1
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Niermann T, Hoppe H, Manthe U. A multi-layer multi-configurational time-dependent Hartree approach to lattice models beyond one dimension. J Chem Phys 2024; 161:134109. [PMID: 39360683 DOI: 10.1063/5.0228399] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2024] [Accepted: 09/18/2024] [Indexed: 10/04/2024] Open
Abstract
The multi-layer multi-configurational time-dependent Hartree (MCTDH) approach is an efficient method to study quantum dynamics in real and imaginary time. The present work explores its potential to describe quantum fluids. The multi-layer MCTDH approach in second quantization representation is used to study lattice models beyond one dimension at finite temperatures. A scheme to map the lattice sites onto the MCTDH tree representation for multi-dimensional lattice models is proposed. A statistical sampling scheme previously used in MCTDH calculations is adapted to facilitate an efficient description of the thermal ensemble. As example, a two-dimensional hard-core Bose-Hubbard model is studied considering up to 64 × 64 lattice sites. The single particle function basis set size required to obtain converged results is found to not increase with the lattice size. The numerical results properly simulate the finite temperature Berezinskii-Kosterlitz-Thouless phase transition.
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Affiliation(s)
- Tristan Niermann
- Theoretische Chemie, Fakultät für Chemie, Universität Bielefeld, Universitätsstr. 25, D-33615 Bielefeld, Germany
| | - Hannes Hoppe
- 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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2
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Dickinson JA, Hammes-Schiffer S. Nonadiabatic Hydrogen Tunneling Dynamics for Multiple Proton Transfer Processes with Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory. J Chem Theory Comput 2024. [PMID: 39259939 DOI: 10.1021/acs.jctc.4c00737] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/13/2024]
Abstract
Proton transfer and hydrogen tunneling play key roles in many processes of chemical and biological importance. The generalized nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method was developed in order to capture hydrogen tunneling effects in systems involving the transfer and tunneling of one or more protons. The generalized NEO-MSDFT method treats the transferring protons quantum mechanically on the same level as the electrons and obtains the delocalized vibronic states associated with hydrogen tunneling by mixing localized NEO-DFT states in a nonorthogonal configuration interaction scheme. Herein, we present the derivation and implementation of analytical gradients for the generalized NEO-MSDFT vibronic state energies and the nonadiabatic coupling vectors between these vibronic states. We use this methodology to perform adiabatic and nonadiabatic dynamics simulations of the double proton transfer reactions in the formic acid dimer and the heterodimer of formamidine and formic acid. The generalized NEO-MSDFT method is shown to capture the strongly coupled synchronous or asynchronous tunneling of the two protons in these processes. Inclusion of vibronically nonadiabatic effects is found to significantly impact the double proton transfer dynamics. This work lays the foundation for a variety of nonadiabatic dynamics simulations of multiple proton transfer systems, such as proton relays and hydrogen-bonding networks.
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Affiliation(s)
- Joseph A Dickinson
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
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3
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Wodraszka R, Carrington T. Using a pruned basis and a sparse collocation grid with more points than basis functions to do efficient and accurate MCTDH calculations with general potential energy surfaces. J Chem Phys 2024; 160:214121. [PMID: 38836450 DOI: 10.1063/5.0214557] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2024] [Accepted: 05/14/2024] [Indexed: 06/06/2024] Open
Abstract
We propose a new collocation multi-configuration time-dependent Hartree (MCTDH) method. It reduces point-set error by using more points than basis functions. Collocation makes it possible to use MCTDH with a general potential energy surface without computing any integrals. The collocation points are associated with a basis larger than the basis used to represent wavefunctions. Both bases are obtained from a direct product basis built from single-particle functions by imposing a pruning condition. The collocation points are those on a sparse grid. Heretofore, collocation MCTDH calculations with more points than basis functions have only been possible if both the collocation grid and the basis set are direct products. In this paper, we exploit a new pseudo-inverse to use both more points than basis functions and a pruned basis and grid. We demonstrate that, for a calculation of the lowest 50 vibrational states (energy levels and wavefunctions) of CH2NH, errors can be reduced by two orders of magnitude by increasing the number of points, without increasing the basis size. This is true also when unrefined time-independent points are used.
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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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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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Hoppe H, Manthe U. Eigenstate calculation in the state-averaged (multi-layer) multi-configurational time-dependent Hartree approach. J Chem Phys 2024; 160:034104. [PMID: 38230812 DOI: 10.1063/5.0188748] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2023] [Accepted: 12/15/2023] [Indexed: 01/18/2024] Open
Abstract
A new approach for the calculation of eigenstates with the state-averaged (multi-layer) multi-configurational time-dependent Hartree (MCTDH) approach is presented. The approach is inspired by the recent work of Larsson [J. Chem. Phys. 151, 204102 (2019)]. It employs local optimization of the basis sets at each node of the multi-layer MCTDH tree and successive downward and upward sweeps to obtain a globally converged result. At the top node, the Hamiltonian represented in the basis of the single-particle functions (SPFs) of the first layer is diagonalized. Here p wavefunctions corresponding to the p lowest eigenvalues are computed by a block Lanczos approach. At all other nodes, a non-linear operator consisting of the respective mean-field Hamiltonian matrix and a projector onto the space spanned by the respective SPFs is considered. Here, the eigenstate corresponding to the lowest eigenvalue is computed using a short iterative Lanczos scheme. Two different examples are studied to illustrate the new approach: the calculation of the vibrational states of methyl and acetonitrile. The calculations for methyl employ the single-layer MCTDH approach, a general potential energy surface, and the correlation discrete variable representation. A five-layer MCTDH representation and a sum of product-type Hamiltonian are used in the acetonitrile calculations. Very fast convergence and order of magnitude reductions in the numerical effort compared to the previously used block relaxation scheme are found. Furthermore, a detailed comparison with the results of Avila and Carrington [J. Chem. Phys. 134, 054126 (2011)] for acetonitrile highlights the potential problems of convergence tests for high-dimensional systems.
