Question #44153

In a standard planar amide, resonance between the nitrogen lone pair and the carbonyl group results in a \ce{C-N} fractional $\pi$-bond order of $0.40$ and a \ce{C=O} stretching frequency of $1650 \text{ cm}^{-1}$. In a completely orthogonal (unresonated) system where the dihedral angle $\theta = 90^\circ$, the \ce{C-N} $\pi$-bond order is $0$ and the \ce{C=O} stretching frequency is $1730 \text{ cm}^{-1}$.

In a highly sterically hindered \ce{N-tert-butyl-N-methylacetamide} derivative at $298 \text{ K}$, steric strain forces the amide plane to twist, resulting in a dihedral angle $\theta = 60^\circ$.

Assuming that the \ce{C-N} $\pi$-bond order is directly proportional to the square of the orbital overlap integral (which is proportional to $\cos \theta$), and that the \ce{C=O} stretching frequency varies linearly with the \ce{C=O} $\pi$-bond order (where $\text{\ce{C-N} } \pi\text{-bond order} + \text{\ce{C=O} } \pi\text{-bond order} = 1.0$), what is the expected \ce{C-N} total bond order and the \ce{C=O} stretching frequency in this sterically hindered amide?