1
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Singh K, Lee KH, Peláez D, Bande A. Accelerating wavepacket propagation with machine learning. J Comput Chem 2024; 45:2360-2373. [PMID: 39031712 DOI: 10.1002/jcc.27443] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2023] [Revised: 05/13/2024] [Accepted: 05/16/2024] [Indexed: 07/22/2024]
Abstract
In this work, we discuss the use of a recently introduced machine learning (ML) technique known as Fourier neural operators (FNO) as an efficient alternative to the traditional solution of the time-dependent Schrödinger equation (TDSE). FNOs are ML models which are employed in the approximated solution of partial differential equations. For a wavepacket propagating in an anharmonic potential and for a tunneling system, we show that the FNO approach can accurately and faithfully model wavepacket propagation via the density. Additionally, we demonstrate that FNOs can be a suitable replacement for traditional TDSE solvers in cases where the results of the quantum dynamical simulation are required repeatedly such as in the case of parameter optimization problems (e.g., control). The speed-up from the FNO method allows for its combination with the Markov-chain Monte Carlo approach in applications that involve solving inverse problems such as optimal and coherent laser control of the outcome of dynamical processes.
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Affiliation(s)
- Kanishka Singh
- Theory of Electron Dynamics and Spectroscopy, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Berlin, Germany
- Institute of Chemistry and Biochemistry, Freie Universität Berlin, Berlin, Germany
| | - Ka Hei Lee
- Theory of Electron Dynamics and Spectroscopy, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Berlin, Germany
- Fachbereich Physik, Freie Universität Berlin, Berlin, Germany
| | - Daniel Peláez
- CNRS, Institut des Sciences Moléculaires d'Orsay, Université Paris-Saclay, Orsay, France
| | - Annika Bande
- Theory of Electron Dynamics and Spectroscopy, Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Berlin, Germany
- Institute of Inorganic Chemistry, Leibniz University Hannover, Hannover, Germany
- Cluster of Excellence PhoenixD, Leibniz University Hannover, Hannover, Germany
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2
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Dwivedi A, Lopez-Ruiz MA, Iyengar SS. Resource Optimization for Quantum Dynamics with Tensor Networks: Quantum and Classical Algorithms. J Phys Chem A 2024; 128:6774-6797. [PMID: 39101545 DOI: 10.1021/acs.jpca.4c03407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/06/2024]
Abstract
The exponential scaling of the quantum degrees of freedom with the size of the system is one of the biggest challenges in computational chemistry and particularly in quantum dynamics. We present a tensor network approach for the time-evolution of the nuclear degrees of freedom of multiconfigurational chemical systems at a reduced storage and computational complexity. We also present quantum algorithms for the resultant dynamics. To preserve the compression advantage achieved via tensor network decompositions, we present an adaptive algorithm for the regularization of nonphysical bond dimensions, preventing the potentially exponential growth of these with time. While applicable to any quantum dynamical problem, our method is particularly valuable for dynamical simulations of nuclear chemical systems. Our algorithm is demonstrated using ab initio potentials obtained for a symmetric hydrogen-bonded system, namely, the protonated 2,2'-bipyridine, and compared to exact diagonalization numerical results.
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Affiliation(s)
- Anurag Dwivedi
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
- Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Miguel Angel Lopez-Ruiz
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
- Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405, United States
- Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
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3
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Li W, Ren J, Yang H, Wang H, Shuai Z. Optimal tree tensor network operators for tensor network simulations: Applications to open quantum systems. J Chem Phys 2024; 161:054116. [PMID: 39105557 DOI: 10.1063/5.0218773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2024] [Accepted: 07/17/2024] [Indexed: 08/07/2024] Open
Abstract
Tree tensor network states (TTNS) decompose the system wavefunction to the product of low-rank tensors based on the tree topology, serving as the foundation of the multi-layer multi-configuration time-dependent Hartree method. In this work, we present an algorithm that automatically constructs the optimal and exact tree tensor network operators (TTNO) for any sum-of-product symbolic quantum operator. The construction is based on the minimum vertex cover of a bipartite graph. With the optimal TTNO, we simulate open quantum systems, such as spin relaxation dynamics in the spin-boson model and charge transport in molecular junctions. In these simulations, the environment is treated as discrete modes and its wavefunction is evolved on equal footing with the system. We employ the Cole-Davidson spectral density to model the glassy phonon environment and incorporate temperature effects via thermo-field dynamics. Our results show that the computational cost scales linearly with the number of discretized modes, demonstrating the efficiency of our approach.
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Affiliation(s)
- Weitang Li
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, People's Republic of China
- Tencent Quantum Lab, Tencent, Shenzhen 518057, People's Republic of China
| | - Jiajun Ren
- MOE Key Laboratory of Theoretical and Computational Photochemistry, College of Chemistry, Beijing Normal University, Beijing 100875, People's Republic of China
| | - Hengrui Yang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084 Beijing, People's Republic of China
| | - Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA
| | - Zhigang Shuai
- School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, People's Republic of China
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, 100084 Beijing, People's Republic of China
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4
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Ellerbrock R, Johnson KG, Seritan S, Hoppe H, Zhang JH, Lenzen T, Weike T, Manthe U, Martínez TJ. QuTree: A tree tensor network package. J Chem Phys 2024; 160:112501. [PMID: 38497471 DOI: 10.1063/5.0180233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2023] [Accepted: 02/20/2024] [Indexed: 03/19/2024] Open
Abstract
We present QuTree, a C++ library for tree tensor network approaches. QuTree provides class structures for tensors, tensor trees, and related linear algebra functions that facilitate the fast development of tree tensor network approaches such as the multilayer multiconfigurational time-dependent Hartree approach or the density matrix renormalization group approach and its various extensions. We investigate the efficiency of relevant tensor and tensor network operations and show that the overhead for managing the network structure is negligible, even in cases with a million leaves and small tensors. QuTree focuses on providing simple, high-level routines while retaining easy access to the backend to facilitate novel developments. We demonstrate the capabilities of the package by computing the eigenstates of coupled harmonic oscillator Hamiltonians and performing random circuit simulations on a virtual quantum computer.
