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Schmidt M, Roy PN. On the accuracy and efficiency of different methods to calculate Raman vibrational shifts of parahydrogen clusters. J Chem Phys 2022; 156:084102. [DOI: 10.1063/5.0076403] [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
The Raman vibrational frequency shifts of pure parahydrogen and orthodeuterium clusters of sizes N = 4–9 are calculated using the Langevin equation path integral ground state method. The shifts are calculated using three different methods; the results obtained from each are compared to experiment and variance properties are assessed. The first method requires the direct calculation of energies from two simulations: one when the cluster is in the v = 0 vibrational state and one when the cluster has v = 1 total quantum of vibration. The shift is directly calculated from the difference in those two energies. The second method requires only a v = 0 simulation to be performed. The ground state energy is calculated as usual and the excited state energy is calculated by using the distribution of the v = 0 simulation and the ratio of the density matrices between the v = 1 state and the v = 0 state. The shift is calculated from the difference in those two energies. These first two are both exact methods. The final method is based on perturbation theory where the shift is calculated by averaging the pairwise difference potential over the pair distribution function. However, this is an approximate approach. It is found that for large enough system sizes, despite the approximations, the perturbation theory method has the strongest balance between accuracy and precision when weighing against computational cost.
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Affiliation(s)
- Matthew Schmidt
- 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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Schmidt M, Roy PN. Ground state chemical potential of parahydrogen clusters of size N = 21-40. J Chem Phys 2022; 156:016101. [PMID: 34998339 DOI: 10.1063/5.0076389] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We report the ground state chemical potential of parahydrogen clusters between N = 21-40 calculated using the Langevin equation Path Integral Ground State method. There has been much debate in the past whether the chemical potential size evolution in this region is jagged (indicating magic number cluster sizes) or if it is smooth (indicating some quantum melting below 1 K). We compare to previous diffusion Monte Carlo and Path Integral Ground State (PIGS) results, including very recent Variational Path Integral Molecular Dynamics (VPIMD) calculations [S. Miura, J. Chem. Phys. 148, 102333 (2018)]. We find that the ground state chemical potential is not a smooth curve and that magic number clusters are present, consistent with VPIMD and PIGS Monte Carlo results.
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Affiliation(s)
- Matthew Schmidt
- 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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Schmidt M, Millar J, Roy PN. Path integral simulations of confined parahydrogen molecules within clathrate hydrates: Merging low temperature dynamics with the zero-temperature limit. J Chem Phys 2022; 156:014303. [PMID: 34998330 DOI: 10.1063/5.0076386] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Clathrate hydrates, or cages comprised solely of water molecules, have long been investigated as a clean storage facility for hydrogen molecules. A breakthrough occurred when hydrogen molecules were experimentally placed within a structure-II clathrate hydrate, which sparked much interest to determine their feasibility for energy storage [Mao et al., Science 297, 2247-2249 (2002)]. We use Path Integral Molecular Dynamics (PIMD) and Langevin equation Path Integral Ground State (LePIGS) for finite temperature and zero-temperature studies, respectively, to determine parahydrogen occupancy properties in the small dodecahedral (512) and large hexakaidecahedral (51264) sized cages that comprise the structure-II unit cell. We look at energetic and structural properties of small clusters of hydrogen, treated as point-like particles, confined within each of the different sized clathrates, and treated as rigid, to determine energetic and structural properties in the zero-temperature limit. Our predicted hydrogen occupancy within these two cage sizes is consistent with previous literature values. We then calculate the energies as a function of temperature and merge the low temperature results calculated using finite temperature PIMD with the zero-temperature results using LePIGS, demonstrating that the two methods are compatible.
