### Abstract

We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H
_{2}
, HD, and D
_{2}
molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 H
_{2}
O molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H
_{2}
in the hydrate domain, based on an ab initio 6D H
_{2}
-H
_{2}
O pair potential for flexible H
_{2}
and rigid H
_{2}
O. They extend to the first excited (v = 1) vibrational state of H
_{2}
, along with two isotopologues, providing a direct computation of vibrational frequency shifts. We show that obtaining a converged v = 1 vibrational state of the caged molecule does not require converging the very large number of intermolecular translation-rotation states belonging to the v = 0 manifold up to the energy of the intramolecular stretch fundamental (≈4100 cm
^{−1}
for H
_{2}
). Only a relatively modest-size basis for the intermolecular degrees of freedom is needed to accurately describe the vibrational averaging over the delocalized wave function of the quantum ground state of the system. For the caged H
_{2}
, our computed fundamental translational excitations, rotational j = 0 → 1 transitions, and frequency shifts of the stretch fundamental are in excellent agreement with recent quantum 5D (rigid H
_{2}
) results [A. Powers et al., J. Chem. Phys. 148, 144304 (2018)]. Our computed frequency shift of −43 cm
^{−1}
for H
_{2}
is only 14% away from the experimental value at 20 K.

Original language | English (US) |
---|---|

Article number | 154303 |

Journal | Journal of Chemical Physics |

Volume | 150 |

Issue number | 15 |

DOIs | |

State | Published - Apr 21 2019 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

_{2}, HD, and D

_{2}in the small cage of structure II clathrate hydrate: Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates.

*Journal of Chemical Physics*,

*150*(15), [154303]. https://doi.org/10.1063/1.5090573

**H
_{2}
, HD, and D
_{2}
in the small cage of structure II clathrate hydrate : Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates.** / Lauvergnat, David; Felker, Peter; Scribano, Yohann; Benoit, David M.; Bacic, Zlatko.

Research output: Contribution to journal › Article

_{2}, HD, and D

_{2}in the small cage of structure II clathrate hydrate: Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates',

*Journal of Chemical Physics*, vol. 150, no. 15, 154303. https://doi.org/10.1063/1.5090573

_{2}, HD, and D

_{2}in the small cage of structure II clathrate hydrate: Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates. Journal of Chemical Physics. 2019 Apr 21;150(15). 154303. https://doi.org/10.1063/1.5090573

}

TY - JOUR

T1 - H 2 , HD, and D 2 in the small cage of structure II clathrate hydrate

T2 - Vibrational frequency shifts from fully coupled quantum six-dimensional calculations of the vibration-translation-rotation eigenstates

AU - Lauvergnat, David

AU - Felker, Peter

AU - Scribano, Yohann

AU - Benoit, David M.

AU - Bacic, Zlatko

PY - 2019/4/21

Y1 - 2019/4/21

N2 - We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H 2 , HD, and D 2 molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 H 2 O molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H 2 in the hydrate domain, based on an ab initio 6D H 2 -H 2 O pair potential for flexible H 2 and rigid H 2 O. They extend to the first excited (v = 1) vibrational state of H 2 , along with two isotopologues, providing a direct computation of vibrational frequency shifts. We show that obtaining a converged v = 1 vibrational state of the caged molecule does not require converging the very large number of intermolecular translation-rotation states belonging to the v = 0 manifold up to the energy of the intramolecular stretch fundamental (≈4100 cm −1 for H 2 ). Only a relatively modest-size basis for the intermolecular degrees of freedom is needed to accurately describe the vibrational averaging over the delocalized wave function of the quantum ground state of the system. For the caged H 2 , our computed fundamental translational excitations, rotational j = 0 → 1 transitions, and frequency shifts of the stretch fundamental are in excellent agreement with recent quantum 5D (rigid H 2 ) results [A. Powers et al., J. Chem. Phys. 148, 144304 (2018)]. Our computed frequency shift of −43 cm −1 for H 2 is only 14% away from the experimental value at 20 K.

AB - We report the first fully coupled quantum six-dimensional (6D) bound-state calculations of the vibration-translation-rotation eigenstates of a flexible H 2 , HD, and D 2 molecule confined inside the small cage of the structure II clathrate hydrate embedded in larger hydrate domains with up to 76 H 2 O molecules, treated as rigid. Our calculations use a pairwise-additive 6D intermolecular potential energy surface for H 2 in the hydrate domain, based on an ab initio 6D H 2 -H 2 O pair potential for flexible H 2 and rigid H 2 O. They extend to the first excited (v = 1) vibrational state of H 2 , along with two isotopologues, providing a direct computation of vibrational frequency shifts. We show that obtaining a converged v = 1 vibrational state of the caged molecule does not require converging the very large number of intermolecular translation-rotation states belonging to the v = 0 manifold up to the energy of the intramolecular stretch fundamental (≈4100 cm −1 for H 2 ). Only a relatively modest-size basis for the intermolecular degrees of freedom is needed to accurately describe the vibrational averaging over the delocalized wave function of the quantum ground state of the system. For the caged H 2 , our computed fundamental translational excitations, rotational j = 0 → 1 transitions, and frequency shifts of the stretch fundamental are in excellent agreement with recent quantum 5D (rigid H 2 ) results [A. Powers et al., J. Chem. Phys. 148, 144304 (2018)]. Our computed frequency shift of −43 cm −1 for H 2 is only 14% away from the experimental value at 20 K.

UR - http://www.scopus.com/inward/record.url?scp=85064476607&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064476607&partnerID=8YFLogxK

U2 - 10.1063/1.5090573

DO - 10.1063/1.5090573

M3 - Article

C2 - 31005099

AN - SCOPUS:85064476607

VL - 150

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 15

M1 - 154303

ER -