The derivation of the rotational potential function from atom–atom potentials. IV. The symmetric tops NH3D+ and NHD+3 and the asymmetric top NH2D+2

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Abstract
A procedure is presented for computing the hindered rotational energy levels of symmetric and asymmetric tops in tetrahedral crystalline fields. By considering the equations used to derive the rotational potential function from atom–atom potentials, the change required in the potential function on going from spherical tops to symmetric and asymmetric tops has been determined. The rotational potential function of NH3D+ and NHD+3 in NH4Cl, (NH4)2SnCl6, (NH4)2SiF6, and NH4F have been derived from atom–atom potentials. The rotational potential functions of NH2D+2 in the first three compounds listed above have also been derived from atom–atom potentials. Only the J=4 term in the rotational potential functions has been found to be significantly different for symmetric and asymmetric tops than for spherical tops. The librational frequencies have been computed for the isotopic forms of the solids listed above. For some of solids that have been studied, tunneling frequencies have also been computed. For the symmetric tops NH3D+ and NHD+3, there are two librational frequencies, one with A symmetry and the other with E symmetry. The difference in energies of these frequencies is due to the changes in both the kinetic energy term and potential energy term in the Hamiltonian on going from a spherical top to a symmetric top. The contributions of each of these terms to the splitting in the librational frequency has been determined for the compounds under study. The tunneling frequencies of CH3D have been computed in phase II for both the methane molecules on the D2d and Oh sites. For the molecules on the D2d sites, only the molecular field is considered. The potential function is due to the crystalline field for molecules on the Oh sites. The computed tunneling frequencies of the molecules on both sites are in good agreement with the observed results of the INS of CH3D in CH4.