Rotational of methane

In equation 5 the parameters a(R) correspond to the (isotropic) group polarizabilities as given in Refs 4 and 16 (and partly in Ref. 5). The parameters /i(R) and v(R) are further rotation parameters associated with the groups directly attached to a particular skeletal carbon atom and with the remote groups, respectively. The parameters a(R) and /x(R) are exactly those which are used to calculate the optical rotations of methane derivatives V according to equation 6 ... 

The elastic (f = 0) and quasi-elastic incoherent structure factors for the isotropic rotation of methane are shown in Fig. 3. It appears from this figure that only the first three terms of the summation in expression 23 have to be considered in the Q range, which is usually covered by QENS instruments. The self-diffusivity will be obtained by first fitting the QENS spectra with expression 23 and then from the broadening of As with Q. 

When a substance is heated, the kinetic energy of atoms and molecules increases. E.g., if methane is heated, the kinetic energy of translation, vibration and rotation of methane molecules increases, as discussed in section 1.2. As heat is applied, higher vibrational states are increasingly populated. In higher vibrational quantum states, the average C-H bond distance increases until finally the C-H bond breaks. The result is the formation of a methyl radical and a hydrogen atom. 

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... 

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].

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

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). 

The chemistry of all of these molecules is fascinating but, concentrating on the origins of life, a detailed look at the organic species is appropriate to see what molecules are present and how they might have been formed. The only alkane detected directly in the ISM is methane but this is due to the problem of detection. All alkanes are non-polar and so do not have a pure rotation spectrum. However, there is one allowed vibration of methane that is infrared active and with the low moment of inertia of methane the vibration-rotation spectrum can be observed and a rotational progression identifies the molecule with confidence. 

The quantity measured in the experimental work on the methane derivatives was the rotation of the Na D-line in ethanol solution (sometimes it was necessary to use another solvent, in which case a correction was applied). The sum (5), as well as its separate terms, was evaluated for 13 different choices of the set of ligands a,b,c,d,x. For eleven of these, the observed sum was less in absolute value than its statistical average calculated from the absolute values of the separate terms. For the other two (as well as for some of the eleven), the mixture contained molecules for which one would expect large deviations from T,rsymmetry, and/or dimerization. For those mixtures for which the sum (5) was small, a least-square fit was made to the data with a function of the form (2). This best fit was interpreted as the T -component, the remainder as the result of deviation from T -symmetry for each molecule. A fit was also made with functions of the form (1), with less quantitative success. 

The first observation one can make is that the correlation effects for the rotational g tensor in HF, H2O, and NH3 are in general small, 1.5-3.5%, and negative, i.e., correlation reduces the values of the rotational g tensor and therefore the amount of coupling between the electronic and rotational motion. Methane is an exception in that respect, because correlation increases the value of the g factor and because some methods, MPn and CCSD, predict much larger correlation corrections. 

Nuclear magnetic resonance measurements of methane adsorbed to various coverages on titanium dioxide have been made by Fuschillo and Renton 16). At a coverage of 0.95 monolayer and at 20.4°K, the X-point for solid bulk methane, these authors observed an abrupt change in the proton resonance line width, presumably due to translational and rotational diffusion of methane molecules. For pure, bulk methane no change has been observed in the line width at the X-point. 

The first polymerizations reported by Kops and Schuerch147 were those of l,4-anhydro-2,3,6-tri-0-methyl-/3-D-galactopyranose and 1,4-anhydro-2,3-di-0-methyl-a -L-arabinopyranose. The latter compound was slightly contaminated with l,4-anhydro-2,3-di-0-methyl-a-D-xy-lopyranose, but the course of the polymerization could nevertheless be monitored reasonably accurately. For the most part, the polymerizations were conducted at 10% concentration (g/mL) in dichloro-methane, or aromatic hydrocarbons, with 1-5 mol% of phosphorus pentafluoride, or boron trifluoride etherate. At low temperature (—78 to —97°), the d.p. of both polymers produced was —90 at increasing temperatures of polymerization, termination processes became more severe, and the d.p. lower. Usually, the reaction times were long (perhaps unnecessarily so), and the conversions were 50 to 90%. The specific rotations of the D-galactans prepared at —28 and —90° differ by only —10° ( — 85 to — 95°), but those of the L-arabinans varied from + 6... 

Estimates of the rotational diffusivity may be made from MD calculations by fitting an exponential function to Legendre polynomials that express the decorrelation of a unit vector that is fixed in the methane coordinate frame (11). The rotational diffusivity was found to increase with concentration (as a result of sorbate-sorbate collisions which act to decorrelate the molecular orientation). The values are of the same order as those for liquid methane and are 2 orders of magnitude larger than those found by Jobic et al. (73) from a quasi-elastic neutron scattering study of methane in NaZSM-5. 

The dipole moment p must be invariant under any rotation of the molecular symmetry group applied to any one of the two molecules [166, 374]. When one of these rotations is applied, the rotation matrix D V(Q) is transformed into a linear combination of the D v, Cl) matrices with different o. The proper linear combinations of the D%V(C1) are invariant under the rotational symmetry group. Such linear combinations are obtained from group-theoretical arguments. For example, for the case of methane pairs in the ground vibrational state, for Ai = 3, 4 and 6, we have the combinations... 

---