Predicted frequency

Yon can use a sin gle poin t calculation that determines energies for ground and excited states, using configuration interaction, to predict frequencies and intensities of an electron ic ultraviolet-visible spectrum. 

This mode corresponds to the IR peak associated with carbonyl stretch, used to identify the C-O double bond. Its predicted frequency is about 1810 (after scaling). This is in reasonable agreement with the experimental value of 1746. Using a larger basis set will improve this value. We ll discuss basis set effects in the next chapter. 

After scaling, the predicted frequencies are generally within the expected range for carbonyl stretch (-1750 cm ). The table below reproduces our values, published theoretical values using the 6-31+G(d) basis set (this basis set includes diffuse functions), and the experimental values, arranged in order of ascending experimental frequency ... 

For the four smaller systems, determine how well the predicted frequencies compare to the experimental IR spectral data given below. Identify the symmetry type for the normal mode associated with each assigned peak. 

For the Cs and K substituents, all three DFT functionals produce similar structures. All three functionals predict frequencies which are somewhat lower than the observed values but which reproduce the trends in the experimental data quite well. The SVWN5 frequencies tend to be higher than those computed by BLYP and B3LYP. 

Here are the predicted frequencies for the first excited state of formaldehyde, along with the corresponding experimental values (the scale factor is the same as for Hartree-Fock frequencies 0.8929) ... 

In addition, compare the predicted frequencies for the first excited state with these experimental results ... 

The frequency job confirms that this structure is a rninimum, finding no imaginary frequencies. Here are the predicted frequencies, compared to the experimental values given earlier ... 

Here are the predicted frequencies (scaled, in cm ) in the gas phase and in solution ... 

Sclutlcn The geometry optimization reveals that the structure of formaldehyde in cyclohexane is essentially the same as it is in acetonitrile. Here are the predicted frequency shifts with respect to the gas phase for the two media ... 

Besides these response properties of a molecule we will also devote one section in this chapter to the experimentally important infrared intensities, which are needed to complement the theoretically predicted frequencies for the complete computational simulation of an IR spectrum. This discussion belongs in the present chapter because the infrared intensities are related to the derivative of the permanent electric dipole moment p with respect to geometrical parameters. 

The selection rules for the QM harmonic oscillator pennit transitions only for An = 1 (see Section 14.5). As Eq. (9.47) indicates diat the energy separation between any two adjacent levels is always hm, the predicted frequency for die = 0 to n = 1 absorption (or indeed any allowed absorption) is simply v = o). So, in order to predict die stretching frequency within the harmonic oscillator equation, all diat is needed is the second derivative of the energy with respect to bond stretching computed at die equilibrium geometry, i.e., k. The importance of k has led to considerable effort to derive analytical expressions for second derivatives, and they are now available for HF, MP2, DFT, QCISD, CCSD, MCSCF and select other levels of theory, although they can be quite expensive at some of the more highly correlated levels of theoiy. 

One final caveat with respect to comparing experimental IR spectra with theoretically predicted frequencies is that the latter do not account for such experimental complications as Fermi resonances (where two nearby fundamentals are shifted to higher and lower frequencies, respectively), overtones, etc. Such details require case-by-case evaluation. 

Atomistic simulations, even though more time-consiuning will also yield valuable information on the dependence of e on chemical structure. One of the advantages of these simulations is that they can, in principle, predict frequency dependence. Work along these lines is in progress. 

The spectrum in Figure 3.65 was found to closely resemble that of a cationic complex observed by the authors in experiments investigating the anodic behaviour of the (Dmbpy)Re[CO]jCl. The complex, (Dmbpy)Re[CO]3 (CHjCN +, showed absorptions at 2039cm-1, 1948cm 1 (as a poorly-resolved shoulder) and 1935 cm -, The predicted frequencies were 2043 cm, 1959 cm 1 and 1944 cm-. In both cases, considerable structure was observed in the C=N absorption region between 2250cm-1 and 2300cm-1 (not... 

Normal vibration calculations, if based on a correct structure and correct potential field, would supposedly permit a unique correlation to be made between predicted and observed absorption bands. In most cases this ideal situation is far from being achieved in the study of high polymer spectra. More usually the structure and force field are to some extent unknown, or normal mode calculations are not available, so that other methods must be used in order to establish the origin of bands in the spectrum. Even if complete calculations were available it would be desirable to check their predictions by means other than a comparison of observed and predicted frequency values. One method of doing so is by studying isotopically substituted molecules, and the most useful case is that in which deuterium is substituted for hydrogen. 

As usual, the actual values for the force constants themselves must be derived by fitting the predicted frequencies of the visible modes to the experimental values. 

The parameters A3 and 0 cwere set arbitrarily of order 102 and 5.0 10 respectively, since it was found by trial and error that these values lead to good qualitative agreement between experimental and model predicted frequencies. However no systematic attempt was made to optimize the values of the unknown parameters in order to improve the agreement with the experimental amplitudes and frequencies. 

Separate values of the parameters were deduced for ortho, meta and para substituents. These values are listed in Table 6. As most chemists would have anticipated the standard deviation of the predicted frequency for the orf/w-substituted iodobenzenes is much higher than for the meta or para derivatives. Likewise, of these two last series it is the /wra-substituted compounds that exhibit the greatest sensitivity to asymmetry parameter. This is probably due to steric factors that may deform the shape of the filled non-bonding p-orbitals on the iodine atom and it is unlikely that in this case the asymmetry parameter can be used as a measure of the -character of the carbon-iodine bond. The meta and para are certainly better candidates for study in this respect, but even here no clear picture of the carbon-iodine 7i-bond arises. 

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