1
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Eraković M, Cvitaš MT. Tunneling splittings in the vibrationally excited states of water trimer. Phys Chem Chem Phys 2024; 26:12965-12981. [PMID: 38634688 DOI: 10.1039/d4cp00013g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/19/2024]
Abstract
Tunneling splitting (TS) patterns in vibrationally excited states of the water trimer are calculated, taking into account six tunneling pathways that describe the flips of free OH bonds and five bifurcation mechanisms that break and reform hydrogen bonds in the trimer ring. A tunneling matrix (TM) model is used to derive the energy shifts due to tunneling in terms of the six distinct TM elements in symbolic form. TM elements are calculated using the recently-developed modified WKB (Wentzel-Kramers-Brillouin) method in full dimensionality. Convergence was achieved for the lowest six excited vibrational modes. Bifurcation widths of the pseudorotational quartets are shown to be of comparable size to the ground-state widths, obtained using instanton theory, or increased for some particular modes of vibration. The largest increase is obtained for the excited out-of-phase flip of two adjacent water monomers with free OH bonds pointing in opposite directions relative to the ring plane. Bifurcation widths in (D2O)3 are found to be two orders of magnitude smaller than in (H2O)3. Geometrical arguments were used to explain the order of states in some TS multiplets in vibrationally excited water trimers.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Ruđer Bošković Institute, Zagreb, Croatia.
| | - Marko T Cvitaš
- Department of Physics, University of Zagreb Faculty of Science, Zagreb, Croatia.
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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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Yang X, Liu R, Xu R, Wang Z. Sequential flipping: the donor-acceptor exchange mechanism in water trimers. Phys Chem Chem Phys 2023; 25:21957-21963. [PMID: 37553960 DOI: 10.1039/d3cp02666c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/10/2023]
Abstract
The donor-acceptor exchange (DAE) is a significant hydrogen bond network rearrangement (HBNR) mechanism because it can lead to the change of the hydrogen bond direction. In this work, we report a new DAE mechanism found in water trimers that is realized by sequential flipping (SF) of all molecules rather than the well-known proton transfer (PT) process. Meanwhile, the SF process has a much smaller potential barrier (0.262 eV) than the previously predicted collective rotation process (about 1.7 eV), implying that the SF process is the main flipping process that can lead to DAE. Importantly, high-precision ab initio calculations show that SF-DAE can make the water ring to show a clear chiral difference from PT-DAE, which brings the prospect of distinguishing the two confusing processes based on circular dichroism spectra. The reaction rate analysis including quantum tunneling indicates an obvious temperature-dependent competitive relationship between the SF and PT processes; specifically, the SF process dominates above 65 K, while the PT process dominates below 65 K. Therefore, in most cases, the contribution for DAE mainly comes from the flipping process, rather than the PT process as previously thought. Our work enriches the understanding of the DAE mechanism in water trimers and provides a piece of the jigsaw that has been sought for the HBNR mechanism.
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Affiliation(s)
- Xinrui Yang
- Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China.
| | - Rui Liu
- Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China.
| | - Ruiqi Xu
- Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China.
| | - Zhigang Wang
- Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, China.
- International Center for Computational Method & Software, College of Physics, Jilin University, Changchun 130012, China
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4
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Trenins G, Meuser L, Bertschi H, Vavourakis O, Flütsch R, Richardson JO. Exact tunneling splittings from symmetrized path integrals. J Chem Phys 2023; 159:034108. [PMID: 37466233 DOI: 10.1063/5.0158879] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2023] [Accepted: 06/13/2023] [Indexed: 07/20/2023] Open
Abstract
We develop a new simulation technique based on path-integral molecular dynamics for calculating ground-state tunneling splitting patterns from ratios of symmetrized partition functions. In particular, molecular systems are rigorously projected onto their J = 0 rotational state by an "Eckart spring" that connects two adjacent beads in a ring polymer. Using this procedure, the tunneling splitting can be obtained from thermodynamic integration at just one (sufficiently low) temperature. Converged results are formally identical to the values that would have been obtained by solving the full rovibrational Schrödinger equation on a given Born-Oppenheimer potential energy surface. The new approach is showcased with simulations of hydronium and methanol, which are in good agreement with wavefunction-based calculations and experimental measurements. The method will be of particular use for the study of low-barrier methyl rotations and other floppy modes, where instanton theory is not valid.
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Affiliation(s)
- George Trenins
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Lars Meuser
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Hannah Bertschi
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Odysseas Vavourakis
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Reto Flütsch
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
| | - Jeremy O Richardson
- Department of Chemistry and Applied Biosciences, ETH Zürich, 8093 Zürich, Switzerland
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5
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Videla PE, Foguel L, Vaccaro PH, Batista VS. Proton-Tunneling Dynamics along Low-Barrier Hydrogen Bonds: A Full-Dimensional Instanton Study of 6-Hydroxy-2-formylfulvene. J Phys Chem Lett 2023:6368-6375. [PMID: 37418693 DOI: 10.1021/acs.jpclett.3c01337] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/09/2023]
Abstract
Understanding the dynamics of proton transfer along low-barrier hydrogen bonds remains an outstanding challenge of great fundamental and practical interest, reflecting the central role of quantum effects in reactions of chemical and biological importance. Here, we combine ab initio calculations with the semiclassical ring-polymer instanton method to investigate tunneling processes on the ground electronic state of 6-hydroxy-2-formylfulvene (HFF), a prototypical neutral molecule supporting low-barrier hydrogen-bonding. The results emerging from a full-dimensional ab initio instanton analysis reveal that the tunneling path does not pass through the instantaneous transition-state geometry. Instead, the tunneling process involves a multidimensional reaction coordinate with concerted reorganization of the heavy-atom skeletal framework to substantially reduce the donor-acceptor distance and drive the ensuing intramolecular proton-transfer event. The predicted tunneling-induced splittings for HFF isotopologues are in good agreement with experimental findings, leading to percentage deviations of only 20-40%. Our full-dimensional results allow us to characterize vibrational contributions along the tunneling path, highlighting the intrinsically multidimensional nature of the attendant hydron-migration dynamics.
