1
|
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.
Collapse
|
2
|
Wu Y, Bian X, Rawlinson JI, Littlejohn RG, Subotnik JE. A phase-space semiclassical approach for modeling nonadiabatic nuclear dynamics with electronic spin. J Chem Phys 2022; 157:011101. [DOI: 10.1063/5.0093345] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. However, for electronic systems with spin degrees of freedom, there are few if any applicable and practical quasiclassical methods. Here, we show that for nonadiabatic dynamics with two electronic states and a complex-valued Hamiltonian that does not obey time-reversal symmetry (as relevant to many coupled nuclear-electronic-spin systems), the optimal semiclassical approach is to generalize Tully’s surface hopping dynamics from coordinate space to phase space. In order to generate the relevant phase-space adiabatic surfaces, one isolates a proper set of diabats, applies a phase gauge transformation, and then diagonalizes the total Hamiltonian (which is now parameterized by both R and P). The resulting algorithm is simple and valid in both the adiabatic and nonadiabatic limits, incorporating all Berry curvature effects. Most importantly, the resulting algorithm allows for the study of semiclassical nonadiabatic dynamics in the presence of spin–orbit coupling and/or external magnetic fields. One expects many simulations to follow as far as modeling cutting-edge experiments with entangled nuclear, electronic, and spin degrees of freedom, e.g., experiments displaying chiral-induced spin selectivity.
Collapse
Affiliation(s)
- Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Jonathan I. Rawlinson
- School of Mathematics, The University of Manchester, Oxford Rd., Manchester M13 9PL, United Kingdom
| | - Robert G. Littlejohn
- Department of Physics, University of California, 366 Physics North MC 7300, Berkeley, California 94720-7300, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| |
Collapse
|
3
|
Lyu N, Soley MB, Batista VS. Tensor-Train Split-Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations. J Chem Theory Comput 2022; 18:3327-3346. [PMID: 35649210 DOI: 10.1021/acs.jctc.2c00209] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Numerically exact simulations of quantum reaction dynamics, including nonadiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of molecular spectroscopy. Here, we introduce the tensor-train split-operator KSL (TT-SOKSL) method for quantum simulations in tensor-train (TT)/matrix product state (MPS) representations. TT-SOKSL propagates the quantum state as a tensor train using the Trotter expansion of the time-evolution operator, as in the tensor-train split-operator Fourier transform (TT-SOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank-adaptive TT-KSL scheme instead of using the scaling and squaring approach as in TT-SOFT. We demonstrate the accuracy and efficiency of TT-SOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including nonadiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a time-dependent wavepacket evolving according to a two-state 25-dimensional model Hamiltonian. We find that TT-SOKSL converges faster than TT-SOFT with respect to the maximally allowed memory requirement of the tensor-train representation and better preserves the norm of the time-evolving state. When compared to the corresponding simulations based on the TT-KSL method, TT-SOKSL has the advantage of avoiding the need to construct the matrix product state Laplacian by exploiting the linear scaling of multidimensional tensor-train Fourier transforms.
