Computational Chemistry

distribution) will have the extra energy needed to traverse the higher-energy regions of this flatter saddle, away from the exac ...

of this region and its curvature. The shape of the hypersurface can be handled as an analytic function of atomic coordinates E¼f ...

Equation (5.198) was used to calculate rate constants for the three unimolecular reactions in Fig.5.30(cf. Fig. 5.21). Reactants ...

unsatisfactory for the reaction of ozone with ethyne and ethene, and CBS-QB3 was singled out for special cautioning; the reactio ...

change in activation free energy of 5 kJ mol#^1 can alter the rate constant or halflife by a factor of about 10: DGz¼100 kJ mol# ...

Our calculations predict room temperature halflives for cyclopropylidene of about 10 #^9 –10#^10 s. Attempts to generate cyclopr ...

temperature from the free energy of activation, for unimolecular isomerizations. This regardsDG{as only a weak function ofT, as ...

Table 5.13 Energy differences (kJ mol ^1 ) of some isomers, calculated at modest ab initio levels; plu s at the G3(MP2) level, a ...

purpose. All the levels predict the correct stability order in these four cases, but are vulnerable to varying extents to a narr ...

The characterization of stationary points by the number of imaginary frequen- cies was discussed inChapter 2, and zero-point ene ...

parabolicE/qrelationship (Fig5.32), i.e. to a steeper curve than the real one, and thus to stiffer bonds. Stiffer bonds need mor ...

higher, thanobservedfrequencies. From the foregoing discussion it appears that the fundamental reason ab initio frequencies are ...

wavenumbers and intensities. The intensity of a vibration is determined by the change in dipole moment accompanying the vibratio ...

be unusual. A few IR spectra calculated at routinely practical levels are shown in Figs.5.33–5.36and compared with gas-phase spe ...

Theshapeof a molecular species can provide clues to the existence of theoreti- cal principles (why is it that benzene has six e ...

Theenergyof a molecular species relative to the energies of other species on a potential energy surface is fundamental to a kno ...

5.5.4.1 Dipole Moments The dipole moment [ 250 ] of a system of two chargesQand#Qseparated by a distanceris, by definition, the ...

moments. It is often convenient to think of the molecular dipole moment in a more pictorial form than that presented by Eq. (5.2 ...

to fluctuate, so that even a spherical atom can have temporary nonzero dipole moments. Another point is that we usually consider ...

usually not much better. Some calculated and experimental dipole moments are compared in Table5.14. These results, which are qui ...