1
|
Lauvergnat D, Nauts A. Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality. Chemphyschem 2023; 24:e202300501. [PMID: 37555577 DOI: 10.1002/cphc.202300501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Revised: 08/08/2023] [Accepted: 08/09/2023] [Indexed: 08/10/2023]
Abstract
In 1963 Smolyak introduced an approach to overcome the exponential scaling with respect to the number of variables of the direct product size [S. A. Smolyak Soviet Mathematics Doklady, 4, 240 (1963)]. The main idea is to replace a single large direct product by a sum of selected small direct products. It was first used in quantum dynamics in 2009 by Avila and Carrington [G. Avila and T. Carrington, J. Chem. Phys., 131, 174103 (2009)]. Since then, several calculations have been published by Avila and Carrington and by other groups. In the present study, and to push the limit to larger and more complex systems, this scheme is combined with the use of an on-the-fly calculation of the kinetic energy operator and a Block-Davidson procedure to obtain eigenstates in our home-made Fortran codes, ElVibRot and Tnum-Tana. This was applied to compute the tunneling splitting of malonaldehyde in full dimensionality (21D) using the potential of Mizukami et al. [W. Mizukami, S. Habershon, and D.P. Tew, J. Chem. Phys. 141, 1443-10 (2014)]. Our tunneling splitting calculations, 21.7±0.3 cm-1 and 2.9±0.1 cm-1 , show excellent agreement with the experimental values, 21.6 cm-1 and 2.9 cm-1 for the normal isotopologue and the mono-deuterated one, respectively.
Collapse
Affiliation(s)
- David Lauvergnat
- Institut de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
| | - André Nauts
- Institut de Chimie Physique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405, Orsay, France
- Institute of Condensed Matter and Nanosciences (NAPS), Université Catholique de Louvain, 2 Chemin du Cyclotron, 1348, Louvain-la-Neuve, Belgium
| |
Collapse
|
2
|
Yanes-Rodríguez R, Prosmiti R. Computational investigations of stable multiple-cage-occupancy He clathrate-like hydrostructures. Phys Chem Chem Phys 2023. [PMID: 37314248 DOI: 10.1039/d3cp00603d] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
One of the several possibilities offered by the interesting clathrate hydrates is the opportunity to encapsulate several atoms or molecules, in such a way that more efficient storage materials could be explored or new molecules that otherwise do not exist could be created. These types of applications are receiving growing attention from technologists and chemists, given the future positive implications that they entail. In this context, we investigated the multiple cage occupancy of helium clathrate hydrates, to establish stable novel hydrate structures or ones similar to those predicted previously by experimental and theoretical studies. To this purpose, we analyzed the feasibility of including an increased number of He atoms inside the small (D) and large (H) cages of the sII structure through first-principles properly assessed density functional approaches. On the one hand, we have computed energetic and structural properties, in which we examined the guest-host and guest-guest interactions in both individual and two-adjacent clathrate-like sII cages by means of binding and evaporation energies. On the other hand, we have carried out a thermodynamical analysis on the stability of such He-containing hydrostructures in terms of changes in enthalpy, ΔH, Gibbs free energy, ΔG, and entropy, ΔS, during their formation process at various temperature and pressure values. In this way, we have been able to make a comparison with experiments, reaffirming the ability of computational DFT approaches to describe such weak guest-host interactions. In principle, the most stable structure involves the encapsulation of one and four He atoms inside the D and H sII cages, respectively; however, more He atoms could be entrapped under lower temperature and/or higher pressure thermodynamic conditions. We foresee such accurate computational quantum chemistry approaches contributing to the current emerging machine-learning model development.
Collapse
Affiliation(s)
- Raquel Yanes-Rodríguez
- Institute of Fundamental Physics (IFF-CSIC), CSIC, Serrano 123, 28006 Madrid, Spain.
- Doctoral Programme in Theoretical Chemistry and Computational Modelling, Doctoral School, Universidad Autónoma de Madrid, Spain
| | - Rita Prosmiti
- Institute of Fundamental Physics (IFF-CSIC), CSIC, Serrano 123, 28006 Madrid, Spain.
| |
Collapse
|
3
|
Chen A, Benoit DM, Scribano Y, Nauts A, Lauvergnat D. Smolyak Algorithm Adapted to a System-Bath Separation: Application to an Encapsulated Molecule with Large-Amplitude Motions. J Chem Theory Comput 2022; 18:4366-4372. [PMID: 35584357 DOI: 10.1021/acs.jctc.2c00108] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A Smolyak algorithm adapted to system-bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system-bath concept in a specific configuration without limitations on the form of the Hamiltonian, thus achieving a highly efficient convergence of the excitation transitions for the "system" part. Our approach provides a general way to overcome the perennial convergence problem for the standard Smolyak algorithm and enables the simulation of floppy molecules with more than a hundred degrees of freedom. The efficiency of the present method is illustrated on the simulation of H2 caged in an sII clathrate hydrate including two kinds of cage modes. The transition energies are converged by increasing the number of normal modes of water molecules. Our results confirm the triplet splittings of both translational and rotational (j = 1) transitions of the H2 molecule. Furthermore, they show a slight increase of the translational transitions with respect to the ones in a rigid cage.
