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Nanni L. Investigating proton tunneling dynamics in the time-dependent Schrödinger equation. J Comput Chem 2024; 45:1614-1623. [PMID: 38523084 DOI: 10.1002/jcc.27348] [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: 12/29/2023] [Revised: 03/02/2024] [Accepted: 03/07/2024] [Indexed: 03/26/2024]
Abstract
Understanding the temporal evolution of the wave function in the proton tunneling reactions allows us to make theoretical predictions on the possible femtosecond spectroscopy patterns. However, the analytical solution of the time-dependent Schrödinger equation of complex molecules is challenging and requires a high computational cost. In this study, we solve the time-dependent Schrödinger equation using the Fourier grid Hamiltonian method, highlighting its simplicity of calculation, even for multidimensional tunneling reactions. The obtained model is applied to studying malonaldehyde's two-dimensional intramolecular proton tunneling, comparing the results with those obtained using other computational methods.
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Affiliation(s)
- Luca Nanni
- Department of Physics, University of Ferrara, Ferrara, Italy
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2
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Eraković M, Cvitaš MT. Tunneling splittings using modified WKB method in Cartesian coordinates: The test case of vinyl radical. J Chem Phys 2024; 160:154112. [PMID: 38639313 DOI: 10.1063/5.0204986] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Accepted: 03/31/2024] [Indexed: 04/20/2024] Open
Abstract
Modified WKB theory for calculating tunneling splittings in symmetric multi-well systems in full dimensionality is re-derived using Cartesian coordinates. It is explicitly shown that the theory rests on the wavefunction that is exact for harmonic potentials. The theory was applied to calculate tunneling splittings in vinyl radical and some of its deuterated isotopologues in their vibrational ground states and the low-lying vibrationally excited states and compared to exact variational results. The exact results are reproduced within a factor of 2 in most states. Remarkably, all large enhancements of tunneling splittings relative to the ground state, up to three orders in magnitude in some excited mode combinations, are well reproduced. It is also shown that in the asymmetrically deuterated vinyl radical, the theory correctly predicts the states that are localized in a single well and the delocalized tunneling states. Modified WKB theory on the minimum action path is computationally inexpensive and can also be applied without modification to much larger systems in full dimensionality; the results of this test case serve to give insight into the expected accuracy of the method.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Ruđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
| | - Marko T Cvitaš
- Department of Physics, University of Zagreb Faculty of Science, Bijenička Cesta 32, 10000 Zagreb, Croatia
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3
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Eraković M, Cvitaš MT. Vibrational Tunneling Spectra of Molecules with Asymmetric Wells: A Combined Vibrational Configuration Interaction and Instanton Approach. J Chem Theory Comput 2022; 18:2785-2802. [PMID: 35439012 PMCID: PMC9097297 DOI: 10.1021/acs.jctc.2c00124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
A combined approach
that uses the vibrational configuration interaction
(VCI) and semiclassical instanton theory was developed to study vibrational
tunneling spectra of molecules with multiple wells in full dimensionality.
The method can be applied to calculate low-lying vibrational states in the systems with an
arbitrary number of minima, which are not necessarily equal in energy
or shape. It was tested on a two-dimensional double-well model system
and on malonaldehyde, and the calculations reproduced the exact quantum
mechanical (QM) results with high accuracy. The method was subsequently
applied to calculate the vibrational spectrum of the asymmetrically
deuterated malonaldehyde with nondegenerate vibrational frequencies
in the two wells. The spectrum is obtained at a cost of single-well
VCI calculations used to calculate the local energies. The interactions
between states of different wells are computed semiclassically using
the instanton theory at a comparatively negligible computational cost.
The method is particularly suited to systems in which the wells are
separated by large potential barriers and tunneling splittings are
small, for example, in some water clusters, when the exact QM methods
come at a prohibitive computational cost.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Rud̵er Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
| | - Marko T Cvitaš
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička Cesta 32, 10000 Zagreb, Croatia
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4
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Cheng YH, Zhu YC, Kang W, Li X, Fang W. Determination of concerted or stepwise mechanism of hydrogen tunneling from isotope effects: Departure between experiment and theory. J Chem Phys 2022; 156:124304. [DOI: 10.1063/5.0085010] [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
Isotope substitution is an important experimental technique that offers deep insight into reaction mechanisms, as the measured kinetic isotope effects (KIEs) can be directly compared with theory. For multiple proton transfer processes, there are two types of mechanisms: stepwise transfer and concerted transfer. The Bell-Limbach model provides a simple theory to determine whether the proton transfer mechanism is stepwise or concerted from KIEs. Recent STM experiments have studied the proton switching process in water tetramers on NaCl(001). Theoretical studies predict that this process occurs via a concerted mechanism, however, the experimental KIEs resemble the Bell-Limbach model for stepwise tunneling, raising question on the underlying mechanism or the validity of the model. We study this system using ab initio instanton theory, and in addition to thermal rates, we also considered microcanonical rates, as well as tunneling splittings. Instanton theory predicts a concerted mechanism, and the KIEs for tunneling rates (both thermal and microcanonical) upon deuteration are consistent with the Bell-Limbach model for concerted tunneling, but could not explain the experiments. For tunneling splittings, partial and full deuteration changes the size of it in a similar fashion to how it changes the rates. We further examined the Bell-Limbach model in another system, porphycene, which has both stepwise and concerted tunneling pathways. The KIEs predicted by instanton theory are again consistent with the Bell-Limbach model. This study highlights differences between KIEs in stepwise and concerted tunneling, and the discrepancy between theory and recent STM experiments. New theory/experiments are desired to settle this problem.
