1
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Lauvergnat D, Nauts A. Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality. Chemphyschem 2023; 24:e202300501. [PMID: 37555577 DOI: 10.1002/cphc.202300501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Revised: 08/08/2023] [Accepted: 08/09/2023] [Indexed: 08/10/2023]
Abstract
In 1963 Smolyak introduced an approach to overcome the exponential scaling with respect to the number of variables of the direct product size [S. A. Smolyak Soviet Mathematics Doklady, 4, 240 (1963)]. The main idea is to replace a single large direct product by a sum of selected small direct products. It was first used in quantum dynamics in 2009 by Avila and Carrington [G. Avila and T. Carrington, J. Chem. Phys., 131, 174103 (2009)]. Since then, several calculations have been published by Avila and Carrington and by other groups. In the present study, and to push the limit to larger and more complex systems, this scheme is combined with the use of an on-the-fly calculation of the kinetic energy operator and a Block-Davidson procedure to obtain eigenstates in our home-made Fortran codes, ElVibRot and Tnum-Tana. This was applied to compute the tunneling splitting of malonaldehyde in full dimensionality (21D) using the potential of Mizukami et al. [W. Mizukami, S. Habershon, and D.P. Tew, J. Chem. Phys. 141, 1443-10 (2014)]. Our tunneling splitting calculations, 21.7±0.3 cm-1 and 2.9±0.1 cm-1 , show excellent agreement with the experimental values, 21.6 cm-1 and 2.9 cm-1 for the normal isotopologue and the mono-deuterated one, respectively.
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Affiliation(s)
- David Lauvergnat
- Institut de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
| | - André Nauts
- Institut de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
- Institute of Condensed Matter and Nanosciences (NAPS), Université Catholique de Louvain, 2 Chemin du Cyclotron, 1348, Louvain-la-Neuve, Belgium
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2
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Segatta F, Ruiz DA, Aleotti F, Yaghoubi M, Mukamel S, Garavelli M, Santoro F, Nenov A. Nonlinear Molecular Electronic Spectroscopy via MCTDH Quantum Dynamics: From Exact to Approximate Expressions. J Chem Theory Comput 2023; 19:2075-2091. [PMID: 36961952 PMCID: PMC10100531 DOI: 10.1021/acs.jctc.2c01059] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/26/2023]
Abstract
We present an accurate and efficient approach to computing the linear and nonlinear optical spectroscopy of a closed quantum system subject to impulsive interactions with an incident electromagnetic field. It incorporates the effect of ultrafast nonadiabatic dynamics by means of explicit numerical propagation of the nuclear wave packet. The fundamental expressions for the evaluation of first- and higher-order response functions are recast in a general form that can be used with any quantum dynamics code capable of computing the overlap of nuclear wave packets evolving in different states. Here we present the evaluation of these expressions with the multiconfiguration time-dependent Hartree (MCTDH) method. Application is made to pyrene, excited to its lowest bright excited state S2 which exhibits a sub-100-fs nonadiabatic decay to a dark state S1. The system is described by a linear vibronic coupling Hamiltonian, parametrized with multiconfiguration electronic structure methods. We show that the ultrafast nonadiabatic dynamics can have a remarkable effect on the spectral line shapes that goes beyond simple lifetime broadening. Furthermore, a widely employed approximate expression based on the time scale separation of dephasing and population relaxation is recast in the same theoretical framework. Application to pyrene shows the range of validity of such approximations.
