Thermal energy correction

To compute zero-point vibration and thermal energy corrections to total energies as well as other thermodynamic quantities of interest such and the enthalpy and entropy of the system. 

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 ... 

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. 

Gaussian predicts various important thermodynamic quantities at the specified temperature and pressure, including the thermal energy correction, heat capacity and entropy. These items are broken down into their source components in the output ... 

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. 

In order to predict the energy of a system at some higher temperature, a thermal energy correction must be added to the total energy, which includes the effects of molecular translation, rotation and vibration at the specified temperature and pressure. Note that the thermal energy includes the zero-point energy automatically do not add both of them to an energy value. 

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. 

Here is how the zero-point and thermal energy-corrected properties appear in the output from a frequency calculation ... 

The raw zero-point energy and thermal energy corrections are listed first, followed by the predicted energy of the system taking them into account. The output also includes corrections to and the final predicted values for the enthalpy and Gibbs free energy. All values are in Hartrees. 

Zero-point and thermal energy corrections are usually computed with the same model chemistry as the geometry optimization. However, you may also choose to follow the common practice of always using the HF/6-31G(d) model chemistry for predicting zero-point and thermal energies (see page 149). Of course, such frequency calculations must follow a HF/6-31G(d) geometry optimization. 

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.)... 

The internal energy at a specific temperature is then determined by the sum of the internal thermal energy correction term and the computed electronic energy. Take 298 K, as an example. 

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