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Affiliation(s)
- Hannes Hoppe
- 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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Lauvergnat D, Nauts A. Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality. Chemphyschem 2023; 24:e202300501. [PMID: 37555577 DOI: 10.1002/cphc.202300501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Revised: 08/08/2023] [Accepted: 08/09/2023] [Indexed: 08/10/2023]
Abstract
In 1963 Smolyak introduced an approach to overcome the exponential scaling with respect to the number of variables of the direct product size [S. A. Smolyak Soviet Mathematics Doklady, 4, 240 (1963)]. The main idea is to replace a single large direct product by a sum of selected small direct products. It was first used in quantum dynamics in 2009 by Avila and Carrington [G. Avila and T. Carrington, J. Chem. Phys., 131, 174103 (2009)]. Since then, several calculations have been published by Avila and Carrington and by other groups. In the present study, and to push the limit to larger and more complex systems, this scheme is combined with the use of an on-the-fly calculation of the kinetic energy operator and a Block-Davidson procedure to obtain eigenstates in our home-made Fortran codes, ElVibRot and Tnum-Tana. This was applied to compute the tunneling splitting of malonaldehyde in full dimensionality (21D) using the potential of Mizukami et al. [W. Mizukami, S. Habershon, and D.P. Tew, J. Chem. Phys. 141, 1443-10 (2014)]. Our tunneling splitting calculations, 21.7±0.3 cm-1 and 2.9±0.1 cm-1 , show excellent agreement with the experimental values, 21.6 cm-1 and 2.9 cm-1 for the normal isotopologue and the mono-deuterated one, respectively.
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Affiliation(s)
- David Lauvergnat
- Institut de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
| | - André Nauts
- Institut de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
- Institute of Condensed Matter and Nanosciences (NAPS), Université Catholique de Louvain, 2 Chemin du Cyclotron, 1348, Louvain-la-Neuve, Belgium
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7
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Dickinson JA, Yu Q, Hammes-Schiffer S. Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory for Multiple Proton Transfer Processes. J Phys Chem Lett 2023:6170-6178. [PMID: 37379485 DOI: 10.1021/acs.jpclett.3c01422] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/30/2023]
Abstract
Proton transfer and hydrogen tunneling play pivotal roles in many chemical and biological processes. The nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) approach was developed to describe hydrogen tunneling systems within the multicomponent NEO framework, where the transferring proton is quantized and treated with molecular orbital techniques on the same level as the electrons. Herein, the NEO-MSDFT framework is generalized to an arbitrary number of quantum protons to allow applications to systems involving the transfer and tunneling of multiple protons. The generalized NEO-MSDFT approach is shown to produce delocalized, bilobal proton densities and accurate tunneling splittings for fixed geometries of the formic acid dimer and asymmetric substituted variants, as well as the porphycene molecule. Investigation of a protonated water chain highlights the applicability of this approach to proton relay systems. This work provides the foundation for nuclear-electronic quantum dynamics simulations of a wide range of multiple proton transfer processes.
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Affiliation(s)
- Joseph A Dickinson
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Qi Yu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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8
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Garashchuk S, Stetzler J, Rassolov V. Factorized Electron-Nuclear Dynamics with an Effective Complex Potential. J Chem Theory Comput 2023; 19:1393-1408. [PMID: 36795898 DOI: 10.1021/acs.jctc.2c01019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/18/2023]
Abstract
We present a quantum dynamics approach for molecular systems based on wave function factorization into components describing the light and heavy particles, such as electrons and nuclei. The dynamics of the nuclear subsystem can be viewed as motion of the trajectories defined in the nuclear subspace, evolving according to the average nuclear momentum of the full wave function. The probability density flow between the nuclear and electronic subsystems is facilitated by the imaginary potential, derived to ensure a physically meaningful normalization of the electronic wave function for each configuration of the nuclei, and conservation of the probability density associated with each trajectory in the Lagrangian frame of reference. The imaginary potential, defined in the nuclear subspace, depends on the momentum variance in the nuclear coordinates averaged over the electronic component of the wave function. An effective real potential, driving the dynamics of the nuclear subsystem, is defined to minimize motion of the electronic wave function in the nuclear degrees of freedom. Illustration and the analysis of the formalism are given for a two-dimensional model system of vibrationally nonadiabatic dynamics.
