Methane, rotation

From what has been said above it is clear that free rotation will be most common in molecular structures which contain small molecules, and indeed a quantitative treatment reveals that it may be expected in many such structures below their melting points. In hydrogen, free rotation of the H2 molecule occurs at the absolute zero, and the crystal structure down to the lowest temperature at which it has been observed is hexagonal close packed. In methane, rotation sets in at about 20 °K, and the transition is accompanied by an anomalous increase in specific heat between 18 and 22 8 °K. Above the latter temperature the structure is cubic close packed. Similar transitions take place in HC1 and HBr, the high-temperature forms of which have close-packed structures while at low temp eratures more complex structures of lower symmetry obtain. F ree rotation is naturally less common in molecular structures containing large molecules, but it is found in certain long-chain compounds, to be discussed later, in which rotation about the axis of the chain takes place ( 14.22). 

H/D exchange in TpPt(H)2(CH3) (Tp=hydrido-tris(pyrazolyl)borate) was investigated with the DFT method [24], where various functionals were used. The reaction takes place through the reductive elimination of methane, methane rotation, and the oxidative addition. Important in this reaction is that the platinum(II) methane complex is very stable the binding energy of methane with the Pt(II) center was evaluated to be 6.0 kcal/mol and the activation barrier for methane loss was 11.9 kcal/mol, where mPWlk functional was... 

An interesting point is that infrared absorptions that are symmetry-forbidden and hence that do not appear in the spectrum of the gaseous molecule may appear when that molecule is adsorbed. Thus Sheppard and Yates [74] found that normally forbidden bands could be detected in the case of methane and hydrogen adsorbed on glass this meant that there was a decrease in molecular symmetry. In the case of the methane, it appeared from the band shapes that some reduction in rotational degrees of freedom had occurred. Figure XVII-16 shows the IR spectrum for a physisorbed H2 system, and Refs. 69 and 75 give the IR spectra for adsorbed N2 (on Ni) and O2 (in a zeolite), respectively. 

Hollenstein H, Marquardt R, Quack M and Suhm M A 1994 Dipole moment function and equilibrium structure of methane In an analytical, anharmonic nine-dimenslonal potential surface related to experimental rotational constants and transition moments by quantum Monte Carlo calculations J. Chem. Phys. 101 3588-602... 

The chemistry of propylene is characterized both by the double bond and by the aHyUc hydrogen atoms. Propylene is the smallest stable unsaturated hydrocarbon molecule that exhibits low order symmetry, ie, only reflection along the main plane. This loss of symmetry, which implies the possibiUty of different types of chemical reactions, is also responsible for the existence of the propylene dipole moment of 0.35 D. Carbon atoms 1 and 2 have trigonal planar geometry identical to that of ethylene. Generally, these carbons are not free to rotate, because of the double bond. Carbon atom 3 is tetrahedral, like methane, and is free to rotate. The hydrogen atoms attached to this carbon are aUyflc. 

Fig. 1. Examples of temperature dependence of the rate constant for the reactions in which the low-temperature rate-constant limit has been observed 1. hydrogen transfer in the excited singlet state of the molecule represented by (6.16) 2. molecular reorientation in methane crystal 3. internal rotation of CHj group in radical (6.25) 4. inversion of radical (6.40) 5. hydrogen transfer in halved molecule (6.16) 6. isomerization of molecule (6.17) in excited triplet state 7. tautomerization in the ground state of 7-azoindole dimer (6.1) 8. polymerization of formaldehyde in reaction (6.44) 9. limiting stage (6.45) of (a) chain hydrobromination, (b) chlorination and (c) bromination of ethylene 10. isomerization of radical (6.18) 11. abstraction of H atom by methyl radical from methanol matrix [reaction (6.19)] 12. radical pair isomerization in dimethylglyoxime crystals [Toriyama et al. 1977].

The di-TT-methane rearrangement is a stereospecific reaction. There are several elements of stereochemistry to be considered. It is known that the double bond that remains uncyclized retains the E or Z configuration present in the starting material. This result excludes any intermediate with a freely rotating terminal radical. The concerted... 

