Symmetric Internal Rotor Research Articles

Internal Rotation of Molecules with Two Inequivalent Methyl Groups: The Microwave Spectrum of N-Methylethylidenimine

The microwave spectra of two isotopic species of trans-N-methylethylidenimine (CH3CH=NCH3) were recorded between 8 and 40 GHz. The rotational transitions clearly demonstrate the coupling with the internal motions of the two methyl groups, which are inequivalent in this molecule. The theory for the over-all and internal rotation was extended to molecules with two inequivalent symmetric internal rotors. The internal axis method (IAM) was used to calculate the internal rotors' splittings of the rotational transitions. They were split into five components according to the different irreducible representations of the symmetry group. In addition to this, the spectra were further complicated by the nuclear quadrupole multiplets of the nitrogen. A least squares analysis of the measured transition frequencies yielded the following rotational and quadrupole coupling constants for CH3CH=NCH3: A=38258.627± 0.048 MHz, B=4078.1354± 0.0058 MHz, C=3862.7391± 0.0072 MHz, χaa=1.578± 0.039 MHz, χbb=−4.601± 0.037 MHz, χcc=3.023± 0.041 MHz; and for CH3CD=NCH3: A=32982.409± 0.050 MHz, B=4076.6142± 0.0066 MHz, C=3799.5528± 0.0079 MHz, χaa=1.551± 0.038 MHz, χbb=−4.595± 0.023 MHz, χcc=3.044± 0.036 MHz. The mean values for the barriers of the two methyl groups were found to be 1642± 19 cal/mole for the C–CH3 top and 2109± 84 cal/mole for the N–CH3 top. A dipole moment of 1.499± 0.007 D was determined from the measured Stark splittings.

Theory of rotation and torsion spectra for a semi-rigid model of molecules with an internal rotor ofC2vsymmetry

The theory of the rotation-internal rotation spectra for a rather general class of molecules with an internal rotor of the symmetry C 2v is developed in the semi-rigid model approximation. Analytical expressions for the classical and quantum-mechanical hamiltonian are given. It is shown that the energy matrix may be analytically calculated in an appropriate zeroth-order basis composed of rotational and trigonometric wave functions. Symmetry properties of the hamiltonian are given and used extensively in factoring the energy matrix. The irreducible blocks of this matrix are of infinite order. The asymptotic behaviour of the matrix elements far from the diagnoal is shown to be O(ηn ) (η < 1; n is the distance from the main diagonal), which is of decisive importance in the numerical diagonalization of such matrices. A few numerical examples for a model are given in order to demonstrate the high precision achievable in the infinite matrix diagonalization. Furthermore the internal rotation problem (J = 0 states) is discussed, including the application to actual barrier determination from far infra-red spectra or microwave spectra as well as a comparison with the symmetric internal rotor case. Finally selection rules for electric dipole transitions and analytical expressions for the line strengths are given. It is shown that the theory can be developed to the same degree of explicitness as in the case of the rigid asymmetric rotor.

Interactions between Ordinary Vibrations and Hindered Internal Rotation. I. Rotational Energies

The effect of vibration-hindered rotation interactions on the rotational energy levels of molecules containing a symmetric internal rotor has been re-examined theoretically. The complete Hamiltonian has been derived and includes terms which are due to Coriolis coupling and to the explicit dependence of the kinetic energy on the angle of internal rotation. Over-all and internal rotation are separated from vibration, in zeroth order, by means of the Eckart and Sayvetz conditions. Difficulties in previous treatments are traced back to the application of these conditions. For each vibrational state, an approximate Hamiltonian for over-all and internal rotation is obtained by a Van Vleck perturbation treatment in which torsional denominators are assumed to be negligible. A correction for these denominators is determined by taking the first term in a power series expansion. A preliminary transformation, similar to that described by Hecht and Dennison, is used to remove zeroth-order coupling between the angular momenta of over-all and internal rotation. Simple product wavefunctions, then, form a suitable basis for evaluating first-order energy corrections due to higher-order coupling of internal and over-all rotation. Symmetric rotors, slightly asymmetric rotors, and asymmetric rotors with relatively high barriers to internal rotation are each treated separately. Empirical frequency expressions for rotational transitions of all three types of molecule are given. The symmetric rotor formula is identical in form to Kivelson's but the empirical constants must be interpreted differently. A symmetric rotor analysis was done on CH3SiF3 and CD3SiF3. K→K, J—1→J transitions of slightly asymmetric rotors obey a particularly simple frequency relation. Two groups of asymmetric rotor transitions are tractable: (1) The 00,0→10,1, ½[11,0→21,1+11,1→21,2], and 22,1→32,2 transitions, where the designation of levels is for a prolate rotor, and (2) transitions between the two members of an asymmetry doublet.

Calculation of Energy Levels for Internal Torsion and Over-All Rotation. II. CH3CHO Type Molecules; Acetaldehyde Spectra

Methods are described for the calculation of energy levels for the over-all rotation and internal torsion of molecules with a plane of symmetry and one symmetric internal rotor. Typical examples are CH3CHO, CH3SiH2D, and CH3OH. Analysis of the microwave spectra of CH3CHO, CD3CDO, CD3CHO, CH2DCHO, CHD2CHO, C13H3CHO, CH3C13HO, C13H3C13HO, and CH3CHO18 yields V3=1162, 1151, 1143±30 cal, and V6&amp;lt;100 cal, respectively, for the first three isotopic species, where the barrier to internal rotation is V=V3(1—cos3α)/2+V6(1—cos6α)/2. The aldehyde oxygen was found to be opposite one of the methyl hydrogens in the equilibrium orientation of the methyl group. The measured moments of inertia of the nine isotopic species lead to a structure with the parameters Methyl group: C–H=1.086 A C–D=1.088 H–C–H=108°16′ D–C–D=108°32′ C–C=1.501 Aldehyde: C–H=1.114 C=0=1.216 C–C–H=117°29′ C–C–O=123°55′ The Stark effect gave a dipole moment of 2.69 debyes.