Collapse
Affiliation(s)
- Ningyi Lyu
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, United States
| | - Micheline B Soley
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, United States.,Yale Quantum Institute, Yale University, P.O. Box 208334, New Haven, Connecticut 06520-8263, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, United States.,Yale Quantum Institute, Yale University, P.O. Box 208334, New Haven, Connecticut 06520-8263, United States
| |
Collapse
|
4
|
Structure and dynamics of electronically excited molecular systems. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1576] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
|
5
|
Seidu I, Neville SP, MacDonell RJ, Schuurman MS. Resolving competing conical intersection pathways: time-resolved X-ray absorption spectroscopy of trans-1,3-butadiene. Phys Chem Chem Phys 2021; 24:1345-1354. [PMID: 34935809 DOI: 10.1039/d1cp05085k] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Time-resolved X-ray absorption spectroscopy is emerging as a uniquely powerful tool to probe coupled electronic-nuclear dynamics in photo-excited molecules. Theoretical studies to date have established that time-resolved X-ray absorption spectroscopy is an atom-specific probe of excited-state wave packet passage through a seam of conical intersections (CIs). However, in many molecular systems, there are competing dynamical pathways involving CIs of different electronic and nuclear character. Discerning these pathways remains an important challenge. Here, we demonstrate that time-resolved X-ray absorption spectroscopy (TRXAS) has the potential to resolve competing channels in excited-state non-adiabatic dynamics. Using the example of 1,3-butadiene, we show how TRXAS discerns the different electronic structures associated with passage through multiple conical intersections. trans-1,3-Butadiene exhibits a branching between polarized and radicaloid pathways associated with ethylenic "twisted-pyramidalized" and excited-state cis-trans isomerization dynamics, respectively. The differing electronic structures along these pathways give rise to different XAS signals, indicating the possibility of resolving them. Furthermore, this indicates that XAS, and other core-level spectroscopic techniques, offer the appealing prospect of directly probing the effects of selective chemical substitution and its ability to affect chemical control over excited-state molecular dynamics.
Collapse
Affiliation(s)
- Issaka Seidu
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada.
| | - Simon P Neville
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada.
| | - Ryan J MacDonell
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, 10 Marie Curie, Ottawa, Ontario, K1N 6N5, Canada
| | - Michael S Schuurman
- National Research Council Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada. .,Department of Chemistry and Biomolecular Sciences, University of Ottawa, 10 Marie Curie, Ottawa, Ontario, K1N 6N5, Canada
| |
Collapse
|
6
|
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.
Collapse
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
| |
Collapse
|
7
|
Abstract
In this article, we review nonadiabatic molecular dynamics (NAMD) methods for modeling spin-crossover transitions. First, we discuss different representations of electronic states employed in the grid-based and direct NAMD simulations. The nature of interstate couplings in different representations is highlighted, with the main focus on nonadiabatic and spin-orbit couplings. Second, we describe three NAMD methods that have been used to simulate spin-crossover dynamics, including trajectory surface hopping, ab initio multiple spawning, and multiconfiguration time-dependent Hartree. Some aspects of employing different electronic structure methods to obtain information about potential energy surfaces and interstate couplings for NAMD simulations are also discussed. Third, representative applications of NAMD to spin crossovers in molecular systems of different sizes and complexities are highlighted. Finally, we pose several fundamental questions related to spin-dependent processes. These questions should be possible to address with future methodological developments in NAMD.
Collapse
Affiliation(s)
- Saikat Mukherjee
- Institut de Chimie Radicalaire, CNRS 7273, Aix-Marseille University, 13013 Marseille, France;
| | - Dmitry A Fedorov
- Oak Ridge Associated Universities, Oak Ridge, Tennessee 37830, USA;
| | - Sergey A Varganov
- Department of Chemistry, University of Nevada, Reno, Nevada 89557-0216, USA;
| |
Collapse
|
8
|
Loaiza I, Izmaylov AF, Brumer P. Computational approaches to efficient generation of the stationary state for incoherent light excitation. J Chem Phys 2021; 154:124126. [PMID: 33810687 DOI: 10.1063/5.0036622] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Light harvesting processes are often computationally studied from a time-dependent viewpoint, in line with ultrafast coherent spectroscopy experiments. Yet, natural processes take place in the presence of incoherent light, which induces a stationary state. Such stationary states can be described using the eigenbasis of the molecular Hamiltonian, but for realistic systems, a full diagonalization is prohibitively expensive. We propose three efficient computational approaches to obtain the stationary state that circumvents system Hamiltonian diagonalization. The connection between the incoherent perturbations, decoherence, and Kraus operators is established.