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Affiliation(s)
- Francesco Segatta
- Dipartimento di Chimica Industriale "Toso Montanari", University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - Daniel Aranda Ruiz
- ICMol, Universidad de Valencia, Catedrático José Beltrán Martínez, 2, 46980 Paterna, Spain
- Istituto di Chimica dei Composti Organometallici (ICCOM-CNR), Area della Ricerca del CNR, Via Moruzzi 1, I-56124 Pisa, Italy
| | - Flavia Aleotti
- Dipartimento di Chimica Industriale "Toso Montanari", University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - Martha Yaghoubi
- Istituto di Chimica dei Composti Organometallici (ICCOM-CNR), Area della Ricerca del CNR, Via Moruzzi 1, I-56124 Pisa, Italy
| | - Shaul Mukamel
- Department of Chemistry and Department of Physics and Astronomy, University of California, Irvine, California 92697, United States
| | - Marco Garavelli
- Dipartimento di Chimica Industriale "Toso Montanari", University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
| | - Fabrizio Santoro
- Istituto di Chimica dei Composti Organometallici (ICCOM-CNR), Area della Ricerca del CNR, Via Moruzzi 1, I-56124 Pisa, Italy
| | - Artur Nenov
- Dipartimento di Chimica Industriale "Toso Montanari", University of Bologna, Viale del Risorgimento, 4, 40136 Bologna, Italy
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3
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Gelin MF, Chen L, Domcke W. Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals. Chem Rev 2022; 122:17339-17396. [PMID: 36278801 DOI: 10.1021/acs.chemrev.2c00329] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.
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Affiliation(s)
- Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching,Germany
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4
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Gelin MF, Velardo A, Borrelli R. Efficient quantum dynamics simulations of complex molecular systems: A unified treatment of dynamic and static disorder. J Chem Phys 2021; 155:134102. [PMID: 34624969 DOI: 10.1063/5.0065896] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
We present a unified and highly numerically efficient formalism for the simulation of quantum dynamics of complex molecular systems, which takes into account both temperature effects and static disorder. The methodology is based on the thermo-field dynamics formalism, and Gaussian static disorder is included into simulations via auxiliary bosonic operators. This approach, combined with the tensor-train/matrix-product state representation of the thermalized stochastic wave function, is applied to study the effect of dynamic and static disorders in charge-transfer processes in model organic semiconductor chains employing the Su-Schrieffer-Heeger (Holstein-Peierls) model Hamiltonian.
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Affiliation(s)
- Maxim F Gelin
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
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5
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Gelin MF, Borrelli R. Simulation of Nonlinear Femtosecond Signals at Finite Temperature via a Thermo Field Dynamics-Tensor Train Method: General Theory and Application to Time- and Frequency-Resolved Fluorescence of the Fenna-Matthews-Olson Complex. J Chem Theory Comput 2021; 17:4316-4331. [PMID: 34076412 DOI: 10.1021/acs.jctc.1c00158] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Addressing needs of contemporary nonlinear femtosecond optical spectroscopy, we have developed a fully quantum, numerically accurate wave function-based approach for the calculation of third-order spectroscopic signals of polyatomic molecules and molecular aggregates at finite temperature. The systems are described by multimode nonadiabatic vibronic-coupling Hamiltonians, in which diagonal terms are treated in harmonic approximation, while off-diagonal interstate couplings are assumed to be coordinate independent. The approach is based on the Thermo Field Dynamics (TFD) representation of quantum mechanics and tensor-train (TT) machinery for efficient numerical simulation of quantum evolution of systems with many degrees of freedom. The developed TFD-TT approach is applied to the calculation of time- and frequency-resolved fluorescence spectra of the Fenna-Matthews-Olson (FMO) antenna complex at room temperature taking into account finite time-frequency resolution in fluorescence detection, orientational averaging, and static disorder.
