Rotational constants of all H/D substituted water trimers: Coupling of intermolecular torsional and symmetric stretching modes

A four-dimensional (4D) intermolecular potential energy surface (IPES) for the water trimer was calculated in the subspace of the three torsional coordinates and the symmetric intermolecular stretch coordinate, employing high-level ab initio theory. Torsionally adiabatic potential energy curves for the intermolecular symmetric stretching vibration were constructed based on this IPES. They were used to calculate the symmetric stretch fundamentals and stretching-averaged interoxygen R(O⋯O) distances 〈R_H〉 and 〈R_D〉, for the n= 0-6 torsional levels of (H₂O)₃ and (D₂O)₃. 〈R_H〉 and 〈R_D〉 increase with «up to n=5, and decrease for n=6. Torsionally averaged rotational constants A, B, and C of all 20 isotopomers of water trimer, for the torsional levels n = 0, 5 and 6, were obtained by averaging the inverse inertia tensor over the 3D torsional wave functions. Two approaches were examined: (i) setting the interoxygen A(O⋯O) distance to a fixed value, independent of torsional excitation; (ii) effectively incorporating the vibrational averaging due to the intermolecular symmetric stretching mode by using the appropriate 〈RH〉 and 〈R_D〉 values to define the R(O⋯O) distances for the isotopomers in the torsional state n. Both approaches yielded n=O, 5 rotational constants in good agreement with experiment. However, only approach (ii) reproduced the experimentally observed decrease in the rotational constants A and B upon 5 ←0 torsional excitation. Fixing the R(O⋯O) distances to R_H and R_D values obtained by fitting the 3D torsionally averaged rotational constants to the experimental values for (H₂O)₃ and (D₂O)₃, only marginally improved the agreement with experiment for other isotopomers.