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Affiliation(s)
| | | | - Wei Kang
- Center for Applied Physics and Technology, Peking University, China
| | | | - Wei Fang
- Dalian Institute of Chemical Physics, China
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5
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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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6
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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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7
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Kay KG. Semiclassical tunneling splittings for arbitrary vibrational states in multidimensional double wells. J Chem Phys 2018; 149:144108. [DOI: 10.1063/1.5047830] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Kenneth G. Kay
- Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
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9
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Smedarchina Z, Siebrand W, Fernández-Ramos A. Entanglement and co-tunneling of two equivalent protons in hydrogen bond pairs. J Chem Phys 2018; 148:102307. [DOI: 10.1063/1.5000681] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Zorka Smedarchina
- Centro Singular de Investigación en Química Biolóxica e Materiais Moleculares (CIQUS), e Departamento de Química Física, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
- National Research Council of Canada, Ottawa, Ontario K1A 0R6 Canada
| | - Willem Siebrand
- National Research Council of Canada, Ottawa, Ontario K1A 0R6 Canada
| | - Antonio Fernández-Ramos
- Centro Singular de Investigación en Química Biolóxica e Materiais Moleculares (CIQUS), e Departamento de Química Física, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
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10
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Affiliation(s)
- Jan Meisner
- 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
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11
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Cvitaš MT. Quadratic String Method for Locating Instantons in Tunneling Splitting Calculations. J Chem Theory Comput 2018; 14:1487-1500. [DOI: 10.1021/acs.jctc.7b00881] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Marko T. Cvitaš
- Department of Physical Chemistry, Ruđer Bošković Institute, Bijenička Cesta 54, 10000 Zagreb, Croatia
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12
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Laude G, Calderini D, Tew DP, Richardson JO. Ab initio instanton rate theory made efficient using Gaussian process regression. Faraday Discuss 2018; 212:237-258. [PMID: 30230495 DOI: 10.1039/c8fd00085a] [Citation(s) in RCA: 38] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.
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Affiliation(s)
- Gabriel Laude
- Laboratory of Physical Chemistry, ETH Zurich, Switzerland. and On exchange from School of Chemistry, University of Edinburgh, UK
| | | | - David P Tew
- Max-Planck-Institut für Festkörperforschung, Heisenbergstraße 1, 70569 Stuttgart, Germany
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13
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Wu F, Ren Y. Primary and secondary isotope effect on tunnelling in malonaldehyde using a quantum mechanical scheme. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1317371] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Feng Wu
- Department of Physics, Yancheng Institute of Technology, Yancheng, China
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing, China
| | - Yinghui Ren
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing, China
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14
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Wu F, Ren Y, Bian W. The hydrogen tunneling splitting in malonaldehyde: A full-dimensional time-independent quantum mechanical method. J Chem Phys 2016; 145:074309. [DOI: 10.1063/1.4960789] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Feng Wu
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yinghui Ren
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
| | - Wensheng Bian
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China
- University of Chinese Academy of Sciences, Beijing 100049, China
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15
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Wu F. Quantum Mechanical Investigation of Mode-Specific Tunneling upon Fundamental Excitation in Malonaldehyde. J Phys Chem A 2016; 120:3849-54. [PMID: 27192182 DOI: 10.1021/acs.jpca.6b00340] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a quantum mechanical study of mode-specific tunneling upon fundamental excitation in malonaldehyde with a multidimensional theory that utilizes the saddle-point normal coordinates. We find that a ring-deformation normal mode is as essential as the well-known imaginary-frequency normal mode in the multidimensional investigation. The changes in tunneling splittings upon fundamental excitation are calculated. The results are competitive with those from a recently developed mixed classical-quantum method. Moreover, the results are qualitatively consistent with experiment for about half of all the modes.
