Before using PARAM for method development, first become familiar with the various utilities that are available. Then run a simple parameter optimization using PARAM. A good starting job would be Optimize-h.dat in FILES.zip. Examine the output, to familiarize yourself with the process. Once the process is understood, make changes to the PARAM data set, and try out various ideas to test your understanding of the process.
Also, before starting any parameter optimization work, decide what the objective is. Is it to develop a new, general purpose method, such as PM6 - that would be a large project taking at least a year. Or is it to develop a high-accuracy method such as RM1 that is limited to a few elements, or to a few molecular species, or to a specific set of bonds.
If the objective is to develop a method for modeling a specific set of molecules, then the database would need to include examples of those systems. The default database (normal_data) is very small, only about 250 files. During the development of PM6, the databases used consisted of over 8,000 normal compounds, over 1,000 special cases, and about 380 atomic states. So the default database is obviously unlikely to have many molecules of interest. The first big task, then, is to assemble reference data for the species of interest, and to convert these data into reference data files.
Use the default method, currently PM6, where possible, for both preliminary cleaning up of reference data set geometries and as a starting point for the values of parameters.
For each data file constructed, first run it using MOPAC to get a good starting geometry. In the case of geometric references, set the optimization flags for the geometric references to zero during this operation.
When a good set of reference data files are available, run a survey of them using PARAM (use SURVEY). This will allow any obvious errors to be quickly identified. Then run PARAM without SURVEY and without optimizing any parameters. The output file will allow more subtle errors to be detected.
Parameter optimization is straightforward. To optimize all parameters for a given element, Ti for example, use (Ti)(all). To optimize several elements, separate the chemical symbols by spaces, e.g., (H C N O)(all). To optimize only some parameters, specify the parameters, either as (H C N O)(Uss betas zs) or as explicit entries:
The style of specifying parameters is the same as that used in EXTERNAL. If there is a need to constrain the values of parameters lower and upper bounds can be set, thus:
ZS H 0.5 2.0
Weak interactions: rules
Use of non-equilibrium structures
Often there is insufficient information to pin down the surface of parameter space. In the case of the rare gases this can occur simply because there are few or no exemplars. When this occurs, one option is to use non-equilibrium structures. These are represented as reference data by rules. A typical example would be the difference in energy of the system at equilibrium and the system with a bond stretched or compressed. As systems of this type do not occur in nature, the best source of reference data is high-level calculation. In practice, diatomics are best. First, the geometry of the system is optimized, then the appropriate bond length is increased by 0.2Å then decreased by 0.2Å. The results are used in the construction of three reference data files: the equilibrium, the stretched and the compressed forms. The geometries of all three reference data files are frozen. Rules are then constructed, relating the heat of formation of the stretched and compressed forms to that of the equilibrium form.
Building sets of reference data files of this type is quite rapid.
Inclusion of even one solid state system in a parameterization calculation would slow it down to such a degree that parameter optimization would be impossible. Instead, small aggregates can be used. Thus for the alkali metal halides, the tetrahedral system M4X4 would be suitable. Its geometry could be obtained from high-level calculations. Likewise, the stability of such a system relative to four isolated MX dimers could be expressed as a rule.
sequence of optimization
Methods that do not involve geometry optimization
All general methods involve geometry optimization. Such methods are, of their nature, unsuitable for modeling many phenomena, such as activation barriers, electronic excited states, pKa, polarizabilities, etc. Methods for modeling these phenomena can be developed by using frozen geometries. The underlying idea is that geometries are optimized using one method, and the desired phenomenon then modeled using a different method.
First, optimize all geometries using a well-defined method. This is easily done using PARAM keywords PRECISE and NEW_REF. Then run parameter optimizations using PARAM keyword 1SCF. This prevents the geometries from changing during the parameterization. This allows the flexibility that was used for modeling geometries accurately to be used for the new phenomenon.
A model example of this process would be to develop a method for predicting UV-Vis spectra. Only data relating to the desired phenomenon would be used, i.e., in the case of UV-Vis, this would consist of the named excited state of various molecules and the energies of the excitation. Only parameters that affect electronics need be optimized. This would exclude all nuclear terms, such as xfac, alpb, alp, fn11, etc.