1
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Yang Y, Zhang S, Ranasinghe KD, Isayev O, Roitberg AE. Machine Learning of Reactive Potentials. Annu Rev Phys Chem 2024; 75:371-395. [PMID: 38941524 DOI: 10.1146/annurev-physchem-062123-024417] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/30/2024]
Abstract
In the past two decades, machine learning potentials (MLPs) have driven significant developments in chemical, biological, and material sciences. The construction and training of MLPs enable fast and accurate simulations and analysis of thermodynamic and kinetic properties. This review focuses on the application of MLPs to reaction systems with consideration of bond breaking and formation. We review the development of MLP models, primarily with neural network and kernel-based algorithms, and recent applications of reactive MLPs (RMLPs) to systems at different scales. We show how RMLPs are constructed, how they speed up the calculation of reactive dynamics, and how they facilitate the study of reaction trajectories, reaction rates, free energy calculations, and many other calculations. Different data sampling strategies applied in building RMLPs are also discussed with a focus on how to collect structures for rare events and how to further improve their performance with active learning.
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Affiliation(s)
- Yinuo Yang
- Department of Chemistry, University of Florida, Gainesville, Florida;
| | - Shuhao Zhang
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania;
| | | | - Olexandr Isayev
- Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania;
| | - Adrian E Roitberg
- Department of Chemistry, University of Florida, Gainesville, Florida;
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2
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Habershon S. Program Synthesis of Sparse Algorithms for Wave Function and Energy Prediction in Grid-Based Quantum Simulations. J Chem Theory Comput 2022; 18:2462-2478. [PMID: 35293216 PMCID: PMC9009083 DOI: 10.1021/acs.jctc.2c00035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We have recently shown how program synthesis (PS), or the concept of "self-writing code", can generate novel algorithms that solve the vibrational Schrödinger equation, providing approximations to the allowed wave functions for bound, one-dimensional (1-D) potential energy surfaces (PESs). The resulting algorithms use a grid-based representation of the underlying wave function ψ(x) and PES V(x), providing codes which represent approximations to standard discrete variable representation (DVR) methods. In this Article, we show how this inductive PS strategy can be improved and modified to enable prediction of both vibrational wave functions and energy eigenvalues of representative model PESs (both 1-D and multidimensional). We show that PS can generate algorithms that offer some improvements in energy eigenvalue accuracy over standard DVR schemes; however, we also demonstrate that PS can identify accurate numerical methods that exhibit desirable computational features, such as employing very sparse (tridiagonal) matrices. The resulting PS-generated algorithms are initially developed and tested for 1-D vibrational eigenproblems, before solution of multidimensional problems is demonstrated; we find that our new PS-generated algorithms can reduce calculation times for grid-based eigenvector computation by an order of magnitude or more. More generally, with further development and optimization, we anticipate that PS-generated algorithms based on effective Hamiltonian approximations, such as those proposed here, could be useful in direct simulations of quantum dynamics via wave function propagation and evaluation of molecular electronic structure.