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Affiliation(s)
- Pablo E Videla
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Lidor Foguel
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Patrick H Vaccaro
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Victor S Batista
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
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6
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Zhu YC, Yang S, Zeng JX, Fang W, Jiang L, Zhang DH, Li XZ. Accurate calculation of tunneling splittings in water clusters using path-integral based methods. J Chem Phys 2023; 158:2895223. [PMID: 37290067 DOI: 10.1063/5.0146562] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2023] [Accepted: 04/03/2023] [Indexed: 06/10/2023] Open
Abstract
Tunneling splittings observed in molecular rovibrational spectra are significant evidence for tunneling motion of hydrogen nuclei in water clusters. Accurate calculations of the splitting sizes from first principles require a combination of high-quality inter-atomic interactions and rigorous methods to treat the nuclei with quantum mechanics. Many theoretical efforts have been made in recent decades. This Perspective focuses on two path-integral based tunneling splitting methods whose computational cost scales well with the system size, namely, the ring-polymer instanton method and the path-integral molecular dynamics (PIMD) method. From a simple derivation, we show that the former is a semiclassical approximation to the latter, despite that the two methods are derived very differently. Currently, the PIMD method is considered to be an ideal route to rigorously compute the ground-state tunneling splitting, while the instanton method sacrifices some accuracy for a significantly smaller computational cost. An application scenario of such a quantitatively rigorous calculation is to test and calibrate the potential energy surfaces of molecular systems by spectroscopic accuracy. Recent progress in water clusters is reviewed, and the current challenges are discussed.
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Affiliation(s)
- Yu-Cheng Zhu
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Materials, Peking University, Beijing 100871, People's Republic of China
| | - Shuo Yang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China
- University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Jia-Xi Zeng
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Materials, Peking University, Beijing 100871, People's Republic of China
| | - Wei Fang
- Department of Chemistry, Fudan University, Shanghai 200438, People's Republic of China
| | - Ling Jiang
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China
| | - Dong H Zhang
- State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, People's Republic of China
| | - Xin-Zheng Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing 100871, People's Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Materials, Peking University, Beijing 100871, People's Republic of China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu 226010, People's Republic of China
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7
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Zhu YC, Yang S, Zeng JX, Fang W, Jiang L, Zhang DH, Li XZ. Torsional Tunneling Splitting in a Water Trimer. J Am Chem Soc 2022; 144:21356-21362. [DOI: 10.1021/jacs.2c09909] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Yu-Cheng Zhu
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing100871, People’s Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Materials, Peking University, Beijing100871, People’s Republic of China
| | - Shuo Yang
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian116023, People’s Republic of China
- University of Chinese Academy of Sciences, Beijing100871, People’s Republic of China
| | - Jia-Xi Zeng
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing100871, People’s Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Materials, Peking University, Beijing100871, People’s Republic of China
| | - Wei Fang
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian116023, People’s Republic of China
- Department of Chemistry, Fudan University, Shanghai200438, People’s Republic of China
| | - Ling Jiang
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian116023, People’s Republic of China
| | - Dong H. Zhang
- State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian116023, People’s Republic of China
| | - Xin-Zheng Li
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Frontier Science Center for Nano-optoelectronics and School of Physics, Peking University, Beijing100871, People’s Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Research Center for Light-Element Advanced Materials, and Collaborative Innovation Center of Quantum Materials, Peking University, Beijing100871, People’s Republic of China
- Peking University Yangtze Delta Institute of Optoelectronics, Nantong, Jiangsu226010, People’s Republic of China
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8
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Pravatto P, Fresch B, Moro GJ. The tunneling splitting and the Kramers theory of activated processes. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2022.111608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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9
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Méndez E, Videla PE, Laria D. Equilibrium and Dynamical Characteristics of Hydrogen Bond Bifurcations in Water-Water and Water-Ammonia Dimers: A Path Integral Molecular Dynamics Study. J Phys Chem A 2022; 126:4721-4733. [PMID: 35834556 DOI: 10.1021/acs.jpca.2c02525] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present path integral molecular dynamics results that describe the effects of nuclear quantum fluctuations on equilibrium and dynamical characteristics pertaining to bifurcation pathways in hydrogen bonded dimers combining water and ammonia, at cryogenic temperatures of the order of 20 K. Along these isomerizations, the hydrogen atoms in the molecules acting as hydrogen-bond donors interchange their original dangling/connective characters. Our results reveal that the resulting quantum transition paths comprise three stages: the initial and final ones involve overall rotations during which the two protons retain their classical-like characteristics. Effects from quantum fluctuation are clearly manifested in the changes operated at the intermediate passages over transition states, as the spatial extents of the protons stretch over typical lengths comparable to the distances between connective and dangling basins of attractions. Consequently, the classical over-the-hill path is replaced by a tunneling controlled mechanism which, within the path integral perspective, can be cast in terms of concerted inter-basin migrations of polymer beads from dangling-to-connective and from connective-to-dangling, at practically no energy costs. We also estimated the characteristic timescales describing such interconversions within the approximate ring polymer rate theory. Effects derived from full and partial deuteration are also discussed.
