Constants calculated

For reactions between atoms, the computation needs to model only the translational energy of impact. For molecular reactions, there are internal energies to be included in the calculation. These internal energies are vibrational and rotational motions, which have quantized energy levels. Even with these corrections included, rate constant calculations tend to lose accuracy as the complexity of the molecular system and reaction mechanism increases. 

Coupling constants, calculated with the aid of McConnel s formula (286) are given in Table 1-42 together with the experimental values. 

Table 7.2 lists a few cross-propagation constants calculated by Eq. (7.20). Far more extensive tabulations than this have been prepared by correlating copolymerization and homopolymerization data for additional systems. Examination of Table 7.2 shows that the general order of increasing radical activity is... 

Fig. 18. Rate constant calculated with the use of (2.80a) plotted against (m/mH). The hydrogen transfer rate is assumed to be 10 s the effective symmetric vibration mass 125mH. The ratio of force constants corresponding to the intra (Kq) and intermolecular (K,) vibrations is (Ki/Ko) = 2.5 x 10 , 5 x 10 and l.Ox 10 for curves 1-3, respectively.

One of the best available texts describing the principles of Raman scattering from crystals. Includes factor group calculations, polarization measurements, force constant calculations, and many other aspects of crystal physics. 

Substituent constants calculated in this way are in good agreement with empirical Of values. The same system was used to calculate values by determining charge accumulation or depletion on the a and p carbons of substituted ethylenes using the 4-3IG method. 

The residence time of the crystallizer in previous example is doubled. If the slurry suspension density is kept constant, calculate the effect of this change on ... 

For Scheme XIV, and for each of the following sets of rate constants, calculate the exact relative concentration cb/ca as a function of time. Also, for each set, calculate the approximate values of cb/ca using both the equilibrium assumption and the steady-state approximation. 

If k2 is sufficiently large that it cannot be neglected (which will be revealed by the inconstancy of the constant calculated as above), then Eq. (6-54) may be put into the forms... 

Force constant calculations are normally done in Cartesian coordinates. Suppose we have N atoms whose position vectors are Ri, R2,. .., Ra - Each of the atoms vibrates about its equilibrium position Ri g, Ri.e, , R v,e-The first step in our treatment is to define mass-weighted displacement coordinates... 

No ab initio coupling constants calculations related to tautomerism are available however, semiempirical calculations using, for instance, INDO have been reported [83THE(94)163]. 

Elastic constants calculated and the experimental lattice constant. Experimental data from Ref. [36]. 

From the L/D values of l-(e), knowing the L/V, using V assumed as constant, calculate the necessity reflux fluid, L. Figure 8-39 indicates a plot of time to produce a constant product composition and the necessary external reflux returned to the tower. 

RCS (.sec Rate-controlling step) Racemization, 49, 95 Rate constant calculation of. 17 composite, 161-164 diffusion-controlled, 200-201 Rate-controlling step, 9, 82-86 Rate-determining step (see Ratecontrolling step)... 

The recipe (5.58) is even more sensitive to the high-frequency dependence of kjj than similar criterion (5.53), which was used before averaging over kinetic energy of collisions E. It is a much better test for validity of microscopic rate constant calculation than the line width s j-dependence, which was checked in Fig. 5.6. Comparison of experimental and theoretical data on ZR for the Ar-N2 system presented in [191] is shown in Fig. 5.7. The maximum value Zr = 22 corresponding to point 3 at 300 K is determined from the rate constants obtained in [220],... 

Pulsed source techniques have been used to study thermal energy ion-molecule reactions. For most of the proton and H atom transfer reactions studied k thermal) /k 10.5 volts /cm.) is approximately unity in apparent agreement with predictions from the simple ion-induced dipole model. However, the rate constants calculated on this basis are considerably higher than the experimental rate constants indicating reaction channels other than the atom transfer process. Thus, in some cases at least, the relationship of k thermal) to k 10.5 volts/cm.) may be determined by the variation of the relative importance of the atom transfer process with ion energy rather than by the interaction potential between the ion and the neutral. For most of the condensation ion-molecule reactions studied k thermal) is considerably greater than k 10.5 volts/cm.). 

In Table III we compare for several reactions the experimental rate constants with rate constants calculated on the basis of ion-induced dipole interactions only from the relation (4) ... 

A strictly entropically controlled tendency for statistical ligand distribution was discussed 150) for ligand exchange when the sum of the Sb—X and Sb—Y bond energies remains constant. Calculations show that due to the electronic interaction in the entire molecule an energetic tendency also exists to form Lewis acids with mixed ligand spheres ... 

The molecule S12, like Se, is of Dsd symmetry but in the soHd state it occupies sites of the much lower C211 symmetry [163]. Due to the low solubihty and the thermal decomposition on melting only solid state vibrational spectra have been recorded [2,79]. However, from carbon disulfide the compound Si2-CS2 crystallizes in which the S12 molecules occupy sites of the high Sg symmetry which is close to 03a [163]. The spectroscopic investigation of this adduct has resulted in a revision [79] of the earher vibrational assignment [2] and therefore also of the earlier force constants calculation [164]. In Fig. 24 the low-temperature Raman spectra of S12 and Si2-CS2 are shown. 

The spectra of S12 and Si2-CS2 clearly reflect the differing site symmetries of the S12 molecule The two Eg vibrations at 188 and 245 cm degenerate in Si2 CS2, split into their components in pure S12 with its non-degenerate site symmetry of C2h- The valence force constants calculated for S12 reproduce the observed wavenumbers within 14 cm [79]. The two most interesting constants are/r = 2.41 and/ r = 0.60 N cm ... 

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