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Affiliation(s)
- Sophya Garashchuk
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Julian Stetzler
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
| | - Vitaly Rassolov
- Department of Chemistry & Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States
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9
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Goli M, Shahbazian S. MC-QTAIM analysis reveals an exotic bond in coherently quantum superposed malonaldehyde. Phys Chem Chem Phys 2023; 25:5718-5730. [PMID: 36744327 DOI: 10.1039/d2cp05499j] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
The proton between the two oxygen atoms of the malonaldehyde molecule experiences an effective double-well potential in which the proton's wavefunction is delocalized between the two wells. Herein we employ a state-of-the-art multi-component quantum theory of atoms in molecules partitioning scheme to obtain the molecular structure, i.e. atoms in molecules and bonding network, from the superposed ab initio wavefunctions of malonaldehyde. In contrast to the familiar clamped-proton portrayal of malonaldehyde, in which the proton forms a hydrogen basin, for the superposed states the hydrogen basin disappears and two novel hybrid oxygen-hydrogen basins appear instead, with an even distribution of the proton population between the two basins. The interaction between the hybrid basins is stabilizing thanks to an unprecedented mechanism. This involves the stabilizing classical Coulomb interaction of the one-proton density in one of the basins with one-electron density in the other basin. This stabilizing mechanism yields a bond foreign to the known bonding modes in chemistry.
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Affiliation(s)
- Mohammad Goli
- School of Nano Science, Institute for Research in Fundamental Sciences (IPM), Tehran 19395-5531, Iran.
| | - Shant Shahbazian
- Department of Physics, Shahid Beheshti University, Evin, Tehran, Iran.
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10
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Yu Q, Roy S, Hammes-Schiffer S. Nonadiabatic Dynamics of Hydrogen Tunneling with Nuclear-Electronic Orbital Multistate Density Functional Theory. J Chem Theory Comput 2022; 18:7132-7141. [PMID: 36378867 DOI: 10.1021/acs.jctc.2c00938] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Proton transfer reactions play a critical role in many chemical and biological processes. The development of computationally efficient approaches to describe the quantum dynamics of proton transfer, which often involves hydrogen tunneling, is challenging. Herein, the nuclear-electronic orbital multistate density functional theory (NEO-MSDFT) method is combined with both Ehrenfest and surface hopping nonadiabatic dynamics methods to describe hydrogen tunneling. The NEO-MSDFT method treats the transferring hydrogen nucleus quantum mechanically on the same level as the electrons and incorporates both static and dynamical correlation by mixing localized NEO-DFT solutions with a nonorthogonal configuration interaction scheme. The other nuclei are propagated on the NEO-MSDFT vibronic surfaces during the Ehrenfest or surface hopping dynamics. These methods are applied to proton transfer in malonaldehyde as a prototypical hydrogen tunneling system. The inclusion of vibronically nonadiabatic effects is found to significantly impact the proton transfer time and tunneling dynamics. This approach is applicable to a wide range of other proton transfer reactions.
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Affiliation(s)
- Qi Yu
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Saswata Roy
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
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Käser S, Richardson JO, Meuwly M. Transfer Learning for Affordable and High-Quality Tunneling Splittings from Instanton Calculations. J Chem Theory Comput 2022; 18:6840-6850. [DOI: 10.1021/acs.jctc.2c00790] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Silvan Käser
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | | | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
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12
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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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13
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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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14
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Yu Q, Schneider PE, Hammes-Schiffer S. Analytical gradients for nuclear–electronic orbital multistate density functional theory: Geometry optimizations and reaction paths. J Chem Phys 2022; 156:114115. [DOI: 10.1063/5.0085344] [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
Hydrogen tunneling plays a critical role in many biologically and chemically important processes. The nuclear–electronic orbital multistate density functional theory (NEO-MSDFT) method was developed to describe hydrogen transfer systems. In this approach, the transferring proton is treated quantum mechanically on the same level as the electrons within multicomponent DFT, and a nonorthogonal configuration interaction scheme is used to produce delocalized vibronic states from localized vibronic states. The NEO-MSDFT method has been shown to provide accurate hydrogen tunneling splittings for fixed molecular systems. Herein, the NEO-MSDFT analytical gradients for both ground and excited vibronic states are derived and implemented. The analytical gradients and semi-numerical Hessians are used to optimize and characterize equilibrium and transition state geometries and to generate minimum energy paths (MEPs), for proton transfer in the deprotonated acetylene dimer and malonaldehyde. The barriers along the resulting MEPs are lower when the transferring proton is quantized because the NEO-MSDFT method inherently includes the zero-point energy of the transferring proton. Analysis of the proton densities along the MEPs illustrates that the proton density can exhibit symmetric or asymmetric bilobal character associated with symmetric or slightly asymmetric double-well potential energy surfaces and hydrogen tunneling. Analysis of the contributions to the intrinsic reaction coordinate reveals that changes in the C–O bond lengths drive proton transfer in malonaldehyde. This work provides the foundation for future reaction path studies and direct nonadiabatic dynamics simulations of a wide range of hydrogen transfer reactions.
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Affiliation(s)
- Qi Yu
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Patrick E. Schneider
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA
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15
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Richter F, Carbonnière P. Vibrational treatment of hydroxylamine in valence coordinates. J Chem Phys 2022; 156:084306. [DOI: 10.1063/5.0081289] [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 valence coordinate H2NOH ground state potential energy surface accurate for all levels up to 6000 cm−1 relative to trans zero point energy has been generated at the coupled-cluster single double triple-F12/aug-cc-pVTZ level encompassing the trans and cis as well as the N–H2 permutational conformers. All cis and trans fundamentals and a complete set of eigenfunctions up to about 3100 cm−1 have been calculated and assigned using the improved relaxation method of the Heidelberg multi-configuration time-dependent Hartree package and an exact expression for the kinetic energy in valence coordinates generated by the TANA program. The average and maximal error to all observed transitions is about 6.3 and 14.6 cm−1, respectively. Local cis eigenfunctions exist with up to two quanta in the isomerization mode ν9. Although no significant inversion splittings have been found up to the considered 3100 cm−1, they are expected within the fundamental energy range in view of the calculated 4261 cm−1 H2 permutation/inversion barrier height. The cis-NH2 symmetric stretch fundamental shows a Fermi resonance with a splitting of about 10 cm−1.