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Affiliation(s)
- Roman Ellerbrock
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
- Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany
| | - K Grace Johnson
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
| | - Stefan Seritan
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
| | - Hannes Hoppe
- Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany
| | - J H Zhang
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
| | - Tim Lenzen
- Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany
| | - Thomas Weike
- Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany
| | - Uwe Manthe
- Bielefeld University, Universitätsstraße 25, 33615 Bielefeld, Germany
| | - Todd J Martínez
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
- SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA
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5
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Tajouo Tela H, Quintas-Sánchez E, Dubernet ML, Scribano Y, Dawes R, Gatti F, Ndengué S. Rovibrational states calculations of the H 2O-HCN heterodimer with the multiconfiguration time dependent Hartree method. Phys Chem Chem Phys 2023; 25:31813-31824. [PMID: 37966067 DOI: 10.1039/d3cp03225f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
Water and hydrogen cyanide are two of the most common species in space and the atmosphere with the ability of binding to form dimers such as H2O-HCN. In the literature, while calculations characterizing various properties of the H2O-HCN cluster (equilibrium distance, vibrational frequencies and rotational constants) have been done in the past, extensive calculations of the rovibrational states of this system using a reliable quantum dynamical approach have yet to be reported. In this work, we intend to mend that by performing the first calculation of the rovibrational states of the H2O-HCN van der Waals complex on a recently developed potential energy surface. We use the block improved relaxation procedure implemented in the Heidelberg MultiConfiguration Time-Dependent Hartree (MCTDH) package to compute the states of the H2O-HCN isomer, from which we extract the transition frequencies and rotational constants of the complex. We further adapt an approach first suggested by Wang and Carrington-and supported here by analysis routines of the Heidelberg MCTDH package-to properly characterize the computed rovibrational states. The subsequent assignment of rovibrational states was done by theoretical analysis and visual inspection of the wavefunctions. Our simulations provide a Zero Point Energy (ZPE) and intermolecular vibrational frequencies in good agreement with past ab initio calculations. The transition frequencies and rotational constants obtained from our simulations match well with the available experimental data. This work has the broad aim to propose the MCTDH approach as a reliable option to compute and characterize rovibrational states of van der Waals complexes such as the current one.
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Affiliation(s)
- Hervé Tajouo Tela
- ICTP-East African Institute for Fundamental Research, University of Rwanda, Kigali, Rwanda.
| | - Ernesto Quintas-Sánchez
- Department of Chemistry, Missouri University of Science and Technology, 65409 Rolla, Missouri, USA
| | - Marie-Lise Dubernet
- LERMA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne University, UPMC Univ Paris 06, 75014 Paris, France
| | - Yohann Scribano
- Laboratoire Univers et Particules de Montpellier, UMR-CNRS 5299, Université de Montpellier, Place Eugène Bataillon, 34095 Montpellier, France
| | - Richard Dawes
- Department of Chemistry, Missouri University of Science and Technology, 65409 Rolla, Missouri, USA
| | - Fabien Gatti
- Institut de Sciences Moleculaires d'Orsay, UMR 8214, Université Paris-Sud - Université Paris-Saclay, 91405 Orsay, France
| | - Steve Ndengué
- ICTP-East African Institute for Fundamental Research, University of Rwanda, Kigali, Rwanda.
- Department of Physics, Trinity College, 06106 Hartford, Connecticut, USA
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6
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Ashani MN, Huang Q, Flowers AM, Brown A, Aerts A, Otero-de-la-Roza A, DiLabio GA. Accurate Potential Energy Surfaces Using Atom-Centered Potentials and Minimal High-Level Data. J Phys Chem A 2023; 127:8015-8024. [PMID: 37712536 DOI: 10.1021/acs.jpca.3c04558] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/16/2023]
Abstract
We demonstrate that a Δ-density functional theory (Δ-DFT) approach based on atom-centered potentials (ACPs) represents a computationally inexpensive and accurate method for representing potential energy surfaces (PESs) for the HONO and HFCO molecules and vibrational frequencies derived therefrom. Using as few as 100 CCSD(T)-F12a reference energies, ACPs developed for use with B3LYP/def2-TZVPP are shown to produce PESs for HONO and HFCO with mean absolute errors of 27.7 and 5.8 cm-1, respectively. Application of the multiconfigurational time-dependent Hartree (MCTDH) method with ACP-corrected B3LYP/def2-TZVPP PESs produces vibrational frequencies for cis- and trans-HONO with mean absolute percent errors (MAPEs) of 0.8 and 1.1, compared to 0.8 obtained for the two isomers with CCSD(T)-F12a/cc-pVTZ-F12/MCTDH. For HFCO, the vibrational frequencies obtained using the present (Δ-DFT)/MCTDH approach give a MAPE of 0.1, which is the error obtained with CCSD(T)-F12a/cc-pVTZ-F12/MCTDH. The ACP approach is therefore successful in representing a PES calculated at a high level of theory (CCSD(T)-F12a) and a promising method for the development of a general protocol for the representation of accurate molecular PESs and the calculation of molecular properties from them.
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Affiliation(s)
- Mahsa Nazemi Ashani
- Department of Chemistry, University of British Columbia, 3247 University Way, Kelowna, British Columbia V1V 1V7, Canada
| | - Qinan Huang
- Department of Chemistry, University of British Columbia, 3247 University Way, Kelowna, British Columbia V1V 1V7, Canada
| | - A Mackenzie Flowers
- Department of Chemistry, University of Alberta, Edmonton, AB T6G 2G2, Canada
| | - Alex Brown
- Department of Chemistry, University of Alberta, Edmonton, AB T6G 2G2, Canada
| | - Antoine Aerts
- Spectroscopy, Quantum Chemistry and Atmospheric Remote Sensing (SQUARES), Université libre de Bruxelles, 50 avenue F. Roosevelt, C.P. 160/09, B-1050 Brussels, Belgium
| | - Alberto Otero-de-la-Roza
- Departamento de Química Física y Analítica and MALTA Consolider Team, Facultad de Química, Universidad de Oviedo, 33006 Oviedo, Spain
| | - Gino A DiLabio
- Department of Chemistry, University of British Columbia, 3247 University Way, Kelowna, British Columbia V1V 1V7, Canada
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7
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Iyengar SS, Kumar A, Saha D, Sabry A. Synthesis of Hidden Subgroup Quantum Algorithms and Quantum Chemical Dynamics. J Chem Theory Comput 2023; 19:6082-6092. [PMID: 37703187 DOI: 10.1021/acs.jctc.3c00404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/15/2023]
Abstract
We describe a general formalism for quantum dynamics and show how this formalism subsumes several quantum algorithms, including the Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Shor algorithms as well as the conventional approach to quantum dynamics based on tensor networks. The common framework exposes similarities among quantum algorithms and natural quantum phenomena: we illustrate this connection by showing how the correlated behavior of protons in water wire systems that are common in many biological and materials systems parallels the structure of Shor's algorithm.
