Analysis and fit of the Fourier-transform microwave spectrum of the two-top molecule N-methylacetamide

The jet-cooled Fourier-transform microwave spectrum of N-methylacetamide (CH₃NHC(O)CH₃), a molecule containing two methyl tops with relatively low barriers to internal rotation, has been recorded and fit to nearly experimental uncertainty. Measurements were carried out between 10 and 26 GHz, with the nitrogen quadrupole splittings resolved for many transitions. The permutation-inversion group for this molecule is G₁₈ (not isomorphic to any point group), with irreducible representations A₁, A₂, E₁, E₂, E₃, and E₄. One of these symmetry species and the usual three asymmetric rotor quantum numbers J_KaKc were assigned to each torsion-rotation level involved in the observed transitions. F values were assigned to hyperfine components, where . Transitions involving levels of A₁ and A₂ species could be fit to an asymmetric rotor Hamiltonian. The other transitions were first fit separately for each symmetry species using a Pickett-like effective rotational Hamiltonian. Constants from these fits show a number of additive properties which can be correlated with sums and differences of effects involving the two tops. A final global fit to 48 molecular parameters for 839 hyperfine components of 216 torsion-rotation transitions involving 152 torsion-rotation levels was carried out using a newly written two-top computer program, giving a root-mean-square deviation of observed-minus-calculated residuals of 4 kHz. This program was written in the principal axis system of the molecule and uses a free-rotor basis set for each top, a symmetric-top basis set for the rotational functions, and a single-step diagonalization procedure. Such an approach requires quite long computation times, but it is much less prone to subtle programming errors (a consideration felt to be important since checking the new program against precise fits of low-barrier two-top molecules in the literature was not possible). The two internal rotation angles in this molecule correspond to the Ramachandran angles ψ and φ often defined to describe polypeptide folding. Barriers to internal rotation about these two angles were found to be 73 and 79 cm⁻¹, respectively. Top-top coupling in both the kinetic and potential energy part of the Hamiltonian is relatively small in this molecule.