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Affiliation(s)
- Scott Habershon
- Department of Chemistry, University of Warwick, Coventry, CV4 7AL, United Kingdom
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3
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Richings GW, Habershon S. Predicting Molecular Photochemistry Using Machine-Learning-Enhanced Quantum Dynamics Simulations. Acc Chem Res 2022; 55:209-220. [PMID: 34982533 DOI: 10.1021/acs.accounts.1c00665] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The processes which occur after molecules absorb light underpin an enormous range of fundamental technologies and applications, including photocatalysis to enable new chemical transformations, sunscreens to protect against the harmful effects of UV overexposure, efficient photovoltaics for energy generation from sunlight, and fluorescent probes to image the intricate details of complex biomolecular structures. Reflecting this broad range of applications, an enormously versatile set of experiments are now regularly used to interrogate light-driven chemical dynamics, ranging from the typical ultrafast transient absorption spectroscopy used in many university laboratories to the inspiring central facilities around the world, such as the next-generation of X-ray free-electron lasers.Computer simulations of light-driven molecular and material dynamics are an essential route to analyzing the enormous amount of transient electronic and structural data produced by these experimental sources. However, to date, the direct simulation of molecular photochemistry remains a frontier challenge in computational chemical science, simultaneously demanding the accurate treatment of molecular electronic structure, nuclear dynamics, and the impact of nonadiabatic couplings.To address these important challenges and to enable new computational methods which can be integrated with state-of-the-art experimental capabilities, the past few years have seen a burst of activity in the development of "direct" quantum dynamics methods, merging the machine learning of potential energy surfaces (PESs) and nonadiabatic couplings with accurate quantum propagation schemes such as the multiconfiguration time-dependent Hartree (MCTDH) method. The result of this approach is a new generation of direct quantum dynamics tools in which PESs are generated in tandem with wave function propagation, enabling accurate "on-the-fly" simulations of molecular photochemistry. These simulations offer an alternative route toward gaining quantum dynamics insights, circumventing the challenge of generating ab initio electronic structure data for PES fitting by instead only demanding expensive energy evaluations as and when they are needed.In this Account, we describe the chronological evolution of our own contributions to this field, focusing on describing the algorithmic developments that enable direct MCTDH simulations for complex molecular systems moving on multiple coupled electronic states. Specifically, we highlight active learning strategies for generating PESs during grid-based quantum chemical dynamics simulations, and we discuss the development and impact of novel diabatization schemes to enable direct grid-based simulations of photochemical dynamics; these developments are highlighted in a series of benchmark molecular simulations of systems containing multiple nuclear degrees of freedom moving on multiple coupled electronic states. We hope that the ongoing developments reported here represent a major step forward in tools for modeling excited-state chemistry such as photodissociation, proton and electron transfer, and ultrafast energy dissipation in complex molecular systems.
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Affiliation(s)
- Gareth W. Richings
- Department of Chemistry, University of Warwick, Coventry, United Kingdom CV4 7AL
| | - Scott Habershon
- Department of Chemistry, University of Warwick, Coventry, United Kingdom CV4 7AL
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4
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Richings GW, Habershon S. Analyzing Grid-Based Direct Quantum Molecular Dynamics Using Non-Linear Dimensionality Reduction. Molecules 2021; 26:molecules26247418. [PMID: 34946499 PMCID: PMC8708769 DOI: 10.3390/molecules26247418] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2021] [Revised: 11/30/2021] [Accepted: 12/02/2021] [Indexed: 11/18/2022] Open
Abstract
Grid-based schemes for simulating quantum dynamics, such as the multi-configuration time-dependent Hartree (MCTDH) method, provide highly accurate predictions of the coupled nuclear and electronic dynamics in molecular systems. Such approaches provide a multi-dimensional, time-dependent view of the system wavefunction represented on a coordinate grid; in the case of non-adiabatic simulations, additional information about the state populations adds a further layer of complexity. As such, wavepacket motion on potential energy surfaces which couple many nuclear and electronic degrees-of-freedom can be extremely challenging to analyse in order to extract physical insight beyond the usual expectation-value picture. Here, we show that non-linear dimensionality reduction (NLDR) methods, notably diffusion maps, can be adapted to extract information from grid-based wavefunction dynamics simulations, providing insight into key nuclear motions which explain the observed dynamics. This approach is demonstrated for 2-D and 9-D models of proton transfer in salicylaldimine, as well as 8-D and full 12-D simulations of cis-trans isomerization in ethene; these simulations demonstrate how NLDR can provide alternative views of wavefunction dynamics, and also highlight future developments.
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5
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Abstract
We demonstrate that a program synthesis approach based on a linear code representation can be used to generate algorithms that approximate the ground-state solutions of one-dimensional time-independent Schrödinger equations constructed with bound polynomial potential energy surfaces (PESs). Here, an algorithm is constructed as a linear series of instructions operating on a set of input vectors, matrices, and constants that define the problem characteristics, such as the PES. Discrete optimization is performed using simulated annealing in order to identify sequences of code-lines, operating on the program inputs that can reproduce the expected ground-state wavefunctions ψ(x) for a set of target PESs. The outcome of this optimization is not simply a mathematical function approximating ψ(x) but is, instead, a complete algorithm that converts the input vectors describing the system into a ground-state solution of the Schrödinger equation. These initial results point the way toward an alternative route for developing novel algorithms for quantum chemistry applications.