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Affiliation(s)
- Falk Richter
- Groupe de Chimie Théorique et Réactivité IPREM-ECP, Université de Pau et des Pays de l’Adour, Pau, France
| | - P. Carbonnière
- Groupe de Chimie Théorique et Réactivité IPREM-ECP, Université de Pau et des Pays de l’Adour, Pau, France
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16
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Weike T, Manthe U. The multi-configurational time-dependent Hartree approach in optimized second quantization: thermal ensembles and statistical sampling. Chem Phys 2021. [DOI: 10.1016/j.chemphys.2021.111413] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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17
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Medel R. Simple models for the quick estimation of ground state hydrogen tunneling splittings in alcohols and other compounds. Phys Chem Chem Phys 2021; 23:17591-17605. [PMID: 34369526 DOI: 10.1039/d1cp02115j] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Models for the quick estimation of energy splittings caused by coherent tunneling of hydrogen atoms are evaluated with available experimental data for alcohols and improvements are proposed. The discussed models are mathematically simple and require only results from routine quantum chemical computations, i.e. hybrid DFT calculation of the equilibrium geometry and the transition state within the harmonic approximation. A benchmark of experimental splittings spanning four orders of magnitude for 27 alcohol species is captured by three evaluated models with a mean symmetric deviation factor of 1.7, 1.5 and 1.4, respectively, i.e. the calculated values deviate on average by this factor in either direction. Limitations of the models are explored with alcohols featuring uncommon properties, such as an inverted conformational energy sequence, a very light molecular frame, an elevated torsional frequency, or a coupling with a second internal degree of freedom. If the splitting of either the protiated or deuterated form of an alcohol is already experimentally determined, the one of the second isotopolog can be estimated by three additional models with a mean symmetric deviation factor of 1.14, 1.19 and 1.15, respectively. It is shown that this can be achieved with a novel approach without any quantum chemical calculation by directly correlating experimental splittings of isotopologs across related species. This is also demonstrated for other classes of compounds with hydrogen tunneling, such as amines, thiols, and phenols. Furthermore, it is found that the isotope effect can even be anticipated without any further knowledge about the system solely from the size of either splitting with a mean symmetric deviation factor of 1.3. This is based on an extensive sample of 77 pairs of splittings spanning eight orders of magnitude for isotopologs of chemically diverse compounds.
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Affiliation(s)
- Robert Medel
- Institute of Physical Chemistry, University of Goettingen, Tammannstr. 6, 37077 Goettingen, Germany.
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18
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Vazquez-Salazar LI, Boittier ED, Unke OT, Meuwly M. Impact of the Characteristics of Quantum Chemical Databases on Machine Learning Prediction of Tautomerization Energies. J Chem Theory Comput 2021; 17:4769-4785. [PMID: 34288675 DOI: 10.1021/acs.jctc.1c00363] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
An essential aspect for adequate predictions of chemical properties by machine learning models is the database used for training them. However, studies that analyze how the content and structure of the databases used for training impact the prediction quality are scarce. In this work, we analyze and quantify the relationships learned by a machine learning model (Neural Network) trained on five different reference databases (QM9, PC9, ANI-1E, ANI-1, and ANI-1x) to predict tautomerization energies from molecules in Tautobase. For this, characteristics such as the number of heavy atoms in a molecule, number of atoms of a given element, bond composition, or initial geometry on the quality of the predictions are considered. The results indicate that training on a chemically diverse database is crucial for obtaining good results and also that conformational sampling can partly compensate for limited coverage of chemical diversity. The overall best-performing reference database (ANI-1x) performs on average by 1 kcal/mol better than PC9, which, however, contains about 2 orders of magnitude fewer reference structures. On the other hand, PC9 is chemically more diverse by a factor of ∼5 as quantified by the number of atom-in-molecule-based fragments (amons) it contains compared with the ANI family of databases. A quantitative measure for deficiencies is the Kullback-Leibler divergence between reference and target distributions. It is explicitly demonstrated that when certain types of bonds need to be covered in the target database (Tautobase) but are undersampled in the reference databases, the resulting predictions are poor. Examples of this include the poor performance of all databases analyzed to predict C(sp2)-C(sp2) double bonds close to heteroatoms and azoles containing N-N and N-O bonds. Analysis of the results with a Tree MAP algorithm provides deeper understanding of specific deficiencies in predicting tautomerization energies by the reference datasets due to inadequate coverage of chemical space. Capitalizing on this information can be used to either improve existing databases or generate new databases of sufficient diversity for a range of machine learning (ML) applications in chemistry.