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Affiliation(s)
- Emilio Méndez
- Departamento de Química Inorgánica, Analítica y Química-Física and INQUIMAE-CONICET, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria, Pabellón II, 1428 Buenos Aires, Argentina
| | - Pablo E Videla
- Department of Chemistry and Energy Sciences Institute, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, United States
| | - Daniel Laria
- Departamento de Física de la Materia Condensada, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, 1429 Buenos Aires, Argentina
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10
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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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11
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Sahoo T, Serwatka T, Roy PN. A path integral ground state approach for asymmetric top rotors with nuclear spin symmetry: Application to water chains. J Chem Phys 2021; 154:244305. [PMID: 34241367 DOI: 10.1063/5.0053051] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A path integral ground state (PIGS) approach for the simulation of asymmetric top rotors is presented. The method is based on Monte Carlo sampling of angular degrees of freedom. A symmetry-adapted rotational density matrix is used to account for nuclear spin statistics. To illustrate the method, ground-state properties of collections of para-water molecules confined to a one-dimensional lattice are computed. Those include energetic and structural observables. An advantage of the PIGS method is that expectation values can be obtained directly since the square of the wavefunction is sampled during a simulation. To benchmark the method, ground state energies and orientational distributions are computed using exact diagonalization for a single para-water molecule in an external field using a finite basis of symmetric top eigenfunctions. Benchmark results are also provided for N = 2 para-water molecules pinned to lattice sites at various distances to sample the crossover from hydrogen bonding to the dipole-dipole interaction regime. Excellent agreement between the PIGS results and the finite basis set calculations is observed. A thorough analysis of the convergence in terms of the imaginary time propagation length and systematic Trotter error is performed. The PIGS approach is then applied to a chain of N = 11 water molecules, and an equation of state is constructed in terms of the intermolecular separation. Ordering effects are also studied, and a transition between hydrogen bonding to dipole-dipole alignment is observed. The method is scalable and can also be applied in higher dimensions.
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Affiliation(s)
- Tapas Sahoo
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Tobias Serwatka
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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12
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Eraković M, Cvitaš MT. Tunnelling splitting patterns in some partially deuterated water trimers. Phys Chem Chem Phys 2021; 23:4240-4254. [PMID: 33586727 DOI: 10.1039/d0cp06135b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We apply our recently developed semiclassical method for calculating tunnelling splittings (TS) in asymmetric systems to make the first characterization of the ground-state TS pattern of some partially deuterated water trimers. Similarly to homoisotopic water trimers, the ground-state TS patterns are explained in terms of six distinct rearrangement mechanisms. TS patterns in (D2O)(H2O)2 and (H2O)(D2O)2 are composed of sextets induced by the dynamics of flips, and each of its levels is further finely split into a quartet of doublets and a doublet of quartets, respectively, due to various bifurcation dynamics. The TS pattern is obtained using 18 distinct tunnelling matrix elements. TS patterns of (HOD)(H2O)2 and (HOD)(D2O)2 each consists of two sextets, belonging to in-bond and out-of-bond substituted isomers. These sextet levels are further split into quartets by bifurcations. The TS pattern is computed in terms of 13 matrix elements. We also derive analytic expressions for bifurcation tunnelling splittings in terms of tunnelling matrix elements using symmetry. The present approach can be applied to other water clusters and also to the low-lying vibrationally excited states and should help in the interpretation and assignment of experimental spectra in the future.
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Affiliation(s)
- Mihael Eraković
- Department of Physical Chemistry, Ruđer Bošković Institute, 10000 Zagreb, Croatia.
| | - Marko T Cvitaš
- Department of Physical Chemistry, Ruđer Bošković Institute, 10000 Zagreb, Croatia.
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13
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Sahu N, Richardson JO, Berger R. Instanton calculations of tunneling splittings in chiral molecules. J Comput Chem 2021; 42:210-221. [PMID: 33259074 DOI: 10.1002/jcc.26447] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2020] [Revised: 08/20/2020] [Accepted: 08/27/2020] [Indexed: 11/11/2022]
Abstract
We report the ground state tunneling splittings (ΔE± ) of a number of axially chiral molecules using the ring-polymer instanton (RPI) method (J. Chem. Phys., 2011, 134, 054109). The list includes isotopomers of hydrogen dichalcogenides H2 X2 (X = O, S, Se, Te, and Po), hydrogen thioperoxide HSOH and dichlorodisulfane S2 Cl2 . Ab initio electronic-structure calculations have been performed on the level of second-order Møller-Plesset perturbation (MP2) theory either with split-valance basis sets or augmented correlation-consistent basis sets on H, O, S, and Cl atoms. Energy-consistent pseudopotential and corresponding triple zeta basis sets of the Stuttgart group are used on Se, Te, and Po atoms. The results are further improved using single point calculations performed at the coupled cluster level with iterative singles and doubles and perturbative triples amplitudes. When available for comparison, our computed values of ΔE± are found to lie within the same order of magnitude as values reported in the literature, although RPI also provides predictions for H2 Po2 and S2 Cl2 , which have not previously been directly calculated. Since RPI is a single-shot method which does not require detailed prior knowledge of the optimal tunneling path, it offers an effective way for estimating the tunneling dynamics of more complex chiral molecules, and especially those with small tunneling splittings.