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Affiliation(s)
- Srinivasan S Iyengar
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
- Quantum Science and Engineering Center (QSEc), Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Anup Kumar
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Debadrita Saha
- Department of Chemistry, Indiana University, Bloomington, Indiana 47405-7102, United States
| | - Amr Sabry
- Quantum Science and Engineering Center (QSEc), Indiana University, Bloomington, Indiana 47405-7102, United States
- Department of Computer Science, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47405-7102, United States
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8
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Schneider M, Born D, Kästner J, Rauhut G. Positioning of grid points for spanning potential energy surfaces-How much effort is really needed? J Chem Phys 2023; 158:144118. [PMID: 37061506 DOI: 10.1063/5.0146020] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
The positions of grid points for representing a multidimensional potential energy surface (PES) have a non-negligible impact on its accuracy and the associated computational effort for its generation. Six different positioning schemes were studied for PESs represented by n-mode expansions as needed for the accurate calculation of anharmonic vibrational frequencies by means of vibrational configuration interaction theory. A static approach, which has successfully been used in many applications, and five adaptive schemes based on Gaussian process regression have been investigated with respect to the number of necessary grid points and the accuracy of the fundamental modes for a small set of test molecules. A comparison with a related, more sophisticated, and consistent approach by Christiansen et al. is provided. The impact of the positions of the ab initio grid points is discussed for multilevel PESs, for which the computational effort of the individual electronic structure calculations decreases for increasing orders of the n-mode expansion. As a result of that, the ultimate goal is not the maximal reduction of grid points but rather the computational cost, which is not directly related.
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Affiliation(s)
- Moritz Schneider
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Daniel Born
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Johannes Kästner
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institute for Theoretical Chemistry, University of Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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9
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Nadoveza N, Panadés-Barrueta RL, Shi L, Gatti F, Peláez D. Analytical high-dimensional operators in canonical polyadic finite basis representation (CP-FBR). J Chem Phys 2023; 158:114109. [PMID: 36948837 DOI: 10.1063/5.0139224] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023] Open
Abstract
In the present work, we introduce a simple means of obtaining an analytical (i.e., grid-free) canonical polyadic (CP) representation of a multidimensional function that is expressed in terms of a set of discrete data. For this, we make use of an initial CP guess, even not fully converged, and a set of auxiliary basis functions [finite basis representation (FBR)]. The resulting CP-FBR expression constitutes the CP counterpart of our previous Tucker sum-of-products-FBR approach. However, as is well-known, CP expressions are much more compact. This has obvious advantages in high-dimensional quantum dynamics. The power of CP-FBR lies in the fact that it requires a grid much coarser than the one needed for the dynamics. In a subsequent step, the basis functions can be interpolated to any desired density of grid points. This is useful, for instance, when different initial conditions (e.g., energy content) of a system are to be considered. We show the application of the method to bound systems of increased dimensionality: H2 (3D), HONO (6D), and CH4 (9D).
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Affiliation(s)
- Nataša Nadoveza
- Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405 Orsay, France
| | | | - Lei Shi
- Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405 Orsay, France
| | - Fabien Gatti
- Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405 Orsay, France
| | - Daniel Peláez
- Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405 Orsay, France
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10
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Kumar A, DeGregorio N, Ricard T, Iyengar SS. Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynamics. J Chem Theory Comput 2022; 18:7243-7259. [PMID: 36332133 DOI: 10.1021/acs.jctc.2c00484] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
Molecular fragmentation methods have revolutionized quantum chemistry. Here, we use a graph-theoretically generated molecular fragmentation method, to obtain accurate and efficient representations for multidimensional potential energy surfaces and the quantum time-evolution operator, which plays a critical role in quantum chemical dynamics. In doing so, we find that the graph-theoretic fragmentation approach naturally reduces the potential portion of the time-evolution operator into a tensor network that contains a stream of coupled lower-dimensional propagation steps to potentially achieve quantum dynamics with reduced complexity. Furthermore, the fragmentation approach used here has previously been shown to allow accurate and efficient computation of post-Hartree-Fock electronic potential energy surfaces, which in many cases has been shown to be at density functional theory cost. Thus, by combining the advantages of molecular fragmentation with the tensor network formalism, the approach yields an on-the-fly quantum dynamics scheme where both the electronic potential calculation and nuclear propagation portion are enormously simplified through a single stroke. The method is demonstrated by computing approximations to the propagator and to potential surfaces for a set of coupled nuclear dimensions within a protonated water wire problem exhibiting the Grotthuss mechanism of proton transport. In all cases, our approach has been shown to reduce the complexity of representing the quantum propagator, and by extension action of the propagator on an initial wavepacket, by several orders, with minimal loss in accuracy.
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Affiliation(s)
- Anup Kumar
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Nicole DeGregorio
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Timothy Ricard
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry, and the Indiana University Quantum Science and Engineering Center (IU-QSEC), Indiana University, Bloomington, Indiana 47405, United States
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11
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Song Q, Zhang X, Peláez D, Meng Q. Direct Canonical-Polyadic-Decomposition of the Potential Energy Surface from Discrete Data by Decoupled Gaussian Process Regression. J Phys Chem Lett 2022; 13:11128-11135. [PMID: 36442084 DOI: 10.1021/acs.jpclett.2c03080] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
A Gaussian process regression (GPR) approach for directly constructing the canonical polyadic decomposition (CPD) of a multidimensional potential energy surface (PES) by discrete training energies is proposed and denoted by CPD-GPR. The present CPD-GPR method requires the kernel function in a product of a series of one-dimensional functions. To test CPD-GPR, the reactive probabilities of H + H2 as a function of kinetics energy are performed. Comparing the dynamics results computed by the CPD-GPR PES with those by the original PES, a good agreement between these results can be clearly found. Discussions on the previous algorithms for building the decomposed form are also given. We further show that the CPD-GPR method might be the general algorithm for building the decomposed form. However, further development is needed to reduce the CPD rank. Therefore, the present CPD-GPR method might be helpful to inspire ideas for developing new tools in building decomposed potential functions.