Collapse
Affiliation(s)
- Ignacio Loaiza
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Artur F Izmaylov
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| |
Collapse
|
9
|
Mukherjee S, Ravi S, Naskar K, Sardar S, Adhikari S. A beyond Born–Oppenheimer treatment of C6H6+ radical cation for diabatic surfaces: Photoelectron spectra of its neutral analog using time-dependent discrete variable representation. J Chem Phys 2021; 154:094306. [DOI: 10.1063/5.0040361] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Soumya Mukherjee
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Satyam Ravi
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Koushik Naskar
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Subhankar Sardar
- Department of Chemistry, Bhatter College, Dantan, Paschim Medinipur 721426, India
| | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| |
Collapse
|
10
|
Sathyamurthy N, Mahapatra S. Time-dependent quantum mechanical wave packet dynamics. Phys Chem Chem Phys 2020; 23:7586-7614. [PMID: 33306771 DOI: 10.1039/d0cp03929b] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Starting from a model study of the collinear (H, H2) exchange reaction in 1959, the time-dependent quantum mechanical wave packet (TDQMWP) method has come a long way in dealing with systems as large as Cl + CH4. The fast Fourier transform method for evaluating the second order spatial derivative of the wave function and split-operator method or Chebyshev polynomial expansion for determining the time evolution of the wave function for the system have made the approach highly accurate from a practical point of view. The TDQMWP methodology has been able to predict state-to-state differential and integral reaction cross sections accurately, in agreement with available experimental results for three dimensional (H, H2) collisions, and identify reactive scattering resonances too. It has become a practical computational tool in predicting the observables for many A + BC exchange reactions in three dimensions and a number of larger systems. It is equally amenable to determining the bound and quasi-bound states for a variety of molecular systems. Just as it is able to deal with dissociative processes (without involving basis set expansion), it is able to deal with multi-mode nonadiabatic dynamics in multiple electronic states with equal ease. We present an overview of the method and its strength and limitations, citing examples largely from our own research groups.
Collapse
|
11
|
Miao G, Bian X, Zhou Z, Subotnik J. A "backtracking" correction for the fewest switches surface hopping algorithm. J Chem Phys 2020; 153:111101. [PMID: 32962370 DOI: 10.1063/5.0022436] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a "backtracking" mechanism within Tully's fewest switches surface hopping (FSSH) algorithm, whereby whenever one detects consecutive (double) hops during a short period of time, one simply rewinds the dynamics backward in time. In doing so, one reduces the number of hopping events and comes closer to a truly fewest switches surface hopping approach with independent trajectories. With this algorithmic change, we demonstrate that surface hopping can be reasonably accurate for nuclear dynamics in a multidimensional configuration space with a complex-valued (i.e., not real-valued) electronic Hamiltonian; without this adjustment, surface hopping often fails. The added computational cost is marginal. Future research will be needed to assess whether or not this backtracking correction can improve the accuracy of a typical FSSH calculation with a real-valued electronic Hamiltonian (that ignores spin).
Collapse
Affiliation(s)
- Gaohan Miao
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| |
Collapse
|
12
|
Stolyarov EV, White AJ, Mozyrsky D. Mixed quantum-classical approach to model non-adiabatic electron-nuclear dynamics: Detailed balance and improved surface hopping method. J Chem Phys 2020; 153:074116. [PMID: 32828087 DOI: 10.1063/5.0014284] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We develop a density matrix formalism to describe coupled electron-nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional "virtual" nuclear wave packets whose interference with the "real" (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phase shifts lead to the detailed balance condition in the strong decoherence limit.
Collapse
Affiliation(s)
- E V Stolyarov
- Institute of Physics of the National Academy of Sciences of Ukraine, pr. Nauky 46, 03028 Kyiv, Ukraine
| | - A J White
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - D Mozyrsky
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
13
|
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.
Collapse
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
| |
Collapse
|
14
|
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.