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Affiliation(s)
- Nityananda Sahu
- Fachbereich Chemie, Theoretische Chemie, Philipps Universität Marburg, Marburg, Germany
| | | | - Robert Berger
- Fachbereich Chemie, Theoretische Chemie, Philipps Universität Marburg, Marburg, Germany
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14
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Méndez E, Laria D. Nuclear quantum effects on the hydrogen bond donor-acceptor exchange in water-water and water-methanol dimers. J Chem Phys 2020; 153:054302. [PMID: 32770908 DOI: 10.1063/5.0016122] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present results from path integral molecular dynamics simulations that describe effects from the explicit incorporation of nuclear quantum fluctuations on the topology of the free energy associated with the geared exchange of hydrogen bonds in the water-water dimer. Compared to the classical treatment, our results reveal important reductions in the free energy barriers and changes at a qualitative level in the overall profile. Most notable are those manifested by a plateau behavior, ascribed to nuclear tunneling, which bridges reactant and product states, contrasting with the usual symmetric double-well profile. The characteristics of the proton localizations along the pathway are examined. An imaginary time analysis of the rotational degrees of freedom of the partners in the dimer at the vicinities of transition states shows a clear "anticorrelation" between intermolecular interactions coupling beads localized in connective and dangling basins of attractions. As such, the transfer is operated by gradual concerted inter-basin migrations in opposite directions, at practically no energy costs. Modifications operated by partial deuteration and by the asymmetries in the hydrogen bonding characteristics prevailing in water-methanol heterodimers are also examined.
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Affiliation(s)
- Emilio Méndez
- Departamento de Química Inorgánica Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428 Buenos Aires, Argentina
| | - Daniel Laria
- Departamento de Química Inorgánica Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428 Buenos Aires, Argentina
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15
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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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16
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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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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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18
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Vaillant CL, Wales DJ, Althorpe SC. Tunneling Splittings in Water Clusters from Path Integral Molecular Dynamics. J Phys Chem Lett 2019; 10:7300-7304. [PMID: 31682130 DOI: 10.1021/acs.jpclett.9b02951] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We present calculations of tunneling splittings in selected small water clusters, based on a recently developed path integral molecular dynamics (PIMD) method. The ground-rotational-state tunneling motions associated with the largest splittings in the water dimer, trimer, and hexamer are considered, and we show that the PIMD predictions are in very good agreement with benchmark quantum and experimental results. As the tunneling spectra are highly sensitive to both the details of the quantum dynamics and the potential energy surface, our calculations are a validation of the MB-Pol surface as well as the accuracy of PIMD. The favorable scaling of PIMD with system size paves the way for calculations of tunneling splittings in large, nonrigid molecular systems with motions that cannot be treated accurately by other methods, such as the semiclassical instanton.
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Affiliation(s)
- C L Vaillant
- Laboratory of Theoretical Physical Chemistry , Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL) , CH-1015 Lausanne , Switzerland
| | - D J Wales
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , United Kingdom
| | - S C Althorpe
- Department of Chemistry , University of Cambridge , Lensfield Road , Cambridge CB2 1EW , United Kingdom
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19
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Lee VGM, McCoy AB. An Efficient Approach for Studies of Water Clusters Using Diffusion Monte Carlo. J Phys Chem A 2019; 123:8063-8070. [DOI: 10.1021/acs.jpca.9b06444] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Affiliation(s)
- Victor G. M. Lee
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Anne B. McCoy
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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20
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Vaillant CL, Wales DJ, Althorpe SC. Tunneling splittings from path-integral molecular dynamics using a Langevin thermostat. J Chem Phys 2018; 148:234102. [DOI: 10.1063/1.5029258] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- C. L. Vaillant
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - D. J. Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - S. C. Althorpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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21
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Wang XG, Carrington T. Using monomer vibrational wavefunctions to compute numerically exact (12D) rovibrational levels of water dimer. J Chem Phys 2018; 148:074108. [DOI: 10.1063/1.5020426] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xiao-Gang Wang
- 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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22
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Kawatsu T, Tachikawa M. Quantum fluctuations of a fullerene cage modulate its internal magnetic environment. Phys Chem Chem Phys 2018; 20:1673-1684. [PMID: 29264598 DOI: 10.1039/c7cp06401b] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Abstract
To investigate the effect of quantum fluctuations on the magnetic environment inside a C60 fullerene cage, we have calculated the nuclear magnetic shielding constant of protons in H2@C60 and HD@C60 systems by on-the-fly ab initio path integral simulation, including both thermal and nuclear quantum effects. The most dominant upfield from an isolated hydrogen molecule occurs due to the diamagnetic current of the C60 cage, which is partly cancelled by the paramagnetic current, where the paramagnetic contribution is enlarged by the zero-point vibrational fluctuation of the C60 carbon backbone structure via a widely distributed HOMO-LUMO gap. This quantum modulation mechanism of the nuclear magnetic shielding constant is newly proposed. Because this quantum effect is independent of the difference between H2 and HD, the H2/HD isotope shift occurs in spite of the C60 cage. The nuclear magnetic constants computed for H2@C60 and HD@C60 are 32.047 and 32.081 ppm, respectively, which are in reasonable agreement with the corresponding values of 32.19 and 32.23 ppm estimated from the experimental values of the chemical shifts.
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Affiliation(s)
- Tsutomu Kawatsu
- Graduate School of Nanobioscience, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236-0027, Japan.
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Vaillant CL, Cvitaš MT. Rotation-tunneling spectrum of the water dimer from instanton theory. Phys Chem Chem Phys 2018; 20:26809-26813. [DOI: 10.1039/c8cp04991b] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A linearly-scaling path-integral method is developed to calculate rotation-tunneling spectra, and is applied to the water dimer.
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Affiliation(s)
| | - Marko T. Cvitaš
- Department of Physical Chemistry, Ruđer Bošković Institute
- 10000 Zagreb
- Croatia
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24
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Karandashev K, Xu ZH, Meuwly M, Vaníček J, Richardson JO. Kinetic isotope effects and how to describe them. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2017; 4:061501. [PMID: 29282447 PMCID: PMC5729036 DOI: 10.1063/1.4996339] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2017] [Accepted: 08/23/2017] [Indexed: 06/01/2023]
Abstract
We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.
