Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 2A / Section B / 22 / b / i / Solution

Let $T_{v^{\prime },v^{\prime \prime }}=T_e+G^{\prime }(v^{\prime })-G^{\prime \prime }(v^{\prime \prime })$. For a fixed row, moving one column to the right therefore givesThus adjacent-column entries decrease by the lower-state vibrational spacing, independent of the upper-state row in the ideal model. If the positive difference is instead defined as left minus right, it is ${\tilde{\omega }}_e^{\prime \prime }-2{\tilde{\omega }}_e^{\prime \prime }{x}_e^{\prime \prime }(v^{\prime \prime }+1)$. Stating the subtraction direction prevents an artificial negative vibrational frequency.