Vibration parameters

In using the combination difference method to obtain vibrational parameters, cOg, etc., for two electronic states between which vibronic transitions are observed, the first step is to organize all the vibronic transition wavenumbers into a Deslandres table. An example is shown in Table 7.7 for the system of carbon monoxide. The electronic... 

The high stability of fluoride complexes maintains the configuration and vibration parameters of different compounds in various media. This special feature enables clear distinguishing of different complex ion types using vibration spectroscopy in solid, liquid and molten media. 

The correlation of structural and vibrational parameters, and a detailed analysis of structural trends based on the available wealth of electron diffraction, microwave and X-ray structural studies on sulphoxides and sulphones, have been reported by Hargittai in a comprehensive study20 which will stand for a long time as a milestone in the structural... 

As at room temperature Bragg reflections contain both nuclear and magnetic structure factors, the nuclear structure was refined from a combination of polarized and unpolarized neutron data. Contrary to the ideal structure where only three atomic sites are present, it has been shown [11, 12] that some Y atoms were substituted by pairs of cobalt. These pairs, parallel to the c-axis are responsible for a structure deformation which shrinks the cobalt hexagons surrounding the substitutions. The amount of these substituted Y was refined to be 0.046 0.008. Furthermore, the thermal vibration parameter of Coi site appeared to be very anisotropic. The nuclear structure factors Fn were calculated from this refined structure and were introduced in the polarized neutron data to get the magnetic structure factors Fu. 

The success of the gas phase electron diffraction analysis of cis-and /ra 5-decalin (123) is another example of the use of MM calculations as an auxiliary technique. Minimum energy conformations and vibrational ampUtudes were calculated by both the Lifson and Boyd force fields (30,31) and were used as the starting values for refinement of the geometrical and vibrational parameters for the least-squares analysis. The results revealed no appreciable strain in cj5-decalin (123) other than that expected from gauche interactions. 

By the early fifties a technique was developed mainly by J. and I. L. Karle to quantitatively treat the experimental data in order to obtain accurate geometrical and vibrational parameters. The new technique was called the sector-microphotometer method. As the name has been used ever since, today it has a wider meaning than just a reference to the experimental technique, and it usually signifies all the experimental, computational, and theoretical developments of the electron diffraction technique. 

Chandrasekhar, K., and Biirgi, H.-B. (1984). Dynamic processes in crystals examined through difference vibrational parameters At/ The low-spin-high-spin transition in tris(dithiocarbamato)iron(III) complexes. Acta Crystallogr., Sect. B 40, 387-397. 

However, the precision of the results derived from a high-quality, low-temperature data set may be just sufficient to distinguish between the isotropic vibrational parameters of hydrogen and deuterium (U > UD). This was demonstrated for the X-ray structure analysis at a temperature of 100 K of ammonium (25,, 3/ )-malate-3-[Pg.380]

Molecular electronic spectroscopy can provide information on vibrational parameters (frequencies and force constants), rotational parameters (moments of inertia and therefore molecular geometries), electronic excitation energies, ionization potentials, and dissociation energies for ground and excited electronic states. Moreover, a knowledge of excited electronic states is important in understanding the course of photochemically induced reactions. 

Shock initiation has been studied in the presence of free-radical donors and getters (Ref 154). Detonation occurs only under particular vibration parameters (Ref 155). A new ACP (Augmented by Collision Pressure) method is said to be simpler and more reliable than conventional initiation procedures (Ref 105)... 

Fig. 6. Structure of the cation (K-6) the K atom and atoms of the benzene ring A were refined with anisotropic vibration parameters (reproduced with permission).

Table 6. Vibrational parameters of SiNH/SiND and CNH/CND4Ib)...

At ambient temperature, it is usually impossible to discern the smearing caused by thermal vibrations (averaged over time) from that caused by static displacements of atoms (averaged over the whole crystal), and the vibrational parameters in fact account for both. Therefore it is now recommended to use the term atomic displacement parameters (ADP) instead. A diffraction study of the same stmcture at different temperatures, however, will show the difference the genuine thermal vibrations diminish on cooling, but the ADP due to static disorder (e.g. in ferrocene ) will remain large. 

Similar considerations apply for modelling dipole and quadrupole changes upon vibrational motion in CS2. In Table 1 the vibrational parameters entering equation (2) are presented. 

An interesting result of this or a more detailed analysis [66] is that the excited-state vibrational parameters can be extracted from this type of time domain experiment even when the corresponding frequency domain observation of vibrational progressions in the Sq - Sj absorption spectrum is impossible due to inhomogeneous broadening of the electronic transition. In malachite green, the vibrational dephasing rate is about twice as rapid in Sj as in So [63]. 

Because the diffraction experiment involves the average of a very large number of unit cells (of the order of 10 in a crystal used for X-ray diffraction analysis), minor static displacements of atoms closely simulate the effects of vibrations on the scattering power of the average atom. In addition, if an atom moves from one disordered position to another, it will be frozen in time during the X-ray diffraction experiment. This means that atomic motion and spatial disorder are difficult to separate from each other by simple experimental measurements of intensity falloff as a function of sm6/X. For this reason, atomic displacement parameter is considered a more suitable term than the terms that have been used historically, such as temperature factor, thermal parameter, or vibration parameter for each of the correction factors included in the structure factor equation. A displacement parameter may be isotropic (with equal displacements in all directions) or anisotropic (with different values in different directions in the crystal). 

Vibration parameter (See temperature factor or atomic displacement parameters.)... 

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