## Sunday, January 13, 2013

### FixSol solvation model and FIXPVA2 tessellation scheme

Contributed by Jan H. Jensen

This paper introduces a variant of the conductor like polarizable continuum model (C-PCM) called FixSol and a modified area tesselation scheme (FIXPVA2) that both serve to increase the numerical stability of geometry optimizations and molecular dynamics simulations.

The C-PCM equation is $${\bf Cq}=-\frac{\varepsilon-1}{\varepsilon}{\bf V}\text{ where } C_{ij}=\frac{1}{r_{ij}}$$Here $r_{ij}$ is the distance between tesserae centers so when atomic spheres and, hence, tesserae points get close the C-PCM equations become numerically unstable.

This has traditionally been dealt with by associating damping functions with each tesserae point (see for example the work by York and Karplus) and FIXPVA2 is a variant of this approach.  However, this study goes even further and modified the $C$ matrix for tesserae that are within a certain cutoff with a smooth transition to C-PCM beyond the cutoff.  The resulting energies are within 0.5 kcal/mol of conventional C-PCM calculations for small molecule ab initio calculations.

However, what really caught my eye was that the demonstration of numerical stability was done by short (10-ps) FixSol-PCM/CHARMM molecular dynamics simulations of a small protein and 13-base pair piece of DNA with energy conservation to within 0.09 kcal/mol.  This is indeed a very stringent text of numerical stability and I don't recall having seeing PCM MD simulations on such large systems, but feel free to correct me in the comments.  Unfortunately timings where not given.

Full disclosure: I was Hui Li's PhD advisor

1. Following up on Jan Jensen's point: A couple of years back, we came up with a COSMO/C-PCM variant suitable for Car-Parrinello MD (Senn, Margl, Schmid, Ziegler, Blöchl, Ab initio molecular dynamics with a continuum solvation model, JCP 2003, 118, 1089-1100, doi:10.1063/1.1528890).

The essential feature was a tesselation/cavity scheme with smooth analytical gradients. Similarly to the work discussed in the post, it used switching functions and a modified potential at short range. We demonstrated the accuracy of the forces in energy-conserving CP-MD simulations

1. OK, thanks! And I see you make the ASCs a dynamic variable like the electronic degrees of freedom. I wonder if one could do that with MM/PCM MDs, but perhaps the step-size will have to be prohibitively small.