Although ab initio HF calculations fail in predicting molecular atomization energies, one can still use HF energies to estimate energy changes for certain types of reactions. Recall that good barriers to internal rotation can usually be obtained from ab initio SCF MO calculations because of a near cancellation in correlation energies between different molecular conformations. As ethane goes from staggered to eclipsed, the number of chemical bonds of each type does not change. More generally, one might hope that a similar near cancellation of correlation energies might occur for an isodesmic chemical reaction; an isodesmic reaction (Greek isos, ==equal==; desm, ==bond==) is one in which the number of bonds of each type does not change [W. J. Hehre et al., J. Am. Chem. Soc., 92, 4796 (1970)]. For example, the isodesmic reaction CH2 == CHCH2OH + CH2 == O ( CH2 == CHOH + CH3CH == O has seven CH bonds, one CC double bond, one CC single bond, one CO double bond, one CO single bond, and one OH bond on each side. A special kind of isodesmic reaction is a bond-separation reaction. Here, one starts with a molecule and converts it to products, each of which contains only one bond between nonhydrogen atoms. For example, starting with CH3 - CH == C == O, one would form the products CH3 - CH3, CH2==CH2, and CH2==O, in which the C-C, C==C, and C==O bonds are separated from one another. To balance the reaction, one adds an appropriate number of hydride molecules (for example, CH4, NH3, H2O) to the left side. The bond-separation reaction for CH3 CHCO is then CH3--CH==C==O + 2CH4S C2H6 + C2H4 + CH2O.
The bond-separation reaction for benzene is C6H6 + 6CH4S 3C2H6 + 3C2H4. (If the energy of a molecule could be represented as the sum of bond energies that were invariant from molecule to molecule, then the energy change for any isodesmic reaction would be zero. The energy change for a bond-separation reaction measures the interactions between the bonds in the molecule.) If an SCF MO calculation could fairly accurately predict the energy change for the bond-separation reaction of a large molecule, then we could use the known energies of the small product molecules like C2H6 to get a reasonably good estimate for the energy of the large molecule from an SCF calculation, without having to use expensive correlation methods.
(a) Write the bond-separation reaction for cyclopropane. Do the same for CH3CHO.
(b) Do HF/6-31G* energy and vibrational frequency calculations on the molecules in the CH3 CHO bond-separation reaction. Scale the vibrational frequencies (Section 15.12) to find the zero-point energies. Find the ∆H0 value predicted by the HF/6-31G* method for the gas-phase CH3CHO bond-separation reaction. Compare with the experimental value of 11.5kcal/mol.
(c) Repeat (b) using MP2/6-31G* calculations. (Although isodesmic-reaction calculations work reasonably well for small molecules, the errors become too large when used with large molecules.)