Ethylenes normal vibrations

Ab initio calculations of the normal vibrational frequencies for the primary and secondary ozonides of ethylene allowed making a few modifications of the earlier assignments, and will serve for assisting in assigning vibrational bands of larger ozonides <1996SAA1479>. 

As a test of the method, we examined the dimerization of ethylene. The first and second excited states are Az and Alt respectively (Fig. 14). For a four-center square species, the normal vibrations which could lead to dimerization are (Alg) and vz (Blg) (Herzberg, 1945). Accordingly, dimerization would be possible but difficult, since the symmetry of vx matches that of the second excited state. This conclusion agrees with the results of orbital-symmetry arguments. 

An unstrained olefinic double bond in the ground state is described by six atoms lying in a plane with bond angles near 120° and bond lengths of about 134.0 pm. Two classes of deformations can be distinguished in nonplanar or out-of-plane (oop) distortions, substituents move perpendicular to the molecular plane, whereas planarity is maintained with the planar or in-plane (ip) distortions of substituents. For a systematic approach, these static distortions can be derived from the normal vibrations of ethylene. 

The normal vibrational modes of ethylene, numbered according to the convention of Herzberg ( Infra-red and Raman spectra , van Nostrand, 1945) are shown in table 1. Since the molecule has a centre of symmetry no mode symmetrical with respect to this centre can be active in the infra-red and no antisymmetrical mode can be active in the Raman spectrum. The twisting mode number 4 is inactive in both. The most recent assignment (Crawford, Lancaster, and Inskeq>, J. Chem. Phys. 1953, 21, 678) of wave-numbers for the remaining eleven modes are given. 

Normal vibrations of the poly(ethylene glycol) chain were treated by Matsuura and Miyazawa (1969a) for the phase differences of 5 = 0 180°. The frequency-dispersion curves were calculated as shown... 

How many normal vibrational modes wiU the following molecules have H2O2, C2H2 (acetylene), C2H4 (ethylene), C2H3CI (ethylene chloride), C He (benzene), C6HsCl (chlorobenzene)... 

Figure 6.33 Three normal modes of vibration of ethylene...

The approach of the carbon atom to ethylene, and the conversion of 30 to 31, thus correspond to one of the normal modes of vibration of the cyclopropane ring, viz ... 

Evidently a large part of the energy liberated in the approach of the carbon atom to ethylene will go into this normal mode — which is the one required for conversion of 30 to 31. Unless the interconversion of vibrational energy is incredibly efficient, one would then expect the initially formed 30 to be converted to 31 even at the lowest temperatures. The fact that allene is formed at -190° is not therefore surprising. On the other hand the existence of a large barrier between 30 and 31 would prohibit rearrangement of 30 if formed under milder conditions free cyclopropyl carbenes do not rearrange to allenes if formed by conventional methods in solution 49). 

Analysis of the rotational fine structure of IR bands yields the moments of inertia 7°, 7°, and 7 . From these, the molecular structure can be fitted. (It may be necessary to assign spectra of isotopically substituted species in order to have sufficient data for a structural determination.) Such structures are subject to the usual errors due to zero-point vibrations. Values of moments of inertia determined from IR work are less accurate than those obtained from microwave work. However, the pure-rotation spectra of many polyatomic molecules cannot be observed because the molecules have no permanent electric dipole moment in contrast, all polyatomic molecules have IR-active vibration-rotation bands, from which the rotational constants and structure can be determined. For example, the structure of the nonpolar molecule ethylene, CH2=CH2, was determined from IR study of the normal species and of CD2=CD2 to be8... 

The infrared spectrum of physically adsorbed methane had a band at 2899 cm.-1 which is not present in the equivalent path-length of either the gas or the liquid. This corresponds to the symmetrical C—H stretching vibration which produces a Raman band at 2916 cm.-1. The spectrum of adsorbed ethylene shows an extra weak shoulder at 3010 cm.-1 which was assumed to be the normally infrared inactive v vibration in which all four hydrogens are vibrating in phase and which produces a Raman band at 3019 cm.-1. 

Detailed analyses of the molar partition functions and the zero-point energies for the various vibrational modes in the ground and ion states indicate that the major contributor to the EIE is the creation of a new mode in the ion, termed the CH2-symmetric twist, arising from the loss of the rotational freedom about the C—C axis in ethylene (Eigure 1). In the absence of this new mode, the computed EIE is normal, K /Ky) = 1.12. The computations also indicated that the ion state undergoes very little rehybridization of the carbons. ... 

We have observed the OH stretching vibrations for a pure sample of monocaprin in carbon tetrachloride and at 0.008M have found a monomer or free OH band at 3620 cm.-1 and a band which we think is caused by the intramolecular hydrogen bond at 3540 cm-1. At 0.04M the OH band is much broader, with a maximum at 3460 cm-1., presumably owing to extensive intermolecular association. It seems therefore that this type of association sets in at similar OH group concentrations in the diols and the monohydric alcohols, as can also be seen in Kuhn s spectrum of tetramethyl-ethylene glycol, in which the intermolecular band in 0.05M solution has approximately the same intensity as in 0.1M solutions of the normal alkanols. 

To evaluate the increment to the isotope effect caused by each vibrational motion in the S + C2H4 reaction, the magnitude of the isotope effect associated with each normal mode was calculated separately. The results obtained for the asymmetrical model of the C2D4/C2H4 reactant pair are collected in Table II. The most important contribution to the isotope effect comes not from the out-of-plane CH bendings but from a single vibration—namely the asymmetric twist mode of the thiirane molecule which is absent in the ethylene. 

These results are valid and apply for all addition reactions involving olefinic double bonds. Addition reactions are characterized by an increase in the number of normal modes of vibration. In this case the ethylene molecule has 12 normal modes of vibration while thiirane has 15. One of these, the CS stretching mode, coincides with the reaction coordinate and does not contribute to the isotope effect. Out of the net gain of two, the CCS bending mode is not sensitive to isotopic substitution and does not generate an isotope effect, but the twist of the CH2 group which... 

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