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Affiliation(s)
- Scott Habershon
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
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6
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Posenitskiy E, Spiegelman F, Lemoine D. On application of deep learning to simplified quantum-classical dynamics in electronically excited states. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2021. [DOI: 10.1088/2632-2153/abfe3f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Abstract
Deep learning (DL) is applied to simulate non-adiabatic molecular dynamics of phenanthrene, using the time-dependent density functional based tight binding (TD-DFTB) approach for excited states combined with mixed quantum–classical propagation. Reference calculations rely on Tully’s fewest-switches surface hopping (FSSH) algorithm coupled to TD-DFTB, which provides electronic relaxation dynamics in fair agreement with various available experimental results. Aiming at describing the coupled electron-nuclei dynamics in large molecular systems, we then examine the combination of DL for excited-state potential energy surfaces (PESs) with a simplified trajectory surface hopping propagation based on the Belyaev–Lebedev (BL) scheme. We start to assess the accuracy of the TD-DFTB approach upon comparison of the optical spectrum with experimental and higher-level theoretical results. Using the recently developed SchNetPack (Schütt et al 2019 J. Chem. Theory Comput.
15 448–55) for DL applications, we train several models and evaluate their performance in predicting excited-state energies and forces. Then, the main focus is given to the analysis of the electronic population of low-lying excited states computed with the aforementioned methods. We determine the relaxation timescales and compare them with experimental data. Our results show that DL demonstrates its ability to describe the excited-state PESs. When coupled to the simplified BL scheme considered in this study, it provides reliable description of the electronic relaxation in phenanthrene as compared with either the experimental data or the higher-level FSSH/TD-DFTB theoretical results. Furthermore, the DL performance allows high-throughput analysis at a negligible cost.
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7
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Westermayr J, Marquetand P. Machine Learning for Electronically Excited States of Molecules. Chem Rev 2021; 121:9873-9926. [PMID: 33211478 PMCID: PMC8391943 DOI: 10.1021/acs.chemrev.0c00749] [Citation(s) in RCA: 167] [Impact Index Per Article: 55.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2020] [Indexed: 12/11/2022]
Abstract
Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.
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Affiliation(s)
- Julia Westermayr
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna
Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Data
Science @ Uni Vienna, University of Vienna, Währinger Strasse 29, 1090 Vienna, Austria
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8
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Abstract
Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.
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Affiliation(s)
- Julia Westermayr
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
| | - Philipp Marquetand
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Vienna Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währinger Strasse 17, 1090 Vienna, Austria
- Data Science @ Uni Vienna, University of Vienna, Währinger Strasse 29, 1090 Vienna, Austria
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9
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Zobel JP, González L. The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes. JACS AU 2021; 1:1116-1140. [PMID: 34467353 PMCID: PMC8397362 DOI: 10.1021/jacsau.1c00252] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2021] [Indexed: 05/15/2023]
Abstract
This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.
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Affiliation(s)
- J. Patrick Zobel
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währingerstr. 19, 1090 Vienna Austria
| | - Leticia González
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währingerstr. 19, 1090 Vienna Austria
- Vienna
Research Platform on Accelerating Photoreaction Discovery, University of Vienna, Währingerstr. 19, 1090 Vienna Austria
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10
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Rassolov V, Garashchuk S. Local Measure of Quantum Effects in Quantum Dynamics. J Phys Chem A 2021; 125:4653-4667. [PMID: 34014096 DOI: 10.1021/acs.jpca.1c02533] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The Madelung-de Broglie-Bohm formulation of the Schrödinger equation casts the time-evolution of a wave function as dynamics of an ensemble of quantum, or Bohmian, trajectories, interacting via the nonlocal quantum potential. This trajectory perspective gives insight into the quantumness (or classicality) of a given system due to clear partitioning of the energy into classical and quantum components. Here, we propose a system-independent measure of the quantumness of dynamics, based on the energy time-change, referred to as "quantum power". This measure is local in the coordinate space. Based on applications to model chemical systems, we argue that during the transition from the quantum to classical regime, defined as compression of quantization, the quantum features in dynamics do not "disappear" but are pushed forward in time. This feature may be used to gauge the validity of the semiclassical and other approximate dynamics approaches in applications to anharmonic systems.
