Energy minimization RMS gradient convergence criterion; GAMESS vs. Tinker.

As per the recommendations of +Jan Jensen  we have in our group been using the convergence criterion, in GAMESS, OPTTOL=0.0005 in the $STATPT input group for minimization of protein structures using various fast quantum mechanical methods ranging from correlated fragment based methods to dispersion corrected Hartree-Fock theory to semi-empirical methods.

Yesterday I was about to carry out a molecular mechanics energy minimization of a PDB structure in order to remove a couple seemingly spurious bond lengths in the structure before putting the coordinates through a full QM calculation. I started Tinker and I was immediately faced with a cryptic question to which I only knew the answer in terms of GAMESS' OPTTOL variable:

Enter RMS Gradient per Atom Criterion [0.01] : 

Firstly, the question is cryptic since there is no mention of units. Secondly, my answer to the question was also not obvious, since I didn't know exactly what OPTTOL=0.0005 (which is in hartree/bohr) really meant. INPUT.DOC in the gamess/ directory was helpful:

OPTTOL = gradient convergence tolerance, in Hartree/Bohr.
         Convergence of a geometry search requires the
         largest component of the gradient to be less
         than OPTTOL, and the root mean square gradient
         less than 1/3 of OPTTOL.  (default=0.0001)

So actually, my convergence criterion of the RMS gradient in GAMESS has been 1/3 * 0.0005 hartree/bohr.

After a bit of detective work, it turns out that the units of the Tinker criterion is in kcal/mol/angstom. So the relevant conversion factors from OPTTOL in GAMESS to RMS gradient in Tinker are can be summed up as:

• 1/3 (GAMESS definition)
• 627.51 (hartree to kcal/mol)
• 1.8897 (angstrom to bohr)

The total conversion factor becomes: 1/3 * 627.51 * 1.8897 = 395.27

All in all OPTTOL=0.0005 in "GAMESS units" (hartree/bohr) amounts to an RMS gradient of 0.2 in "Tinker units" (kcal/mol/angstom).

Happy Tinkering!