Vibrations, intramolecular lattice

In the crystal, the total number of vibrations is determined by the number of atoms per molecule, N, and the nmnber of molecules per primitive cell, Z, multiplied by the degrees of freedom of each atom 3ZN. In the case of a-Sg (Z =4, N =8) this gives a total of 96 vibrations ( ) which can be separated in (3N-6)—Z = 72 intramolecular or "internal" vibrations and 6Z = 24 intermo-lecular vibrations or lattice phonons ("external" vibrations). The total of the external vibrations consists of 3Z = 12 librational modes due to the molecular rotations, 3Z-3 = 9 translational modes, and 3 acoustic phonons, respectively. 

Polymerization changes both the microscopic and the macroscopic properties of the material. The intramolecular lattice vibrations change relatively little, but because the symmetry is lowered a large number of previously forbidden lines appear in the Raman and IR spectra. This was observed already in pioneering experiments on polymeric C60 [6-8], and a very large number of spectroscopic studies have been carried out on polymeric materials with different structures... 

Probably the most important experimental work which confirms the cooperative nature of the spin crossover transition is the heat capacity measurements on Fe(phenanthroline)2(NCS)2 and Fe(phenanthroline)2-(NCSe)2 by Sorai Seki (1974). The variation in the molar heat capacity of the latter compound with temperature is shown in Figure 3.27. Not only does the heat capacity show a sharp peak at the transition temperature (see Table 3.9), but there is also a change in the heat capacity, for the two different spin states (see Figure 3.27) at the transition. These authors propose that the total heat capacity of each spin state is made up of contributions from lattice vibrations, intramolecular vibrations, and electron thermal excitation. From this they have determined the changes in enthalpy and entropy associated with the change in spin state at the crossover. The results of these calculations are given in Table 3.9 and they... 

The normal modes for solid Ceo can be clearly subdivided into two main categories intramolecular and intermolecular modes, because of the weak coupling between molecules. The former vibrations are often simply called molecular modes, since their frequencies and eigenvectors closely resemble those of an isolated molecule. The latter are also called lattice modes or phonons, and can be further subdivided into librational, acoustic and optic modes. The frequencies for the intermolecular modes are low, reflecting, the... 

The Raman and infrared spectra for C70 are much more complicated than for Cfio because of the lower symmetry and the large number of Raman-active modes (53) and infrared active modes (31) out of a total of 122 possible vibrational mode frequencies. Nevertheless, well-resolved infrared spectra [88, 103] and Raman spectra have been observed [95, 103, 104]. Using polarization studies and a force constant model calculation [103, 105], an attempt has been made to assign mode symmetries to all the intramolecular modes. Making use of a force constant model based on Ceo and a small perturbation to account for the weakening of the force constants for the belt atoms around the equator, reasonable consistency between the model calculation and the experimentally determined lattice modes [103, 105] has been achieved. 

The first Raman and infrared studies on orthorhombic sulfur date back to the 1930s. The older literature has been reviewed before [78, 92-94]. Only after the normal coordinate treatment of the Sg molecule by Scott et al. [78] was it possible to improve the earlier assignments, especially of the lattice vibrations and crystal components of the intramolecular vibrations. In addition, two technical achievements stimulated the efforts in vibrational spectroscopy since late 1960s the invention of the laser as an intense monochromatic light source for Raman spectroscopy and the development of Fourier transform interferometry in infrared spectroscopy. Both techniques allowed to record vibrational spectra of higher resolution and to detect bands of lower intensity. 

Experimental studies of liquid crystals have been used for many years to probe the dynamics of these complex molecules [12]. These experiments are usually divided into high and low-frequency spectral regions [80]. This distinction is very important in the study of liquid crystalline phases because, in principle, it can discriminate between inter- and intramolecular dynamics. For many organic materials vibrations above about 150 cm are traditionally assigned to internal vibrations and those below this value to so-called lattice modes . However, the distinction is not absolute and coupling between inter- and intramolecular modes is possible. 