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Affiliation(s)
| | - Eric D Boittier
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Oliver T Unke
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany.,DFG Cluster of Excellence "Unifying Systems in Catalysis" (UniSysCat), Technische Universität Berlin, 10623 Berlin, Germany
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland.,Department of Chemistry, Brown University, Providence, Rhode Island 02912, United States
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19
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Weike T, Manthe U. Symmetries in the multi-configurational time-dependent Hartree wavefunction representation and propagation. J Chem Phys 2021; 154:194108. [PMID: 34240912 DOI: 10.1063/5.0054105] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In multi-configurational time-dependent Hartree (MCTDH) approaches, different multi-layered wavefunction representations can be used to represent the same physical wavefunction. Transformations between different equivalent representations of a physical wavefunction that alter the tree structure used in the multi-layer MCTDH wavefunction representation interchange the role of single-particle functions (SPFs) and single-hole functions (SHFs) in the MCTDH formalism. While the physical wavefunction is invariant under these transformations, this invariance does not hold for the standard multi-layer MCTDH equations of motion. Introducing transformed SPFs, which obey normalization conditions typically associated with SHFs, revised equations of motion are derived. These equations do not show the singularities resulting from the inverse single-particle density matrix and are invariant under tree transformations. Based on the revised equations of motion, a new integration scheme is introduced. The scheme combines the advantages of the constant mean-field approach of Beck and Meyer [Z. Phys. D 42, 113 (1997)] and the singularity-free integrator suggested by Lubich [Appl. Math. Res. Express 2015, 311]. Numerical calculations studying the spin boson model in high dimensionality confirm the favorable properties of the new integration scheme.
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Affiliation(s)
- Thomas Weike
- 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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20
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Wodraszka R, Carrington T. A rectangular collocation multi-configuration time-dependent Hartree (MCTDH) approach with time-independent points for calculations on general potential energy surfaces. J Chem Phys 2021; 154:114107. [PMID: 33752363 DOI: 10.1063/5.0046425] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We introduce a collocation-based multi-configuration time-dependent Hartree (MCTDH) method that uses more collocation points than basis functions. We call it the rectangular collocation MCTDH (RC-MCTDH) method. It does not require that the potential be a sum of products. RC-MCTDH has the important advantage that it makes it simple to use time-independent collocation points. When using time-independent points, it is necessary to evaluate the potential energy function only once and not repeatedly during an MCTDH calculation. It is inexpensive and straightforward to use RC-MCTDH with combined modes. Using more collocation points than basis functions enables one to reduce errors in energy levels without increasing the size of the single-particle function basis. On the contrary, whenever a discrete variable representation is used, the only way to reduce the quadrature error is to increase the basis size, which then also reduces the basis-set error. We demonstrate that with RC-MCTDH and time-independent points, it is possible to calculate accurate eigenenergies of CH3 and CH4.
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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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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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Wang H, Meyer HD. Importance of Appropriately Regularizing the ML-MCTDH Equations of Motion. J Phys Chem A 2021; 125:3077-3087. [DOI: 10.1021/acs.jpca.0c11221] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, United States
| | - Hans-Dieter Meyer
- Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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23
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Bauer B, Bravyi S, Motta M, Chan GKL. Quantum Algorithms for Quantum Chemistry and Quantum Materials Science. Chem Rev 2020; 120:12685-12717. [DOI: 10.1021/acs.chemrev.9b00829] [Citation(s) in RCA: 134] [Impact Index Per Article: 33.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Bela Bauer
- Microsoft Quantum, Station Q, University of California
, Santa Barbara, California 93106, United States
| | - Sergey Bravyi
- IBM Quantum, IBM T. J. Watson Research Center
, Yorktown Heights, New York 10598, United States
| | - Mario Motta
- IBM Quantum, IBM Research Almaden
, San Jose, California 95120, United States
| | - Garnet Kin-Lic Chan
- Division of Chemistry and Chemical Engineering, California Institute of Technology
, Pasadena, California 91125, United States
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24
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Eraković M, Cvitaš MT. Tunneling splittings of vibrationally excited states using general instanton paths. J Chem Phys 2020; 153:134106. [PMID: 33032414 DOI: 10.1063/5.0024210] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
A multidimensional semiclassical method for calculating tunneling splittings in vibrationally excited states of molecules using Cartesian coordinates is developed. It is an extension of the theory by Mil'nikov and Nakamura [J. Chem. Phys. 122, 124311 (2005)] to asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. Additionally, new terms are introduced in the description of the semiclassical wavefunction that drastically improves the splitting estimates for certain systems. The method is based on the instanton theory and builds the semiclassical wavefunction of the vibrationally excited states from the ground-state instanton wavefunction along the minimum action path and its harmonic neighborhood. The splittings of excited states are thus obtained at a negligible added numerical effort. The cost is concentrated, as for the ground-state splittings, in the instanton path optimization and the hessian evaluation along the path. The method can thus be applied without modification to many mid-sized molecules in full dimensionality and in combination with on-the-fly evaluation of electronic potentials. The tests were performed on several model potentials and on the water dimer.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Ruder Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
| | - Marko T Cvitaš
- Department of Physical Chemistry, Ruder Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
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25
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Afshar Ghahremani F, Zahedi-Tabrizi M, Faramarz Tayyari S. The nature of intramolecular hydrogen bond in Naphthazarin. Chem Phys 2020. [DOI: 10.1016/j.chemphys.2020.110907] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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26
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Scivetti I, Sen K, Elena AM, Todorov I. Reactive Molecular Dynamics at Constant Pressure via Nonreactive Force Fields: Extending the Empirical Valence Bond Method to the Isothermal-Isobaric Ensemble. J Phys Chem A 2020; 124:7585-7597. [PMID: 32820921 DOI: 10.1021/acs.jpca.0c05461] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The Empirical Valence Bond (EVB) method offers a suitable framework to obtain reactive potentials through the coupling of nonreactive force fields. In this formalism, most of the implemented coupling terms are built using functional forms that depend on spatial coordinates, while parameters are fitted against reference data to model the change of chemistry between the participating nonreactive states. In this work, we demonstrate that the use of such coupling terms precludes the computation of the stress tensor for condensed phase systems and prevents the possibility to carry out EVB molecular dynamics in the isothermal-isobaric (NPT) ensemble. Alternatively, we make use of coupling terms that depend on the energy gaps, defined as the energy differences between the participating nonreactive force fields, and derive a general expression for the EVB stress tensor suitable for computation. Implementation of this new methodology is tested for a model of a single reactive malonaldehyde solvated in nonreactive water. Mass densities and probability distributions for the values of the energy gaps computed in the NPT ensemble reveal a negligible role of the reactive potential in the limit of low concentrated solutions, thus corroborating for the first time the validity of approximations based on the canonical NVT ensemble, customarily adopted for EVB simulations. The presented formalism also aims to contribute to future implementations and extensions of the EVB method to research the limit of highly concentrated solutions.
