The parameterization of MNDO and AM1 had been done essentially by hand, taking the Gss, Gsp, Gpp, Gp2 and Hsp parameters from atomic data and varying the rest until a satisfactory fit had been obtained. Since the optimization was done by hand, only relatively few reference compounds could be included. J. J. P. Stewart made the optimization process automatic by deriving and implementing formulas for the derivative of a suitable error function with respect to the parameters.50 All parameters could then be optimized simultaneously, including the two-electron terms, and a significantly larger training set with several hundred data could be employed. In this re-parameterization, the AMI expression for the core-core repulsion (eq. (3.85)) was kept, except that only two Gaussians were assigned to each atom. These Gaussian parameters were included as an integral part of the model, and allowed to vary freely. The resulting method was denoted Modified Neglect of Diatomic Overlap, Parametric Method Number 3 (MNDO-PM3 or PM3 for short), and is essentially AMI with all the parameters fully optimized. In a sense, it is the best set of parameters (or at least a good local minimum) for the given set of experimental data. The optimization process, however, still requires some human intervention in selecting the experimental data and assigning appropriate weight factors to each set of data.
Some known limitations of the PM3 model are:
(1) Almost all sp3-nitrogens are predicted to be pyramidal, which is contrary to experimental data.
(3) The gauche conformation in ethanol is predicted to be more stable than the trans.
(4) Bonds between Si and Cl, Br and I are underestimated, the Si—I bond in H3SiI, for example, is too short by ~0.4 A.
(5) H2NNH2 is predicted to have a C2h structure, while the experimental result is C2, and ClF3 is predicted to have a D3h structure, while the experimental result is C2v.
(6) The charge on nitrogen atoms is often of "incorrect" sign and "unrealistic" magnitude.
Some common limitations of MNDO, AMI and PM3 are:
(1) Rotational barriers for bonds that have partly double bond character are significantly too low. The barrier for rotation around the central bond in butadiene is calculated to be only 2-8kJ/mol, in contrast to the experimental value of 25 kJ/mol.51 Similarly, the rotational barrier around the C—N bond in amides is calculated to be 30-50 kJ/mol, which is roughly a factor of two smaller than the experimental value. A purely ad hoc fix has been made by adding a force field rotational term to the C—N bond that raises the value to ~100 kJ/mol and brings it into better agreement with experimental data.
(2) Weak interactions, such as van der Waals complexes or hydrogen bonds, are poorly predicted. Either the interaction is too weak, or the minimum energy geometry is wrong.
(3) Conformational energies for peptides are poorly reproduced.52
(4) The bond length to nitrosyl groups is underestimated. The N—N bond in N2O3, for example, is ~0.7 A too short.
(5) Although MNDO,AM1 and PM3 have parameters for some metals, these are often based on only a few experimental data. Calculations involving metals should thus be treated with care.
The MNDO, AM1 and PM3 methods have been parameterized for most of the main group elements,53 and parameters for many of the transition metals are also being developed under the name PM3(tm), which includes d-orbitals. The PM3(tm) set of parameters are determined exclusively from geometrical data (X-ray) since there are very few reliable energetic data available for transition metal compounds
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