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Affiliation(s)
- Qingfei Song
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072Xi'an, China
- Institut des Sciences Moléculaires d'Orsay, CNRS-UMR 8214, Université Paris-Saclay, Bâtiment 520, F-91405Orsay, France
| | - Xingyu Zhang
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072Xi'an, China
| | - Daniel Peláez
- Institut des Sciences Moléculaires d'Orsay, CNRS-UMR 8214, Université Paris-Saclay, Bâtiment 520, F-91405Orsay, France
| | - Qingyong Meng
- Department of Chemistry, Northwestern Polytechnical University, West Youyi Road 127, 710072Xi'an, China
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12
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Schröder M, Gatti F, Lauvergnat D, Meyer HD, Vendrell O. The coupling of the hydrated proton to its first solvation shell. Nat Commun 2022; 13:6170. [PMID: 36257946 PMCID: PMC9579203 DOI: 10.1038/s41467-022-33650-w] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2022] [Accepted: 09/28/2022] [Indexed: 11/30/2022] Open
Abstract
The Zundel ([Formula: see text]) and Eigen ([Formula: see text]) cations play an important role as intermediate structures for proton transfer processes in liquid water. In the gas phase they exhibit radically different infrared (IR) spectra. The question arises: is there a least common denominator structure that explains the IR spectra of both, the Zundel and Eigen cations, and hence of the solvated proton? Full dimensional quantum simulations of these protonated cations demonstrate that two dynamical water molecules and an excess proton constitute this fundamental subunit. Embedded in the static environment of the parent Eigen cation, this subunit reproduces the positions and broadenings of its main excess-proton bands. In isolation, its spectrum reverts to the well-known Zundel ion. Hence, the dynamics of this subunit polarized by an environment suffice to explain the spectral signatures and anharmonic couplings of the solvated proton in its first solvation shell.
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Affiliation(s)
- Markus Schröder
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120, Heidelberg, Germany.
| | - Fabien Gatti
- Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay UMR 8214, 91405, Orsay, France
| | - David Lauvergnat
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR 8000, 91405, Orsay, France
| | - Hans-Dieter Meyer
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120, Heidelberg, Germany
| | - Oriol Vendrell
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, 69120, Heidelberg, Germany.
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13
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Zhu X, Iyengar SS. Graph Theoretic Molecular Fragmentation for Multidimensional Potential Energy Surfaces Yield an Adaptive and General Transfer Machine Learning Protocol. J Chem Theory Comput 2022; 18:5125-5144. [PMID: 35994592 DOI: 10.1021/acs.jctc.1c01241] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Over a series of publications we have introduced a graph-theoretic description for molecular fragmentation. Here, a system is divided into a set of nodes, or vertices, that are then connected through edges, faces, and higher-order simplexes to represent a collection of spatially overlapping and locally interacting subsystems. Each such subsystem is treated at two levels of electronic structure theory, and the result is used to construct many-body expansions that are then embedded within an ONIOM-scheme. These expansions converge rapidly with many-body order (or graphical rank) of subsystems and have been previously used for ab initio molecular dynamics (AIMD) calculations and for computing multidimensional potential energy surfaces. Specifically, in all these cases we have shown that CCSD and MP2 level AIMD trajectories and potential surfaces may be obtained at density functional theory cost. The approach has been demonstrated for gas-phase studies, for condensed phase electronic structure, and also for basis set extrapolation-based AIMD. Recently, this approach has also been used to derive new quantum-computing algorithms that enormously reduce the quantum circuit depth in a circuit-based computation of correlated electronic structure. In this publication, we introduce (a) a family of neural networks that act in parallel to represent, efficiently, the post-Hartree-Fock electronic structure energy contributions for all simplexes (fragments), and (b) a new k-means-based tessellation strategy to glean training data for high-dimensional molecular spaces and minimize the extent of training needed to construct this family of neural networks. The approach is particularly useful when coupled cluster accuracy is desired and when fragment sizes grow in order to capture nonlocal interactions accurately. The unique multidimensional k-means tessellation/clustering algorithm used to determine our training data for all fragments is shown to be extremely efficient and reduces the needed training to only 10% of data for all fragments to obtain accurate neural networks for each fragment. These fully connected dense neural networks are then used to extrapolate the potential energy surface for all molecular fragments, and these are then combined as per our graph-theoretic procedure to transfer the learning process to a full system energy for the entire AIMD trajectory at less than one-tenth the cost as compared to a regular fragmentation-based AIMD calculation.
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Affiliation(s)
- Xiao Zhu
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington 47405, Indiana, United States
| | - Srinivasan S Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington 47405, Indiana, United States
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Han S, Schröder M, Gatti F, Meyer HD, Lauvergnat D, Yarkony DR, Guo H. Representation of Diabatic Potential Energy Matrices for Multiconfiguration Time-Dependent Hartree Treatments of High-Dimensional Nonadiabatic Photodissociation Dynamics. J Chem Theory Comput 2022; 18:4627-4638. [PMID: 35839299 DOI: 10.1021/acs.jctc.2c00370] [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
Conventional quantum mechanical characterization of photodissociation dynamics is restricted by steep scaling laws with respect to the dimensionality of the system. In this work, we examine the applicability of the multi-configurational time-dependent Hartree (MCTDH) method in treating nonadiabatic photodissociation dynamics in two prototypical systems, taking advantage of its favorable scaling laws. To conform to the sum-of-product form, elements of the ab initio diabatic potential energy matrix (DPEM) are re-expressed using the recently proposed Monte Carlo canonical polyadic decomposition method, with enforcement of proper symmetry. The MCTDH absorption spectra and product branching ratios are shown to compare well with those calculated using conventional grid-based methods, demonstrating its promise for treating high-dimensional nonadiabatic photodissociation problems.