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Affiliation(s)
- Ivan Scivetti
- Daresbury Laboratory, Sc. Tech., Keckwick Lane, Daresbury, Warrington WA4 4AD, U.K.,Department of Chemistry, University of Liverpool, Liverpool L69 3BX, U.K
| | - Kakali Sen
- Daresbury Laboratory, Sc. Tech., Keckwick Lane, Daresbury, Warrington WA4 4AD, U.K
| | - Alin M Elena
- Daresbury Laboratory, Sc. Tech., Keckwick Lane, Daresbury, Warrington WA4 4AD, U.K
| | - Ilian Todorov
- Daresbury Laboratory, Sc. Tech., Keckwick Lane, Daresbury, Warrington WA4 4AD, U.K
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27
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Jahr E, Laude G, Richardson JO. Instanton theory of tunneling in molecules with asymmetric isotopic substitutions. J Chem Phys 2020; 153:094101. [PMID: 32891112 DOI: 10.1063/5.0021831] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We consider quantum tunneling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to a semiclassical expression for the tunneling matrix element and hence the energy-level splitting. We benchmark the method using a set of one- and two-dimensional models, for which the results compare favorably with numerically exact quantum calculations. Using the ring-polymer instanton approach, we apply the method to compute the level splittings in various isotopomers of malonaldehyde in full dimensionality and analyze the relative contributions from the zero-point energy difference and tunneling effects.
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Affiliation(s)
- Elena Jahr
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Gabriel Laude
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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28
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Wodraszka R, Carrington T. A collocation-based multi-configuration time-dependent Hartree method using mode combination and improved relaxation. J Chem Phys 2020; 152:164117. [DOI: 10.1063/5.0006081] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [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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Burd TAH, Clary DC. Analytic Route to Tunneling Splittings Using Semiclassical Perturbation Theory. J Chem Theory Comput 2020; 16:3486-3493. [DOI: 10.1021/acs.jctc.0c00207] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Timothy A. H. Burd
- Physical and Theoretical Chemical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - David C. Clary
- Physical and Theoretical Chemical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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30
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Pavošević F, Culpitt T, Hammes-Schiffer S. Multicomponent Quantum Chemistry: Integrating Electronic and Nuclear Quantum Effects via the Nuclear–Electronic Orbital Method. Chem Rev 2020; 120:4222-4253. [DOI: 10.1021/acs.chemrev.9b00798] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Fabijan Pavošević
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Tanner Culpitt
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
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31
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Gutiérrez-Quintanilla A, Chevalier M, Platakyte R, Ceponkus J, Crépin C. Intramolecular hydrogen tunneling in 2-chloromalonaldehyde trapped in solid para-hydrogen. Phys Chem Chem Phys 2020; 22:6115-6121. [PMID: 32096505 DOI: 10.1039/c9cp06866j] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The internal dynamics of a 2-chloromalonaldehyde (2-ClMA) molecule, possessing a strong internal hydrogen bond (IHB), was examined by means of matrix isolation spectroscopy in a soft host: para-hydrogen (pH2). 2-ClMA is a chlorinated derivative of malonaldehyde (MA), a model molecule in hydrogen transfer studies, better suited to low temperature experiments than its parent molecule. The infrared absorption spectra of 2-ClMA isolated in pH2 exhibit temperature dependent structures which are explained as transitions occurring from split vibrational levels induced by hydrogen tunneling. The doublet components associated with higher and lower energy levels are changing reversibly with the increase/decrease of the matrix temperature. The ground state splitting is measured to be 7.9 ± 0.1 cm-1. The presence of oH2 impurities in the pH2 matrix close to the neighborhood of the 2-ClMA molecule is found to quench the H tunneling. The data provide a powerful insight into the dynamical picture of intramolecular hydrogen tunneling in a molecule embedded in a very weakly perturbing environment.