Collapse
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
| |
Collapse
|
15
|
Martinazzo R, Burghardt I. Local-in-Time Error in Variational Quantum Dynamics. PHYSICAL REVIEW LETTERS 2020; 124:150601. [PMID: 32357037 DOI: 10.1103/physrevlett.124.150601] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/08/2019] [Accepted: 03/26/2020] [Indexed: 06/11/2023]
Abstract
The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrödinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact expressions are provided for this error, which are then evaluated in illustrative cases, notably the widely used mean-field approach and the adiabatic quantum molecular dynamics. Based on these findings, we demonstrate the rigorous formulation of an adaptive scheme that resizes on the fly the underlying variational manifold and, hence, optimizes the overall computational cost of a quantum dynamical simulation. Such adaptive schemes are a crucial requirement for devising and applying direct quantum dynamical methods to molecular and condensed-phase problems.
Collapse
Affiliation(s)
- Rocco Martinazzo
- Department of Chemistry, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy
- Istituto di Scienze e Tecnologie Molecolari, CNR, via Golgi 19, 20133 Milano, Italy
| | - Irene Burghardt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Strasse 7, D-60438 Frankfurt/Main, Germany
| |
Collapse
|
16
|
Mandal A, Hunt KLC. Variance of the energy of a quantum system in a time-dependent perturbation: Determination by nonadiabatic transition probabilities. J Chem Phys 2020; 152:104110. [DOI: 10.1063/1.5140009] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Anirban Mandal
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Katharine L. C. Hunt
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| |
Collapse
|
17
|
Titov E, Humeniuk A, Mitrić R. Comparison of moving and fixed basis sets for nonadiabatic quantum dynamics at conical intersections. Chem Phys 2020. [DOI: 10.1016/j.chemphys.2019.110526] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
|
18
|
Shen L, Tang D, Xie B, Fang WH. Quantum Trajectory Mean-Field Method for Nonadiabatic Dynamics in Photochemistry. J Phys Chem A 2019; 123:7337-7350. [PMID: 31373814 DOI: 10.1021/acs.jpca.9b03480] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
The mixed quantum-classical dynamical approaches have been widely used to study nonadiabatic phenomena in photochemistry and photobiology, in which the time evolutions of the electronic and nuclear subsystems are treated based on quantum and classical mechanics, respectively. The key issue is how to deal with coherence and decoherence during the propagation of the two subsystems, which has been the subject of numerous investigations for a few decades. A brief description on Ehrenfest mean-field and surface-hopping (SH) methods is first provided, and then different algorithms for treatment of quantum decoherence are reviewed in the present paper. More attentions were paid to quantum trajectory mean-field (QTMF) method under the picture of quantum measurements, which is able to overcome the overcoherence problem. Furthermore, the combined QTMF and SH algorithm is proposed in the present work, which takes advantages of the QTMF and SH methods. The potential to extend the applicability of the QTMF method was briefly discussed, such as the generalization to other type of nonadiabatic transitions, the combination with multiscale computational models, and possible improvements on its accuracy and efficiency by using machine-learning techniques.
Collapse
Affiliation(s)
- Lin Shen
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , P. R. China
| | - Diandong Tang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , P. R. China
| | - Binbin Xie
- Hangzhou Institute of Advanced Studies , Zhejiang Normal University , 1108 Gengwen Road , Hangzhou 311231 , Zhejiang P. R. China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry of Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , P. R. China
| |
Collapse
|
19
|
Murakami T, Frankcombe TJ. Non-adiabatic quantum molecular dynamics by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method: Multi-set and single-set formalisms. J Chem Phys 2019; 150:144112. [DOI: 10.1063/1.5084749] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Tatsuhiro Murakami
- School of Science, University of New South Wales, Canberra, ACT 2600, Australia
| | - Terry J. Frankcombe
- School of Science, University of New South Wales, Canberra, ACT 2600, Australia
| |
Collapse
|
20
|
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.
