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ChargeCalculator:Theoretical background

320 bytes added, 17:47, 29 May 2015
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EEM is an empirical method developed as a cost-effective alternative to quantum mechanics (QM) based methods, as it enables the determination of atomic charges that are sensitive to the molecule's topology and three-dimensional structure. EEM has been successfully applied to zeolites, small organic molecules, polypeptides and proteins.
ACC implements one the classical EEM formalism(''Full EEM''), along with two additional modifications(''EEM Cutoff'', ''EEM Cutoff Cover''). We give a brief description of each below. Please refer to the literature for a more in-depth description of EEM and examples of applications (e.g., <ref name="Ionescu_2013"/><ref name="Svobodova_2013"/>).
=Full EEM=
The classical EEM formalism estimates atomic charges via a set of coupled linear equations:
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 first ''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 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 proportionally 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. The , and for each such calculation returns the charge on each of the atom in at the molecule is then computed as center of the sum of its charge contributions from each fragment. FurtherOnce all fragments have been processed, each atomic charge is corrected in such adjusted by a way constant value to ensure that the sum of all atomic charges equals 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 the classical Full EEM) if the cutoff radius is relevant (over 8 angstromAngstrom).
=EEM Cutoff Cover=
* each atom in the molecule has at least one neighbor (within two bonds) included in this subset.
The fragments for ''EEM Cutoff Cover'' are generated in the same way as for ''EEM Cutoff'', according to the ''cutoff radius''. Thus, the average size of the resulting EEM matrices will not differ. However, since fewer fragments are generated for ''EEM Cutoff Cover'', the final number of EEM matrices to be solved will be up to 4 times lower than for ''EEM Cutoff''. The charge on each atom in the molecule is then computed as the sum of its charge contributions from each fragment. Further, each atomic charge is corrected in such a way that the sum of all atomic charges equals the total molecular charge. ''EEM Cutoff Cover'' has also proven robust and sufficiently accurate (RMSD less than 0.003e compared to the ''EEM Cutoff'' of comparable cutoff radius), and is the method of choice for biomolecular complexes of tens of thousands of atoms and higher.
The only notable issue which may arise with the ''EEM Cutoff Cover'' has also proven robust and sufficiently accurate (RMSD less than 0approach is when the molecular system contains atoms for which there are no EEM parameters.003e compared to Unlike in the ''full EEM'' and ''EEM Cutoff'' approaches, these atoms are not entirely ignored here. Specifically, these atoms are included in the subset of comparable cutoff radius)atoms used in the fragment generation step. In extremely rare cases, the molecular system might contain atoms which are only connected to atoms without EEM parameters and is which have been included in the method of choice fragment generation step. In this case, ''EEM Cutoff Cover'' will not be able to calculate charges for these uniquely bonded atoms, even when EEM parameters are available for biomolecular complexes of tens of thousands of them. This problem is very unlikely to arise if H atoms are present, and higherwill only affect a small number of charges even if it does.
The only notable issue which may arise with the ''EEM Cutoff Cover'' approach is when the molecular system contains atoms for which there are no EEM parameters. Unlike in the ''full EEM'' and ''EEM Cutoff'' approaches, these atoms are not entirely ignored here. Specifically, they atoms are included in the subset of atoms used in the fragment generation step. In extremely rare cases, the molecular system might contain atoms which are only connected to atoms without EEM parameters and which have been included in the fragment generation step. In this case, ''EEM Cutoff Cover'' will not be able to calculate charges for these uniquely bonded atoms, even when EEM parameters are available for them. This problem is very unlikely to arise if H atoms are present, and will only affect a small number of charges even if it does.

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