Frequency molecular rotation

The standard microwave frequency used for synthesis is 2450 MHz. At this frequency, molecular rotation occurs as molecular dipoles or ions try to align with the alternating electric field of the microwave by processes called dipole rotation or ionic conduction [24, 25). On the basis of the Arrhenius equation, (k = g-Ka/j r j the reaction rate constant depends on two factors, the frequency of collisions between molecules that have the correct geometry for a reaction to occur, A, and the fraction of those molecules that have the minimum energy required to overcome the activation energy barrier,... 

It is well known that y or X photons have energies suitable for excitation of inner electrons. We can use ultraviolet and visible radiation to initiate chemical reactions (photochemistry). Infrared radiation excites bond vibrations only whereas hyperfrequencies excite molecular rotation. In Tab. 1.1 the energies associated with chemical bonds and Brownian motion are compared with the microwave photon corresponding to the frequency used in microwave heating systems such as domestic and industrial ovens (2.45 GHz, 12.22 cm). 

In conclusion, for condensed phases molecular rotations have quite a short lifetime, because of collisions. The eventual oscillations induced by the electric field are then dissipated in the liquid state leading to vibration. At collision densities corresponding to liquids the frequency of the collisions become comparable with the frequency of a single rotation, and because the probability of a change in rotational state on collision is high, the time a molecule exists in a given state is small. It is, therefore, obvious that the electric field cannot induce organization in condensed phases such as in the liquid state. 

Vibrational spectroscopy can help us escape from this predicament due to the exquisite sensitivity of vibrational frequencies, particularly of the OH stretch, to local molecular environments. Thus, very roughly, one can think of the infrared or Raman spectrum of liquid water as reflecting the distribution of vibrational frequencies sampled by the ensemble of molecules, which reflects the distribution of local molecular environments. This picture is oversimplified, in part as a result of the phenomenon of motional narrowing The vibrational frequencies fluctuate in time (as local molecular environments rearrange), which causes the line shape to be narrower than the distribution of frequencies [3]. Thus in principle, in addition to information about liquid structure, one can obtain information about molecular dynamics from vibrational line shapes. In practice, however, it is often hard to extract this information. Recent and important advances in ultrafast vibrational spectroscopy provide much more useful methods for probing dynamic frequency fluctuations, a process often referred to as spectral diffusion. Ultrafast vibrational spectroscopy of water has also been used to probe molecular rotation and vibrational energy relaxation. The latter process, while fundamental and important, will not be discussed in this chapter, but instead will be covered in a separate review [4],... 

Assume now that weak forces have been applied to the molecular rotations and translations so that the eigenvalues X of the Fm matrix correspond to the 3N — 6 (3N - 5 for a linear molecule) real frequencies X = 4tt2v12 of the molecule plus six (or five) very low frequencies (ordinarily calculated as zero frequencies) that correspond to translations and rotations, uncoupled from the larger molecular vibrations. Then, if one recognizes that (1) the determinant of a diagonal matrix is just the product of its diagonal elements, and (2) if a matrix A can be written as a matrix product of B and C, then... 

Spohr found a significant reduction in the dipole reorientation time for a different model of water (but using the same water/Pt potential). In that paper, the reorientation dynamics are characterized by the spectral densities for rotation around the three principal axes of the water molecule. These calculations demonstrated the hindered rotation of water molecules in the plane parallel to the surface. In addition, a reduction in the frequency of rotation about the molecular dipole for water molecules in the adsorbed... 

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. 

Infrared radiation of frequencies less than about 100 cm-1 is absorbed and converted by an organic molecule into energy of molecular rotation. This absorption is quantized thus a molecular rotation spectrum consists of discrete lines. 

In the isotropic potential approximation, the complete binary spectrum is obtained by superimposing basic line profiles, Ga,a2al( T), shifted by sums of molecular rotational frequencies which may be positive,... 

The dielectric constants and molecular rotations of solid and liquid arsine have been determined 6 from the temperature of liquid hydrogen to the boiling point over the frequency range 0-5 to 50 kilocycles. The molecule rotates freely down to 80-1° Abs. 