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Affiliation(s)
- Shanyu Han
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
| | - Markus Schröder
- Theoretische Chemie, Physikalisch Chemisches Institut, Ruprecht-Karls Universität Heidelberg, D-69120 Heidelberg, Germany
| | - Fabien Gatti
- ISMO, Institut des Sciences Moléculaires d'Orsay─UMR 8214 CNRS/Université Paris-Saclay, F-91405 Orsay, France
| | - Hans-Dieter Meyer
- Theoretische Chemie, Physikalisch Chemisches Institut, Ruprecht-Karls Universität Heidelberg, D-69120 Heidelberg, Germany
| | - David Lauvergnat
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, Orsay 91405, France
| | - David R Yarkony
- Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, United States
| | - Hua Guo
- Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, United States
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15
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Aerts A, Schaefer MR, Brown A. Adaptive Fitting of Potential Energy Surfaces of Small to Medium-Sized Molecules in Sum-of-Product Form: Application to Vibrational Spectroscopy. J Chem Phys 2022; 156:164106. [DOI: 10.1063/5.0089570] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A semi-automatic sampling and fitting procedure for generating sum-of-product (Born-Oppenheimer) potential energy surfaces based on a high-dimensional model representation is presented. The adaptive sampling procedure and subsequent fitting relies on energies only and can be used for re-fitting existing analytic potential energy surfaces in sum-of-product form or for direct fits from ab initio computa- tions. The method is tested by fitting ground electronic state potential energy surfaces for small to medium sized semi-rigid molecules, i.e., HFCO, HONO, and HCOOH, based upon ab initio computations at the CCSD(T)-F12/cc-pVTZ-F12 or MP2/aug-cc-pVTZ levels of theory. Vibrational eigenstates are computed using block improved relaxation in the Heidelberg MCTDH package and compared to available experimental and theoretical data. The new potential energy surfaces are compared to the best ones currently available for these molecules, in terms of accuracy, including of resulting vibrational states, required numbers of sampling points, and number of fitting parameters. The present procedure leads to compact expansions and scales well with the number of dimensions for simple potentials such as single or double wells.
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Affiliation(s)
| | | | - Alex Brown
- Department of Chemistry, University of Alberta, Canada
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16
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Ellerbrock R, Manthe U. A non-hierarchical correlation discrete variable representation. J Chem Phys 2022; 156:134107. [PMID: 35395891 DOI: 10.1063/5.0088509] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The correlation discrete variable representation (CDVR) facilitates (multi-layer) multi-configurational time-dependent Hartree (MCTDH) calculations with general potentials. It employs a layered grid representation to efficiently evaluate all potential matrix elements appearing in the MCTDH equations of motion. The original CDVR approach and its multi-layer extension show a hierarchical structure: the size of the grids employed at the different layers increases when moving from an upper layer to a lower one. In this work, a non-hierarchical CDVR approach, which uses identically structured quadratures at all layers of the MCTDH wavefunction representation, is introduced. The non-hierarchical CDVR approach crucially reduces the number of grid points required, compared to the hierarchical CDVR, shows superior scaling properties, and yields identical results for all three representations showing the same topology. Numerical tests studying the photodissociation of NOCl and the vibrational states of CH3 demonstrate the accuracy of the non-hierarchical CDVR approach.
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Affiliation(s)
- Roman Ellerbrock
- Department of Chemistry and The PULSE Institute, Stanford University, Stanford, California 94305, USA
| | - Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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17
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Manzhos S, Ihara M. Computational vibrational spectroscopy of molecule-surface interactions: what is still difficult and what can be done about it. Phys Chem Chem Phys 2022; 24:15158-15172. [DOI: 10.1039/d2cp01389d] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Interactions of molecules with solid surfaces are responsible for key functionalities for a range of currently actively pursued technologies, including heterogeneous catalysis for synthesis or decomposition of molecules, sensitization, surface...
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18
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Kumar A, DeGregorio N, Iyengar SS. Graph-Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Dimensions. J Chem Theory Comput 2021; 17:6671-6690. [PMID: 34623129 DOI: 10.1021/acs.jctc.1c00065] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
We present a multitopology molecular fragmentation approach, based on graph theory, to calculate multidimensional potential energy surfaces in agreement with post-Hartree-Fock levels of theory but at the density functional theory cost. A molecular assembly is coarse-grained into a set of graph-theoretic nodes that are then connected with edges to represent a collection of locally interacting subsystems up to an arbitrary order. Each of the subsystems is treated at two levels of electronic structure theory, the result being used to construct many-body expansions that are embedded within an ONIOM scheme. These expansions converge rapidly with the many-body order (or graphical rank) of subsystems and capture many-body interactions accurately and efficiently. However, multiple graphs, and hence multiple fragmentation topologies, may be defined in molecular configuration space that may arise during conformational sampling or from reactive, bond breaking and bond formation, events. Obtaining the resultant potential surfaces is an exponential scaling proposition, given the number of electronic structure computations needed. We utilize a family of graph-theoretic representations within a variational scheme to obtain multidimensional potential surfaces at a reduced cost. The fast convergence of the graph-theoretic expansion with increasing order of many-body interactions alleviates the exponential scaling cost for computing potential surfaces, with the need to only use molecular fragments that contain a fewer number of quantum nuclear degrees of freedom compared to the full system. This is because the dimensionality of the conformational space sampled by the fragment subsystems is much smaller than the full molecular configurational space. Additionally, we also introduce a multidimensional clustering algorithm, based on physically defined criteria, to reduce the number of energy calculations by orders of magnitude. The molecular systems benchmarked include coupled proton motion in protonated water wires. The potential energy surfaces and multidimensional nuclear eigenstates obtained are shown to be in very good agreement with those from explicit post-Hartree-Fock calculations that become prohibitive as the number of quantum nuclear dimensions grows. The developments here provide a rigorous and efficient alternative to this important chemical physics problem.
