Bond rotation frequencies

When rotation occurs about a bond there are two sources of strain energy. The first arises from the nonbonded interactions between the atoms attached to the two atoms of the bond (1,4-interactions) and these interactions are automatically included in most molecular mechanics models. The second source arises from reorganization of the electron density about the bonded atoms, which alters the degree of orbital overlap. The values for the force constants can be determined if a frequency for rotation about a bond in a model compound can be determined. For instance, the bond rotation frequencies of ethane and ethylamine have been determined by microwave spectroscopy. From the temperature dependence of the frequencies, the barriers to rotation have been determined as 12.1 and 8.28 kJ mol-1, respectively1243. The contribution to this barrier that arises from the nonbonded 1,4-interactions is then calculated using the potential functions to be employed in the force field. 

Pure rotational spectra only appear for molecules with permanent dipole moments and vibrational spectra require a change of dipole during the motion. However, electronic spectra are observed for all molecules, and changes in the electron distribution in a molecule are always accompanied by dipole changes. As a result even homonuclear molecules (H2 or N2) which have no rotation or vibration spectra, do give electronic spectra with vibrational and rotational structure from which rotational constants and bond vibration frequencies may be derived. 

A particularly interesting example of the effect of molecular motions on NMR line widths was observed by Murray and Waugh for Co(NH3)6Cl i (92). Theoretical line shapes for the proton resonance of Co(NH3)6C13 are shown in Fig. 22 for (1) a rigid lattice, (2) rotation about the Co—N bond, and (3) rotation of the entire Co(NH3)63+ ion in the crystal lattice. Experimental points for II1 spectra at 100°K and 300°K are seen to fall quite well on curves calculated for, respectively, models (2) and (3). Thus even at 100°K rotation about the Co—N bond at frequencies in excess of about 104 sec-1 is occurring. Between 100°K and 300°K, the frequency of rotation of the Co(NH3)63+ ion exceeds 104 sec-1. 

Bond Rotational Moment of Inertia (GHz) Frequency Vj Energy Eq... 

Although some of the speculation about non-thermal microwave effects appears to emanate from a misconception that microwave radiation can excite rotational transitions, the frequencies at which these occur are much higher than 2.45 GHz. For example, the first absorption lines of OCS, CO, HF and MeF occur at 12.2, 115, 1230 and 51 GHz, respectively. Internal bond rotations (torsional vibrations) also require higher frequencies, in the order of 100-400 cm-1 or 3000-12 000 GHz, for excitation61,62. 

It is interesting to compare the results obtained for ordinary and heavy water. To interpret the difference, we show in Fig. 33 by solid curves the total absorption attained in the R-band (i.e., near the frequency 200 cm-1). Dashed curves and dots show the components of this absorption determined, respectively, by a constant (in time) and by a time-varying parts of a dipole moment. In the case of D20, the R-absorption peak vR is stipulated mainly by nonrigidity of the H-bonded molecules, while in the case of H20 both contributions (due to vibration and reorientation) are commensurable. Therefore one may ignore, in a first approximation, the vibration processes in ordinary water as far as it concerns the wideband absorption frequency dependences (actually this assumption was accepted in Section V, as well is in many other publications (VIG), [7, 12b, 33, 34]. However, in the case of D20, where the mean free-rotation-frequency is substantially less than in the case of H20, neglecting of the vibrating mechanism due to nonrigid dipoles appears to be nonproductive. 

Figure 58. Density distributions of angular deflections P (a), internal-rotation frequencies (b), transverse librations (c), and their frequencies (d). Solid, dashed, and dashed-and-dotted curves refer to the H-bond length /, — 1.42,1.54, and 1.85 A. Water H2O at T — 3(X) K.

Figure 60. Effect of stretching and bending of H-bond on rotational dynamics of H20 molecule. Solid lines account for the effect of the full torque, and dashed lines account for the effect of only the stretching, (a) Reduced potential u versus angular deflection p. (b,c) Distributions of amplitudes P0 (b) and a (c). (d) Distribution of restricted-rotation frequencies vstr. (e) The dependence of the RR frequency vstr on amplitude P0. k = 6000dyn cm-1, T = 300K, Cq = 0.1, r = 1.02 A.

The microwave experiment studies rotational structure at a given vibrational level. The spectra are analyzed in terms of rotational models of various symmetries. The vibration of a diatomic molecule is, for instance, approximated by a Morse potential and the rotational frequencies are related to a molecular moment of inertia. For a rigid classical diatomic molecule the moment of inertia I = nr2 and the equilibrium bond length may be calculated from the known reduced mass and the measured moment, assuming zero centrifugal distortion. 

II), RRKM calculations were performed to determine the rate constants. The program Fall-Off", available from the Quantum Chemistry Exchange Program (2J) and modified by Shandross and Howard (24) was used lor the RRKM calculations. Transition states were located at the centrifugal barrier on the minimum energy path from reactants to products. Bond vibration and rotation frequencies were estimated using the techniques of Benson (25). 

Recently, Neue [54] published another paper on an application of WT in dynamic NMR spectroscopy which could simplify the analysis of the free induction decay (FID) signal. Dynamic NMR spectroscopy is a technique used to measure rate parameters for a molecule [55]. The measured resonance frequencies represent the spatial coordinates of spins. Any motion, such as bond rotation and other molecular gymnastics, may change these frequencies as a function of time. The localization property of WT gives a better picture... 

---