Notes on the Accuracy of PM7 and PM6-D3H4

(All solids - Periodic Table - Home - PM7 and PM6-D3H4 Accuracy - Manual)


A frequently asked question is, "Which method in MOPAC is the most accurate?"  Although apparently a simple question, there is no simple answer other than that PM7 and PM6-D3H4 are the two most accurate methods in MOPAC.  These methods should be used for all routine use. There are several other methods, but they should only be used when necessary.  The data in the PM7 and PM6-D3H4 Accuracy web-page provides an unbroken chain of logic from raw experimental data to a summary of a statistical analysis of the errors in various properties, and provides enough information to allow users of MOPAC to decide which method to use.

The methods in MOPAC were designed to provide practical chemists with a tool for modeling chemical systems.  To this end, the focus has been on main-stream chemistry - think sulfuric acid - and on systems with common but interesting structures, for example hydrogen bonds in enzymes.  Modeling methods are of little practical use unless they can be used without much effort, i.e., in a reasonable time on readily available hardware.  These objectives can be contrasted with the philosophy behind many high-level methods, where the objective is to generate accurate data on small systems, or to model exotic systems or exotic phenomena.  Such methods are often very time consuming.  This is not an attempt to disparage such methods: if semiempirical methods are to be improved, they will have to depend on reference data generated using high level methods. 

Purpose of these tables

1 Research

Before starting any research that uses the methods in MOPAC, an estimate should be made of how accurately the two most important methods, PM7 and PM6-D3H4, predict properties of interest. This section of the manual contains a large number of tables and summaries that provide information that should be useful in making that estimate. 

2 Teaching

Information on a large number of chemical systems - atoms, molecules, biomolecular systems, and solids is presented, both as graphics and as text. Examples of data-sets for different types of calculation are given in the form of .arc files; these can be run directly using MOPAC, although it would normally be preferable to re-name them as .mop files to avoid over-writing the .arc file.

3. Development

Method developers can use the tables to identify strengths and weaknesses in semiempirical methods, and the automated tools for generating these tables can be used in determining the accuracy of a new method.  Provided the raw data are selected in an unbiased manner, and given that the automated tools do not introduce any bias, the resulting tables and statistics can be regarded as unbiased.

Summary of PM7

Advantages: The best method for general chemistry, and for solids. Optimized to reproduce the Standard Heat of Formation, ΔHf.

Disadvantages: Less accurate than PM6-D3H4 for geometries in organic chemistry. See crystal urea.

Faults: There is a fault in the hydrogen-bond calculation that can cause a severe error in vibrational frequencies. This fault occurs when there is a hydrogen atom attached to an acceptor atom and the angle between that hydrogen atom, the acceptor atom, and the hydrogen atom involved in the hydrogen bond are near to 180°. Although the fault originated in the calculation of the hydrogen-bond energy, it only becomes significant when the derivative of the hydrogen-bond energy with respect to geometry is calculated.  An example of such a situation is shown in the figure nearby.  In this figure, the angle H6 makes with O4 and H3 is 179.8°, and the lowest-energy vibrational mode is i14533.1.  This is printed as -14533.1 cm-1, a completely nonsensical value.

Data-set that shows the fault in calculated vibrational frequencies

Orientation of two water molecules showing the almost collinear atoms

   force let
   FORCE calculation on a water dimer

   O   0.00000000 +1   0.0000000 +1    0.0000000 +1
   H   0.97355715 +1   0.0000000 +1    0.0000000 +1 1 0 0
   H   1.02564937 +1 106.0267800 +1    0.0000000 +1 1 2 0
   O   4.60167391 +1 155.5013383 +1   98.8837966 +1 3 1 2
   H   0.97322361 +1  78.1005920 +1 -160.7983157 +1 4 3 1
   H   0.99799606 +1 179.8194280 +1  -37.8616995 +1 4 3 1

It should be emphasized that this fault only occurs very infrequently, because the specific condition for its appearance, the three atoms being almost collinear, does not occur in most hydrogen bonding environments, but in the rare case that it does occur the results will be nonsense.

Because PM7 has been used for many years, this fault has not been corrected, instead it is documented here as information for users and developers.

Summary of PM6-D3H4

Advantages: Very good for biochemistry and organic and organometallic chemistry. Very good for non-covalent interactions.   Errors in intermolecular interactions are much smaller than in PM7

Disadvantages:  Often there are severe errors in inorganic solids. Errors in ΔHf are much larger than in PM7. This is a consequence of the fact that the D3H4 modification was added on to the PM6 method. PM6 was optimized to reproduce ΔHf, and the addition of D3H4 resulted in extra stabilization. 

When to use PM7 and when to use PM6-D3H4

For all organic chemistry, use PM6-D3H4.

For inorganic solids, use PM7.

For more information, consult the statistics in the PM7 and PM6-D3H4 Accuracy web-page.