Only the more recent methods PM6 and PM7 will be addressed here, older methods, such as PM3, and more specialized methods, such as RM1, will not be described.
The methods in MOPAC are designed to be general-purpose, that is, they are intended for the study of a very wide range of chemical systems. There are biases in the recent methods towards increased emphasis on heats of formation and geometry, and also biases in favor of organic chemistry, but with these exceptions the fundamental objective of all the methods is the same - to model chemical phenomena.
PM6 provides a good example of how methods evolve. Its direct ancestor was PM3. When PM3 was first released, it marked an improvement over its immediate ancestor, AM1, but as time went by several faults were found in PM3. These faults were collected into a list, and an attempt was made to correct them when the project that resulted in PM6 was started. Put another way, PM6 was designed to correct the faults in PM3.
At the time of its release, PM6 was a large improvement on PM3 but after it had been used for a while, two types of faults were discovered. One type involved cases where PM6 gave severely inaccurate results for some heats of formation and for some geometries, Faults of this type were collected into a list, and stored until a new method (PM7) could be developed.
The other type of fault dealt with weak interactions between molecules, specifically VDW and hydrogen-bond interactions. Interactions of this type are of great importance, particularly in biochemistry, and errors of the type that would be acceptable in heats of formation and in geometries would be completely unacceptable here. In addition, faults of this type could be corrected by the addition of a post-SCF modification to the energy, i.e., to the heat of formation, of the system. Like earlier methods, PM6 did not do a good job of reproducing intermolecular interactions; in all cases it underestimated the binding energy. Several attempts were made to correct this fault, these attempts were given specific names such as PM6-DH, PM6-DH2, PM6-DH+ , PM6-DH2X, and PM6-D3. All these methods were designed to reproduce intermolecular interactions, but, since they added a significant stabilization energy to the system, they could not be used as a substitute for PM6 for predicting heats of formation.
When the project that resulted in PM7 was started, information on both of the types of errors that had been found in PM6 was used in the design. The set of approximations was modified to include the ideas of the PM6-ABC methods, and reference data was used that would allow the severely inaccurate predictions of PM6 to be corrected. As a result, PM7 was able to simultaneously predict intermolecular interactions with good accuracy and also to predict heats of formation and geometries with good accuracy.
Recently, faults have been found in the way PM7 treats intermolecular interactions. For small systems, everything looks good, but PM7 apparently over-estimates the VDW bonding when large molecules are used. Also, some specific faults in individual molecules have been identified. This is similar to the sequence that occurred after PM6 was released, and the process for handling these faults is similar. Specifically, a list of single-molecule faults will be constructed, and, for intermolecular interactions, attempts will be made to correct the energies. These attempts will be given names of the type PM7-ABC.
At some date in the future, another project (PM8?) will be started that will attempt to correct the faults in PM7. As with the other projects of this type, great care will need to be taken in the design of the new method. For example, in recent years there have been several benchmark publications describing the results of very high level calculations. These benchmark results could be a source of valuable reference data. Indeed, as the semiempirical methods become more accurate, there have been increasing problems with conventional reference data of the type found in e.g., the WebBook.
An objective of each new method has been to reduce the average unsigned error in important quantities by several tens of percent. This objective has been achieved in both PM6 and PM7, and should be an objective of PM8. Of course, since PM7 represented the best that could be done at the time, the challenge in designing PM8 will be very hard.