Thermal energy correction scaling

You should be aware that the optimal scaling factors vary by basis set. For example, Bauschlicher and Partridge computed the B3LYP/6-311+G(3df,2p) ZPE/thermal energy correction scaling factor to be 0.989. Additional scaling factors have also been computed by Wong and by Scott and Radom. 

Frequencies computed with methods other than Hartree-Fock are also scaled to similarly eliminate known systematic errors in calculated frequencies. The followng table lists the recommended scale factors for frequencies and for zero-point energies and for use in computing thermal energy corrections (the latter two items are discussed later in this chapter), for several important calculation types ... 

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. 

When comparing energy results to experiments performed at particular temperatures, the thermal energy correction given in the output should be added to the total energy (this sum is also given in the output). In order to apply the appropriate scale factor to a thermal energy correction, you must specify a scale factoi via input to the Readlsotopes option. The quantity reported in the output cannot simply be multiplied by the scale factor itself as it is composed of several terms, only some of which should be scaled. 

Compute the isomerization energy between acetaldehyde and ethylene oxide at STP with the QCISD(T)/6-31G(d) model chemistry, and compare the performance of the various model chemistries. Use HF/6-31G(d) to compute the thermal energy corrections. Remember to specify the scaling factor via the Freq=Recxllso option. (Note that we have already optimized the stmcture of acetaldehyde.)... 

Example 4. Calculation of CBS-Q Energy for CH4 The geometry is first optimized at the HF/6-31G(d ) level and the HF/6-31G(d ) vibrational frequencies are calculated. The 6-31G(d ) basis set combines the sp functions of 6-31G with the polarization exponents of 6-311G(d,p). A scale factor of 0.91844 is applied to the vibrational frequencies that are used to calculate the zero-point energies and the thermal correction to 298 K. Next the MP2(FC)/6-31G(d ) optimization is performed and this geometry is used in all subsequent single-point energy calculations. In a frozen-core (FC) calculation, only valence electrons are correlated. 

The fact is that the reaction free energies are hardly ever determined experimentally, but are simply calculated from the Rehm-Weller equation which will be discussed in detail in the next section [26]. There are still considerable technical problems in direct experimental measurements, because standard methods of calorimetry cannot cope with reactions in time scales of ns or ps but this is slowly changing with the advent of fast calorimetric techniques such as time-resolved photoacoustic spectroscopy [27] and thermal lensing [28] these are considered in the following section. Nevertheless, it appears that all the data currently used in the rate constant-energy plots simply use the Rehm-Weller equation (sometimes with various corrections) and it is obviously important to consider the assumptions built into this equation, its limitations, and possible improvements. 

A second caveat concerns the dependence of the numerical values of the free energies and entropies of complexation on the concentration scale used. AH" must be calculated by applying the van t Hoff equation to or values, the complexation constants on the mole fraction or molal concentration scales, respectively. If one uses Kc (molar concentration), enthalpies mnst be corrected for the thermal expansion of the solvent. 

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