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Affiliation(s)
- Maxim F Gelin
- School of Sciences, Hangzhou Dianzi University, Hangzhou 310018, China
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6
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Chen L, Borrelli R, Shalashilin DV, Zhao Y, Gelin MF. Simulation of Time- and Frequency-Resolved Four-Wave-Mixing Signals at Finite Temperatures: A Thermo-Field Dynamics Approach. J Chem Theory Comput 2021; 17:4359-4373. [PMID: 34107216 DOI: 10.1021/acs.jctc.1c00259] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We propose a new approach to simulate four-wave-mixing signals of molecular systems at finite temperatures by combining the multiconfigurational Ehrenfest method with the thermo-field dynamics theory. In our approach, the four-time correlation functions at finite temperatures are mapped onto those at zero temperature in an enlarged Hilbert space with twice the vibrational degrees of freedom. As an illustration, we have simulated three multidimensional spectroscopic signals, time- and frequency-resolved fluorescence spectra, transient-absorption pump-probe spectra, and electronic two-dimensional (2D) spectra at finite temperatures, for a conical intersection-mediated singlet fission model of a rubrene crystal. It is shown that a detailed dynamical picture of the singlet fission process can be extracted from the three spectroscopic signals. An increasing temperature leads to lower intensities of the signals and broadened vibrational peaks, which can be attributed to faster singlet-triplet population transfer and stronger bath-induced electronic dephasing at higher temperatures.
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Affiliation(s)
- Lipeng Chen
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str 38, 01187 Dresden, Germany
| | - Raffaele Borrelli
- Department of Agricultural, Forestry and Food Science, Universitá di Torino, I-10095 Grugliasco, TO, Italy
| | | | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore
| | - Maxim F Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
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7
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Wang H, Meyer HD. Importance of Appropriately Regularizing the ML-MCTDH Equations of Motion. J Phys Chem A 2021; 125:3077-3087. [DOI: 10.1021/acs.jpca.0c11221] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
| | - Hans-Dieter Meyer
- Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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8
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Sun K, Xu Q, Chen L, Gelin MF, Zhao Y. Temperature effects on singlet fission dynamics mediated by a conical intersection. J Chem Phys 2020; 153:194106. [DOI: 10.1063/5.0031435] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kewei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Quan Xu
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
| | - Lipeng Chen
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
| | - Maxim F. Gelin
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Yang Zhao
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Singapore
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9
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Sasmal S, Vendrell O. Non-adiabatic quantum dynamics without potential energy surfaces based on second-quantized electrons: Application within the framework of the MCTDH method. J Chem Phys 2020; 153:154110. [PMID: 33092359 DOI: 10.1063/5.0028116] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
A first principles quantum formalism to describe the non-adiabatic dynamics of electrons and nuclei based on a second quantization representation (SQR) of the electronic motion combined with the usual representation of the nuclear coordinates is introduced. This procedure circumvents the introduction of potential energy surfaces and non-adiabatic couplings, providing an alternative to the Born-Oppenheimer approximation. An important feature of the molecular Hamiltonian in the mixed first quantized representation for the nuclei and the SQR representation for the electrons is that all degrees of freedom, nuclear positions and electronic occupations, are distinguishable. This makes the approach compatible with various tensor decomposition Ansätze for the propagation of the nuclear-electronic wavefunction. Here, we describe the application of this formalism within the multi-configuration time-dependent Hartree framework and its multilayer generalization, corresponding to Tucker and hierarchical Tucker tensor decompositions of the wavefunction, respectively. The approach is applied to the calculation of the photodissociation cross section of the HeH+ molecule under extreme ultraviolet irradiation, which features non-adiabatic effects and quantum interferences between the two possible fragmentation channels, He + H+ and He+ + H. These calculations are compared with the usual description based on ab initio potential energy surfaces and non-adiabatic coupling matrix elements, which fully agree. The proof-of-principle calculations serve to illustrate the advantages and drawbacks of this formalism, which are discussed in detail, as well as possible ways to overcome them. We close with an outlook of possible application domains where the formalism might outperform the usual approach, for example, in situations that combine a strong static correlation of the electrons with non-adiabatic electronic-nuclear effects.