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Affiliation(s)
- Anup Kumar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Nicole DeGregorio
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
| | - Srinivasan S Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Avenue, Bloomington, Indiana 47405, United States
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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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20
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Christopoulou G, Freibert A, Worth GA. Improved algorithm for the direct dynamics variational multi-configurational Gaussian method. J Chem Phys 2021; 154:124127. [PMID: 33810697 DOI: 10.1063/5.0043720] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Direct Dynamics variational Multi-Configurational Gaussian (DD-vMCG) method provides a fully quantum mechanical solution to the time-dependent Schrödinger equation for the time evolution of nuclei with potential surfaces calculated on-the-fly using a quantum chemistry program. Initial studies have shown its potential for flexible and accurate simulations of non-adiabatic excited-state molecular dynamics. In this paper, we present developments to the DD-vMCG algorithm that improve both its accuracy and efficiency. First, a new, efficient parallel algorithm to control the DD-vMCG database of quantum chemistry points is presented along with improvements to the Shepard interpolation scheme. Second, the use of symmetry in describing the potential surfaces is introduced along with a new phase convention in the propagation diabatization. Benchmark calculations on the allene radical cation including all degrees of freedom then show that the new scheme is able to produce a consistent non-adiabatic coupling vector field. This new DD-vMCG version thus opens the route for effectively and accurately treating complex chemical systems using quantum dynamics simulations.
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Affiliation(s)
| | - Antonia Freibert
- Department of Chemistry, University College London, London WC1H 0AJ, United Kingdom
| | - Graham A Worth
- Department of Chemistry, University College London, London WC1H 0AJ, United Kingdom
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21
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Zhao B, Manthe U. Direct product-type grid representations for angular coordinates in extended space and their application in the MCTDH approach. J Chem Phys 2021; 154:104115. [PMID: 33722051 DOI: 10.1063/5.0045054] [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
Multi-configurational time-dependent Hartree (MCTDH) calculations using time-dependent grid representations can be used to accurately simulate high-dimensional quantum dynamics on general ab initio potential energy surfaces. Employing the correlation discrete variable representation, sets of direct product type grids are employed in the calculation of the required potential energy matrix elements. This direct product structure can be a problem if the coordinate system includes polar and azimuthal angles that result in singularities in the kinetic energy operator. In the present work, a new direct product-type discrete variable representation (DVR) for arbitrary sets of polar and azimuthal angles is introduced. It employs an extended coordinate space where the range of the polar angles is taken to be [-π, π]. The resulting extended space DVR resolves problems caused by the singularities in the kinetic energy operator without generating a very large spectral width. MCTDH calculations studying the F·CH4 complex are used to investigate important properties of the new scheme. The scheme is found to allow for more efficient integration of the equations of motion compared to the previously employed cot-DVR approach [G. Schiffel and U. Manthe, Chem. Phys. 374, 118 (2010)] and decreases the required central processing unit times by about an order of magnitude.
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Affiliation(s)
- Bin Zhao
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
| | - Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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22
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Sinha S, Saalfrank P. “Inverted” CO molecules on NaCl(100): a quantum mechanical study. Phys Chem Chem Phys 2021; 23:7860-7874. [DOI: 10.1039/d0cp05198e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Inverted (“O-down”) CO adsorbates on NaCl(100), recently observed experimentally after IR vibrational excitation (Lau et al., Science, 2020, 367, 175–178), are characterized using periodic DFT and a quantum mechanical description of vibrations.
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Affiliation(s)
- Shreya Sinha
- Theoretical Chemistry
- Institute of Chemistry
- University of Potsdam
- 14476 Potsdam
- Germany
| | - Peter Saalfrank
- Theoretical Chemistry
- Institute of Chemistry
- University of Potsdam
- 14476 Potsdam
- Germany
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23
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Panadés-Barrueta RL, Peláez D. Low-rank sum-of-products finite-basis-representation (SOP-FBR) of potential energy surfaces. J Chem Phys 2020; 153:234110. [PMID: 33353311 DOI: 10.1063/5.0027143] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
The sum-of-products finite-basis-representation (SOP-FBR) approach for the automated multidimensional fit of potential energy surfaces (PESs) is presented. In its current implementation, the method yields a PES in the so-called Tucker sum-of-products form, but it is not restricted to this specific ansatz. The novelty of our algorithm lies in the fact that the fit is performed in terms of a direct product of a Schmidt basis, also known as natural potentials. These encode in a non-trivial way all the physics of the problem and, hence, circumvent the usual extra ad hoc and a posteriori adjustments (e.g., damping functions) of the fitted PES. Moreover, we avoid the intermediate refitting stage common to other tensor-decomposition methods, typically used in the context of nuclear quantum dynamics. The resulting SOP-FBR PES is analytical and differentiable ad infinitum. Our ansatz is fully general and can be used in combination with most (molecular) dynamics codes. In particular, it has been interfaced and extensively tested with the Heidelberg implementation of the multiconfiguration time-dependent Hartree quantum dynamical software package.
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Affiliation(s)
- Ramón L Panadés-Barrueta
- Laboratoire de Physique des Lasers, Atomes et Molécules (PhLAM), Université Lille 1, Villeneuve d'Ascq Cedex, France
| | - Daniel Peláez
- Institut des Sciences Moléculaires d'Orsay (ISMO) - UMR 8214, Bât. 520, Université Paris-Saclay, 91405 Orsay Cedex, France
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24
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Ren J, Li W, Jiang T, Shuai Z. A general automatic method for optimal construction of matrix product operators using bipartite graph theory. J Chem Phys 2020; 153:084118. [PMID: 32872857 DOI: 10.1063/5.0018149] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
Constructing matrix product operators (MPOs) is at the core of the modern density matrix renormalization group (DMRG) and its time dependent formulation. For the DMRG to be conveniently used in different problems described by different Hamiltonians, in this work, we propose a new generic algorithm to construct the MPO of an arbitrary operator with a sum-of-products form based on the bipartite graph theory. We show that the method has the following advantages: (i) it is automatic in that only the definition of the operator is required; (ii) it is symbolic thus free of any numerical error; (iii) the complementary operator technique can be fully employed so that the resulting MPO is globally optimal for any given order of degrees of freedom; and (iv) the symmetry of the system could be fully employed to reduce the dimension of MPO. To demonstrate the effectiveness of the new algorithm, the MPOs of Hamiltonians ranging from the prototypical spin-boson model and the Holstein model to the more complicated ab initio electronic Hamiltonian and the anharmonic vibrational Hamiltonian with the sextic force field are constructed. It is found that for the former three cases, our automatic algorithm can reproduce exactly the same MPOs as the optimally hand-crafted ones already known in the literature.