Electrons of still lower energy have been called subvibrational (Mozumder and Magee, 1967). These electrons are hot (epithermal) and must still lose energy to become thermal with energy (3/2)kBT — 0.0375 eV at T = 300 K. Subvibrational electrons are characterized not by forbiddenness of intramolecular vibrational excitation, but by their low cross section. Three avenues of energy loss of subvibrational electrons have been considered (1) elastic collision, (2) excitation of rotation (free or hindered), and (3) excitation of inter-molecular vibration (including, in crystals, lattice vibrations). 

In those cases when no sharp groups of slow electrons are observed, the unselective deformation of the distribution curve can be ascribed to the excitation of intramolecular and intermolecnlar vibrations in the lattice. The appearance of sharp groups of slow electrons is to be ascribed to the electronic excitation of the molecular ions formed, as was the case for the photoionization of similar compounds in the gas phase, dealt with in the previous sections. As recently found, energy losses of 0.3-0.4 e.v. may be due to the excitation of electrons from traps. 

For intramolecular vibrations, each site was considered independently. However, the reorganizations in the surrounding solvent are necessarily properties of both sites since some of the solvent molecules involved are shared between reactants. The critical motions in the solvent are reorientations of the solvent dipoles. These motions are closely related to rotations of molecules in the gas phase but are necessarily collective in nature because of molecule—molecule interactions in the condensed phase of the solution. They have been treated theoretically as vibrations by analogy with lattice vibrations of phonons which occur in the solid state.32,33... 

For large spin-orbital interactions a marked anisotropic -factor is expected and provides an important mechanism for relaxation of the electron spin from the upper to the lower state. Once again, if this relaxation is too efficient, there will be an uncertainty-principle broadening of the lines, which may be so great that no absorption can be detected. The relaxation is due to coupling between the orbital component and vibrational and other motions of the lattice , which includes any inter- or intramolecular motions, and hence it may be necessary to cool to very low temperatures in order to obtain narrow lines. Fortunately this situation rarely arises for organic radicals since iS.g is almost invariably very small. 

Isochoric heat capacity of crystals can be presented as a sum of contributions from lattice vibrations (6 degrees of freedom) and intramolecular vibrations (3n-6 degrees of freedom, where n is a number of atoms in a molecule)... 

The total set of resonant sublevels participating in the RLT typically consists of a small number of active acceptor modes with nonzero matrix elements (2.59) and many inactive modes with Fi( = 0. The latter play the role of the reservoir and ensure the resonance condition Et = Ef. For aromatic hydrocarbon molecules, for example, the main acceptor modes are strongly anharmonic C-H vibrations that accept most of the electronic energy in singlet-triplet transitions. The inactive modes in this case are the stretching and bending vibrations of the carbon skeleton. The value of p( afforded by these intramolecular vibrations is often so large that they behave as an essentially continuous bath even in the absence of intermolecular vibrations. This statement is supported by the observation that RLT rates for many molecules embedded in crystal lattices are similar to those of the isolated gas-phase molecules. 

Cp.iatvib is the contribution from lattice vibrations, CPtintravaj the contribution from intramolecular vibrations, and CPimag is the magnetic or electronic heat capacity arising from thermal excitation of electrons. 

This intermolecular potential for ADN ionic crystal has further been developed to describe the lowest phase of ammonium nitrate (phase V) [150]. The intermolecular potential contains similar potential terms as for the ADN crystal. This potential was extended to include intramolecular potential terms for bond stretches, bond bending and torsional motions. The corresponding set of force constants used in the intramolecular part of the potential was parameterized based on the ab initio calculated vibrational frequencies of the isolated ammonium and nitrate ions. The temperature dependence of the structural parameters indicate that experimental unit cell dimensions can be well reproduced, with little translational and rotational disorder of the ions in the crystal over the temperature range 4.2-250 K. Moreover, the anisotropic expansion of the lattice dimensions, predominantly along a and b axes were also found in agreement with experimental data. These were interpreted as being due to the out-of-plane motions of the nitrate ions which are positions perpendicular on both these axes. 

Figure 3-4 (a) Raman spectra of the symmetric (vj) and the anti-symmetric (V3) stretching modes in solid H2S at various pressures. The phase transition occurs at about 11 GPa. (b) Pressure dependence of the intramolecular and the lattice vibrational frequencies in solid H2S at 300 K. (Reproduced with permission from Ref. 12.)... 

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