The frequencies of rotational transitions are much smaller than vibrational frequencies, which means that the rotational motion is slower than the vibrational one. For a free molecule, the period of rotational motion is within 10 12-10 9 s. In condensed media the rotational motion is even slower, its period being respectively greater. At this stage it is more correct to speak of the relaxation time of the molecules. The latter essentially depends on the phase state of the medium. For example, in liquid water the relaxation time of molecular dipoles in an external electric field is about 10 11 s, whereas in ice (at 0°C) it is — 1 () 5 s. 

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. 

Absorption of microwave radiation to excite molecular rotation is allowed only if the molecule has a permanent dipole moment. This restriction is less severe than it may sound, however, because centrifugal distortion can disturb the molecular symmetry enough to allow weak absorption, especially in transitions between the higher rotational states which may appear in the far IR (c. 100cm-1). Microwave spectroscopy can provide a wealth of other molecular data, mostly of interest to physical chemists rather than inorganic chemists. Because of the ways in which molecular rotation is affected by vibration, it is possible to obtain vibrational frequencies from pure rotational spectra, often more accurately than is possible by direct vibrational spectroscopy. 

In view of the calculations considered in Section V and in other publications (VIG), these interactions, giving rise to FIR absorption and to low-frequency Debye loss, resemble interactions pertinent to strongly polar nonassociated liquids. However, if we compare water with a nonassociated liquid (e.g., CH3F), then we shall find that in the latter (i) the R-band is absent (ii) the number mvjb of the reorientation cycles is much less, so that the reduced collision frequency y is substantially greater thus, molecular rotation is more damped and chaotic and (iii) the fitted form factor/is greater. 

We now consider hydrogen transfer reactions between the excited impurity molecules and the neighboring host molecules in crystals. Prass et al. [1988, 1989] and Steidl et al. [1988] studied the abstraction of an hydrogen atom from fluorene by an impurity acridine molecule in its lowest triplet state. The fluorene molecule is oriented in a favorable position for the transfer (Figure 6.18). The radical pair thus formed is deactivated by the reverse transition. H atom abstraction by acridine molecules competes with the radiative deactivation (phosphorescence) of the 3T state, and the temperature dependence of transfer rate constant is inferred from the kinetic measurements in the range 33-143 K. Below 72 K, k(T) is described by Eq. (2.30) with n = 1, while at T>70K the Arrhenius law holds with the apparent activation energy of 0.33 kcal/mol (120 cm-1). The value of a corresponds to the thermal excitation of the symmetric vibration that is observed in the Raman spectrum of the host crystal. The shift in its frequency after deuteration shows that this is a libration i.e., the tunneling is enhanced by hindered molecular rotation in crystal. 

Here the parameters ge, /rB, coz, /, Mh and rr were the g-factor of the free electron, the Bohr magneton, the microwave frequency of measurement, the nuclear spin quantum number, its projection, and the molecular rotational correlation time in solution. The anisotropic parameters, A g, A a and eQVj 1(21 — 1) were estimated from line width coefficients, K, K2 and K4, respectively. Thus the analysis of the temperature dependences of coefficients K, K2 and K4 gave the anisotropic parameters, A g, A a and eQV/1(21 — 1) for all molecules. On the other hand,... 

B. Protein Solutions. The dielectric properties of proteins and nucleic acids have been extensively reviewed (10, 11). Protein solutions exhibit three major dispersion ranges. One occurs at RF s and is believed to arise from molecular rotation in the applied electric field. Typical characteristic frequencies range from about 1 to 10 MHz, depending on the protein size. Dipole moments are of the order of 200-500 Debyes and low-frequency increments of dielectric permittivity vary between 1 and 10 units/g protein/100 ml of solution. The high-frequency dielectric permittivity of this dispersion is lower than that of water because of the low dielectric permittivity of the protein leading to a high-frequency decrement of the order of 1 unit/g protein/... 

R-type transition in spectroscopy. As a result of light absorption in this transition the difference A — J — J" between the quantum numbers of the angular momentum in excited (J ) and ground (J") state equals +1, and the angular momentum of the molecule increases. The transition with transition dipole moment d l at frequency u>o — fl corresponds to a diminution in the angular momentum of molecular rotation, and we have A = J — J" = — 1. Such a transition is called a P-type transition. 

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