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Affiliation(s)
- Sudip Sasmal
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuneheimer Feld 229, 69120 Heidelberg, Germany
| | - Oriol Vendrell
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuneheimer Feld 229, 69120 Heidelberg, Germany
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10
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Binz M, Bruder L, Chen L, Gelin MF, Domcke W, Stienkemeier F. Effects of high pulse intensity and chirp in two-dimensional electronic spectroscopy of an atomic vapor. OPTICS EXPRESS 2020; 28:25806-25829. [PMID: 32906864 DOI: 10.1364/oe.396108] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 06/06/2020] [Indexed: 06/11/2023]
Abstract
The effects of high pulse intensity and chirp on two-dimensional electronic spectroscopy signals are experimentally investigated in the highly non-perturbative regime using atomic rubidium vapor as clean model system. Data analysis is performed based on higher-order Feynman diagrams and non-perturbative numerical simulations of the system response. It is shown that higher-order contributions may lead to a fundamental change of the static appearance and beating-maps of the 2D spectra and that chirped pulses enhance or suppress distinct higher-order pathways. We further give an estimate of the threshold intensity beyond which the high-intensity effects become visible for the system under consideration.
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11
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Gao X, Geva E. A Nonperturbative Methodology for Simulating Multidimensional Spectra of Multiexcitonic Molecular Systems via Quasiclassical Mapping Hamiltonian Methods. J Chem Theory Comput 2020; 16:6491-6502. [DOI: 10.1021/acs.jctc.0c00843] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Xing Gao
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
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12
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Palacino-González E, Gelin MF, Domcke W. Analysis of transient-absorption pump-probe signals of nonadiabatic dissipative systems: “Ideal” and “real” spectra. J Chem Phys 2019; 150:204102. [DOI: 10.1063/1.5094485] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Maxim F. Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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13
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Wang H, Shao J. Quantum Phase Transition in the Spin-Boson Model: A Multilayer Multiconfiguration Time-Dependent Hartree Study. J Phys Chem A 2019; 123:1882-1893. [DOI: 10.1021/acs.jpca.8b11136] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
- Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
| | - Jiushu Shao
- College of Chemistry and Center for Advanced Quantum Studies and Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, Beijing Normal University, Beijing 100875, China
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14
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Wang H, Liu X, Liu J. Accurate calculation of equilibrium reduced density matrix for the system-bath model: A multilayer multiconfiguration time-dependent Hartree approach and its comparison to a multi-electronic-state path integral molecular dynamics approach. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1805122] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver CO 80217-3364, USA
| | - Xinzijian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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15
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
| | - Hans-Dieter Meyer
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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16
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Vendrell O. Coherent dynamics in cavity femtochemistry: Application of the multi-configuration time-dependent Hartree method. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2018.02.008] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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17
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Wang H, Thoss M. A multilayer multiconfiguration time-dependent Hartree simulation of the reaction-coordinate spin-boson model employing an interaction picture. J Chem Phys 2017; 146:124112. [PMID: 28388113 DOI: 10.1063/1.4978901] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The multilayer multiconfiguration time-dependent Hartree method is applied in an interaction picture to simulate dynamics of the spin-boson model in the reaction-coordinate representation. The use of the interaction picture allows a more effective description of correlation effects, especially when the coupling strength between the reaction coordinate and the bath is very strong. Examples show that in most physical regimes the efficiency is improved significantly, in some cases up to several orders of magnitude. This opens up new avenues for studying quantum dynamical problems.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No.10 East Xibeiwang Road, Haidian District, Beijing 100193, China
| | - Michael Thoss
- Institute for Theoretical Physics and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, Erlangen D-91058, Germany
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18
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Wang H, Thoss M. On the accuracy of the noninteracting electron approximation for vibrationally coupled electron transport. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.06.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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19