Collapse
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
| |
Collapse
|
21
|
Mandal S, Ghosh S, Sardar S, Adhikari S. The TDDVR approach for molecular photoexcitation, molecule–surface and triatomic reactive scattering processes. INT REV PHYS CHEM 2018. [DOI: 10.1080/0144235x.2018.1548103] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Souvik Mandal
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India
| | - Sandip Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India
| | | | - Satrajit Adhikari
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, India
| |
Collapse
|
22
|
Murakami T, Frankcombe TJ. Accurate quantum molecular dynamics for multidimensional systems by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method. J Chem Phys 2018; 149:134113. [DOI: 10.1063/1.5046643] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Tatsuhiro Murakami
- School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, ACT 2600, Australia
| | - Terry J. Frankcombe
- School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, ACT 2600, Australia
| |
Collapse
|
23
|
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.
Collapse
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
| |
Collapse
|
24
|
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
| |
Collapse
|
25
|
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.
Collapse
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
| |
Collapse
|
26
|
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
| |
Collapse
|
27
|
Kowalewski M, Fingerhut BP, Dorfman KE, Bennett K, Mukamel S. Simulating Coherent Multidimensional Spectroscopy of Nonadiabatic Molecular Processes: From the Infrared to the X-ray Regime. Chem Rev 2017; 117:12165-12226. [DOI: 10.1021/acs.chemrev.7b00081] [Citation(s) in RCA: 81] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Markus Kowalewski
- Department
of Chemistry and Department of Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
| | - Benjamin P. Fingerhut
- Max-Born-Institut für Nichtlineare Optik und Kurzzeitspektroskopie, D-12489 Berlin, Germany
| | - Konstantin E. Dorfman
- State
Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai 200062, China
| | - Kochise Bennett
- Department
of Chemistry and Department of Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
| | - Shaul Mukamel
- Department
of Chemistry and Department of Physics and Astronomy, University of California, Irvine, California 92697-2025, United States
| |
Collapse
|
28
|
Greene SM, Batista VS. Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics. J Chem Theory Comput 2017; 13:4034-4042. [DOI: 10.1021/acs.jctc.7b00608] [Citation(s) in RCA: 61] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Samuel M. Greene
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O. Box 27394, West Haven, Connecticut 06516-7394, United States
| | - Victor S. Batista
- Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, United States
- Energy Sciences Institute, Yale University, P.O. Box 27394, West Haven, Connecticut 06516-7394, United States
| |
Collapse
|
29
|
Izmaylov AF, Joubert-Doriol L. Quantum Nonadiabatic Cloning of Entangled Coherent States. J Phys Chem Lett 2017; 8:1793-1797. [PMID: 28375623 DOI: 10.1021/acs.jpclett.7b00596] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We propose a systematic approach to the basis set extension for nonadiabatic dynamics of entangled combination of nuclear coherent states (CSs) evolving according to the time-dependent variational principle (TDVP). The TDVP provides a rigorous framework for fully quantum nonadiabatic dynamics of closed systems; however, the quality of results strongly depends on available basis functions. Starting with a single nuclear CS replicated vertically on all electronic states, our approach clones this function when replicas of the CS on different electronic states experience increasingly different forces. Created clones move away from each other (decohere), extending the basis set. To determine a moment for cloning, we introduce generalized forces based on derivatives that maximally contribute to a variation of the total quantum action and thus account for entanglement of all basis functions.
Collapse
Affiliation(s)
- 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
| | - 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
| |
Collapse
|
30
|
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.