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Affiliation(s)
- Konstantin Karandashev
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Zhen-Hao Xu
- 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
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jeremy O Richardson
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, Eidgenössische Technische Hochschule Zürich (ETHZ), CH-8093 Zürich, Switzerland
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25
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Richardson JO, Pérez C, Lobsiger S, Reid AA, Temelso B, Shields GC, Kisiel Z, Wales DJ, Pate BH, Althorpe SC. Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism. Science 2016; 351:1310-3. [PMID: 26989250 DOI: 10.1126/science.aae0012] [Citation(s) in RCA: 201] [Impact Index Per Article: 25.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
The nature of the intermolecular forces between water molecules is the same in small hydrogen-bonded clusters as in the bulk. The rotational spectra of the clusters therefore give insight into the intermolecular forces present in liquid water and ice. The water hexamer is the smallest water cluster to support low-energy structures with branched three-dimensional hydrogen-bond networks, rather than cyclic two-dimensional topologies. Here we report measurements of splitting patterns in rotational transitions of the water hexamer prism, and we used quantum simulations to show that they result from geared and antigeared rotations of a pair of water molecules. Unlike previously reported tunneling motions in water clusters, the geared motion involves the concerted breaking of two hydrogen bonds. Similar types of motion may be feasible in interfacial and confined water.
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Affiliation(s)
- Jeremy O Richardson
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK. Department of Chemistry, Durham University, South Road Durham DH1 3LE, UK
| | - Cristóbal Pérez
- Department of Chemistry, University of Virginia, McCormick Road, Charlottesville, VA 22903, USA
| | - Simon Lobsiger
- Department of Chemistry, University of Virginia, McCormick Road, Charlottesville, VA 22903, USA
| | - Adam A Reid
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | - Berhane Temelso
- Dean's Office, College of Arts and Sciences, and Department of Chemistry, Bucknell University, Lewisburg, PA 17837, USA
| | - George C Shields
- Dean's Office, College of Arts and Sciences, and Department of Chemistry, Bucknell University, Lewisburg, PA 17837, USA
| | - Zbigniew Kisiel
- Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
| | - Brooks H Pate
- Department of Chemistry, University of Virginia, McCormick Road, Charlottesville, VA 22903, USA
| | - Stuart C Althorpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, UK
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26
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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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27
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Ng YH, Bettens RPA. Comparing Vibrationally Averaged Nuclear Shielding Constants by Quantum Diffusion Monte Carlo and Second-Order Perturbation Theory. J Phys Chem A 2016; 120:1297-306. [PMID: 26835785 DOI: 10.1021/acs.jpca.6b00036] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Using the method of modified Shepard's interpolation to construct potential energy surfaces of the H2O, O3, and HCOOH molecules, we compute vibrationally averaged isotropic nuclear shielding constants ⟨σ⟩ of the three molecules via quantum diffusion Monte Carlo (QDMC). The QDMC results are compared to that of second-order perturbation theory (PT), to see if second-order PT is adequate for obtaining accurate values of nuclear shielding constants of molecules with large amplitude motions. ⟨σ⟩ computed by the two approaches differ for the hydrogens and carbonyl oxygen of HCOOH, suggesting that for certain molecules such as HCOOH where big displacements away from equilibrium happen (internal OH rotation), ⟨σ⟩ of experimental quality may only be obtainable with the use of more sophisticated and accurate methods, such as quantum diffusion Monte Carlo. The approach of modified Shepard's interpolation is also extended to construct shielding constants σ surfaces of the three molecules. By using a σ surface with the equilibrium geometry as a single data point to compute isotropic nuclear shielding constants for each descendant in the QDMC ensemble representing the ground state wave function, we reproduce the results obtained through ab initio computed σ to within statistical noise. Development of such an approach could thereby alleviate the need for any future costly ab initio σ calculations.
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Affiliation(s)
- Yee-Hong Ng
- Department of Chemistry, National University of Singapore , 3 Science Drive 3, 117543 Singapore
| | - Ryan P A Bettens
- Department of Chemistry, National University of Singapore , 3 Science Drive 3, 117543 Singapore
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28
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Videla PE, Rossky PJ, Laria D. Communication: Isotopic effects on tunneling motions in the water trimer. J Chem Phys 2016; 144:061101. [DOI: 10.1063/1.4941701] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Pablo E. Videla
- Departamento de Química Inorgánica Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428 Buenos Aires, Argentina
| | - Peter J. Rossky
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
| | - D. Laria
- Departamento de Química Inorgánica Analítica y Química-Física e INQUIMAE, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón II, 1428 Buenos Aires, Argentina
- Departamento de Física de la Materia Condensada, Comisión Nacional de Energía Atómica, Avenida Libertador 8250, 1429 Buenos Aires, Argentina
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29
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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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30
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Koman VB, Santschi C, von Moos NR, Slaveykova VI, Martin OJ. Portable oxidative stress sensor: Dynamic and non-invasive measurements of extracellular H 2 O 2 released by algae. Biosens Bioelectron 2015; 68:245-252. [DOI: 10.1016/j.bios.2014.12.044] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2014] [Revised: 12/17/2014] [Accepted: 12/20/2014] [Indexed: 01/12/2023]
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31
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On the fly nodal searches in importance sampled fixed-node diffusion Monte Carlo using a parallel, fine-grained, genetic algorithm. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2014.11.054] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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32
