DFT frequencies

The vibrational spectra of 1,2-dithiole-3-thione 46 and 1,2-dithiol-3-one 47 were computed at the DFT and MP2 levels (Scheme 31) [98VS77]. Most remarkably, the uniformly scaled MP2 fundamentals are in better agreement with experimental data than the corresponding DFT frequencies. 

Florian and Johnson50 calculated vibrational frequencies in isolated formamide using the DFT calculations at the LDA (SVWN) and post-LDA (B88/LYP) levels. The DFT frequencies were compared with the ones derived from the Hartree-Fock and MP2 calculations, and from experiment. The authors found that the DFT(B88/LYP) frequencies were more in line with experiment then the MP2 ones. The DFT(SVWN) calculations led to geometry, force constants, and infrared spectra fully comparable to the MP2 results. The equilibrium geometry and vibrational frequencies of formamide were also the subject of studies by Andzelm et al.51. It was found that the DFT(B88/P86) calculations led to frequencies in a better agreement with experiment than those obtained from the CISD calculations. 

Table 7.8. Experimental and calculated (DFT) frequencies of the Si-H and SiO-H stretching vibrations for H-related centers in Si02 and their fluorine-containing low-molecular analogs...

As the result of the DFT frequency calculations in LS, we have Nai totally symmetric normal coordinates Qk (k = I... Na ), which are the eigenvectors of the Hessian. The corresponding eigenvalues are Ak = (2 rvk), I k is a frequency of a normal mode which is connected to the wave numbers, i3k, that are usually used, by a simple relation Vk = kc, where c is the speed of light. The normal modes are displacement vectors in generalized displacement coordinates, i.e. ... 

In addition, the stretching vibrations from the DFT frequency analysis agreed with the experimental values. 

Unlike ab initio and semiempirical frequencies, DFT frequencies are not always significantly lower than observed ones (indeed, calculated values slightly higher than experimental frequencies have been reported). Flere are some correction factors that have been calculated for various functionals, as well as for some ab initio and semiempirical methods (slightly different factors were recommended for accurate calculations of ZPE) [62] except for F1F/3-21G the basis set for the ab initio and DFT methods is6-31G ... 

In all our molecular modeling, special care was taken not only to reproduce the DFT frequencies, but also the eigenvectors. Indeed, a great deal of spectroscopic experiments on photosynthetic RC involve directly or indirectly the nuclear dynamics of the chromophores. In Fig. 3 we present... 

The far-left column in the cluster-adsorbate system. Adjacent three columns (steric/donation/back donation) give in the change in frequency due to each contribution, calculated with respect to the uncoordinated DFT frequency of 2095 cm" for CO. The main entries have been calculated in the order as given in the Table, i.e., steric-donation-back donation, whereas the entries within parentheses refer to the order steric-back donation-donation. The column rest refers to the residual frequency shift upon adsorption not accounted for by the sum of steric/donation/back donation. The far-right column gives the coordinated C-0 vibrational frequency. 

As an example, a window size of 4096 samples at a sampling rate of 22,050 Hz would give us a resolution of 5 Hz between adjacent frequency samples in the DFT, but would also act to average all events that happen within 0.2 seconds of each other. In contrast, a window size of 100 samples would allow us to inspect an event that takes place in 4.5 milliseconds, but our spectral frequency resolution (space between DFT frequency bins) would be 220 Hz per bin. 

Figure 4 Theoretically simulated, Lorentzian lineshape of 5 cm > half width at half height, and experimental (Reference 119) VCD and IR spectra of 1-azabicyclo-[3.1.0]hexane 17 in the region 600-1600 cm->. SCF, MP2, and DFT frequencies are scaled by 0.90, 0.95, and 0.97, respectively.

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