Collapse
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
| |
Collapse
|
31
|
Curchod BFE, Sisto A, Martínez TJ. Ab Initio Multiple Spawning Photochemical Dynamics of DMABN Using GPUs. J Phys Chem A 2017; 121:265-276. [DOI: 10.1021/acs.jpca.6b09962] [Citation(s) in RCA: 44] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Basile F. E. Curchod
- Department
of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, United States
| | - Aaron Sisto
- Department
of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, United States
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, 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
| |
Collapse
|
32
|
Heaps CW, Mazziotti DA. Accurate non-adiabatic quantum dynamics from pseudospectral sampling of time-dependent Gaussian basis sets. J Chem Phys 2016. [DOI: 10.1063/1.4959872] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Charles W. Heaps
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| | - David A. Mazziotti
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
| |
Collapse
|
33
|
Curchod BFE, Rauer C, Marquetand P, González L, Martínez TJ. Communication: GAIMS—Generalized Ab Initio Multiple Spawning for both internal conversion and intersystem crossing processes. J Chem Phys 2016; 144:101102. [DOI: 10.1063/1.4943571] [Citation(s) in RCA: 77] [Impact Index Per Article: 9.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Basile F. E. Curchod
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Clemens Rauer
- Institute of Theoretical Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Institute of Theoretical Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Leticia González
- Institute of Theoretical Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Todd J. Martínez
- Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| |
Collapse
|
34
|
Makhov DV, Martinez TJ, Shalashilin DV. Toward fully quantum modelling of ultrafast photodissociation imaging experiments. Treating tunnelling in the ab initio multiple cloning approach. Faraday Discuss 2016; 194:81-94. [DOI: 10.1039/c6fd00073h] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present an account of our recent effort to improve simulation of the photodissociation of small heteroaromatic molecules using the Ab Initio Multiple Cloning (AIMC) algorithm. The ultimate goal is to create a quantitative and converged technique for fully quantum simulations which treats both electrons and nuclei on a fully quantum level. We calculate and analyse the total kinetic energy release (TKER) spectra and Velocity Map Images (VMI), and compare the results directly with experimental measurements. In this work, we perform new extensive calculations using an improved AIMC algorithm that now takes into account the tunnelling of hydrogen atoms. This can play an extremely important role in photodissociation dynamics.
Collapse
|
35
|
Kondorskiy AD, Nanbu S. Electronically nonadiabatic wave packet propagation using frozen Gaussian scattering. J Chem Phys 2015; 143:114103. [DOI: 10.1063/1.4930923] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alexey D. Kondorskiy
- P. N. Lebedev Physical Institute of the Russian Academy of Sciences, 53, Leninsky Prospekt, Moscow 119991, Russia
| | - Shinkoh Nanbu
- Department of Materials and Life Sciences, Faculty of Science and Technology, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan
| |
Collapse
|
36
|
Polyak I, Allan CSM, Worth GA. A complete description of tunnelling using direct quantum dynamics simulation: Salicylaldimine proton transfer. J Chem Phys 2015; 143:084121. [DOI: 10.1063/1.4929478] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Iakov Polyak
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - Charlotte S. M. Allan
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| | - Graham A. Worth
- School of Chemistry, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom
| |
Collapse
|
37
|
Ouyang W, Dou W, Subotnik JE. Surface hopping with a manifold of electronic states. I. Incorporating surface-leaking to capture lifetimes. J Chem Phys 2015; 142:084109. [PMID: 25725714 DOI: 10.1063/1.4908032] [Citation(s) in RCA: 27] [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 investigate the incorporation of the surface-leaking (SL) algorithm into Tully's fewest-switches surface hopping (FSSH) algorithm to simulate some electronic relaxation induced by an electronic bath in conjunction with some electronic transitions between discrete states. The resulting SL-FSSH algorithm is benchmarked against exact quantum scattering calculations for three one-dimensional model problems. The results show excellent agreement between SL-FSSH and exact quantum dynamics in the wide band limit, suggesting the potential for a SL-FSSH algorithm. Discrepancies and failures are investigated in detail to understand the factors that will limit the reliability of SL-FSSH, especially the wide band approximation. Considering the easiness of implementation and the low computational cost, we expect this method to be useful in studying processes involving both a continuum of electronic states (where electronic dynamics are probabilistic) and processes involving only a few electronic states (where non-adiabatic processes cannot ignore short-time coherence).