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Affiliation(s)
- Jiajun Ren
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Weitang Li
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Tong Jiang
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
| | - Zhigang Shuai
- MOE Key Laboratory of Organic OptoElectronics and Molecular Engineering, Department of Chemistry, Tsinghua University, Beijing 100084, People's Republic of China
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25
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Schröder M. Transforming high-dimensional potential energy surfaces into a canonical polyadic decomposition using Monte Carlo methods. J Chem Phys 2020; 152:024108. [DOI: 10.1063/1.5140085] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Markus Schröder
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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26
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DeGregorio N, Iyengar SS. Challenges in constructing accurate methods for hydrogen transfer reactions in large biological assemblies: rare events sampling for mechanistic discovery and tensor networks for quantum nuclear effects. Faraday Discuss 2020; 221:379-405. [DOI: 10.1039/c9fd00071b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present two methods that address the computational complexities arising in hydrogen transfer reactions in enzyme active sites.
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Affiliation(s)
- Nicole DeGregorio
- Department of Chemistry
- Department of Physics
- Indiana University
- Bloomington
- USA
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27
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Larsson HR. Computing vibrational eigenstates with tree tensor network states (TTNS). J Chem Phys 2019; 151:204102. [DOI: 10.1063/1.5130390] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023] Open
Affiliation(s)
- Henrik R. Larsson
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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28
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Wodraszka R, Carrington T. A pruned collocation-based multiconfiguration time-dependent Hartree approach using a Smolyak grid for solving the Schrödinger equation with a general potential energy surface. J Chem Phys 2019; 150:154108. [DOI: 10.1063/1.5093317] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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29
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DeGregorio N, Iyengar SS. Adaptive Dimensional Decoupling for Compression of Quantum Nuclear Wave Functions and Efficient Potential Energy Surface Representations through Tensor Network Decomposition. J Chem Theory Comput 2019; 15:2780-2796. [DOI: 10.1021/acs.jctc.8b01113] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Nicole DeGregorio
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Ave, Bloomington, Indiana 47405, United States
| | - Srinivasan S. Iyengar
- Department of Chemistry and Department of Physics, Indiana University, 800 E. Kirkwood Ave, Bloomington, Indiana 47405, United States
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30
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Intermolecular rovibrational bound states of H2O H2 dimer from a MultiConfiguration Time Dependent Hartree approach. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2018.11.035] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
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31
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Dawes R, Quintas‐Sánchez E. THE CONSTRUCTION OF AB INITIO‐BASED POTENTIAL ENERGY SURFACES. REVIEWS IN COMPUTATIONAL CHEMISTRY 2018. [DOI: 10.1002/9781119518068.ch5] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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32
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Ziegler B, Rauhut G. Rigorous use of symmetry within the construction of multidimensional potential energy surfaces. J Chem Phys 2018; 149:164110. [DOI: 10.1063/1.5047912] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Benjamin Ziegler
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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33
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Otto F, Chiang YC, Peláez D. Accuracy of Potfit-based potential representations and its impact on the performance of (ML-)MCTDH. Chem Phys 2018. [DOI: 10.1016/j.chemphys.2017.11.013] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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34
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Wodraszka R, Carrington T. A new collocation-based multi-configuration time-dependent Hartree (MCTDH) approach for solving the Schrödinger equation with a general potential energy surface. J Chem Phys 2018; 148:044115. [DOI: 10.1063/1.5018793] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Robert Wodraszka
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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35
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Schröder M, Meyer HD. Transforming high-dimensional potential energy surfaces into sum-of-products form using Monte Carlo methods. J Chem Phys 2017; 147:064105. [DOI: 10.1063/1.4991851] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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36
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Brown A, Pradhan E. Fitting potential energy surfaces to sum-of-products form with neural networks using exponential neurons. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2017. [DOI: 10.1142/s0219633617300014] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this paper, the use of the neural network (NN) method with exponential neurons for directly fitting ab initio data to generate potential energy surfaces (PESs) in sum-of-product form will be discussed. The utility of the approach will be highlighted using fits of CS2, HFCO, and HONO ground state PESs based upon high-level ab initio data. Using a generic interface between the neural network PES fitting, which is performed in MATLAB, and the Heidelberg multi-configuration time-dependent Hartree (MCTDH) software package, the PESs have been tested via comparison of vibrational energies to experimental measurements. The review demonstrates the potential of the PES fitting method, combined with MCTDH, to tackle high-dimensional quantum dynamics problems.
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Affiliation(s)
- Alex Brown
- Department of Chemistry, University of Alberta, Edmonton, AB, T6G 2G2, Canada
| | - E. Pradhan
- Department of Chemistry, University of Alberta, Edmonton, AB, T6G 2G2, Canada
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37
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Larsson HR, Tannor DJ. Dynamical pruning of the multiconfiguration time-dependent Hartree (DP-MCTDH) method: An efficient approach for multidimensional quantum dynamics. J Chem Phys 2017; 147:044103. [DOI: 10.1063/1.4993219] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- H. R. Larsson
- Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
| | - D. J. Tannor
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
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38
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Manthe U. Wavepacket dynamics and the multi-configurational time-dependent Hartree approach. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:253001. [PMID: 28430111 DOI: 10.1088/1361-648x/aa6e96] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
Multi-configurational time-dependent Hartree (MCTDH) based approaches are efficient, accurate, and versatile methods for high-dimensional quantum dynamics simulations. Applications range from detailed investigations of polyatomic reaction processes in the gas phase to high-dimensional simulations studying the dynamics of condensed phase systems described by typical solid state physics model Hamiltonians. The present article presents an overview of the different areas of application and provides a comprehensive review of the underlying theory. The concepts and guiding ideas underlying the MCTDH approach and its multi-mode and multi-layer extensions are discussed in detail. The general structure of the equations of motion is highlighted. The representation of the Hamiltonian and the correlated discrete variable representation (CDVR), which provides an efficient multi-dimensional quadrature in MCTDH calculations, are discussed. Methods which facilitate the calculation of eigenstates, the evaluation of correlation functions, and the efficient representation of thermal ensembles in MCTDH calculations are described. Different schemes for the treatment of indistinguishable particles in MCTDH calculations and recent developments towards a unified multi-layer MCTDH theory for systems including bosons and fermions are discussed.
