Essentials of Computational Chemistry

5.6 GENERAL PERFORMANCE OVERVIEW OF BASIC NDDO MODELS 149
approach, the fragments are larger and N is smaller than the total number of atoms. Over
583 neutral, closed-shell molecules, Repasky, Chandrasekhar, and Jorgensen found that
the mean unsigned errors from MNDO, AM1, and PM3 were reduced from 8.2, 6.6, and
4.2 kcal mol −1 , respectively, to 3.0, 2.3, and 2.2 kcal mol −1 , respectively, when bond/group
equivalents were used in place of atoms as the fundamental fragments.
5.6.1.2 Other energetic quantities
Another energetic quantity of some interest is the ionization potential (IP). Recall that in
HF theory, the eigenvalue associated with each MO is the energy of an electron in that
MO. Thus, a good estimate of the negative of the IP is the energy of the highest occupied
MO – this simple approximation is one result from a more general statement known
as Koopmans’ theorem (Koopmans, 1933; this was Koopmans’ only independent paper in
theoretical physics/chemistry–immediately thereafter he turned his attention to economics
and went on to win the 1975 Nobel Prize in that field). Employing this approximation, all
of the semiempirical methods do reasonably well in predicting IPs for organic molecules.
On a test set of 207 molecules containing H, C, N, O, F, Al, S, P, Cl, Br, and I, the average
error in predicted IP for MNDO, AM1, and PM3 is 0.7, 0.6, and 0.5 eV, respectively. For
purely inorganic compounds, PM3 shows essentially unchanged performance, while MNDO
and AM1 have errors increased by a few tenths of an electron volt.
With respect to the energetics associated with conformational changes and reactions, a few
general comments can be made. MNDO has some well-known shortcomings; steric crowding
tends to be too strongly disfavored and small ring compounds are predicted to be too stable.
The former problem leads to unrealistically high heats of formation for sterically congested
molecules (e.g., neopentane) and similarly too high heats of activation for reactions characterized
by crowded TS structures. For the most part, these problems are corrected in AM1
and PM3 through use of Eq. (5.16) to modify the non-bonded interactions. Nevertheless,
activation enthalpies are still more likely to be too high than too low for the semiempirical
methods because electron correlation energy tends to be more important in TS structures
than in minima (see also Table 8.3), and since correlation energy is introduced in only an
average way by parameterization of the semiempirical HF equations, it cannot distinguish
well between the two kinds of structures.
For intermolecular interactions that are weak in nature, e.g., those arising from London
forces (dispersion) or hydrogen bonding, semiempirical methods are in general unreliable.
Dispersion is an electron correlation phenomenon, so it is not surprising that HF-based
semiempirical models fail to make accurate predictions. As for hydrogen bonding, one of
the primary motivations for moving from MNDO to AM1 was to correct for the very weak
hydrogen bond interactions predicted by the former. Much of the focus in the parameterization
efforts of AM1 and PM3 was on reproducing the enthalpy of interaction of the
water dimer, and both methods do better in matching the experimental value of 3.6 kcal
mol −1 than does MNDO. However, detailed analyses of hydrogen bonding in many different
systems have indicated that in most instances the interaction energies are systematically too
small by up to 50 percent and that the basic NDDO methods are generally not well suited
to the characterization of hydrogen bonded systems (Dannenberg 1997). Bernal-Uruchurtu