Collapse
Affiliation(s)
- Wenjun Ouyang
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Wenjie Dou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| |
Collapse
|
38
|
Makhov DV, Glover WJ, Martinez TJ, Shalashilin DV. Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics. J Chem Phys 2014; 141:054110. [DOI: 10.1063/1.4891530] [Citation(s) in RCA: 139] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Dmitry V. Makhov
- Department of Chemistry, University of Leeds, Leeds LS2 9JT, United Kingdom
| | - William J. Glover
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | - Todd J. Martinez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA
| | | |
Collapse
|
39
|
Herman MF. Improving the efficiency of Monte Carlo surface hopping calculations. J Phys Chem B 2014; 118:8026-33. [PMID: 24650188 DOI: 10.1021/jp501139s] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
A surface hopping method with a Monte Carlo procedure for deciding whether to hop at each step along the classical trajectories used in the semiclassical calculation is discussed. It is shown for a simple one-dimensional model problem that the numerical efficiency of the method can be improved by averaging over several copies of the sections of each trajectory that span the interaction regions. The use of Sobol sequences in the selection of the initial momentum for the trajectories is also explored. It is found that accurate results can be obtained with relatively small trajectory samples.
Collapse
Affiliation(s)
- Michael F Herman
- Department of Chemistry, Tulane University , New Orleans, Louisiana 70118, United States
| |
Collapse
|
40
|
An overview of nonadiabatic dynamics simulations methods, with focus on the direct approach versus the fitting of potential energy surfaces. Theor Chem Acc 2014. [DOI: 10.1007/s00214-014-1526-1] [Citation(s) in RCA: 102] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
41
|
Ouyang W, Subotnik JE. Estimating the entropy and quantifying the impurity of a swarm of surface-hopping trajectories: A new perspective on decoherence. J Chem Phys 2014; 140:204102. [DOI: 10.1063/1.4876491] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
|
42
|
Yamamoto K, Takatsuka K. Electronic quantum effects mapped onto non-Born-Oppenheimer nuclear paths: Nonclassical surmounting over potential barriers and trapping above the transition states due to nonadiabatic path-branching. J Chem Phys 2014; 140:124111. [DOI: 10.1063/1.4869191] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
|
43
|
Herman MF. Analysis of a surface hopping expansion that includes hops in classically forbidden regions. Chem Phys 2014. [DOI: 10.1016/j.chemphys.2014.01.013] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
44
|
Akimov AV, Neukirch AJ, Prezhdo OV. Theoretical Insights into Photoinduced Charge Transfer and Catalysis at Oxide Interfaces. Chem Rev 2013; 113:4496-565. [DOI: 10.1021/cr3004899] [Citation(s) in RCA: 402] [Impact Index Per Article: 36.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Alexey V. Akimov
- Department of Chemistry, University of Rochester, Rochester, New York 14627,
United States
- Chemistry
Department, Brookhaven National Laboratory, Upton, New York 11973-5000,
United States
| | - Amanda J. Neukirch
- Department
of Physics and Astronomy, University of Rochester, Rochester, New York 14627,
United States
| | - Oleg V. Prezhdo
- Department of Chemistry, University of Rochester, Rochester, New York 14627,
United States
| |
Collapse
|
45
|
Yonehara T, Takatsuka K. Path-Branching Representation for Nonadiabatic Electron Dynamics in Conical Intersection. J Phys Chem A 2013; 117:8599-608. [DOI: 10.1021/jp402655q] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Takehiro Yonehara
- Department of Basic
Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
| | - Kazuo Takatsuka
- Department of Basic
Sciences, Graduate School of Arts and Sciences, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan
| |
Collapse
|
46
|
Izmaylov AF. Perturbative wave-packet spawning procedure for non-adiabatic dynamics in diabatic representation. J Chem Phys 2013; 138:104115. [DOI: 10.1063/1.4794047] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|
47
|
Zamstein N, Tannor DJ. Non-adiabatic molecular dynamics with complex quantum trajectories. I. The diabatic representation. J Chem Phys 2013; 137:22A517. [PMID: 23249054 DOI: 10.1063/1.4739845] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We extend a recently developed quantum trajectory method [Y. Goldfarb, I. Degani, and D. J. Tannor, J. Chem. Phys. 125, 231103 (2006)] to treat non-adiabatic transitions. Each trajectory evolves on a single surface according to Newton's laws with complex positions and momenta. The transfer of amplitude between surfaces stems naturally from the equations of motion, without the need for surface hopping. In this paper we derive the equations of motion and show results in the diabatic representation, which is rarely used in trajectory methods for calculating non-adiabatic dynamics. We apply our method to the first two benchmark models introduced by Tully [J. Chem. Phys. 93, 1061 (1990)]. Besides giving the probability branching ratios between the surfaces, the method also allows the reconstruction of the time-dependent wavepacket. Our results are in quantitative agreement with converged quantum mechanical calculations.