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Affiliation(s)
- Vitaly Rassolov
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sophya Garashchuk
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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11
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Friederich P, Häse F, Proppe J, Aspuru-Guzik A. Machine-learned potentials for next-generation matter simulations. NATURE MATERIALS 2021; 20:750-761. [PMID: 34045696 DOI: 10.1038/s41563-020-0777-6] [Citation(s) in RCA: 117] [Impact Index Per Article: 39.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2019] [Accepted: 07/17/2020] [Indexed: 05/18/2023]
Abstract
The choice of simulation methods in computational materials science is driven by a fundamental trade-off: bridging large time- and length-scales with highly accurate simulations at an affordable computational cost. Venturing the investigation of complex phenomena on large scales requires fast yet accurate computational methods. We review the emerging field of machine-learned potentials, which promises to reach the accuracy of quantum mechanical computations at a substantially reduced computational cost. This Review will summarize the basic principles of the underlying machine learning methods, the data acquisition process and active learning procedures. We highlight multiple recent applications of machine-learned potentials in various fields, ranging from organic chemistry and biomolecules to inorganic crystal structure predictions and surface science. We furthermore discuss the developments required to promote a broader use of ML potentials, and the possibility of using them to help solve open questions in materials science and facilitate fully computational materials design.
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Affiliation(s)
- Pascal Friederich
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada
- Department of Computer Science, University of Toronto, Toronto, Ontario, Canada
- Institute of Nanotechnology, Karlsruhe Institute of Technology, Eggenstein-Leopoldshafen, Germany
- Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany
| | - Florian Häse
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada
- Department of Computer Science, University of Toronto, Toronto, Ontario, Canada
- Vector Institute for Artificial Intelligence, Toronto, Ontario, Canada
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA
| | - Jonny Proppe
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada
- Department of Computer Science, University of Toronto, Toronto, Ontario, Canada
- Institute of Physical Chemistry, Georg-August University, Göttingen, Germany
| | - Alán Aspuru-Guzik
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada.
- Department of Computer Science, University of Toronto, Toronto, Ontario, Canada.
- Vector Institute for Artificial Intelligence, Toronto, Ontario, Canada.
- Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA, USA.
- Lebovic Fellow, Canadian Institute for Advanced Research (CIFAR), Toronto, Ontario, Canada.
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12
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Abstract
Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.
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13
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Liu Z, Lin L, Jia Q, Cheng Z, Jiang Y, Guo Y, Ma J. Transferable Multilevel Attention Neural Network for Accurate Prediction of Quantum Chemistry Properties via Multitask Learning. J Chem Inf Model 2021; 61:1066-1082. [PMID: 33629839 DOI: 10.1021/acs.jcim.0c01224] [Citation(s) in RCA: 42] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
The development of efficient models for predicting specific properties through machine learning is of great importance for the innovation of chemistry and material science. However, predicting global electronic structure properties like Frontier molecular orbital highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy levels and their HOMO-LUMO gaps from the small-sized molecule data to larger molecules remains a challenge. Here, we develop a multilevel attention neural network, named DeepMoleNet, to enable chemical interpretable insights being fused into multitask learning through (1) weighting contributions from various atoms and (2) taking the atom-centered symmetry functions (ACSFs) as the teacher descriptor. The efficient prediction of 12 properties including dipole moment, HOMO, and Gibbs free energy within chemical accuracy is achieved by using multiple benchmarks, both at the equilibrium and nonequilibrium geometries, including up to 110,000 records of data in QM9, 400,000 records in MD17, and 280,000 records in ANI-1ccx for random split evaluation. The good transferability for predicting larger molecules outside the training set is demonstrated in both equilibrium QM9 and Alchemy data sets at the density functional theory (DFT) level. Additional tests on nonequilibrium molecular conformations from DFT-based MD17 data set and ANI-1ccx data set with coupled cluster accuracy as well as the public test sets of singlet fission molecules, biomolecules, long oligomers, and protein with up to 140 atoms show reasonable predictions for thermodynamics and electronic structure properties. The proposed multilevel attention neural network is applicable to high-throughput screening of numerous chemical species in both equilibrium and nonequilibrium molecular spaces to accelerate rational designs of drug-like molecules, material candidates, and chemical reactions.