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Affiliation(s)
- Matthew Schmidt
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Jayme Millar
- 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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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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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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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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Schmidt M, Roy PN. Path integral molecular dynamic simulation of flexible molecular systems in their ground state: Application to the water dimer. J Chem Phys 2018; 148:124116. [DOI: 10.1063/1.5017532] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matthew Schmidt
- 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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Bishop KP, Roy PN. Quantum mechanical free energy profiles with post-quantization restraints: Binding free energy of the water dimer over a broad range of temperatures. J Chem Phys 2018; 148:102303. [DOI: 10.1063/1.4986915] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kevin P. Bishop
- 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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Kamibayashi Y, Miura S. Variational path integral molecular dynamics and hybrid Monte Carlo algorithms using a fourth order propagator with applications to molecular systems. J Chem Phys 2016; 145:074114. [DOI: 10.1063/1.4961149] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Affiliation(s)
- Yuki Kamibayashi
- Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
| | - Shinichi Miura
- Graduate School of Natural Science and Technology, Kanazawa University, Kakuma, Kanazawa 920-1192, Japan
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Schmidt M, Fernández JM, Faruk N, Nooijen M, Le Roy RJ, Morilla JH, Tejeda G, Montero S, Roy PN. Raman Vibrational Shifts of Small Clusters of Hydrogen Isotopologues. J Phys Chem A 2015; 119:12551-61. [DOI: 10.1021/acs.jpca.5b08852] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Matthew Schmidt
- Department
of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - José M. Fernández
- Laboratory
of Molecular Fluid Dynamics, Instituto de Estructura de la Materia, CSIC, Serrano 121, E-28006 Madrid, Spain
| | - Nabil Faruk
- Department
of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Marcel Nooijen
- Department
of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Robert J. Le Roy
- Department
of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Juan H. Morilla
- Laboratory
of Molecular Fluid Dynamics, Instituto de Estructura de la Materia, CSIC, Serrano 121, E-28006 Madrid, Spain
| | - Guzmán Tejeda
- Laboratory
of Molecular Fluid Dynamics, Instituto de Estructura de la Materia, CSIC, Serrano 121, E-28006 Madrid, Spain
| | - Salvador Montero
- Laboratory
of Molecular Fluid Dynamics, Instituto de Estructura de la Materia, CSIC, Serrano 121, E-28006 Madrid, Spain
| | - Pierre-Nicholas Roy
- Department
of Chemistry, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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Faruk N, Schmidt M, Li H, Le Roy RJ, Roy PN. First-principles prediction of the Raman shifts in parahydrogen clusters. J Chem Phys 2014; 141:014310. [DOI: 10.1063/1.4885275] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nabil Faruk
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Matthew Schmidt
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Hui Li
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
- Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin University, 2519 Jiefang Road, Changchun 130023, People's Republic of China
| | - Robert J. Le Roy
- 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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Schmidt M, Constable S, Ing C, Roy PN. Inclusion of trial functions in the Langevin equation path integral ground state method: Application to parahydrogen clusters and their isotopologues. J Chem Phys 2014; 140:234101. [DOI: 10.1063/1.4882184] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Zeng T, Roy PN. Microscopic molecular superfluid response: theory and simulations. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:046601. [PMID: 24647079 DOI: 10.1088/0034-4885/77/4/046601] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
Since its discovery in 1938, superfluidity has been the subject of much investigation because it provides a unique example of a macroscopic manifestation of quantum mechanics. About 60 years later, scientists successfully observed this phenomenon in the microscopic world though the spectroscopic Andronikashvili experiment in helium nano-droplets. This reduction of scale suggests that not only helium but also para-H2 (pH2) can be a candidate for superfluidity. This expectation is based on the fact that the smaller number of neighbours and surface effects of a finite-size cluster may hinder solidification and promote a liquid-like phase. The first prediction of superfluidity in pH2 clusters was reported in 1991 based on quantum Monte Carlo simulations. The possible superfluidity of pH2 was later indirectly observed in a spectroscopic Andronikashvili experiment in 2000. Since then, a growing number of studies have appeared, and theoretical simulations have been playing a special role because they help guide and interpret experiments. In this review, we go over the theoretical studies of pH2 superfluid clusters since the experiment of 2000. We provide a historical perspective and introduce the basic theoretical formalism along with key experimental advances. We then present illustrative results of the theoretical studies and comment on the possible future developments in the field. We include sufficient theoretical details such that the review can serve as a guide for newcomers to the field.
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Affiliation(s)
- Tao Zeng
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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