Editing ChargeCalculator:Theoretical background (section)

=EEM Cutoff=

While EEM is very fast compared to QM methods, handling large molecules or complexes still requires significant time and memory resources. In order to make such calculations accessible to you in real time, ACC implements two special EEM approximations.

The ''EEM Cutoff'' approximation employs a cutoff for the size of a given system of equations being solved. Specifically, for each atom, ACC solves a system containing only the equations for atoms within a certain distance in Angstrom (''cutoff radius'') from the given atom. The number of equations considered depends on the density of the molecular structure and overall shape of the molecule in the area of that particular atom.

Thus, for a molecule with 10000 atoms and a cutoff radius of 10, instead of solving one matrix with 10000 x 10000 elements, ACC will solve 10000 matrices of much smaller size (approximately from 50 x 50 up to 400 x 400). The essence of the ''EEM Cutoff'' method is that, instead of a very large calculation, ACC will run many small calculations, each of them being less memory and time demanding than the original one. ''EEM Cutoff'' is therefore efficient only for large molecules, containing at least several thousands of atoms. 

In other words, running ''EEM Cutoff'' is like running ''EEM'' for a set of overlapping fragments of the original molecule. A fragment is generated for each atom. The position and type of the atoms in each fragment are the same as in the original molecule. The only issue is the total charge of the fragment. ''EEM Cutoff'' assigns each fragment a quota of the total molecular charge proportional to the number of atoms in the fragment, and irrespective of the nature of these atoms. Then ACC solves the EEM equation for each fragment, and for each such calculation returns the charge of the atom at the center of the fragment. Once all fragments have been processed, each atomic charge is adjusted by a constant value to ensure that the sum of all atomic charges is the total molecular charge. While this algorithm may not be chemically rigorous, it has proven both robust and sufficiently accurate (RMSD less than 0.003e compared to Full EEM) if the cutoff radius is relevant (over 8 Angstrom).