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Affiliation(s)
- Ziteng Liu
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, P. R. China
| | - Liqiang Lin
- National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210023, P. R. China
| | - Qingqing Jia
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, P. R. China
| | - Zheng Cheng
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, P. R. China
| | - Yanyan Jiang
- National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210023, P. R. China
| | - Yanwen Guo
- National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing 210023, P. R. China
| | - Jing Ma
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, P. R. China.,Jiangsu Key Laboratory of Advanced Organic Materials, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, P. R. China
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14
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Richings GW, Habershon S. Direct Grid-Based Nonadiabatic Dynamics on Machine-Learned Potential Energy Surfaces: Application to Spin-Forbidden Processes. J Phys Chem A 2020; 124:9299-9313. [DOI: 10.1021/acs.jpca.0c06125] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Gareth W. Richings
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
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15
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Conti I, Cerullo G, Nenov A, Garavelli M. Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going. J Am Chem Soc 2020; 142:16117-16139. [PMID: 32841559 PMCID: PMC7901644 DOI: 10.1021/jacs.0c04952] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
![]()
Computational spectroscopy is becoming a mandatory tool for the interpretation of the
complex, and often congested, spectral maps delivered by modern non-linear multi-pulse
techniques. The fields of Electronic Structure Methods,
Non-Adiabatic Molecular Dynamics, and Theoretical
Spectroscopy represent the three pillars of the virtual ultrafast
optical spectrometer, able to deliver transient spectra in
silico from first principles. A successful simulation strategy requires a
synergistic approach that balances between the three fields, each one having its very
own challenges and bottlenecks. The aim of this Perspective is to demonstrate that,
despite these challenges, an impressive agreement between theory and experiment is
achievable now regarding the modeling of ultrafast photoinduced processes in complex
molecular architectures. Beyond that, some key recent developments in the three fields
are presented that we believe will have major impacts on spectroscopic simulations in
the very near future. Potential directions of development, pending challenges, and
rising opportunities are illustrated.
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Affiliation(s)
- Irene Conti
- Dipartimento di Chimica Industriale, Università degli Studi di Bologna, Viale del Risorgimento 4, I-40136 Bologna, Italy
| | - Giulio Cerullo
- Dipartimento di Fisica, Politecnico di Milano, IFN-CNR, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy
| | - Artur Nenov
- Dipartimento di Chimica Industriale, Università degli Studi di Bologna, Viale del Risorgimento 4, I-40136 Bologna, Italy
| | - Marco Garavelli
- Dipartimento di Chimica Industriale, Università degli Studi di Bologna, Viale del Risorgimento 4, I-40136 Bologna, Italy
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16
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Abstract
We present a machine learning (ML) method to accelerate the nuclear ensemble approach (NEA) for computing absorption cross sections. ML-NEA is used to calculate cross sections on vast ensembles of nuclear geometries to reduce the error due to insufficient statistical sampling. The electronic properties-excitation energies and oscillator strengths-are calculated with a reference electronic structure method only for a relatively few points in the ensemble. The KREG model (kernel-ridge-regression-based ML combined with the RE descriptor) as implemented in MLatom is used to predict these properties for the remaining tens of thousands of points in the ensemble without incurring much of additional computational cost. We demonstrate for two examples, benzene and a 9-dicyanomethylene derivative of acridine, that ML-NEA can produce statistically converged cross sections even for very challenging cases and even with as few as several hundreds of training points.