Collapse
Affiliation(s)
- Noa Zamstein
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | | |
Collapse
|
48
|
Zamstein N, Tannor DJ. Non-adiabatic molecular dynamics with complex quantum trajectories. II. The adiabatic representation. J Chem Phys 2013; 137:22A518. [PMID: 23249055 DOI: 10.1063/1.4739846] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a complex quantum trajectory method for treating non-adiabatic dynamics. Each trajectory evolves classically on a single electronic surface but with complex position and momentum. The equations of motion are derived directly from the time-dependent Schrödinger equation, and the population exchange arises naturally from amplitude-transfer terms. In this paper the equations of motion are derived in the adiabatic representation to complement our work in the diabatic representation [N. Zamstein and D. J. Tannor, J. Chem. Phys. 137, 22A517 (2012)]. We apply our method to two benchmark models introduced by John Tully [J. Chem. Phys. 93, 1061 (1990)], and get very good agreement with converged quantum-mechanical calculations. Specifically, we show that decoherence (spatial separation of wavepackets on different surfaces) is already contained in the equations of motion and does not require ad hoc augmentation.
Collapse
Affiliation(s)
- Noa Zamstein
- Department of Chemical Physics, Weizmann Institute of Science, Rehovot 76100, Israel
| | | |
Collapse
|
49
|
Zimmermann T, Vaníček J. Evaluation of the importance of spin-orbit couplings in the nonadiabatic quantum dynamics with quantum fidelity and with its efficient "on-the-fly" ab initio semiclassical approximation. J Chem Phys 2013; 137:22A516. [PMID: 23249053 DOI: 10.1063/1.4738878] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose to measure the importance of spin-orbit couplings (SOCs) in the nonadiabatic molecular quantum dynamics rigorously with quantum fidelity. To make the criterion practical, quantum fidelity is estimated efficiently with the multiple-surface dephasing representation (MSDR). The MSDR is a semiclassical method that includes nuclear quantum effects through interference of mixed quantum-classical trajectories without the need for the Hessian of potential energy surfaces. Two variants of the MSDR are studied, in which the nuclei are propagated either with the fewest-switches surface hopping or with the locally mean field dynamics. The fidelity criterion and MSDR are first tested on one-dimensional model systems amenable to numerically exact quantum dynamics. Then, the MSDR is combined with "on-the-fly" computed electronic structure to measure the importance of SOCs and nonadiabatic couplings in the photoisomerization dynamics of CH(2)NH(2)(+) considering 20 electronic states and in the collision of F + H(2) considering six electronic states.
Collapse
Affiliation(s)
- Tomáš Zimmermann
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | | |
Collapse
|
50
|
Mendive-Tapia D, Lasorne B, Worth GA, Robb MA, Bearpark MJ. Towards converging non-adiabatic direct dynamics calculations using frozen-width variational Gaussian product basis functions. J Chem Phys 2012; 137:22A548. [DOI: 10.1063/1.4765087] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
|