The next best thing to seeing real atoms is to mimic them in silico: we assign interactions between the atoms and then — pouf –They’re alive!
The number of particles in a visible sample is on the order of Avogadro’s constant, say ~1023, whereas a fairly muscular computer can only follow ~105-107 atoms at a time. To compensate, computational scientists typically replicate their simulation boxes infinitely in space. This creates a quandary for calculating forces across replication boxes. The simplest option, which is to neglect forces beyond a chosen cut-off, suffices for many interactions, is too crude for the particularly long-range interactions that occur between charges. To accurately account for these interactions, it is customary to use a clever 90-year-old (!) technique, called the Ewald sum.(1)
The problem with the Ewald sum is that it requires imposing a long-range periodicity that is inappropriately short for macromolecules.(2) To avoid artifacts, a number of alternatives have been suggested. One intuitive approach, called “force shifting”, smooths the interaction energy and its first derivative (the force) at the chosen cutoff. However, this creates new artifacts (see figure) when particles have very large or varying charges, as in some ionic liquids. Brandeis scientists Seyit Kale and Judith Herzfeld, have found that this problem can be solved by also smoothing the second derivative of the interaction energy (the acceleration).(3) This approach performs virtually as well as the Ewald sum in a new reactive force field that they have been developing (see figure).
The neighbor frequencies for bulk water calculated with force shifting at a cutoff of 9 Å (red) and 12 Å (magenta) versus with the authors’ new approach at a 9 Å cutoff (blue) and the Ewald sum (black). The blue and black curves are virtually the same while the red and magenta curves contain artifacts. The inset shows a representation of a water molecule from the force field that the authors are developing.
- Ewald P (1921) The Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 369: 253-287.
- Hunenberger PH, McCammon JA (1999) Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: A continuum electrostatics study. Biophys. Chem. 78: 69-88.
- Kale S, Herzfeld J (2011) Pairwise Long-range Compensation for Strongly Ionic Systems. J. Chem. Theory Comput. 7: 3620-3624.