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Affiliation(s)
- Bao-Xin Xue
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
| | | | - Pavlo O Dral
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China
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17
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Dral PO, Owens A, Dral A, Csányi G. Hierarchical machine learning of potential energy surfaces. J Chem Phys 2020; 152:204110. [DOI: 10.1063/5.0006498] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Pavlo O. Dral
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Alec Owens
- Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom
| | - Alexey Dral
- BigData Team, 1A Tormoznoye Shosse Off 17, Yaroslavl, Yaroslavl 150022, Russian Federation
| | - Gábor Csányi
- Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
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18
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Richings GW, Habershon S. A new diabatization scheme for direct quantum dynamics: Procrustes diabatization. J Chem Phys 2020; 152:154108. [DOI: 10.1063/5.0003254] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gareth W. Richings
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry, University of Warwick, Coventry CV4 7AL, United Kingdom
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19
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Neville SP, Seidu I, Schuurman MS. Propagative block diagonalization diabatization of DFT/MRCI electronic states. J Chem Phys 2020; 152:114110. [DOI: 10.1063/1.5143126] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Affiliation(s)
- Simon P. Neville
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, 10 Marie Curie, Ottawa, Ontario K1N 6N5, Canada
| | - Issaka Seidu
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, 10 Marie Curie, Ottawa, Ontario K1N 6N5, Canada
| | - Michael S. Schuurman
- Department of Chemistry and Biomolecular Sciences, University of Ottawa, 10 Marie Curie, Ottawa, Ontario K1N 6N5, Canada
- National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada
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20
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Abstract
As the quantum chemistry (QC) community embraces machine learning (ML), the number of new methods and applications based on the combination of QC and ML is surging. In this Perspective, a view of the current state of affairs in this new and exciting research field is offered, challenges of using machine learning in quantum chemistry applications are described, and potential future developments are outlined. Specifically, examples of how machine learning is used to improve the accuracy and accelerate quantum chemical research are shown. Generalization and classification of existing techniques are provided to ease the navigation in the sea of literature and to guide researchers entering the field. The emphasis of this Perspective is on supervised machine learning.
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Affiliation(s)
- Pavlo O Dral
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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21
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Dutra M, Wickramasinghe S, Garashchuk S. Quantum Dynamics with the Quantum Trajectory-Guided Adaptable Gaussian Bases. J Chem Theory Comput 2019; 16:18-34. [DOI: 10.1021/acs.jctc.9b00844] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Matthew Dutra
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sachith Wickramasinghe
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sophya Garashchuk
- Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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22
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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.
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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
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23
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Polyak I, Richings GW, Habershon S, Knowles PJ. Direct quantum dynamics using variational Gaussian wavepackets and Gaussian process regression. J Chem Phys 2019; 150:041101. [PMID: 30709252 DOI: 10.1063/1.5086358] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The method of direct variational quantum nuclear dynamics in a basis of Gaussian wavepackets, combined with the potential energy surfaces fitted on-the-fly using Gaussian process regression, is described together with its implementation. Enabling exact and efficient analytic evaluation of Hamiltonian matrix elements, this approach allows for black-box quantum dynamics of multidimensional anharmonic molecular systems. Example calculations of intra-molecular proton transfer on the electronic ground state of salicylaldimine are provided, and future algorithmic improvements as well as the potential for multiple-state non-adiabatic dynamics are discussed.
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Affiliation(s)
- Iakov Polyak
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
| | - Gareth W Richings
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Peter J Knowles
- School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom
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24
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Richings G, Robertson C, Habershon S. Can we use on-the-fly quantum simulations to connect molecular structure and sunscreen action? Faraday Discuss 2019; 216:476-493. [DOI: 10.1039/c8fd00228b] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Abstract
Direct MCTDH quantum dynamics simulations, with automatic active coordinate generation, applied to potential molecular sunscreens.
