Knowledge Bank

Double-minimum functions have been determined which fit the energy levels of the out-of-plane bending potential of the $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A2$ and $\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}A2$ states of both $H2CO$ and $D2CO$. The squares of the wave functions of the levels give the probability distribution for the out-of-plane bending angle $\theta$. The other three geometrical parameters are assumed to be rigid during the bending vibration. Effective values for the rigid parameters have been determined from the observed rotational constants by making trial calculations of the expectation values of the reciprocals of inertia. The effective geometrical structure was determined for each state and a corresponding set of rotational constants was determined for each vibrational level. It was found that the rotational constant $A(1+)$ is perturbed for both the $\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A2$ and $\mathrm{<mrow\; data-mjx-texclass="ORD">3</mrow>}A2$ states of $H2CO$. The use of a variable reduced mass allows the calculation of the bending angle at vibrational equilibrium in close agreement with the bending angles calculated by Dixon from an approximate SCF MO calculation.