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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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Petit AS, Ford JE, McCoy AB. Simultaneous Evaluation of Multiple Rotationally Excited States of H3+, H3O+, and CH5+ Using Diffusion Monte Carlo. J Phys Chem A 2013; 118:7206-20. [DOI: 10.1021/jp408821a] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Andrew S. Petit
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Jason E. Ford
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
| | - Anne B. McCoy
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United States
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34
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Affiliation(s)
- Andrew S. Petit
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United
States
| | - Anne B. McCoy
- Department of Chemistry and Biochemistry, The Ohio State University, Columbus, Ohio 43210, United
States
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Fujita T, Tanaka S, Fujiwara T, Kusa MA, Mochizuki Y, Shiga M. Ab initio path integral Monte Carlo simulations for water trimer with electron correlation effects. COMPUT THEOR CHEM 2012. [DOI: 10.1016/j.comptc.2012.07.029] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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Ramilowski JA, Farrelly D. Fixed node diffusion Monte Carlo using a genetic algorithm: a study of the CO-(4)He(N) complex, N = 1…10. Phys Chem Chem Phys 2012; 14:8123-36. [PMID: 22538980 DOI: 10.1039/c2cp40541e] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The diffusion Monte Carlo (DMC) method is a widely used algorithm for computing both ground and excited states of many-particle systems; for states without nodes the algorithm is numerically exact. In the presence of nodes approximations must be introduced, for example, the fixed-node approximation. Recently we have developed a genetic algorithm (GA) based approach which allows the computation of nodal surfaces on-the-fly [Ramilowski and Farrelly, Phys. Chem. Chem. Phys., 2010, 12, 12450]. Here GA-DMC is applied to the computation of rovibrational states of CO-(4)He(N) complexes with N≤ 10. These complexes have been the subject of recent high resolution microwave and millimeter-wave studies which traced the onset of microscopic superfluidity in a doped (4)He droplet, one atom at a time, up to N = 10 [Surin et al., Phys. Rev. Lett., 2008, 101, 233401; Raston et al., Phys. Chem. Chem. Phys., 2010, 12, 8260]. The frequencies of the a-type (microwave) series, which correlate with end-over-end rotation in the CO-(4)He dimer, decrease from N = 1 to 3 and then smoothly increase. This signifies the transition from a molecular complex to a quantum solvated system. The frequencies of the b-type (millimeter-wave) series, which evolves from free rotation of the rigid CO molecule, initially increase from N = 0 to N∼ 6 before starting to decrease with increasing N. An interesting feature of the b-type series, originally observed in the high resolution infra-red (IR) experiments of Tang and McKellar [J. Chem. Phys., 2003, 119, 754] is that, for N = 7, two lines are observed. The GA-DMC algorithm is found to be in good agreement with experimental results and possibly detects the small (∼0.7 cm(-1)) splitting in the b-series line at N = 7. Advantages and disadvantages of GA-DMC are discussed.
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Affiliation(s)
- Jordan A Ramilowski
- Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322-0300, USA
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37
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Richardson JO, Althorpe SC, Wales DJ. Instanton calculations of tunneling splittings for water dimer and trimer. J Chem Phys 2011; 135:124109. [DOI: 10.1063/1.3640429] [Citation(s) in RCA: 72] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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38
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Richardson JO, Althorpe SC. Ring-polymer instanton method for calculating tunneling splittings. J Chem Phys 2011; 134:054109. [DOI: 10.1063/1.3530589] [Citation(s) in RCA: 86] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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39
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40
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Ramilowski JA, Farrelly D. Computation of nodal surfaces in fixed-node diffusion Monte Carlo calculations using a genetic algorithm. Phys Chem Chem Phys 2010; 12:12450-6. [DOI: 10.1039/c0cp00373e] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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41
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Takayanagi T, Yoshikawa T, Motegi H, Shiga M. Path-integral molecular dynamics simulations for water anion clusters (H2O)5- and (D2O)5-. Chem Phys Lett 2009. [DOI: 10.1016/j.cplett.2009.09.107] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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42
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Pathak AK, Mukherjee T, Maity DK. Theoretical studies on photoelectron and IR spectral properties of Br2∙−(H2O)n clusters. J Chem Phys 2007; 127:044304. [PMID: 17672687 DOI: 10.1063/1.2756535] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
We report vertical detachment energy (VDE) and IR spectra of Br2.-.(H2O)n clusters (n=1-8) based on first principles electronic structure calculations. Cluster structures and IR spectra are calculated at Becke's half-and-half hybrid exchange-correlation functional (BHHLYP) with a triple split valence basis function, 6-311++G(d,p). VDE for the hydrated clusters is calculated based on second order Moller-Plesset perturbation (MP2) theory with the same set of basis function. On full geometry optimization, it is observed that conformers having interwater hydrogen bonding among solvent water molecules are more stable than the structures having double or single hydrogen bonded structures between the anionic solute, Br2.-, and solvent water molecules. Moreover, a conformer having cyclic interwater hydrogen bonded network is predicted to be more stable for each size hydrated cluster. It is also noticed that up to four solvent H2O units can reside around the solute in a cyclic interwater hydrogen bonded network. The excess electron in these hydrated clusters is localized over the solute atoms. Weighted average VDE is calculated for each size (n) cluster based on statistical population of the conformers at 150 K. A linear relationship is obtained for VDE versus (n+3)(-1/3) and bulk VDE of Br2.- aqueous solution is calculated as 10.01 eV at MP2 level of theory. BHHLYP density functional is seen to make a systematic overestimation in VDE values by approximately 0.5 eV compared to MP2 data in all the hydrated clusters. It is observed that hydration increases VDE of bromine dimer anion system by approximately 6.4 eV. Calculated IR spectra show that the formation of Br2.--water clusters induces large shifts from the normal O-H stretching bands of isolated water keeping bending modes rather insensitive. Hydrated clusters, Br2.-.(H2O)n, show characteristic sharp features of O-H stretching bands of water in the small size clusters.