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Affiliation(s)
- Gareth W. Richings
- Department of Chemistry and Centre for Scientific Computing
- University of Warwick
- Coventry
- UK
| | - Christopher Robertson
- Department of Chemistry and Centre for Scientific Computing
- University of Warwick
- Coventry
- UK
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing
- University of Warwick
- Coventry
- UK
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25
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Richings GW, Robertson C, Habershon S. Improved on-the-Fly MCTDH Simulations with Many-Body-Potential Tensor Decomposition and Projection Diabatization. J Chem Theory Comput 2018; 15:857-870. [DOI: 10.1021/acs.jctc.8b00819] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Gareth W. Richings
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, U.K
| | - Christopher Robertson
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, U.K
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, U.K
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26
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Chen WK, Liu XY, Fang WH, Dral PO, Cui G. Deep Learning for Nonadiabatic Excited-State Dynamics. J Phys Chem Lett 2018; 9:6702-6708. [PMID: 30403870 DOI: 10.1021/acs.jpclett.8b03026] [Citation(s) in RCA: 100] [Impact Index Per Article: 16.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
In this work we show that deep learning (DL) can be used for exploring complex and highly nonlinear multistate potential energy surfaces of polyatomic molecules and related nonadiabatic dynamics. Our DL is based on deep neural networks (DNNs), which are used as accurate representations of the CASSCF ground- and excited-state potential energy surfaces (PESs) of CH2NH. After geometries near conical intersection are included in the training set, the DNN models accurately reproduce excited-state topological structures; photoisomerization paths; and, importantly, conical intersections. We have also demonstrated that the results from nonadiabatic dynamics run with the DNN models are very close to those from the dynamics run with the pure ab initio method. The present work should encourage further studies of using machine learning methods to explore excited-state potential energy surfaces and nonadiabatic dynamics of polyatomic molecules.
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Affiliation(s)
- Wen-Kai Chen
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , China
| | - Xiang-Yang Liu
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , China
| | - Pavlo O Dral
- Max-Planck-Institut für Kohlenforschung , Kaiser-Wilhelm-Platz 1 , 45470 Mülheim an der Ruhr , Germany
| | - Ganglong Cui
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry , Beijing Normal University , Beijing 100875 , China
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27
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Eisenbrandt P, Ruckenbauer M, Burghardt I. Gaussian-based multiconfiguration time-dependent Hartree: A two-layer approach. III. Application to nonadiabatic dynamics in a charge transfer complex. J Chem Phys 2018; 149:174102. [DOI: 10.1063/1.5053417] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- P. Eisenbrandt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
| | - M. Ruckenbauer
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
| | - I. Burghardt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Str. 7, 60438 Frankfurt, Germany
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28
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Dral PO, Barbatti M, Thiel W. Nonadiabatic Excited-State Dynamics with Machine Learning. J Phys Chem Lett 2018; 9:5660-5663. [PMID: 30200766 PMCID: PMC6174422 DOI: 10.1021/acs.jpclett.8b02469] [Citation(s) in RCA: 101] [Impact Index Per Article: 16.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2018] [Accepted: 09/10/2018] [Indexed: 05/23/2023]
Abstract
We show that machine learning (ML) can be used to accurately reproduce nonadiabatic excited-state dynamics with decoherence-corrected fewest switches surface hopping in a 1-D model system. We propose to use ML to significantly reduce the simulation time of realistic, high-dimensional systems with good reproduction of observables obtained from reference simulations. Our approach is based on creating approximate ML potentials for each adiabatic state using a small number of training points. We investigate the feasibility of this approach by using adiabatic spin-boson Hamiltonian models of various dimensions as reference methods.
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Affiliation(s)
- Pavlo O. Dral
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | | | - Walter Thiel
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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29
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Arai Y, Suzuki K, Kanno M, Kono H. Automatic spatial extension of a time-dependent wavefunction expanded in terms of Gaussians: Application to multidimensional tunneling. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.07.022] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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30
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Hu D, Xie Y, Li X, Li L, Lan Z. Inclusion of Machine Learning Kernel Ridge Regression Potential Energy Surfaces in On-the-Fly Nonadiabatic Molecular Dynamics Simulation. J Phys Chem Lett 2018; 9:2725-2732. [PMID: 29732893 DOI: 10.1021/acs.jpclett.8b00684] [Citation(s) in RCA: 94] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
We discuss a theoretical approach that employs machine learning potential energy surfaces (ML-PESs) in the nonadiabatic dynamics simulation of polyatomic systems by taking 6-aminopyrimidine as a typical example. The Zhu-Nakamura theory is employed in the surface hopping dynamics, which does not require the calculation of the nonadiabatic coupling vectors. The kernel ridge regression is used in the construction of the adiabatic PESs. In the nonadiabatic dynamics simulation, we use ML-PESs for most geometries and switch back to the electronic structure calculations for a few geometries either near the S1/S0 conical intersections or in the out-of-confidence regions. The dynamics results based on ML-PESs are consistent with those based on CASSCF PESs. The ML-PESs are further used to achieve the highly efficient massive dynamics simulations with a large number of trajectories. This work displays the powerful role of ML methods in the nonadiabatic dynamics simulation of polyatomic systems.
