Evaluate the difference between change in energy at 0 K in the absence of zero point vibration and both change in enthalpy and in free energy for real molecules at 298 K. Consider both a uni-molecular iso-merization that does not lead to a net change in the number of molecules and a thermal decomposition reaction that leads to an increase in the number of molecules.

a. Calculate ΔU, ΔH (298), and ΔG (298) for the following isomerization reaction:

CH₃N≡C → CH₃C≡N

Obtain equilibrium geometries for both methyl isocyanide and acetonitrile using the B3LYP/6-31G* density functional model. Do the calculated values for ΔU and ΔH (298) differ significantly (by more than 10%)? If so, is the difference due primarily to the temperature correction or to the inclusion of zero point energy (or to a combination of both)? Is the calculated value for ΔG (298) significantly different from that of ΔH (298)?

b. Repeat your analysis (again using the B3LYP/6-31G* model) for the following pyrolysis reaction:

HCO₂CH₂CH₃ → HCO₂H + H₂C ≡ CH2

Do these two reactions provide a similar or a different picture as to the importance of relating experimental thermo-chemical data to calculated ΔG values rather than ΔU values? If different, explain your result.