Question

Following is a complete list of observed transitions involving levels J = 0, 1, and 2 for two isotopomers of formaldehyde in their vibrational ground states H212c16O H2 13C160 71.14 MHz 4829.66 14488.65 72837.97 140839.54 145602.98 150498.36 4593.09 13778.86 71024.80 137449.97 141983.75 146635.69 Note that in a real spectrum you could not arrange to see only transitions involving/ = 0,1, and 2. In fact, there are more than 54 observed H21c16O transitions below 150498.36 MHz. Explain why the inertial defect is a good test for planarity. Why does H2CO appear NOT to be planar from the microwave spectrum?

Answer 1

$\alpha$ Morino's general formula for inertial defect has been applied to planar molecule with very low out of plane vibrations in order to explain negative inertial defects reported for such molecules.The obtained simple formula is combined with an empirical proportionality relation between zero point inertial defect $\Delta$ 0 and $\sqrt{}$ Icc for ordinary molecules to give semi- empirical relations between the inertial defect $\Delta$ 0, the wavenumber of the lowest out of plane vibration v1 and $\sqrt{}$ Icc. The relation explains well the observed negative inertial defects and allows us to estimate the value of v1 from the observed $\Delta }$ 0

The inertial defect of a molecule is defined as

$\Delta$ =Icc- Iaa-Ibb

Where I $\alpha$ $\alpha$ ( $\alpha$ =a,b,c) are the principal moments of inertia of the molecule

According to the convention, we choose the molecule fixed axes such that Iaa $\leq$ Ibb $\leq$ Icc . Because of the definition of moments of inertia.

Planar molecules which have been obseved to show negative inertial defects in the ground vibrational state. Planar molecules showed abnormally small or negative inertial defects.force constants.These constants may be estimated for simple planar moleculesThe inertia defect is a strong function of the vibrational  

The microwave spectrum is usually defined as a range of freequencies ranging from 1 GHz to over 100 GHz

A molecule's shape depends on the atoms that make it up and the electrons that belong to the central atom. If the atoms arrange themselves around the central molecule so that they exist on a single two dimensional plane,the molecule is planar.