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Affiliation(s)
- Deping Hu
- CAS Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy and Bioprocess Technology , Chinese Academy of Sciences , Qingdao 266101 , China
- University of Chinese Academy of Sciences , Beijing 100049 , China
| | - Yu Xie
- CAS Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy and Bioprocess Technology , Chinese Academy of Sciences , Qingdao 266101 , China
| | - Xusong Li
- CAS Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy and Bioprocess Technology , Chinese Academy of Sciences , Qingdao 266101 , China
- University of Chinese Academy of Sciences , Beijing 100049 , China
| | - Lingyue Li
- University of Chinese Academy of Sciences , Beijing 100049 , China
| | - Zhenggang Lan
- CAS Key Laboratory of Biobased Materials, Qingdao Institute of Bioenergy and Bioprocess Technology , Chinese Academy of Sciences , Qingdao 266101 , China
- University of Chinese Academy of Sciences , Beijing 100049 , China
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31
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Komarova KG, Remacle F, Levine R. On the fly quantum dynamics of electronic and nuclear wave packets. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2018.03.050] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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32
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Richings GW, Habershon S. MCTDH on-the-fly: Efficient grid-based quantum dynamics without pre-computed potential energy surfaces. J Chem Phys 2018; 148:134116. [DOI: 10.1063/1.5024869] [Citation(s) in RCA: 54] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gareth W. Richings
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
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33
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Spinlove KE, Richings GW, Robb MA, Worth GA. Curve crossing in a manifold of coupled electronic states: direct quantum dynamics simulations of formamide. Faraday Discuss 2018; 212:191-215. [PMID: 30238103 DOI: 10.1039/c8fd00090e] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Abstract
Quantum dynamics simulations are an important tool to evaluate molecular behaviour including the, often key, quantum nature of the system. In this paper we present an algorithm that is able to simulate the time evolution of a molecule after photo-excitation into a manifold of states. The direct dynamics variational multi-configurational Gaussian (DD-vMCG) method circumvents the computational bottleneck problems of traditional grid-based methods by computing the potential energy functions on-the-fly, i.e. only where required. Unlike other commonly used direct dynamics methods, DD-vMCG is fully quantum mechanical. Here, the method is combined with a novel on-the-fly diabatisation scheme to simulate the short-time dynamics of the key molecule formamide and its acid analogue formimidic acid. This is a challenging test system due to the nature and large number of excited states, and eight coupled states are included in the calculations. It is shown that the method is able to provide unbiased information on the product channels open after excitation at different energies and demonstrates the potential to be a practical scheme, limited mainly by the quality of the quantum chemistry used to describe the excited states.
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Affiliation(s)
- K Eryn Spinlove
- Dept. of Chemistry, University College London, 20 Gordon St., London, UK. and School of Chemistry, University of Birmingham, Birmingham, B15 2TT, UK and Dept. of Chemistry, Imperial College London, London, SW7 2AZ, UK
| | - Gareth W Richings
- Dept. of Chemistry, University of Warwick, Gibbet Hill, Coventry, CV4 7AL, UK
| | - Michael A Robb
- Dept. of Chemistry, Imperial College London, London, SW7 2AZ, UK
| | - Graham A Worth
- Dept. of Chemistry, University College London, 20 Gordon St., London, UK.
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34
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Richings GW, Habershon S. Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.01.063] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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