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32
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Eraković M, Vaillant CL, Cvitaš MT. Instanton theory of ground-state tunneling splittings with general paths. J Chem Phys 2020; 152:084111. [PMID: 32113369 DOI: 10.1063/1.5145278] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive a multidimensional instanton theory for calculating ground-state tunneling splittings in Cartesian coordinates for general paths. It is an extension of the method by Mil'nikov and Nakamura [J. Chem. Phys. 115, 6881 (2001)] to include asymmetric paths that are necessary for calculating tunneling splitting patterns in multi-well systems, such as water clusters. The approach avoids multiple expensive matrix diagonalizations to converge the fluctuation prefactor in the ring-polymer instanton (RPI) method, and instead replaces them by an integration of a Riccati differential equation. When combined with the string method for locating instantons, we avoid the need to converge the calculation with respect to the imaginary time period of the semiclassical orbit, thereby reducing the number of convergence parameters of the optimized object to just one: the number of equally spaced system replicas used to represent the instanton path. The entirety of the numerical effort is thus concentrated in optimizing the shape of the path and evaluating hessians along the path, which is a dramatic improvement over RPI. In addition to the standard instanton approximations, we neglect the coupling of vibrational modes to external rotations. The method is tested on the model potential of malonaldehyde and on the water dimer and trimer, giving close agreement with RPI at a much-reduced cost.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Rudđđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
| | - Christophe L Vaillant
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Marko T Cvitaš
- Department of Physical Chemistry, Rudđđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
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33
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Weike T, Manthe U. The multi-configurational time-dependent Hartree approach in optimized second quantization: Imaginary time propagation and particle number conservation. J Chem Phys 2020; 152:034101. [DOI: 10.1063/1.5140984] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Thomas Weike
- 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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34
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Wu Y, Car R. Quantum momentum distribution and quantum entanglement in the deep tunneling regime. J Chem Phys 2020; 152:024106. [PMID: 31941303 DOI: 10.1063/1.5133053] [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
In this paper, we consider the momentum operator of a quantum particle directed along the displacement of two of its neighbors. A modified open-path path integral molecular dynamics is presented to sample the distribution of this directional momentum distribution, where we derive and use a new estimator for this distribution. Variationally enhanced sampling is used to obtain this distribution for an example molecule, malonaldehyde, in the very low temperature regime where deep tunneling happens. We find no secondary feature in the directional momentum distribution and that its absence is due to quantum entanglement through a further study of the reduced density matrix.
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Affiliation(s)
- Yantao Wu
- The Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Roberto Car
- The Department of Chemistry and the Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
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35
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Ronto M, Pollak E. Upper and lower bounds for tunneling splittings in a symmetric double-well potential. RSC Adv 2020; 10:34681-34689. [PMID: 35514393 PMCID: PMC9056815 DOI: 10.1039/d0ra07292c] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2020] [Accepted: 09/02/2020] [Indexed: 11/21/2022] Open
Abstract
Ground state tunneling gaps: solid circles are mean of eigenvalues and lower bound gaps.
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Affiliation(s)
- Miklos Ronto
- Chemical and Biological Physics Department
- Weizmann Institute of Science
- 76100 Rehovot
- Israel
- School of Chemistry
| | - Eli Pollak
- Chemical and Biological Physics Department
- Weizmann Institute of Science
- 76100 Rehovot
- Israel
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36
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Baiardi A, Stein CJ, Barone V, Reiher M. Optimization of highly excited matrix product states with an application to vibrational spectroscopy. J Chem Phys 2019; 150:094113. [DOI: 10.1063/1.5068747] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Alberto Baiardi
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Christopher J. Stein
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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37
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Thaunay F, Calvo F, Nicol E, Ohanessian G, Clavaguéra C. Infrared Spectra of Deprotonated Dicarboxylic Acids: IRMPD Spectroscopy and Empirical Valence‐Bond Modeling. Chemphyschem 2019; 20:803-814. [PMID: 30695125 DOI: 10.1002/cphc.201800947] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2018] [Revised: 01/28/2019] [Indexed: 01/08/2023]
Abstract
Experimental infrared multiple-photon dissociation (IRMPD) spectra recorded for a series of deprotonated dicarboxylic acids, HO2 (CH2 )n CO 2 - (n=2-4), are interpreted using a variety of computational methods. The broad bands centered near 1600 cm-1 can be reproduced neither by static vibrational calculations based on quantum chemistry nor by a dynamical description of individual structures using the many-body polarizable AMOEBA force field, strongly suggesting that these molecules experience dynamical proton sharing between the two carboxylic ends. To confirm this assumption, AMOEBA was combined with a two-state empirical valence-bond (EVB) model to allow for proton transfer in classical molecular dynamics simulations. Upon suitable parametrization based on ab initio reference data, the EVB-AMOEBA model satisfactorily reproduces the experimental infrared spectra, and the finite temperature dynamics reveals a significant amount of proton sharing in such systems.
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Affiliation(s)
| | - Florent Calvo
- LIPhyUniversité Grenoble Alpes, CNRS, LiPhy 38000 Grenoble France
| | - Edith Nicol
- LCM, CNRSEcole Polytechnique 91128 Palaiseau Cedex France
| | | | - Carine Clavaguéra
- Laboratoire de Chimie PhysiqueCNRS – Université Paris Sud, Université Paris-Saclay 15 avenue Jean Perrin 91405 Orsay Cedex France
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Gutiérrez-Quintanilla A, Chevalier M, Platakyte R, Ceponkus J, Crépin C. Selective photoisomerisation of 2-chloromalonaldehyde. J Chem Phys 2019; 150:034305. [PMID: 30660154 DOI: 10.1063/1.5082916] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Isomerization of 2-chloromalonaldehyde (2-ClMA) is explored giving access to new experimental data on this derivative of malonaldehyde, not yet studied much. Experiments were performed isolating 2-ClMA in argon, neon, and para-hydrogen matrices. UV irradiation of the matrix samples induced isomerization to three open enolic forms including two previously observed along with the closed enolic form after deposition. IR spectra of these specific conformers were recorded, and a clear assignment of the observed bands was obtained with the assistance of theoretical calculations. UV spectra of the samples were measured, showing a blue shift of the π* ← π absorption with the opening of the internal hydrogen bond of the most stable enol form. Specific sequences of UV irradiation at different wavelengths allowed us to obtain samples containing only one enol conformer. The formation of conformers is discussed. The observed selectivity of the process among the enol forms is analyzed.