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Affiliation(s)
- Feng Wu
- Beijing National Laboratory for Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences , Beijing 100190, China.,University of Chinese Academy of Sciences , Beijing 100049, China
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16
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Mátyus E, Wales DJ, Althorpe SC. Quantum tunneling splittings from path-integral molecular dynamics. J Chem Phys 2016; 144:114108. [DOI: 10.1063/1.4943867] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Edit Mátyus
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - David J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Stuart C. Althorpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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17
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Alves TV, Simón-Carballido L, Ornellas FR, Fernández-Ramos A. Hindered rotor tunneling splittings: an application of the two-dimensional non-separable method to benzyl alcohol and two of its fluorine derivatives. Phys Chem Chem Phys 2016; 18:8945-53. [PMID: 26960818 DOI: 10.1039/c5cp05307b] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this work we present a novel application of the two-dimensional non-separable (2D-NS) method to the calculation of torsional tunneling splittings in systems with two hindered internal rotors. This method could be considered an extension of one-dimensional methods for the case of compounds with two tops. The 2D-NS method includes coupling between torsions in the kinetic and potential energy. Specifically, it has been applied to benzyl alcohol (BA) and two of its fluorine derivatives: 3-fluorobenzyl alcohol (3FBA) and 4-fluorobenzyl alcohol (4FBA). These molecules present two torsions, i.e., about the -CH2OH (ϕ1) and -OH (ϕ2) groups. The electronic structure calculations to build the two-dimensional torsional potential energy surface were performed at the DF-LMP2-F12//DF-LMP2/cc-pVQZ level of theory. For BA and 4FBA the calculated ground-state vibrational level splittings are 429 and 453 MHz, respectively, in good agreement with the experimental values of 337.10 and 492.82 MHz, respectively. In these two cases there are four equivalent wells and the tunneling splitting is the result of transitions between the two closer minima along ϕ1. The analysis of the wavefunctions, as well as the previous experimental work on the system, supports this conclusion. For 3FBA the observed ground-state splitting is 0.82 MHz, whereas in this case the calculated value amounts only to 0.02 MHz. The 2D-NS method, through the analysis of the wavefunctions, shows that this tiny tunneling splitting occurs between the two most stable minima of the potential energy surface. Additionally, we predict that the first vibrationally excited tunneling splitting will also be small and exclusively due to the interconversion between the second lowest minima.
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Affiliation(s)
- Tiago Vinicius Alves
- Departamento de Química Fundamental, Instituto de Química, Universidade de São Paulo, Av. Prof. Lineu Prestes 748, São Paulo, SP 05508-000, Brazil
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18
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Cvitaš MT, Althorpe SC. Locating Instantons in Calculations of Tunneling Splittings: The Test Case of Malonaldehyde. J Chem Theory Comput 2016; 12:787-803. [PMID: 26756608 DOI: 10.1021/acs.jctc.5b01073] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The recently developed ring-polymer instanton (RPI) method [J. Chem. Phys. 2011, 134, 054109] is an efficient technique for calculating approximate tunneling splittings in high-dimensional molecular systems. The key step is locating the instanton tunneling-path at zero temperature. Here, we show that techniques previously designed for locating instantons in finite-temperature rate calculations can be adapted to the RPI method, where they become extremely efficient, reducing the number of potential energy calls by 2 orders of magnitude. We investigate one technique that employs variable time steps to minimize the action integral, and two that employ equally spaced position steps to minimize the abbreviated (i.e., Jacobi) action integral, using respectively the nudged elastic band (NEB) and string methods. We recommend use of the latter because it is parameter-free, but all three methods give comparable efficiency savings. Having located the instanton pathway, we then interpolate the instanton path onto a fine grid of imaginary time points, allowing us to compute the fluctuation prefactor. The crucial modification needed to the original finite-temperature algorithms is to allow the end points of the zero-temperature instanton path to describe overall rotations, which is done using a standard quaternion algorithm. These approaches will allow the RPI method to be combined effectively with expensive potential energy surfaces or on-the-fly electronic structure methods.
