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Academic Commons Search Resultsen-usH2, HD, and D2 inside C60: Coupled translation-rotation eigenstates of the endohedral molecules from quantum five-dimensional calculations
http://academiccommons.columbia.edu/catalog/ac:125416
Xu, Minzhong; Sebastianelli, Francesco; Bačić, Zlatko; Lawler, Ronald; Turro, Nicholas J.http://hdl.handle.net/10022/AC:P:8605Wed, 24 Mar 2010 00:00:00 +0000We have performed rigorous quantum five-dimensional (5D) calculations of the translation-rotation (T-R) energy levels and wave functions of H2, HD, and D2 inside C60. This work is an extension of our earlier investigation of the quantum T-R dynamics of H2@C60 [M. Xu et al., J. Chem. Phys. 128, 011101 (2008)] and uses the same computational methodology. Two 5D intermolecular potential energy surfaces (PESs) were employed, differing considerably in their well depths and the degree of confinement of the hydrogen molecule. Our calculations revealed pronounced sensitivity of the endohedral T-R dynamics to the differences in the interaction potentials, and to the large variations in the masses and the rotational constants of H2, HD, and D2. The T-R levels vary significantly in their energies and ordering on the two PESs, as well as from one isotopomer to another. Nevertheless, they all display the same distinctive patterns of degeneracies, which can be qualitatively understood and assigned in terms the model which combines the isotropic three-dimensional harmonic oscillator, the rigid rotor, and the coupling between the orbital and the rotational angular momenta of H2/HD/D2. The quantum number j associated with the rotation of H2, HD, and D2 was found to be a good quantum number for H2 and D2 on both PESs, while most of the T-R levels of HD exhibit strong mixing of two or more rotational basis functions with different j values.Chemistrynjt3Chemistry, Earth and Environmental Engineering, Chemical EngineeringArticlesQuantum dynamics of coupled translational and rotational motions of H2 inside C60
http://academiccommons.columbia.edu/catalog/ac:125413
Xu, Minzhong; Sebastianelli, Francesco; Gibbons, Brittney R.; Bačić, Zlatko; Lawler, Ronald; Turro, Nicholas J.http://hdl.handle.net/10022/AC:P:8604Wed, 24 Mar 2010 00:00:00 +0000We report rigorous quantum calculations of the translation-rotation (T-R) eigenstates of the H_2 molecule in C60. The resulting level structure can be explained in terms of a few dominant features. These include the coupling between the orbital and the rotational angular momenta of H_2 to give the total angular momentum λ, and the splitting of the sevenfold degeneracy of T-R levels with λ = 3 by the nonsphericity of C60, according to the rules of the icosahedral I_h group.Chemistrynjt3Chemistry, Earth and Environmental Engineering, Chemical EngineeringArticlesCoupled translation-rotation eigenstates of H2 in C60 and C70 on the spectroscopically optimized interaction potential: Effects of cage anisotropy on the energy level structure and assignments
http://academiccommons.columbia.edu/catalog/ac:125410
Xu, Minzhong; Sebastianelli, Francesco; Gibbons, Brittney R.; Bačić, Zlatko; Lawler, Ronald; Turro, Nicholas J.http://hdl.handle.net/10022/AC:P:8603Wed, 24 Mar 2010 00:00:00 +0000We have developed a quantitatively accurate pairwise additive five-dimensional (5D) potential energy surface (PES) for H2 in C60 through fitting to the recently published infrared (IR) spectroscopic measurements of this system for H2 in the vibrationally excited ν = 1 state. The PES is based on the three-site H2-C pair potential introduced in this work, which in addition to the usual Lennard-Jones (LJ) interaction sites on each H atom of H2 has the third LJ interaction site located at the midpoint of the H-H bond. For the optimal values of the three adjustable parameters of the potential model, the fully coupled quantum 5D calculations on this additive PES reproduce the six translation-rotation (T-R) energy levels observed so far in the IR spectra of H2@C60 to within 0.6%. This is due in large part to the greatly improved description of the angular anisotropy of the H2-fullerene interaction afforded by the three-site H2-C pair potential. The same H2-C pair potential spectroscopically optimized for H2@C60 was also used to construct the pairwise additive 5D PES of H2 (v = 1) in C70. This PES, because of the lower symmetry of C70 (D5h) relative to that of C60 (Ih), exhibits pronounced anisotropy with respect to the direction of the translational motion of H2 away from the cage center, unlike that of H2 in C60. As a result, the T-R energy level structure of H2 in C70 from the quantum 5D calculations on the optimized PES, the quantum numbers required for its assignment, and the degeneracy patterns which arise from the T-R coupling for translationally excited H2 are all qualitatively different from those determined previously for H2@C60 [M. Xu et al., J. Chem. Phys. 128, 011101 (2008)].Chemistrynjt3Chemistry, Earth and Environmental Engineering, Chemical EngineeringArticles