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Affiliation(s)
- A K Pathak
- Radiation and Photochemistry Division, Chemistry Group, Bhabha Atomic Research Centre, Mumbai 400085, India
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43
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Mikosz AA, Ramilowski JA, Farrelly D. Quantum solvation dynamics of HCN in a helium-4 droplet. J Chem Phys 2006; 125:014312. [PMID: 16863303 DOI: 10.1063/1.2213253] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Ultracold nanodroplets of helium-4, containing several thousands of He atoms, offer considerable promise as microscopic cryogenic chambers. Potential applications include the creation of tailor-made chemical or biomolecular complexes and studies of superfluidity in nanoscale systems. Recent experiments have succeeded in interrogating droplets of quantum solvent which consist of as few as 1-20 helium-4 atoms and which contain a single solute molecule. This allows the transition from a floppy, but essentially molecular, complex to a dissolved molecule to be followed and, surprisingly, the transition is found to occur quite rapidly, in some cases for as few as N = 7-20 solvent atoms. For example, in experiments on helium-4 droplets seeded with CO molecules [Tang and McKellar, J. Chem. Phys. 119, 754 (2003)], two series of transitions are observed which correlate with the a-type (Delta K = 0) and b-type (Delta K = +/-1) lines of the binary complex, CO-He (K is the quantum number associated with the projection of the total angular momentum onto the vector connecting the atom and the molecular center of mass). The a-type series, which evolves from the end-over-end rotational motion of the CO-He binary complex, saturates to the nanodroplet limit for as few as 10-15 helium-4 atoms, i.e., the effective moment of inertia of the molecule converges to its asymptotic (solvated) value quite rapidly. In contrast, the b-type series, which evolves from the free-molecule rotational mode, disappears altogether for N approximately 7 atoms. Similar behavior is observed in recent computational studies of HCN(4He)N droplets [Paolini et al., J. Chem. Phys. 123, 114306 (2005)]. In this article the quantum solvation of HCN in small helium-4 droplets is studied using a new fixed-node diffusion Monte Carlo (DMC) procedure. In this approach a Born-Oppenheimer-type separation of radial and angular motions is introduced as a means of computing nodal surfaces of the many-body wave functions which are required in the fixed-node DMC method. Excited rotational energies are calculated for HCN(4He)N droplets with N = 1-20: the adiabatic node approach also allows concrete physical mechanisms to be proposed for the predicted disappearance of the b-type series as well as the rapid convergence of the a-type series to the nanodroplet limit with increasing N. The behavior of the a-type series is traced directly to the mechanics of angular momentum coupling-and decoupling-between identical bosons and the molecular rotor. For very small values of N there exists significant angular momentum coupling between the molecule and the helium atoms: at N approximately 10 solvation appears to be complete as evidenced by significant decoupling of the molecule and solvent angular momenta. The vanishing of the b-type series is predicted to be a result of increasing He-He repulsion as the number of solvent atoms increases.
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Affiliation(s)
- Aleksandra A Mikosz
- Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300, USA
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An approach based on genetic algorithms and DFT for studying clusters: (H2O)n (2⩽n⩽13) cluster analysis. Chem Phys 2006. [DOI: 10.1016/j.chemphys.2005.10.034] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Hobza P, Zahradník R, Müller-Dethlefs K. The World of Non-Covalent Interactions: 2006. ACTA ACUST UNITED AC 2006. [DOI: 10.1135/cccc20060443] [Citation(s) in RCA: 166] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
The review focusses on the fundamental importance of non-covalent interactions in nature by illustrating specific examples from chemistry, physics and the biosciences. Laser spectroscopic methods and both ab initio and molecular modelling procedures used for the study of non-covalent interactions in molecular clusters are briefly outlined. The role of structure and geometry, stabilization energy, potential and free energy surfaces for molecular clusters is extensively discussed in the light of the most advanced ab initio computational results for the CCSD(T) method, extrapolated to the CBS limit. The most important types of non-covalent complexes are classified and several small and medium size non-covalent systems, including H-bonded and improper H-bonded complexes, nucleic acid base pairs, and peptides and proteins are discussed with some detail. Finally, we evaluate the interpretation of experimental results in comparison with state of the art theoretical models: this is illustrated for phenol...Ar, the benzene dimer and nucleic acid base pairs. A review with 270 references.
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Jiang H, Sarsa A, Murdachaew G, Szalewicz K, Bacić Z. (HCl)2 and (HF)2 in small helium clusters: Quantum solvation of hydrogen-bonded dimers. J Chem Phys 2005; 123:224313. [PMID: 16375482 DOI: 10.1063/1.2136358] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a rigorous theoretical study of the solvation of (HCl)(2) and (HF)(2) by small ((4)He)(n) clusters, with n=1-14 and 30. Pairwise-additive potential-energy surfaces of He(n)(HX)(2) (X=Cl and F) clusters are constructed from highly accurate four-dimensional (rigid monomer) HX-HX and two-dimensional (rigid monomer) He-HX potentials and a one-dimensional He-He potential. The minimum-energy geometries of these clusters, for n=1-6 in the case of (HCl)(2) and n=1-5 for (HF)(2), correspond to the He atoms in a ring perpendicular to and bisecting the HX-HX axis. The quantum-mechanical ground-state energies and vibrationally averaged structures of He(n)(HCl)(2) (n=1-14 and 30) and He(n)(HF)(2) (n=1-10) clusters are calculated exactly using the diffusion Monte Carlo (DMC) method. In addition, the interchange-tunneling splittings of He(n)(HCl)(2) clusters with n=1-14 are determined using the fixed-node DMC approach, which was employed by us previously to calculate the tunneling splittings for He(n)(HF)(2) clusters, n=1-10 [A. Sarsa et al., Phys. Rev. Lett. 88, 123401 (2002)]. The vibrationally averaged structures of He(n)(HX)(2) clusters with n=1-6 for (HCl)(2) and n=1-5 for (HF)(2) have the helium density localized in an effectively one-dimensional ring, or doughnut, perpendicular to and at the midpoint of the HX-HX axis. The rigidity of the solvent ring varies with n and reaches its maximum for the cluster size at which the ring is filled, n=6 and n=5 for (HCl)(2) and (HF)(2), respectively. Once the equatorial ring is full, the helium density spreads along the HX-HX axis, eventually solvating the entire HX dimer. The interchange-tunneling splitting of He(n)(HCl)(2) clusters hardly varies at all over the cluster size range considered, n=1-14, and is virtually identical to that of the free HCl dimer. This absence of the solvent effect is in sharp contrast with our earlier results for He(n)(HF)(2) clusters, which show a approximately 30% reduction of the tunneling splitting for n=4. A tentative explanation for this difference is proposed. The implications of our results for the interchange-tunneling dynamics of (HCl)(2) in helium nanodroplets are discussed.
