Cyclopropane normal vibrations

Figure 4.1-10 Typical normal vibrations of cyclopropane. The length of the vector arrow and the diameter of its head are proportional to the amplitude. The name of the characteristic vibrations, the vibrational species of the point group D3/, and the calculated frequencies are given (Spiekermann et al, 1980).

In the case of cyclopropane, the vibrational force field and infrared intensities have been examined in some detail both experimentally and via calculation. One of the more interesting observations is that the dipole moment derivatives for the C-H stretching modes are relatively small (corresponding to their low intensities). There is a relationship between the derivatives and the bond dipoles The low value for cyclopropane is a reflection of the smaller than normal electron population at its hydrogens (Table 3). 

The allyl radical [115] trapped in an argon matrix can be photolytically (A = 410 nm) converted into the cyclopropyl radical [116] (Holtzhauer er a/., 1990). Dicyclopropane and cyclopropane were formed when the photolysed matrix was warmed from 18 to 35 K. The intermediate [116] was shown to be a cr-type (Cs symmetry) and not a rr-type symmetry) radical. Normal coordinate analysis of the radical [116] has been carried out and the IR band at 3118 cm has been assigned to the stretching vibration of the C—H bond at the radical centre. 

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 ... 

Trajectories were initiated by generating initial conditions with the efficient microcanonical sampling or quasiclassical normal-mode sampling procedures at 54.6 or 146.0 kcalmoC1 of vibrational energy for trimethylene. Trimethylene was then placed in the center of a box, with periodic boundary conditions, and surrounded by an argon bath with an equilibrium temperature and density. Initially, trimethylene was in a nonequilibrium state with respect to the bath, since its coordinates and momenta were held fixed while the bath was equilibrated, and the trajectories were propagated until either cyclopropane or propene was formed. 

One interesting conclusion that can be drawn from the work with hot molecules relates to the problem of energy flow between normal modes. If there were little energy flow it would be expected that a hot molecule of methylcyclopropane produced from CH2 and cyclopropane would show different behaviour from one made from CH2 and propene, since the energy would be distributed differently in the two cases. No difference in kinetic behaviour is detected, however, in this and similar systems, and this indicates that there is rapid flow of energy between the modes of vibration. 

A characterization of vibrational normal modes in terms of adiabatic internal modes is straightforward with the definitions given in the previous sections. As an example, the vibrational modes of cyclopropane [28] will be discussed. They have been calculated at the FIF/6-31G(d,p) level of theory and they are compared with experimental frequencies in Table 1. 

All frequencies in cm l. Scaled HF/6-31G(d,p) and MP2/(9s5pld/4slp)[4s2pld/2slp] frequencies scaling factors are 0.87 (HF) and 0.95 (MP2), respectively. Each normal mode is dissected into adiabatic internal vibrations [28]. The notation CH (6 x 16%) implies that all six CH stretching modes (each with 16%) of cyclopropane contribute to the normal mode 1. 

In the vapor phase, there are two additional considerations that are very important in understanding of carbene chemistry. The first point reflects the fact that carbene reactions are normally highly exothermic (about 90kcal mol for insertions or additions). Thus, a product molecule is frequently produced with a large amount of excess internal energy. In the vapor phase without solvent molecules to help dissipate the excess vibrational energy, the molecule may be subject to further reactions. Such reactions are often called hot molecule reactions. Cyclopropanes from cycloaddition reactions are particularly susceptible to hot molecule decomposition to the thermodynamically more stable olefin, since for cyclopropane isomerization is only 64kcal mol . ... 

L. B. Sims, H. P. E. Sachse and E. Mei, Report on research Vibrational Assignments and Descriptions of Normal Modes of Vibration of Cyclopropane Molecules, Department of Chemistry, University of Arkansas, Fayetteville, 1972. 

From infrared and Raman spectra of bicyclobutane and appropriate deuterated isomers a new vibrational assignment was made with the help of the spectrum calculated using the 6-3IG basis set. A normal coordinate analysis furnished atomic polar tensors and related properties. The results were compared with similar data for cyclopropane and [l.l.l]propellane. 

So what happens if we change our consideration to a molecule of different complexity In practice, there are many variables which complicate the analysis, for not only will the and d change, but /<, and Aoo will also be different. Let us imagine a hypothetical molecule C3D3 which possesses the same internal relaxation rate constant as does cyclopropane, and which reacts to form some product with the same values of and of A. We will also assume that it has the same two moments of inertia as does cyclopropane, so that the only thing different about it is its vibrational frequencies it has 12 normal modes of vibration instead of 21, and for the purposes of this illustration, I have simply made an arbitrary deletion of nine of the original modes of the cyclopropane molecule. 

Vibrational analysis has turned out to be an additional valuable tool for giving better insight into details of the changes of molecular properties upon interaction with the zeolite surface. In the case of polyatomics the bonds which are mainly affected by interaction, and to what extent, must be traced out. This is accomplished by comparing the force constants of the free and adsorbed molecules. Furthermore, information on the geometry of the sorption complex may be obtained. Normal coordinate analysis using a harmonic valence force field has been carried out for cyclopropane in faujasites and mordenites, propene in different zeolites A and Y and cis-and /ra/25-but-2-ene in zeolites A [58-61]. 

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