
- Department of Physics , Universidade Federal de Santa Catarina , Florianópolis , SC 88040-900 , Brazil
| | - Graziele Bortolini
- Department of Physics , Universidade Federal de Santa Catarina , Florianópolis , SC 88040-900 , Brazil
| | - Luis G C Rego
- Department of Physics , Universidade Federal de Santa Catarina , Florianópolis , SC 88040-900 , Brazil
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19
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Sandoval C. JS, Mandal A, Huo P. Symmetric quasi-classical dynamics with quasi-diabatic propagation scheme. J Chem Phys 2018; 149:044115. [DOI: 10.1063/1.5036787] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
| | - Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, USA
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20
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Mignolet B, Curchod BFE. A walk through the approximations of ab initio multiple spawning. J Chem Phys 2018; 148:134110. [PMID: 29626896 DOI: 10.1063/1.5022877] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Full multiple spawning offers an in principle exact framework for excited-state dynamics, where nuclear wavefunctions in different electronic states are represented by a set of coupled trajectory basis functions that follow classical trajectories. The couplings between trajectory basis functions can be approximated to treat molecular systems, leading to the ab initio multiple spawning method which has been successfully employed to study the photochemistry and photophysics of several molecules. However, a detailed investigation of its approximations and their consequences is currently missing in the literature. In this work, we simulate the explicit photoexcitation and subsequent excited-state dynamics of a simple system, LiH, and we analyze (i) the effect of the ab initio multiple spawning approximations on different observables and (ii) the convergence of the ab initio multiple spawning results towards numerically exact quantum dynamics upon a progressive relaxation of these approximations. We show that, despite the crude character of the approximations underlying ab initio multiple spawning for this low-dimensional system, the qualitative excited-state dynamics is adequately captured, and affordable corrections can further be applied to ameliorate the coupling between trajectory basis functions.
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Affiliation(s)
- Benoit Mignolet
- Theoretical Physical Chemistry, UR MolSYS, B6c, University of Liège, B4000 Liège, Belgium
| | - Basile F E Curchod
- Department of Chemistry, Durham University, South Road, Durham DH1 3LE, United Kingdom
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21
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Joubert-Doriol L, Izmaylov AF. Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians. J Phys Chem A 2018; 122:6031-6042. [DOI: 10.1021/acs.jpca.8b03404] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- 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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22
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Joubert-Doriol L, Izmaylov AF. Variational nonadiabatic dynamics in the moving crude adiabatic representation: Further merging of nuclear dynamics and electronic structure. J Chem Phys 2018; 148:114102. [PMID: 29566517 DOI: 10.1063/1.5020655] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new approach is the elimination of any global or local model representation of electronic potential energy surfaces; instead, the electron-nuclear interaction is treated explicitly using the Gaussian integration. As a result, the new scheme does not introduce any uncontrolled approximations. The employed variational principle ensures the energy conservation and leaves the number of electronic and nuclear basis functions as the only parameter determining the accuracy. To assess performance of the approach, a model with two electronic and two nuclear spacial degrees of freedom containing conical intersections between potential energy surfaces has been considered. Dynamical features associated with nonadiabatic transitions and nontrivial geometric (or Berry) phases were successfully reproduced within a limited basis expansion.
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Affiliation(s)
- Loïc Joubert-Doriol
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada and 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 and Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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23
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Mandal A, Yamijala SSRKC, Huo P. Quasi-Diabatic Representation for Nonadiabatic Dynamics Propagation. J Chem Theory Comput 2018; 14:1828-1840. [DOI: 10.1021/acs.jctc.7b01178] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Arkajit Mandal
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Sharma SRKC Yamijala
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
| | - Pengfei Huo
- Department of Chemistry, University of Rochester, 120 Trustee Road, Rochester, New York 14627, United States
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24
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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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25
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Faraji S, Matsika S, Krylov AI. Calculations of non-adiabatic couplings within equation-of-motion coupled-cluster framework: Theory, implementation, and validation against multi-reference methods. J Chem Phys 2018; 148:044103. [DOI: 10.1063/1.5009433] [Citation(s) in RCA: 31] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Shirin Faraji
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
- Zernike Institute for Advanced Materials, Groningen, The Netherlands
| | - Spiridoula Matsika
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Anna I. Krylov
- Department of Chemistry, University of Southern California, Los Angeles, California 90089, USA
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26
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Robust and Efficient Spin Purification for Determinantal Configuration Interaction. J Chem Theory Comput 2017; 13:4162-4172. [DOI: 10.1021/acs.jctc.7b00466] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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27
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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: 78] [Impact Index Per Article: 11.1] [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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28
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Abstract
Conical intersections represent critical topological features of potential energy surfaces and open ultrafast nonradiative deactivation channels for photoexcited molecules. In the following, we investigate how this funneling picture is transposed in the eyes of the exact factorization formalism for a 2D model system. The exact factorization of the total molecular wave function leads to the fundamental concept of time-dependent potential energy surface and time-dependent vector potential, whose behavior during a dynamics through a conical intersection has up to now remained unexplored. Despite the fact that these quantities might be viewed as time-dependent generalizations of the adiabatic potential energy surfaces and the nonadiabatic coupling vectors, characteristic quantities appearing in the Born-Oppenheimer framework, we observe that they do not exhibit particular topological features in the region of conical intersection but still reflect the complex dynamics of the nuclear wavepacket.
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Affiliation(s)
- Basile F E Curchod
- Centre for Computational Chemistry, School of Chemistry, University of Bristol , Bristol BS8 1TS, United Kingdom
| | - Federica Agostini
- Laboratoire de Chimie Physique, UMR 8000 CNRS/University Paris-Sud, University Paris-Saclay , 91405 Orsay, France
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29
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Joubert-Doriol L, Sivasubramanium J, Ryabinkin IG, Izmaylov AF. Topologically Correct Quantum Nonadiabatic Formalism for On-the-Fly Dynamics. J Phys Chem Lett 2017; 8:452-456. [PMID: 28036173 DOI: 10.1021/acs.jpclett.6b02660] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from electronic structure programs. However, conical intersections frequently occurring in this representation introduce nontrivial geometric or Berry phases which require a special treatment for adequate modeling of the nuclear dynamics. We analyze two approaches for nonadiabatic dynamics using the time-dependent variational principle and the adiabatic representation. The first approach employs adiabatic electronic functions with global parametric dependence on the nuclear coordinates. The second approach uses adiabatic electronic functions obtained only at the centers of moving localized nuclear basis functions (e.g., frozen-width Gaussians). Unless a gauge transformation is used to enforce single-valued boundary conditions, the first approach fails to capture the geometric phase. In contrast, the second approach accounts for the geometric phase naturally because of the absence of the global nuclear coordinate dependence in the electronic functions.
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Affiliation(s)
- 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
| | - Janakan Sivasubramanium
- Department of Physical and Environmental Sciences, University of Toronto Scarborough , Toronto, Ontario M1C 1A4, Canada
| | - 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
| | - 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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