Examples of Quantum Chemical Methods

Using the atomic energies for carbon atom and hydrogen atom from Ref. 25, we calculate the enthalpy of formation of CH4 at 298 K as follows  

The calculation of the enthalpies of formation from other total energies such as from B3LYP, G2(MP2), G3, or CBS-Q is done in a similar manner except that different total energies for the molecule and atoms are used. In subsequent examples, only calculations of the total energies are described. 

The same procedure is used for geometries and frequencies as was done for the G2 energy in Example 1. Note that all the energies listed below can be obtained from two single-point energy calculations QCISD(T)/6-311G(d,p) and MP2/6-311+G(3df,2p). 

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. 

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