Page 284 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

Table 3.5 includes the B3LYP/6−311 + G 3df 2p results for some small hydro- 265
carbons. MO and DFT calculations pertain to molecules at 0 K without any molecular
motion. In order to make comparisons with thermodynamic data at 298 K, correc- SECTION 3.1
tions for both zero-point energy (ZPE) and the difference in thermal energy must be Thermodynamic Stability
made. The corrections are normally incorporated into calculations intended for thermo-
chemical comparisons. The corrections are based on calculation of the vibrations and
rotations that contribute to ZPE and thermal energy. Table 3.5 gives a comparison of
some calculated H with experimental values for some simple hydrocarbons. The
f
absolute errors are small for methods such as G2, CBS-Q, and CBS-QB. There are some
indications that B3LYP calculations tend to underestimate the stability of hydrocarbons
as the size of the molecule increases. For example, using the 6-311 ++G 3df 2p
basis set, the error increased systematically from propane −1 5kcal/mol to hexane
−9 3 and octane −14 0 . 31 Similarly, the effect of successively adding methyl
groups to ethane resulted in an error of 21.1 kcal/mol for 2,2,3,3-tetramethylbutane. 32
MO methods can also be used to calculate heats of reaction by comparing the
heats of formation of reactants and products. The total energy calculated for even a
small hydrocarbon, relative to the separate nuclei and electrons, is enormous (typically
50,000 and 100,000 kcal/mol for C and C compounds, respectively) relative to the
2 4
energy of reaction. Sometimes the energy is tabulated as the energy of atomization,
corresponding to the difference in total energy of the molecule and that of the separate
atom, which is the energy required to break all the bonds. These values, too, are
very large in comparison with the heat of reaction. The energy differences that are
of principal chemical interest, such as H for a reaction, are likely to be in the
range of 0–30 kcal/mol. A very small error relative to the total energy in an MO
calculation becomes a very large error in a calculated H. Fortunately, the absolute
errors for compounds of similar structure are likely to be comparable and tend to
cancel in calculation of the energy differences between related molecules. Calculation
of heats of formation and heats of reaction is frequently done on the basis of isodesmic
reactions, 33 in order to provide for maximum cancellation of errors in total binding
energies. An isodesmic reaction is defined as a process in which the number of formal
bonds of each type is kept constant; that is, there are the same number of C−H, C=C,
C=O, etc., bonds on each side of the equation. 34 For example, an isodesmic reaction
to evaluate the stability of benzene would be:

+ 3 H C
2
3 H C CH 2 3 CH 3 + 6 CH 4
3 C C 3 C C
3 C C 3 C C
30 C H 30 C H

The comparison can be further refined by use of homodesmotic reactions in which
there is matching not only of bond types, but also of hybridization. Thus in the reaction

31
L. A. Curtiss, K. Raghavachari, P. C. Redfern, and J. A. Pople, J. Chem. Phys., 112, 7374 (2000).
32
C. E. Check and T. M. Gilbert, J. Org. Chem., 70, 9828 (2005).
33 W. J. Hehre, R. Ditchfield, L. Radom, and J. A. Pople, J. Am. Chem. Soc., 92, 4796 (1970).
34
D. A. Ponomarev and V. V. Takhistov, J. Chem. Ed., 74, 201 (1997).