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Wang H, Thoss M. Employing an interaction picture to remove artificial correlations in multilayer multiconfiguration time-dependent Hartree simulations. J Chem Phys 2016; 145:164105. [DOI: 10.1063/1.4965712] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA
| | - Michael Thoss
- Institute for Theoretical Physics and Interdisciplinary Center for Molecular Materials, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058, Germany
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20
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Jones JR, Rouet FH, Lawler KV, Vecharynski E, Ibrahim KZ, Williams S, Abeln B, Yang C, McCurdy W, Haxton DJ, Li XS, Rescigno TN. An efficient basis set representation for calculating electrons in molecules. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1176262] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Jeremiah R. Jones
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | | | - Keith V. Lawler
- Department of Chemistry, University of Nevada-Las Vegas, Las Vegas, NV, USA
| | - Eugene Vecharynski
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Khaled Z. Ibrahim
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Samuel Williams
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Brant Abeln
- Department of Chemistry, University of California, Davis, Davis, CA, USA
- Ultrafast X-Ray Science Laboratory, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Chao Yang
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - William McCurdy
- Department of Chemistry, University of California, Davis, Davis, CA, USA
- Ultrafast X-Ray Science Laboratory, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Daniel J. Haxton
- Ultrafast X-Ray Science Laboratory, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Xiaoye S. Li
- Computing Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
| | - Thomas N. Rescigno
- Chemical Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA, USA
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21
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Martinez F, Hanna G. Mixed Quantum-Classical Simulations of Transient Absorption Pump–Probe Signals for a Photo-Induced Electron Transfer Reaction Coupled to an Inner-Sphere Vibrational Mode. J Phys Chem A 2016; 120:3196-205. [DOI: 10.1021/acs.jpca.5b11727] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Franz Martinez
- Department
of Chemistry, University of Alberta, Edmonton, Alberta T6G 2R3, Canada
| | - Gabriel Hanna
- Department
of Chemistry, University of Alberta, Edmonton, Alberta T6G 2R3, Canada
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22
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Abstract
Multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory is a rigorous and powerful method to simulate quantum dynamics in complex many-body systems. This approach extends the original MCTDH theory of Meyer, Manthe, and Cederbaum to include dynamically contracted layers in a recursive way, within which the equations of motion are determined from the Dirac-Frenkel variational principle. This paper presents the general derivation of the theory and analyzes the important features that make the ML-MCTDH method numerically efficient. Furthermore, we discuss the generalization of the theory to treat many-body identical particles (fermions or bosons) as well as calculating energy eigenstates via the improved relaxation method.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
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23
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Sun KW, Gelin MF, Chernyak VY, Zhao Y. Davydov Ansatz as an efficient tool for the simulation of nonlinear optical response of molecular aggregates. J Chem Phys 2015; 142:212448. [DOI: 10.1063/1.4921575] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Ke-Wei Sun
- School of Science, Hangzhou Dianzi University, Hangzhou 310018, China
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
| | - Maxim F. Gelin
- Department of Chemistry, Technische Universität München, Garching D-85747, Germany
| | - Vladimir Y. Chernyak
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
- Department of Chemistry, Wayne State University, Detroit, Michigan 48202, USA
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore
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24
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Chen L, Gelin MF, Domcke W, Zhao Y. Theory of femtosecond coherent double-pump single-molecule spectroscopy: Application to light harvesting complexes. J Chem Phys 2015; 142:164106. [DOI: 10.1063/1.4919240] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Lipeng Chen
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
| | - Maxim F. Gelin
- Department of Chemistry, Technische Universität München, Garching D-85747, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technische Universität München, Garching D-85747, Germany
| | - Yang Zhao
- Division of Materials Science, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798
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Wang H. Iterative Calculation of Energy Eigenstates Employing the Multilayer Multiconfiguration Time-Dependent Hartree Theory. J Phys Chem A 2014; 118:9253-61. [DOI: 10.1021/jp503351t] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Haobin Wang
- Beijing Computational Science Research Center, No.
