Frequency analysis scale factors

The scale factor is optional. If Included, it says to scale the frequencies before performing the thermochemicai analysis. Note that including the factor affects the thermochemistry output only (including the ZPE) the frequencies printed earlier in the output remain unsealed. This parameter is the means by which scale foctors are applied to thermal energy corrections. 

Fonnylcarbene ( CHCHO), 116 Free Radicals, carbon, 110-114 RSE, table of, 114 structure, 110 substituents on, 111 Frequency analysis, 32-33 scale factors, 33 Fulvene, 268 SHMO, 268 Furan, 267 SHMO, 267... 

The discussion of the previous section suggests that the linear combination of the shifted and scaled Fourier transforms of the analysis window in Equation (9.72) must be explicitly accounted for in achieving separation. The (complex) scale factor applied to each such transform corresponds to the desired sine-wave amplitude and phase, and the location of each transform is the desired sine-wave frequency. Parameter estimation is difficult, however, due to the nonlinear dependence of the sine-wave representation on phase and frequency. 

The most efficient way to speed up spin diffusion is the so-called r.f.-driven spin-diffusion experiment [15, 19] where the chemical-shift differences are removed by r.f. irradiation. For small chemical-shift differences, r.f.-driven spin diffusion can be implemented by applying a continuous-wave r.f. field to the S-spins which can theoretically be described by a transformation into a tilted rotating frame (see Appendix B). To zeroth-order average Hamiltonian theory the chemical-shift differences are removed (fl, — fty = 0 for all spins i and j) and the dipolar-coupling frequencies are scaled by a factor s = -1/2. The scaled-down (or ideally vanishing) chemical-shift difference allows one to keep the zero-quantum line narrow by decoupling the protons. This results in fast spin-diffusion rates. Furthermore, the rate constants are now determined by the S-spin coupling network, and the proton spins need not be considered for the data analysis. 

The character of each stationary point (either energy minimum, for which all vibrational frequencies are real, or saddle point, characterized by one imaginary frequency) has been confirmed by vibrational analysis done at the MP2/6-31G(d,p) level. Relative energies have been corrected for zero-point vibrational energies (ZPE) using carefully scaled vibrational wave numbers. The MP2 scaling factor has been deduced from our previous theoretical study on the HCN and HNC systems [60]. It is equal to 0.969 and has been applied to all molecules studied in this section. 

In order to consider a specific example, we have mainly used in our analysis the material parameters of Phase 5. However, in order to study specifically the effects of flexoelectricity, a theoretical scaling factor has been introduced to tune the strength of the flexoelectricity, i.e. we use (ei—63) instead of (61—63) and (ei+63) instead of (ej 4-63). In Fig. 4.4 the calculated critical voltage f/c(/) as a function of the AC frequency / is shown for three different values of. In line with the standard... 

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