Pentadienyl radical, 240 Perturbation theory, 11, 46 Propane, 16, 165 n-Propyi anion conformation, 34 n-Propyl cation, 48, 163 rotational barrier, 34 Propylene, 16, 139 Protonated methane, 72 Pyrazine, 266 orbital ordering, 30 through-bond interactions, 27 Pyridine, 263 Pyrrole, 231... 

Fig. 3.13. Density-dependence of the Qo, branch line width y of methane (the dashed line is for pure vibrational dephasing, supposed to be Unear in density), (o) experimental data (with error bars) [162] Top part rotational contribution yR and its theoretical estimation in motional narrowing limit [162] (solid line) the points were obtained by subtraction of dephasing contribution y

With formulae (3.58), (3.59) and (3.66) Q-branch contours are calculated for CARS spectra of spherical rotators at various pressures and for various magnitudes of parameter y (Fig. 3.14). For comparison with experimental data, obtained in [162], the characteristic parameters of the spectra were extracted from these contours half-widths and shifts of the maximum subject to the density. They are plotted in Fig. 3.15 and Fig. 3.16. The corresponding experimental dependences for methane were plotted by one-parameter fitting. As a result, the cross-section for rotational energy relaxation oe is found ... 

Fig. 3.15, The CARS spectrum rotational width versus methane density for various values of parameter y (1) y = 0, (2) y = 0.3, (3) y = 0.5, (4) y = 0.7, (5) y = 0.75, (6) y = 0.9, (7) y = 0.95, (8) y = 1. Curves (4) and (6) are obtained by subtraction of the dephasing contribution from the line width calculated taking account of vibrational broadening. The other dependences are found assuming purely rotational broadening (vibrational relaxation neglected).

In [162] experiments on methane provided a linear pressure dependence of the contour width. This made it possible to find the dephasing cross-section and to discriminate between contributions of rotational and vibrational relaxation to the contour width. This was done under the above-mentioned simplifying assumption that they are additive. (Let us note that processing of experimental data on linear molecules was always performed under this assumption.) The points found by this method are shown in Fig. 3.15, curves (4) and (6). 

Eagles T. E., McClung R. E. D. Rotational diffusion of spherical top molecules in liquids and gases. IV. Semiclassical theory and applications to the v3 and v4 band shapes of methane in high pressure gas mixtures, J. Chem. Phys. 61, 4070-82 (1974). 

A nonlinear molecule, such as water, methane, or benzene, can rotate about any of three perpendicular axes, and so it has three rotational modes of motion. The average rotational energy of such a molecule is therefore 3 X jkT = ]kT. The contribution of rotation to the molar internal energy of a gas of nonlinear molecules is therefore... 

Further measurements on the flame speed have been obtained with the use of a rotating tube [11] and vortex ring combustion [12]. Figure 4.2.4 shows the flame speed in vortex rings [12]. The values of slope in the V( -plane is nearly equal to unity for the near stoichiometric methane/air mixtures. Thus, this value is much lower than the predictions of JPi/P, and flPn/P >. 

Subsequently, the problem was investigated by Karpov and Severin [6]. They used closed vessels with a diameter of 10cm and 10, 5, and 2.5cm width, initially at atmospheric pressure. The vessels were filled with different lean hydrogen and methane/air mixtures and rotational speeds in the range of 130-4201/s were employed. They also included data from the study of Babkin et al. [3] in their analysis. Unfortunately, they did not observe the flame itself and measured only the pressure rise in the vessel, which was compared with pressure development in the vessel without rotahon, to draw a conclusion with respect to flame speeds and quenching. 

Flame speeds as a function of time for an 8.45% methane/air mixture and different rotation rates. Vessel vented on the axis of rotation. 

Methane/Air Flame Parameters and Rotational Speeds (a>i) for Which the Tangential and Normal Speeds in an Expanding Flame are Equal... 

The calculations were performed into two basis sets, with full geometiy optimization except for the torsional angles a and 6. Two non planar conformations were considered, which correspond to minima on the potential energy surface into the GVB approximation [21]. In these conformations, the molecule adopts a pyramidal conformation, as in methanal. In addition, the hydroxilic group is rotated up or down the OCO plane. 

R. Y. Dong, M. Bloom 1970, (Determination of spin-rotation constants in flu-orinated methane molecules by means of nuclear spin relaxation measurements), Can. J. Phys. 48, 793. 

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