3 He-Qing Road, Hai-Dian District, Beijing 100084, P.R. China
- Department of Chemistry
and
Biochemistry, MSC 3C, New Mexico State University, Las Cruces, New Mexico 88003, United States
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Huynh TD, Sun KW, Gelin M, Zhao Y. Polaron dynamics in two-dimensional photon-echo spectroscopy of molecular rings. J Chem Phys 2014; 139:104103. [PMID: 24050324 DOI: 10.1063/1.4820135] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have developed a new approach to the computation of third-order spectroscopic signals of molecular rings, by incorporating the Davydov soliton theory into the nonlinear response function formalism. The Davydov D1 and D Ansätze have been employed to treat the interactions between the excitons and the primary phonons, allowing for a full description of arbitrary exciton-phonon coupling strengths. As an illustration, we have simulated a series of optical 2D spectra for two models of molecular rings.
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Affiliation(s)
- Thanh Duc Huynh
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798
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Lauvergnat D, Nauts A. Quantum dynamics with sparse grids: a combination of Smolyak scheme and cubature. Application to methanol in full dimensionality. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2014; 119:18-25. [PMID: 23859892 DOI: 10.1016/j.saa.2013.05.068] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2013] [Revised: 05/12/2013] [Accepted: 05/19/2013] [Indexed: 06/02/2023]
Abstract
Quantum dynamical approaches based on product-grids are limited to the studies of molecular systems with few degrees of freedom, typically less than ten. Recently, Avila et al. [G. Avila, T. Carrington, J. Chem. Phys., 131 (2009) 174103] have introduced the Smolyak scheme [S.A. Smolyak, Sov. Math. Dokl., 4 (1963) 240], which considerably reduces the size of the grids. This approach has pushed back the present calculation limits on the vibrational spectra of polyatomic molecules. In the present study, we have developed an extension of the standard Smolyak scheme in which this scheme is combined with multidimensional grids, such as cubatures, to obtain new sparse grids. This scheme has been applied to the study of the torsional energy levels of methanol in full dimensionality (12D).
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Affiliation(s)
- David Lauvergnat
- Laboratoire de Chimie Physique, Bâtiment 349, CNRS, UMR8000, Univ Paris-Sud, Orsay F-91405, France.
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Krčmář J, Gelin MF, Domcke W. Calculation of third-order signals via driven Schrödinger equations: General results and application to electronic 2D photon echo spectroscopy. Chem Phys 2013. [DOI: 10.1016/j.chemphys.2013.01.002] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Martinez F, Rekik N, Hanna G. Simulation of nonlinear optical signals via approximate solutions of the quantum–classical Liouville equation: Application to the pump–probe spectroscopy of a condensed phase electron transfer reaction. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.04.018] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Tempelaar R, van der Vegte CP, Knoester J, Jansen TLC. Surface hopping modeling of two-dimensional spectra. J Chem Phys 2013; 138:164106. [DOI: 10.1063/1.4801519] [Citation(s) in RCA: 50] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wang H, Thoss M. Numerically exact, time-dependent study of correlated electron transport in model molecular junctions. J Chem Phys 2013; 138:134704. [DOI: 10.1063/1.4798404] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Wang H, Shao J. Dynamics of a two-level system coupled to a bath of spins. J Chem Phys 2012; 137:22A504. [DOI: 10.1063/1.4732808] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Zhou Y, Shao J, Wang H. Dynamics of electron transfer in complex glassy environment modeled by the Cole–Davidson spectral density. Mol Phys 2012. [DOI: 10.1080/00268976.2012.670281] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Wang H, Pshenichnyuk I, Härtle R, Thoss M. Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions. J Chem Phys 2011; 135:244506. [DOI: 10.1063/1.3660206] [Citation(s) in RCA: 62] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
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Gelin MF, Egorova D, Domcke W. Optical N-wave-mixing spectroscopy with strong and temporally well-separated pulses: the doorway-window representation. J Phys Chem B 2011; 115:5648-58. [PMID: 21425818 DOI: 10.1021/jp112055h] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
We have extended the doorway-window representation of optical pump-probe spectroscopy with weak pulses toward N-wave-mixing spectroscopy with temporally well-separated pulses of arbitrary strength. The expressions for the signals in the strong-pulse doorway-window representation are derived in the framework of the nonperturbative theory of N-wave-mixing spectroscopy. The strong-pulse doorway-window representation is complementary to the equation-of-motion phase-matching approach. The latter fully accounts for pulse-overlap effects in signals induced by weak pulses but is computationally more expensive. The performance of the doorway-window approximation for temporally well-separated strong pulses is illustrated for an electronic two-level system with an underdamped Condon-active vibrational mode.