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Affiliation(s)
- Marko T Cvitaš
- Department of Physical Chemistry, Ruđer Bošković Institute , Bijenička Cesta 54, 10000 Zagreb, Croatia
| | - Stuart C Althorpe
- Department of Chemistry, University of Cambridge , Lensfield Road, Cambridge CB2 1EW, United Kingdom
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19
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Isotope effects of ammonia umbrella flip using semiclassical instanton calculations based on discretized path integrals. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.05.072] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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20
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Jain A, Sibert EL. Tunneling splittings in formic acid dimer: An adiabatic approximation to the Herring formula. J Chem Phys 2015; 142:084115. [DOI: 10.1063/1.4908565] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Amber Jain
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Edwin L. Sibert
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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21
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Smedarchina Z, Siebrand W, Fernández-Ramos A. Tunneling splitting in double-proton transfer: Direct diagonalization results for porphycene. J Chem Phys 2014; 141:174312. [DOI: 10.1063/1.4900717] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Kawatsu T, Miura S. The isotope effects on a hydrogen transfer using path integral instanton method. MOLECULAR SIMULATION 2014. [DOI: 10.1080/08927022.2014.951641] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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23
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Fernández-Ramos A, Smedarchina Z, Siebrand W. Multidimensional Hamiltonian for tunneling with position-dependent mass. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:033306. [PMID: 25314563 DOI: 10.1103/physreve.90.033306] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2014] [Indexed: 06/04/2023]
Abstract
A multidimensional Hamiltonian for tunneling is formulated, based on the mode with imaginary frequency of the transition state as a reaction coordinate. To prepare it for diagonalization, it is transformed into a lower-dimension Hamiltonian by incorporating modes that move faster than the tunneling into a coordinate-dependent kinetic energy operator, for which a Hermitian form is chosen and tested for stability of the eigenvalues. After transformation to a three-dimensional form, which includes two normal modes strongly coupled to the tunneling mode, this Hamiltonian is diagonalized in terms of a basis set of harmonic oscillator functions centered at the transition state. This involves a sparse matrix which is easily partially diagonalized to yield tunneling splittings for the zero-point level and the two fundamental levels of the coupled modes. The method is tested on the well-known benchmark molecule malonaldehyde and a deuterium isotopomer, for which these splittings have been measured. Satisfactory agreement with experiment results is obtained.
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Affiliation(s)
- Antonio Fernández-Ramos
- Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
| | - Zorka Smedarchina
- Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
| | - Willem Siebrand
- Department of Physical Chemistry and Center for Research in Biological Chemistry and Molecular Materials, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
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24
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Kawatsu T, Miura S. Efficient algorithms for semiclassical instanton calculations based on discretized path integrals. J Chem Phys 2014; 141:024101. [DOI: 10.1063/1.4885437] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Tsutomu Kawatsu
- Institute for Molecular Science, National Institute of Natural Science, 38 Nishigonaka, Myodaiji, Okazaki 222-8585, Japan
- School of Mathematics and Physics, Kanazawa University, Kanazawa 920-1192, Japan
| | - Shinichi Miura
- School of Mathematics and Physics, Kanazawa University, Kanazawa 920-1192, Japan
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25
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Smedarchina Z, Siebrand W, Fernández-Ramos A. Zero-Point Tunneling Splittings in Compounds with Multiple Hydrogen Bonds Calculated by the Rainbow Instanton Method. J Phys Chem A 2013; 117:11086-100. [DOI: 10.1021/jp4073608] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Zorka Smedarchina
- National Research Council of Canada, 100 Sussex Drive, Ottawa, K1A 0R6 Canada
| | - Willem Siebrand
- National Research Council of Canada, 100 Sussex Drive, Ottawa, K1A 0R6 Canada
| | - Antonio Fernández-Ramos
- Department
of Physical Chemistry and Center for Research in Biological Chemistry
and Molecular Materials (CIQUS), University of Santiago de Compostela, 15706 Santiago de Compostela, Santiago de
Compostela, Spain
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26
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Siebrand W, Smedarchina Z, Fernández-Ramos A. Communication: Selection rules for tunneling splitting of vibrationally excited levels. J Chem Phys 2013; 139:021101. [DOI: 10.1063/1.4813002] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
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27
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Lüttschwager NO, Wassermann TN, Coussan S, Suhm MA. Vibrational tuning of the Hydrogen transfer in malonaldehyde – a combined FTIR and Raman jet study†. Mol Phys 2013. [DOI: 10.1080/00268976.2013.798042] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Nils O.B. Lüttschwager
- Institut für Physikalische Chemie, Georg-August-Universität Göttingen , Tammannstr. 6, Göttingen, D-37077, Germany
| | - Tobias N. Wassermann
- Institut für Physikalische Chemie, Georg-August-Universität Göttingen , Tammannstr. 6, Göttingen, D-37077, Germany
- Laboratoire PIIM, Université de Provence, Centre Saint-Jérôme , F-13 397 cedex 20, Marseille, France
| | - Stéphane Coussan
- Laboratoire PIIM, Université de Provence, Centre Saint-Jérôme , F-13 397 cedex 20, Marseille, France
| | - Martin A. Suhm
- Institut für Physikalische Chemie, Georg-August-Universität Göttingen , Tammannstr. 6, Göttingen, D-37077, Germany
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Mengesha ET, Sepioł J, Borowicz P, Waluk J. Vibrations of porphycene in the S0 and S1 electronic states: Single vibronic level dispersed fluorescence study in a supersonic jet. J Chem Phys 2013; 138:174201. [DOI: 10.1063/1.4802769] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
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