Theory of the Interaction of Hindered Internal Rotation with Over-All Rotations. I. Symmetric Rotors: Methyl Silane

Abstract

An approximate theory of the interactions of hindered internal rotation with over‐all rotations of symmetric rotors is given. This treatment considers the interdependence of hindered internal rotation and vibrations and their effect upon the rotational energy levels. The resulting expression for the frequencies of ΔK = 0, ΔJ = 1 transitions is $${\text{ν=2J[B}}_v{\mathrm{+F}}_v\text{(m|1−}\cos {\text{3θ|m)+G}}_v\mathrm{(m|}{\mathbf{\Pi }}_z^2{\mathrm{|m)+L}}_v\mathrm{K(m|}{\mathbf{\Pi }}_z\mathrm{|m)],}$$ where B_v, F_v, G_v, and L_v are constants independent of the rotational quantum numbers, m represents the basis that diagonalizes the Hamiltonian corresponding to pure internal rotation, π_z is the internal angular momentum operator, and θ is the angle of internal rotation. Procedures for evaluating (m|1—cos3θ|m) and (m|π_zⁿ|m) in terms of a parameter α are given. This theory has been applied to the J=0→1 transitions of methyl silane. The parameters B_v, F_v, G_v, and α were obtained empirically and were then used to calculate frequencies. The agreement between observed and calculated values was quite good. Furthermore, the anomalous ordering of the lines observed by Lide and Coles¹ is explained by these calculations. Assuming a cosine potential, the barrier height V₀ is proportional to the parameter α. The value of V₀ was set at 558 cm^‐1±17 cm^‐1. The constant B_v, which is the rotational constant in the ground torsional state for the limiting case of V₀=0, is 10985.79 Mc/sec and 9636.50 Mc/sec for CH₃SiH₃ and CH₃SiD₃, respectively.