Vibrational Coupled Cluster Computations in Polyspherical Coordinates with the Exact Analytical Kinetic Energy Operator

We present the first use of curvilinear vibrational coordinates, specifically polyspherical coordinates, in combination with vibrational coupled cluster theory. The polyspherical coordinates are used in the context of both the adaptive density-guided approach to potential energy surface construction and in the subsequent vibrational coupled cluster calculations of anharmonic vibrational states. Results obtained based on the polyspherical coordinate parametrization are compared to results obtained with the use of rectilinear vibrational coordinates, namely, normal coordinates and hybrid optimized and localized coordinates for the formaldehyde molecule. This comparison is carried out with the full vibrational configuration interaction model, using the respective fully coupled potential energy surfaces and untruncated kinetic energy operators. The polyspherical coordinates are shown to facilitate an acceleration of convergence for truncated methods when compared to the use of normal coordinates. We furthermore report on calculations on the hydrogen peroxide molecule in the polyspherical coordinate parametrization. The polyspherical vibrational coordinates are shown to perform very well, even for truncated methods, especially when considering the difficulty that rectilinear vibrational coordinates can exhibit in treating complicated internal molecular motion.