We examine here how the accuracy of reaction energy calculations depends upon the choice of basis set and the inclusion of correlation in ab initio MO calculations. Semi-empirical Hamiltonians do not generally perform well in these kinds of calculations, since they are parameterized to give good energies for individual molecules; however, if all species in the reaction channel are "close" in structure to the molecules of the training set for the particular Hamiltonian, good results may nonetheless be obtained.

We categorize the reactions according to the conservation of electron spin and the conservation of bonding vs non-bonding (unshared) electron pairs since these properties have great impact on whether inclusion of correlation is necessary.

A. Reactions Not Conserving the Number of Paired Electrons (non-isogyric reactions)

1. Homolytic Bond Dissociations

   Example: CH₄ ===> CH₃. + H.

   Homolytic dissociations, of course, produce two doublet species.

   • Since the extent of electron correlation changes significantly, calculation of bond dissociation energies requires the use of large basis sets and high levels of correlation.

   • For the example reaction, a 6-31G**//6-31-G* calculation gives a BDE of 87 kcal/mol for the above reaction.

   • Addition of correlation at the MP2 level raises this to 109 kcal/mol; MP4 correlation gives a value of 110 kcal/mol.

   • The experimental value is 113 kcal/mol.

2. Absolute Activation Energies

   represent the energy change for a reaction in which a ground state is converted to a transition state. At first glance, it is not obvious that this necessarily should involve a change in the numbers of paired electrons.

   However, because of the presence of partial bonds, transition states are often best represented as hybrids of ionic and diradical states. Hence, again, we seek to use large basis sets and all possible correlation.

1. Heterolytic Bond Dissociations

   Reactions such as the S_N1 and acid ionizations fall into this category:

   (CH₃)₃CBr ===> (CH₃)₃C⁺ + Br^-

   CH₃CO₂H + H₂O ===> CH₃CO₂^- + H₃O⁺

2. Some Isomerization Reactions

   CH₂=O ===> HC-OH

   CH₂=CH₂ ===> CH₃-C-H

   Charged species generally are best modeled with basis sets containing polarization functions, since the charge distorts the electron distribution.

   In addition, anions and neutral species with multiple unshared pairs require inclusion of diffuse functions in order for those electrons to remain bound.

   Consequently, a minimum basis for the above kinds of reactions is something like 6-31+G*. Inclusion of correlation at the MP2 level should significantly increase accuracy.

1. Some Isomerizations

   CH₃CHO ===> CH₂CH₂O

2. Formal Hydrogenation Reactions

   These are (hypothetical) reactions that can be used to assess many kinds of relative stabilities. The molecule of interest is reacted with sufficient hydrogen for complete reduction to the set of one-heavy-atom hydrides. Thus:

   CH3OH + H2 ===> CH4 + H2O

• For example, using experimental enthalpies of formation, the hydrogenation reaction shown has DH = -30 kcal/mol.

• The STO-3G basis yields -16 kcal/mol, the 3-21G* -28 kcal/mol, and 6-31G**//6-31G* -30 kcal/mol, respectively

D. Isodesmic Reactions

Isodesmic (bond conserving) reactions not only maintain the division of electrons into shared and unshared pairs, but maintain the numbers of heavy atom to heavy atom bonds of each type. Whenever possible, comparisons of reactivity and stability should be made using isodesmic reactions to allow the errors inherent in computations for different types of molecules to cancel.

1. Bond Separation Reactions

   In this subgroup of isodesmic reactions, all formal single, double, and triple bonds between heavy atoms are broken until what remains is the set of simplest two-heavy-atom parents containing the same kinds of links.

   The parents are: CH₃CH₃; H₂C=CH₂; HCCH; CH₃NH₂; CH₂=NH; HCN; CH₃OH; CH₂=O; CH₃F; H₂NNH₂; HN=NH; HONH₂; HN=O; FNH₂; H₂O₂; HOF.

   To maintain atom balance, one-heavy-atom hydrides are added.

   For example:

   CH₃CH=C=O + 2CH₄ ===> CH₃CH₃ + CH₂=CH₂ + CH₂=O

   CH₃CH₂CH₃ + CH₄ ===> 2 CH₃CH₃

   Reactions such as these can be used to convert computed reaction energies to enthalpies of formation. Thus, DH_f for propane could be obtained from the second reaction as follows:

   DH_f (propane) = -DE (reaction) - DH_f (methane) + 2 DH_f (ethane)

2. Other Isodesmics

   Many other reactivity comparisons can be written in isodesmic form:

   CH₃OCH₃ + H₂O ===> 2 CH₃OH

   (CH₃)₃NH⁺ + NH₃ ===> (CH₃)₃N + NH₄⁺

Because isodesmic reactions are written so that correlation effects largely cancel, there is little gain from application of models that explicitly include correlation.

None of the above discussion should be taken to imply that if molecular sizes allow, very large basis sets and sophisticated correlation treatments will not give the best possible results. However, the molecules of interest to organic chemists often are far too large, and available computational facilities far to limited, to allow such an approach. In those cases, a rational analysis of what information is required, and careful formulation of comparisons, can lead to reliable results from lower level calculations.