The effective Hamiltonian for the coupling between inversion–torsion states of hydrazine

Abstract

In the present paper, a procedure to calculate matrix elements of the group-theoretical Hamiltonian for hydrazine is described and explained in detail, and a complete set of rovibrational matrix elements responsible for interstate interactions is presented. The transformation properties of the framework functions under the symmetry operators of the double group G ð2Þ 16 are explained in a simple way using the MS Excel spreadsheet.

Rotational spectrum and structure of asymmetric dinitrogen trioxide, N2O3

“…From this point of view, the prototype of the NAN single bond is found in hydrazine, N 2 H 4 . Although it has been extensively studied by microwave spectroscopy [65] and by electron diffraction [66], there is no equilibrium structure available, the highest level of ab initio calculation being MP2/6-311+G(3df, 2p) Table 9 Symmetry coordinates of N 2 O 3 Symmetry coordinate…”

The symmetric amino-wagging band of hydrazine: Assignment and analysis

“…As presented in Fig. 1 of [10], because of that high value of splitting the third torsion state extends from about 780 to 840 cm À1 so one can expect that the lower part of the state will interact directly with the symmetric wagging. This has been confirmed by what we have observed in the spectrum.…”

“…Moreover, the 3m 7 state is predicted not far in energy from the m 6 ( Fig. 1 of paper [10]) so it can easily affect the series belonging to the symmetric wagging.…”

“…But according to the rule for anharmonic resonances [10], two rovibrational states of hydrazine can interact effectively only when they are both of the same vibrational symmetry. This was thoroughly explained in paper [10] where matrix elements for A-A and A-B type interactions were derived. Most of the resulting matrix elements for A-B type coupling vanish.…”

“…Both states are symmetric with respect to the rotation about the C 2 axis of hydrazine (an A-A type of interaction) [10] and therefore a Fermi-type coupling is allowed. Moreover, the 3m 7 state is predicted not far in energy from the m 6 ( Fig.…”