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Affiliation(s)
- Alejandro Gutiérrez-Quintanilla
- Institut des Sciences Moléculaires d'Orsay (ISMO), UMR 8214, CNRS, Université Paris- Sud, Université Paris-Saclay, F-91405 Orsay, France
| | - Michèle Chevalier
- Institut des Sciences Moléculaires d'Orsay (ISMO), UMR 8214, CNRS, Université Paris- Sud, Université Paris-Saclay, F-91405 Orsay, France
| | - Rasa Platakyte
- Institut des Sciences Moléculaires d'Orsay (ISMO), UMR 8214, CNRS, Université Paris- Sud, Université Paris-Saclay, F-91405 Orsay, France
| | - Justinas Ceponkus
- Institute of Chemical Physics, Vilnius University, Sauletekio ave. 9 bat. III, L-10222 Vilnius, Lithuania
| | - Claudine Crépin
- Institut des Sciences Moléculaires d'Orsay (ISMO), UMR 8214, CNRS, Université Paris- Sud, Université Paris-Saclay, F-91405 Orsay, France
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Naskar P, Talukder S, Chaudhury P, Ghosh S. The effect of stochastic barrier fluctuation on semiclassical transmission probability and Shannon entropy of a symmetric double well potential. INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2018; 118:e25667. [DOI: 10.1002/qua.25667] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/19/2023]
Affiliation(s)
- Pulak Naskar
- Department of Chemistry; University of Calcutta, 92 A P C Road; Kolkata 700 009 India
| | - Srijeeta Talukder
- Department of Physical Chemistry; Indian Association for the Cultivation of Science, Jadavpur; Kolkata 700 032 India
| | - Pinaki Chaudhury
- Department of Chemistry; University of Calcutta, 92 A P C Road; Kolkata 700 009 India
| | - Subhasree Ghosh
- Department of Chemistry; Serampore College; Serampore, Hooghly, West Bengal 712201 India
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Affiliation(s)
- Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
| | - Hans-Dieter Meyer
- Theoretische Chemie, Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
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Etinski M, Ensing B. Puzzle of the Intramolecular Hydrogen Bond of Dibenzoylmethane Resolved by Molecular Dynamics Simulations. J Phys Chem A 2018; 122:5945-5954. [DOI: 10.1021/acs.jpca.8b01930] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Mihajlo Etinski
- Faculty of Physical Chemistry, University of Belgrade Studentski trg 12-16 11000 Belgrade, Serbia
| | - Bernd Ensing
- Van ’t Hoff Institute for Molecular Sciences (HIMS), University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands
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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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Gutiérrez-Quintanilla A, Chevalier M, Platakyte R, Ceponkus J, Rojas-Lorenzo GA, Crépin C. 2-Chloromalonaldehyde, a model system of resonance-assisted hydrogen bonding: vibrational investigation. Phys Chem Chem Phys 2018; 20:12888-12897. [PMID: 29700529 DOI: 10.1039/c7cp06481k] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The chelated enol isomer of 2-chloromalonaldehyde (2-ClMA) is experimentally characterized for the first time by IR and Raman spectroscopies. The spectra are obtained by trapping the molecule in cryogenic matrices and analyzed with the assistance of theoretical calculations. Experiments were performed in argon, neon and para-hydrogen matrices. The results highlight puzzling matrix effects, beyond site effects, which are interpreted as due to a tunneling splitting of the vibrational levels related to the proton transfer along the internal hydrogen bond (IHB). 2-ClMA is thus one of the very few molecules in which the H tunneling has been observed in cryogenic matrices. The comparison with its parent molecule (malonaldehyde) shows experimentally and theoretically the weakening of the IHB upon chlorination, with a reduced cooperative effect in the resonance assisted hydrogen bond. In addition, the Cl substitution induces an important stabilization of two open enol conformers. These two open forms appear in the spectra of as-deposited samples, meaning that, in contrast with other well-studied molecules of the same family (β-dialdehydes and β-diketones), they are present in the gas phase at room temperature.
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Affiliation(s)
- Alejandro Gutiérrez-Quintanilla
- Institut des Sciences Moléculaires d'Orsay (ISMO), UMR 8214, CNRS, Univ. Paris-Sud, Université Paris-Saclay UMR 8214, F-91405 Orsay, France
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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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Affiliation(s)
- Hans-Dieter Meyer
- Physikalisch-Chemisches Institut, Universität Heidelberg, Im Neuenheimer Feld 229, D-69120 Heidelberg, Germany
| | - Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
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Richter F, Carbonnière P. Vibrational treatment of the formic acid double minimum case in valence coordinates. J Chem Phys 2018; 148:064303. [DOI: 10.1063/1.5005989] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Falk Richter
- Groupe de Chimie Théorique et Réactivité IPREM-ECP, Université de Pau et des Pays de l’Adour, Pau F-64000, France
| | - P. Carbonnière
- Groupe de Chimie Théorique et Réactivité IPREM-ECP, Université de Pau et des Pays de l’Adour, Pau F-64000, France
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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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Naeini FG, Nowroozi A. Evaluation the origin of conformational preferences in trifluoroacetylacetaldehyde by detail analysis of the intramolecular hydrogen bond and π-electron delocalization in the ground and first excited states. J STRUCT CHEM+ 2017. [DOI: 10.1134/s0022476617060257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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