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Affiliation(s)
- Maxim F Gelin
- Department of Chemistry, Technische Universität München, D-85747 Garching, Germany
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Gelin MF, Egorova D, Domcke W. Manipulating electronic couplings and nonadiabatic nuclear dynamics with strong laser pulses. J Chem Phys 2009; 131:124505. [DOI: 10.1063/1.3236577] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gelin MF, Egorova D, Domcke W. Efficient calculation of time- and frequency-resolved four-wave-mixing signals. Acc Chem Res 2009; 42:1290-8. [PMID: 19449854 DOI: 10.1021/ar900045d] [Citation(s) in RCA: 72] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
"Four-wave-mixing" is the generic name for a family of nonlinear electronic and vibrational spectroscopies. These techniques are widely used to explore dissipation, dephasing, solvation, and interstate coupling mechanisms in various material systems. Four-wave-mixing spectroscopy needs a firm theoretical support, because it delivers information on material systems indirectly, through certain transients, which are measured as functions of carrier frequencies, durations, and relative time delays of the laser pulses. The observed transients are uniquely determined by the three-pulse-induced third-order polarization. There exist two conceptually different approaches to the calculation of the nonlinear polarization. In the standard perturbative approach to nonlinear spectroscopy, the third-order polarization is expressed in terms of the nonlinear response functions. As the material systems become more complex, the evaluation of the response functions becomes cumbersome and the calculation of the signals necessitates a number of approximations. Herein, we review alternative methods for the calculation of four-wave-mixing signals, in which the relevant laser pulses are incorporated into the system Hamiltonian and the driven system dynamics is simulated numerically exactly. The emphasis is on the recently developed equation-of-motion phase-matching approach (EOM-PMA), which allows us to calculate the three-pulse-induced third-order polarization in any phase-matching direction by performing three (with the rotating wave approximation) or seven (without the rotating wave approximation) independent propagations of the density matrix. The EOM-PMA is limited to weak laser fields (its domain of validity is equivalent to the approach based on the third-order response functions) but allows for arbitrary pulse durations and automatically accounts for pulse-overlap effects. As an illustration, we apply the EOM-PMA to the calculation of optical three-pulse photon-echo two-dimensional (2D) signals for a generic model system, which represents a characteristic photophysical dynamics of large molecules or chromophores in condensed phases. The EOM-PMA is easy to implement and can straightforwardly be incorporated into any computational scheme, which provides the time-dependent density matrix or wave function of the material system of interest. In particular, EOM-PMA-based computer codes can efficiently be implemented on parallel computers. The EOM-PMA facilitates considerably the computation of four-wave-mixing signals and 2D spectra, in both vibrational and electronic spectroscopy. The EOM-PMA can be extended to higher order optical responses, e.g., heterodyned 3D IR, transient 2D IR, and other six-wave-mixing techniques.
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Affiliation(s)
- Maxim F. Gelin
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
| | - Dassia Egorova
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
| | - Wolfgang Domcke
- Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
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Gelin MF, Egorova D, Domcke W. Efficient calculation of the polarization induced by N coherent laser pulses. J Chem Phys 2009; 131:194103. [DOI: 10.1063/1.3265213] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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