Collapse
Affiliation(s)
- Ahai Chen
- Maison de la Simulation, UVSQ, CNRS, CEA, Université Paris-Saclay, 91191 Gif-sur-Yvette, France.,Institut de Chimie Physique, UMR-CNRS 8000, Université Paris-Saclay, CNRS, 91405 Orsay, France
| | - David M Benoit
- E.A. Milne Centre for Astrophysics, The University of Hull, Cottingham Road, Kingston upon Hull HU6 7RX, U.K
| | - Yohann Scribano
- Laboratoire Univers et Particules de Montpellier, UMR-CNRS 5299, Université de Montpellier, 34095 Montpellier Cedex, France
| | - André Nauts
- Institut de Chimie Physique, UMR-CNRS 8000, Université Paris-Saclay, CNRS, 91405 Orsay, France.,Institute of Condensed Matter and Nanosciences (NAPS), Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
| | - David Lauvergnat
- Institut de Chimie Physique, UMR-CNRS 8000, Université Paris-Saclay, CNRS, 91405 Orsay, France
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
Smolyak representations with absorbing boundary conditions for reaction path Hamiltonian model of reactive scattering. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2021.139241] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
6
|
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.
Collapse
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
| |
Collapse
|
7
|
Felker PM, Lauvergnat D, Scribano Y, Benoit DM, Bačić Z. Intramolecular stretching vibrational states and frequency shifts of (H2)2 confined inside the large cage of clathrate hydrate from an eight-dimensional quantum treatment using small basis sets. J Chem Phys 2019; 151:124311. [DOI: 10.1063/1.5124051] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Peter M. Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA
| | - David Lauvergnat
- Laboratoire de Chimie Physique, UMR-CNRS 8000, Université de Paris-Sud, Orsay F-91405, France
| | - Yohann Scribano
- Laboratoire Univers et Particule de Montpellier, Université de Montpellier, UMR-CNRS 5299, 34095 Montpellier Cedex, France
| | - David M. Benoit
- Department of Physics and Mathematics, E. A. Milne Centre for Astrophysics and G. W. Gray Centre for Advanced Materials, The University of Hull, Cottingham Road, Kingston upon Hull HU6 7RX, United Kingdom
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
| |
Collapse
|
8
|
Lauvergnat D, Felker P, Scribano Y, Benoit DM, Bačić Z. H2, HD, and D2in the small cage of structure II clathrate hydrate: Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates. J Chem Phys 2019; 150:154303. [DOI: 10.1063/1.5090573] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- David Lauvergnat
- Laboratoire de Chimie Physique, UMR-CNRS 8000, Université de Paris-Sud, Orsay F-91405, France
| | - Peter Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA
| | - Yohann Scribano
- Laboratoire Univers et Particules de Montpellier, Université de Montpellier, UMR-CNRS 5299, 34095 Montpellier Cedex, France
| | - David M. Benoit
- Department of Physics and Mathematics, E.A. Milne Centre for Astrophysics and G. W. Gray Centre for Advanced Materials, The University of Hull, Cottingham Road, Kingston upon Hull HU6 7RX, United Kingdom
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China
| |
Collapse
|
9
|
Qu C, Bowman JM. Assessing the Importance of the H 2-H 2O-H 2O Three-Body Interaction on the Vibrational Frequency Shift of H 2 in the sII Clathrate Hydrate and Comparison with Experiment. J Phys Chem A 2019; 123:329-335. [PMID: 30525619 DOI: 10.1021/acs.jpca.8b11675] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The vibrational frequency shift of H2 in the 512 cage of the sII clathrate hydrate with and without surrounding water molecules is reported at 0 K, using diffusion Monte Carlo calculations for the ground and first excited vibrational states of H2. Approximate 1d calculations of the frequency shift are also reported with the H2 at the equilibrium position in the clathrate hydrate. These calculations make use of full-dimensional potential energy surfaces for the H2-H2O 2-body and H2-H2O-H2O 3-body interactions. The inclusion of the 3-body interaction is shown to make roughly a 33% contribution to the frequency shift and to bring the calculated value of -40 ± 4 cm-1 to within just 3 cm-1 of the experimental value at 20 K. This level of agreement with experiment may be somewhat fortuitous; however, the importance of the 3-body interaction is firmly established by these calculations. The frequency shift reported here with 2-body interactions does not agree with a previously reported calculation using just 2-body interactions from a different ab initio potential energy surface and with a different method to obtain the frequency shift. A similar 1d calculation of the frequency shift using that potential is reported and agrees to within roughly 10% of the one previously reported. Therefore, this suggests that the difference between the present calculations and the previous one using just 2-body interactions is mainly due to differences in the potential energy surfaces.
Collapse
Affiliation(s)
- Chen Qu
- Cherry L. Emerson Center for Scientifc Computations and Department of Chemistry , Emory University , Atlanta , Georgia 30322 , United States
| | - Joel M Bowman
- Cherry L. Emerson Center for Scientifc Computations and Department of Chemistry , Emory University , Atlanta , Georgia 30322 , United States
| |
Collapse
|