Internal rotor hindered

An important property of chain molecules is that a major contribution to the standard entropy is conformational in nature, i.e. is due to hindered internal rotations around single bonds. This property is most relevant to cyclisation phenomena, since a significant change of conformational entropy is expected to take place upon cyclisation. Pitzer (1940) has estimated that the entropy contribution on one C—C internal rotor amounts to 4.43 e.u, A slightly different estimate, namely, 4.52 e.u. has been reported by Person and Pimentel (1953). Thus, it appears that nearly one-half of the constant CH2 increment of 9.3 e.u. arises from the conformational contribution of the additional C—C internal rotor. 

The transfer of an H atom from one site to another, as in the HCN — NCH isomerization, can be viewed as a special type of internal rotation. A hindered internal rotor treatment of such motions was found [148, 149] to yield an increase in the reactant state density by a factor of 3 to 4 for both HCN and HCCH at the thresholds for CH bond dissociations. Furthermore, for HCN, where the dissociation energy is well known, the resulting low pressure limit rate coefficients were found to be in much improved agreement with experiment. This study also provided a simple general formula for estimating the effect of such corrections for arbitrary isomerizations (Eq. (2.31) in [149]). Illustrative calculations suggested that such effects may be important even in larger molecules. 

There are two modes that are not applied to the above statistical treatment of thermodynamic properties that may be a major factor in some molecular species. The first is contribution to entropy, S, and heat capacity, Cp(T) from internal rotors, which for some species can be significant. Molecular species that do not have internal rotors are represented by the above statistical analysis representation. However, for molecular species that have hindered internal rotors, the contributions to S and Cp(T) need to be separately calculated and incorporated into the thermodynamic properties. One method to estimate the hinder rotor contributions is by using the vibration frequency for the torsion. 

In most quantum chemical program packages, these equations are used only to calculate the temperamre dependence of thermodynamic properties. Internal free and hindered rotation contributions to the partition functions are normally neglected or implicitly use the pseudo-vibration approach for the internal rotor. 

The effect of using different internal rotor treatments (harmonic oscillator or free rotator approximations) instead of hindered rotor treatment on the calculated reaction rate coefficient is also shown there [63]. 

Corrections accounting for hindered rotations are included for rotations about the C-C bond and about the reaction coordinate C H C. To obtain these corrections, we computed the potential energy of the hindered internal rotor,... 

How such a method survives for realistic, appreciably anisotropic potentials is the focus of this discussion. As a test system, we consider the intermolecular potential between Ar and HF(v=l). This is best described as a strongly hindered internal rotor complex, and on which we have data for the (10 0), (11 0) and (12 0) from the slit jet spectrometer. These three states, respectively, correlate in the limit of weak anisotropy with precisely the three states (the s," and the II and S oriented "p" orbitals) in the above paragraph that sample the full range of angular coordinates. 

This permits a reconstruction of full 2-D potential energy surface for Ar + HF(v l), which is shown in Fig. 3, and exhibits the double minimum behavior (ArHF and ArFH configurations) predicted from multiproperty fits on rare gas-HCi complexes by Hutson and Howard.The barrier between the two minima is considerably above the j l HF rotor energy, and thus the Ar-HF complex is an example of a strongly hindered internal rotor. 

The difference in termination rate constants between secondary (and primary) alkylperoxys and tertiary alkylperoxys is, therefore, almost entirely due to differences in the rate constants for irreversible tetroxide decay. Thus at 303K 2k- for t-Bu0a = 1.2 X 10 M s and 2k+ for s-BuOa = 10 M" s . That is kt/k-j = 8.3 X 10. Now Ingold (bl) has suggested that AS° for (27) fn-lk.k cal deg mol because of the entropy loss from four hindered internal rotors (i+x3.6 cal deg mol ). Thus A /A and E-b-E-t should be 10 and 9.6 kcal mol , respectively, for t-BuOa and s-BuOa, i.e., E should be ca 1 kcal mol negative. Neither of these predictions are observed experimentally and we are forced to conclude that kinetic data for self-reaction of S-RO2 provides further evidence against the complete acceptance of the Russell mechanism. 

Internal rotation involves the rotation of one part of a molecule relative to the other about a single bond. The appearance of the rotational spectrum depends on the type of internal rotor and on the barrier height hindering internal rotation. Rotation of a methyl group, hindered by a barrier on the order of 3 kcal/mole, leads to a splitting of the... 

The reason that A converges so readily can be ascertained by examining the individual components of the partition functions. The mass component is trivial. The vibrational terms for frequencies above 200 cm are all close to unity (recall vib = [l -exp(-/iv/A Br)] ) and their ratios, in GVG, converges readily. Frequencies lower than 200 cm"l are all treated as hindered internal rotors, whose partition function is determined largely by the geometry it is well established that geometries can be calculated accurately at a relatively low level of quantum theory. The same holds for the external rotations (which comprise only those of the monomer for propagation of a macroradical). 

Before the calculation can be begun we must have some idea of the structure of the complex as well as a classification of the internal orientational motions (free rotor, hindered rotor, or... 

In this section, we will analyze the scattering wavefunction (s,p,y) in the transition-state region for total angular momentum J = 0 and a near-resonant energy of 0.36 eV (measured from the bottom of the entrance valley), with H2 starting in its ground vibration-rotation state. As mentioned in section II, we build the scattering wavefunction at each value of s from products of Morse oscillator functions times hindered-internal-rotor functions. For the calculations reported here, we used a basis of 10 vibrational functions with the rotational distribution 6, 6, 6, 4, 3, 1, 1, 1, 1, 1. This means that there are 6 even-j odd-j functions in the v = 0 manifold,... 

The above treatment has made some assumptions, such as harmonic frequencies and sufficiently small energy spacing between the rotational levels. If a more elaborate treatment is required, the summation for the partition functions must be carried out explicitly. Many molecules also have internal rotations with quite small barriers, hi the above they are assumed to be described by simple harmonic vibrations, which may be a poor approximation. Calculating the energy levels for a hindered rotor is somewhat complicated, and is rarely done. If the barrier is very low, the motion may be treated as a free rotor, in which case it contributes a constant factor of RT to the enthalpy and R/2 to the entropy. 

S. E. Stein and B. S. Rabinovitch. Accurate Evaluation of Internal Energy Level Sums and Densities Including Anharmonic Oscillators and Hindered Rotors. J. Chem. Phys., 58 2438-2445,1973. 

Kivelson, D. Theory of the Interactions of Hindered Internal Rotation with Over-All Rotations. I. Symmetric Rotors Methyl Silane. J. chem. Physics 22, 1733-1739 (1954). 

The vibrational qv) and rotational (q r) partition functions may be calculated within the harmonic and rigid rotor approximations, respectively. In addition, in this work, the qy values were corrected by replacing some of the large amplitude vibrations by the corresponding hindered internal rotations, when necessary. 

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