Two-dimensional vibrational potential energy surface for phthalan: The effect of large coupling on vibrational quantum states

The low-frequency analysis of the phthalan ring-puckering vibration shows a highly irregular pattern of energy levels which cannot be adequately described by a one-dimensional potential energy function. Because the ring-puckering mode interacts strongly with the ring-flapping vibration of the same symmetry, a two-dimensional analysis involving these two motions is required. Two-dimensional kinetic energy (reciprocal reduced mass) expansions were calculated for the puckering, flapping, and interaction terms and these were utilized in the calculation of the two-dimensional potential energy surface. This surface does an excellent job of reproducing the irregular pattern of observed energy spacings for the ring-puckering vibration in both the ground and excited flapping states. The potential-energy surface has a barrier to planarity of 35 cm−1 and energy minima at x1=0.09 Å, x2=−0.03 Å, and x1=−0.09 Å, x2=0.03 Å where x1=puckering and x2=flapping. Although the minima correspond to puckered conformations with a slight amount of flapping, the molecule for practical purposes is planar since the energy barrier is so small. The calculations demonstrate that the unusual irregular pattern of the puckering levels arises primarily from the kinetic-energy interactions of the two vibrations.