TY - JOUR

T1 - Translation-rotation states of H2 in C60

T2 - New insights from a perturbation-theory treatment

AU - Felker, Peter M.

AU - Bačić, Zlatko

N1 - Funding Information:
Z.B. is grateful to the National Science Foundation for its partial support of this research through Grant CHE-1112292. P.M.F. thanks Professor Daniel Neuhauser for generously allowing access to his computational resources and Professor Christian M?ller for hosting him at Ruhr Universit?t Bochum while some of this research was done.
Publisher Copyright:
© 2016 Author(s).
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2016/8/28

Y1 - 2016/8/28

N2 - We report an investigation of the translation-rotation (TR) level structure of H2 entrapped in C60, in the rigid-monomer approximation, by means of a low-order perturbation theory (PT). We focus in particular on the degree to which PT can accurately account for that level structure, by comparison with the variational quantum five-dimensional calculations. To apply PT to the system, the interaction potential of H2@C60 is decomposed into a sum over bipolar spherical tensors. A zeroth-order Hamiltonian, Ĥ0, is then constructed as the sum of the TR kinetic-energy operator and the one term in the tensor decomposition of the potential that depends solely on the radial displacement of the H2 center of mass (c.m.) from the cage center. The remaining terms in the potential are treated as perturbations. The eigenstates of Ĥ0, constructed to also account for the coupling of the angular momentum of the H2 c.m. about the cage center with the rotational angular momentum of the H2 about the c.m., are taken as the PT zeroth-order states. This zeroth-order level structure is shown to be an excellent approximation to the true one except for two types of TR-level splittings present in the latter. We then show that first-order PT accounts very well for these splittings, with respect to both their patterns and magnitudes. This allows one to connect specific features of the level structure with specific features of the potential-energy surface, and provides important new physical insight into the characteristics of the TR level structure.

AB - We report an investigation of the translation-rotation (TR) level structure of H2 entrapped in C60, in the rigid-monomer approximation, by means of a low-order perturbation theory (PT). We focus in particular on the degree to which PT can accurately account for that level structure, by comparison with the variational quantum five-dimensional calculations. To apply PT to the system, the interaction potential of H2@C60 is decomposed into a sum over bipolar spherical tensors. A zeroth-order Hamiltonian, Ĥ0, is then constructed as the sum of the TR kinetic-energy operator and the one term in the tensor decomposition of the potential that depends solely on the radial displacement of the H2 center of mass (c.m.) from the cage center. The remaining terms in the potential are treated as perturbations. The eigenstates of Ĥ0, constructed to also account for the coupling of the angular momentum of the H2 c.m. about the cage center with the rotational angular momentum of the H2 about the c.m., are taken as the PT zeroth-order states. This zeroth-order level structure is shown to be an excellent approximation to the true one except for two types of TR-level splittings present in the latter. We then show that first-order PT accounts very well for these splittings, with respect to both their patterns and magnitudes. This allows one to connect specific features of the level structure with specific features of the potential-energy surface, and provides important new physical insight into the characteristics of the TR level structure.

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U2 - 10.1063/1.4961650

DO - 10.1063/1.4961650

M3 - Article

AN - SCOPUS:84985010392

VL - 145

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 8

M1 - 084310

ER -