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Affiliation(s)
- Uwe Manthe
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
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39
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Wodraszka R, Carrington T. Systematically expanding nondirect product bases within the pruned multi-configuration time-dependent Hartree (MCTDH) method: A comparison with multi-layer MCTDH. J Chem Phys 2017; 146:194105. [PMID: 28527461 DOI: 10.1063/1.4983281] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We propose a pruned multi-configuration time-dependent Hartree (MCTDH) method with systematically expanding nondirect product bases and use it to solve the time-independent Schrödinger equation. No pre-determined pruning condition is required to select the basis functions. Using about 65 000 basis functions, we calculate the first 69 vibrational eigenpairs of acetonitrile, CH3CN, to an accuracy better than that achieved in a previous pruned MCTDH calculation which required more than 100 000 basis functions. In addition, we compare the new pruned MCTDH method with the established multi-layer MCTDH (ML-MCTDH) scheme and determine that although ML-MCTDH is somewhat more efficient when low or intermediate accuracy is desired, pruned MCTDH is more efficient when high accuracy is required. In our largest calculation, the vast majority of the energies have errors smaller than 0.01 cm-1.
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Affiliation(s)
- Robert Wodraszka
- Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Department of Chemistry, Queen's University, Kingston, Ontario K7L 3N6, Canada
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40
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Rai P, Sargsyan K, Najm H, Hermes MR, Hirata S. Low-rank canonical-tensor decomposition of potential energy surfaces: application to grid-based diagrammatic vibrational Green's function theory. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1288937] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Prashant Rai
- Sandia National Laboratories, Livermore, CA, USA
| | | | - Habib Najm
- Sandia National Laboratories, Livermore, CA, USA
| | - Matthew R. Hermes
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, USA
| | - So Hirata
- Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, IL, USA
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41
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Pradhan E, Brown A. A ground state potential energy surface for HONO based on a neural network with exponential fitting functions. Phys Chem Chem Phys 2017; 19:22272-22281. [DOI: 10.1039/c7cp04010e] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Using CCSD(T)-F12/cc-pVTZ-F12 and CCSD(T)/CBS ab initio energies, two different six-dimensional ground state potential energy surfaces for HONO have been fit in sum-of-products form using neural network exponential fitting functions and tested by computing vibrational energies with MCTDH.
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Affiliation(s)
| | - Alex Brown
- Department of Chemistry
- University of Alberta
- Edmonton
- Canada
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42
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Larsson HR, Hartke B, Tannor DJ. Efficient molecular quantum dynamics in coordinate and phase space using pruned bases. J Chem Phys 2016; 145:204108. [DOI: 10.1063/1.4967432] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- H. R. Larsson
- Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - B. Hartke
- Institut für Physikalische Chemie, Christian-Albrechts-Universität zu Kiel, 24098 Kiel, Germany
| | - D. J. Tannor
- Department of Chemical Physics, Weizmann Institute of Science, 76100 Rehovot, Israel
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43
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Alborzpour JP, Tew DP, Habershon S. Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression. J Chem Phys 2016; 145:174112. [DOI: 10.1063/1.4964902] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jonathan P. Alborzpour
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
| | - David P. Tew
- School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
| | - Scott Habershon
- Department of Chemistry and Centre for Scientific Computing, University of Warwick, Coventry CV4 7AL, United Kingdom
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44
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Pradhan E, Brown A. Vibrational energies for HFCO using a neural network sum of exponentials potential energy surface. J Chem Phys 2016; 144:174305. [DOI: 10.1063/1.4948440] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ekadashi Pradhan
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
| | - Alex Brown
- Department of Chemistry, University of Alberta, Edmonton, Alberta T6G 2G2, Canada
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45
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Ziegler B, Rauhut G. Efficient generation of sum-of-products representations of high-dimensional potential energy surfaces based on multimode expansions. J Chem Phys 2016; 144:114114. [DOI: 10.1063/1.4943985] [Citation(s) in RCA: 47] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Benjamin Ziegler
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
| | - Guntram Rauhut
- Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany
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46
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Gu B, Garashchuk S. Quantum Dynamics with Gaussian Bases Defined by the Quantum Trajectories. J Phys Chem A 2016; 120:3023-31. [DOI: 10.1021/acs.jpca.5b10029] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Bing Gu
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Sophya Garashchuk
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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47
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Thomas PS, Carrington T. Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms. J Phys Chem A 2015; 119:13074-91. [DOI: 10.1021/acs.jpca.5b10015] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Phillip S. Thomas
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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48
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Baranov V, Oseledets I. Fitting high-dimensional potential energy surface using active subspace and tensor train (AS+TT) method. J Chem Phys 2015; 143:174107. [DOI: 10.1063/1.4935017] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Vitaly Baranov
- Skolkovo Institute of Science and Technology, Novyaa St. 100, Skolkovo, Moscow 143025, Russia
| | - Ivan Oseledets
- Skolkovo Institute of Science and Technology, Novyaa St. 100, Skolkovo, Moscow 143025, Russia
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49
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Avila G, Carrington T. Using multi-dimensional Smolyak interpolation to make a sum-of-products potential. J Chem Phys 2015; 143:044106. [DOI: 10.1063/1.4926651] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Gustavo Avila
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
| | - Tucker Carrington
- Chemistry Department, Queen’s University, Kingston, Ontario K7L 3N6, Canada
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50
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Abstract
Multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory is a rigorous and powerful method to simulate quantum dynamics in complex many-body systems. This approach extends the original MCTDH theory of Meyer, Manthe, and Cederbaum to include dynamically contracted layers in a recursive way, within which the equations of motion are determined from the Dirac-Frenkel variational principle. This paper presents the general derivation of the theory and analyzes the important features that make the ML-MCTDH method numerically efficient. Furthermore, we discuss the generalization of the theory to treat many-body identical particles (fermions or bosons) as well as calculating energy eigenstates via the improved relaxation method.
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
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