Hindered internal rotation model

The molecular structure is the nonplanar configuration from the electron diffraction study of Akishin et al. (8). A planar model (also point group < 2 ) was assumed by Hisatsune et al. (9) in their approximate normal coordinate analysis of the infrared and Raman spectra. The frequency assignments of these authors are listed above in the order for the planar model, although the vibrations for the nonplanar form will separate differently into the species 5A, 3A2, 3B and 4B2. Hisatsune et al. (9) estimated the N-O -N deformation frequency (8 cm ) from combination bands in the solid and gas phase spectra. The JANAF thermodynamic functions were obtained using these frequencies and assuming the two N0 groups to be hindered internal rotators. 

We have discussed the ideal-chain model in Sect. 2.2 by incorporating short-range restrictions into the freely-jointed-chain model first the fixed bond angles, then the hindered internal rotation. In this way, we reached the description of semiflexibility of the real polymer chains. The mean-square end-to-end distances of chains in different models are given below. 

Thus the use of an equivalent gaussian link chain, which appeared artificial in the case of the freely hinged chain, is quite acceptable for the freely rotating chain, the chain with hindered internal rotation, or the rotational isomeric model. In these cases there is no pretense of reality of the equivalent links, so they need not be given fixed lengths /eit- This equivalent chain is therefore a summary of the chainlike character of flexible polymer chains, and its simplicity enables the investigation of those properties of polymer systems which are solely dependent on the flexible chainlike nature of the polymer molecules. It is then only natural to attempt to formulate simple models which are characteristic of stiff... 

This approach employs an effective analytical approximation of the partition function for a one-dimensional hindered internal rotation that reproduces the accurate values with a maximum error of about 2% for a number of reference systems [257]. The one-dimensional rotor treatment is generalized to give useful approximations of multidimensional rotor thermodynamic functions, and in the HRAO model, is further coupled to the simple perturbation theory (SPT) approach to the partition function for the other internal degrees of freedom [72]. 

As early as 1940 the American chemist F. Stitt demonstrated that in B2H0 the barrier hindering the internal rotation about the hypothetical B—B bond is much higher as compared to ethane. Then some more experimental data appeared to promote the hydrogen bridge structure. Dilthey s model was again taken up in the publications by B. V. Nekrasov, Ya. K. Syrkin, M. E. Dyatkina in the USSR, and some foreign chemists. 

In the case of our model chain, which has no energy barrier hindering the rotation of the segments, the internal energy of the chain is the same for all conformations. Thus the first term on the right side of equation (d) is zero, and... 

The second question addressed during the discussion deals with the calculation of the density of VdW states N(E). The major conclusion of the interpretation of the data reported by E.R. Bernstein is to point out this density of states, as being the primary factor controlling the IVR/VP dynamics. These conclusions are based on the comparison between the behaviours of the aniline-Ar complex and the aniline-CH4 complex. It is clear that, within the framework of the serial IVR/VP model, a proper counting of the VdW modes is essential since it drastically affects N(E) and consequently the predictions of the model. The simplest approach is to remark that, besides the three usual VdW modes (one stretch and two bends) aniline-CH4 complex offers three hindered rotation degrees of freedom. But the proper way to take them into account may be non trivial, due to selection rules imposed by symmetry and spin statistics. Simultaneously the exact values of associated (vibrational) frequencies may depend very much on the relative magnitude of the barrier to internal rotation compared to the free rotation frequency. These factors are expected to reduce the density of states. 

Concerning the proper treatment of torsional anharmonicity, which still represents a challenging aspect for accurate thermochemical calculations of complex molecules [257-265], a hindered-rotor anharmonic oscilattor (HRAO) model has been shown to provide accurate results[62, 72, 117, 204]. The HRAO model is based on a generalization to anharmonic force fields of the hindered-rotor harmonic oscillator (HRHO) model [257] that automatically identifies internal rotation modes and rotating groups during the normal-mode vibrational analysis. 

Prop. Spectra IR (957), (far) IR, Raman and assignment (I3I5, 208l), NMR (259, 582, 735, 1821), microwave (957, 1556), Coriolis coefficient and ground state centrifugal distortions (869), dipole moment (582), deuterium effect on dipole moment (1556), nonbonded electron effect on internal rotation (II6I), electrostatic model to treat hindered rotation force constant (I38,... 

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