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Affiliation(s)
- Hao Jiang
- Department of Chemistry, New York University, New York, NY 10003, USA
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Kim Y, Kim Y. Dynamics of the Concerted Triple Proton Transfer in Cyclic Water Trimer Using the Multiconfiguration Molecular Mechanics Algorithm. J Phys Chem A 2005; 110:600-8. [PMID: 16405332 DOI: 10.1021/jp0530193] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
Cyclic water clusters are important molecular species to understand the nature of hydrogen bonded networks. Theoretical studies for the dynamics of triple proton transfer in the cyclic water trimer were performed. The potential energy surface (PES) of triple proton transfer is generated by the multiconfiguration molecular mechanics (MCMM) algorithm. We have used the MP2/6-31G(d,p) level for high-level ab initio data (energies, gradients, and Hessians), which are used in the Shepard interpolation. Eight high-level reference points were added step by step, including two points for the critical configurations of the large curvature tunneling paths. The more high-level points are used, the better the potential energy surfaces become. The rate constant and kinetic isotope effect (KIE) for the triple proton transfer at 300 K, which have been calculated by the canonical variational transition-state theory with microcanonical optimized multidimensional semiclassical tunneling approximation, are 1.6 x 10(-3) s(-1) and 230, respectively. Tunneling is very important not only for the triple proton transfer but also for the triple deuterium transfer. The MCMM results show good agreement with those from the direct ab initio dynamics calculations.
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Affiliation(s)
- Yangsoo Kim
- Department of Chemistry, Kyung Hee University, Yong-In City, Kyunggi-Do, 449-701, Korea
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Takahashi M, Watanabe Y, Taketsugu T, Wales DJ. An ab initio study of tunneling splittings in the water trimer. J Chem Phys 2005; 123:044302. [PMID: 16095353 DOI: 10.1063/1.1954768] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Tunneling splittings in the water trimer have been determined by the semiclassical WKB method, based on pathways characterized at the computational level of second-order Møller-Plesset theory with basis sets of aug-cc-pVTZ quality. This calculation takes into account the single-flip and bifurcation tunneling rearrangements of the water trimer. The predicted splittings are 37.93 cm(-1) for the flip and 6.50x10(-3) cm(-1) for bifurcation, which agree quite well with the corresponding experimental values of 43.52 cm(-1) and 9.63x10(-3) cm(-1).
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Affiliation(s)
- Mariko Takahashi
- Department of Chemistry, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan
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Goldman N, Leforestier C, Saykally RJ. A 'first principles' potential energy surface for liquid water from VRT spectroscopy of water clusters. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2005; 363:493-508. [PMID: 15664895 DOI: 10.1098/rsta.2004.1504] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We present results of gas phase cluster and liquid water simulations from the recently determined VRT(ASP-W)III water dimer potential energy surface (the third fitting of the Anisotropic Site Potential with Woermer dispersion to vibration-rotation-tunnelling data). VRT(ASP-W)III is shown to not only be a model of high 'spectroscopic' accuracy for the water dimer, but also makes accurate predictions of vibrational ground-state properties for clusters up through the hexamer. Results of ambient liquid water simulations from VRT(ASP-W)III are compared with those from ab initio molecular dynamics, other potentials of 'spectroscopic' accuracy and with experiment. The results herein represent the first time to the authors' knowledge that a 'spectroscopic' potential surface is able to correctly model condensed phase properties of water.
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Affiliation(s)
- Nir Goldman
- Lawrence Livermore National Laboratory, Chemistry and Materials Science Directorate, L-268, Livermore, CA 94551, USA
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Crittenden DL, Thompson KC, Chebib M, Jordan MJT. Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo. J Chem Phys 2004; 121:9844-54. [PMID: 15549857 DOI: 10.1063/1.1756580] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A modified Shepard interpolation scheme is used to construct global potential energy surfaces (PES) in order to calculate quantum observables--vibrationally averaged internal coordinates, fully anharmonic zero-point energies and nuclear radial distribution functions--for a prototypical loosely bound molecular system, the water dimer. The efficiency of PES construction is examined with respect to (a) the method used to sample configurational space, (b) the method used to choose which points to add to the PES data set, and (c) the use of either a one- or two-part weight function. The most efficient method for constructing the PES is found to require a quantum sampling regime, a combination of both h-weight and rms methods for choosing data points and use of the two-part weight function in the interpolation. Using this regime, the quantum diffusion Monte Carlo zero-point energy converges to the exact result within addition of 50 data points. The vibrationally averaged O-O distance and O-O radial distribution function, however, converge more slowly and require addition of over 500 data points. The methods presented here are expected to be applicable to both other loosely bound complexes as well as tightly bound molecular species. When combined with high quality ab initio calculations, these methods should be able to accurately characterize the PES of such species.
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