ChargeCalculator:Theoretical background - Revision history

Crina at 17:47, 29 May 2015

2015-05-29T17:47:30Z

← Older revision		Revision as of 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.		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~~ classical EEM formalism, along with two additional modifications. 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"/>).		ACC implements 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"/>).

	=EEM=		=Full EEM=

	The classical EEM formalism estimates atomic charges via a set of coupled linear equations:		The classical EEM formalism estimates atomic charges via a set of coupled linear equations:
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	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.		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~~ 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.		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.		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~~ 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~~ 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. While this algorithm may not be chemically rigorous, has proven both robust and sufficiently accurate (RMSD less than 0.003e compared to ~~the classical~~ EEM) if the cutoff radius is relevant (over 8 ~~angstrom~~).		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).

	=EEM Cutoff Cover=		=EEM Cutoff Cover=
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	* each atom in the molecule has at least one neighbor (within two bonds) included in this subset.		* 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 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.

	''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'' 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, these 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.

	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.

Crina: /* EEM Cutoff Cover */

2015-03-04T18:12:33Z

EEM Cutoff Cover

← Older revision		Revision as of 18:12, 4 March 2015
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	''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.		''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'' approach is when the molecular system contains atoms for which there are no EEM parameters. Unlike the ''full EEM'' and ''EEM Cutoff'' approaches, these atoms are not entirely ignored here. Specifically, they ~~contribute to the pivot selection step, and may be selected as pivots.~~		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.

	~~This problem is enhanced when some~~ atoms are ~~missing (e.g., missing H atoms). At~~ the ~~end~~ of the ~~EEM Cover calculation~~, the atoms which ~~appeared to be~~ connected ~~only~~ to ~~these problematic~~ atoms ~~will also not have atomic charges, even if they have~~ EEM parameters, ~~due to the nature of the~~ EEM Cover ~~approach.~~

	~~Anyway, the principle oriented solution would~~ be to ~~correct the pivot selection scheme so as to ignore the~~ atoms ~~without~~ EEM parameters~~, consistent with the full EEM and EEM Cutoff approaches~~. ~~However, this would mean full testing and benchmarking of the corrected algorithm, and I am not really looking forward to that :) Moreover, as David pointed out, this~~ is unlikely to ~~happen in cases where~~ H are present, ~~since~~ it ~~solely affects atoms which are connected only to atoms without EEM parameters, and not connected to any other atoms~~.

Crina: /* EEM Cutoff Cover */

2015-03-04T18:01:02Z

EEM Cutoff Cover

← Older revision		Revision as of 18:01, 4 March 2015
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	''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.		''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'' approach is when the molecular system contains atoms for which there are no EEM parameters. Unlike the ''full EEM'' and ''EEM Cutoff'' approaches, these atoms are not entirely ignored here. Specifically, they contribute to the pivot selection step, and may be selected as pivots.

			This problem is enhanced when some atoms are missing (e.g., missing H atoms). At the end of the EEM Cover calculation, the atoms which appeared to be connected only to these problematic atoms will also not have atomic charges, even if they have EEM parameters, due to the nature of the EEM Cover approach.

			Anyway, the principle oriented solution would be to correct the pivot selection scheme so as to ignore the atoms without EEM parameters, consistent with the full EEM and EEM Cutoff approaches. However, this would mean full testing and benchmarking of the corrected algorithm, and I am not really looking forward to that :) Moreover, as David pointed out, this is unlikely to happen in cases where H are present, since it solely affects atoms which are connected only to atoms without EEM parameters, and not connected to any other atoms.

Crina: /* EEM Cutoff Cover */

2014-12-08T15:27:59Z

EEM Cutoff Cover

← Older revision		Revision as of 15:27, 8 December 2014
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	To further enhance the time and memory efficiency of EEM, ACC implements an additional approximation with specific focus on large biomolecular complexes with hundreds of thousands of atoms. This additional approximation is applied to the ''EEM Cutoff'' method in order to reduce the number of EEM matrices that will be solved.		To further enhance the time and memory efficiency of EEM, ACC implements an additional approximation with specific focus on large biomolecular complexes with hundreds of thousands of atoms. This additional approximation is applied to the ''EEM Cutoff'' method in order to reduce the number of EEM matrices that will be solved.

	While in the ''EEM Cutoff'' method ACC generates one fragment for each atom in the molecule, this further approximation generates fragments only for a subset of atoms. The algorithm by which this subset of atoms is obtained ensures that each atom in the molecule will ~~eventualy~~ contribute to at least one fragment. In other words, the entire volume of the molecule is covered, and the method is thus termed ''EEM Cutoff Cover''.		While in the ''EEM Cutoff'' method ACC generates one fragment for each atom in the molecule, this further approximation generates fragments only for a subset of atoms. The algorithm by which this subset of atoms is obtained ensures that each atom in the molecule will eventually contribute to at least one fragment. In other words, the entire volume of the molecule is covered, and the method is thus termed ''EEM Cutoff Cover''.

	In ''EEM Cutoff Cover'', the subset of fragment generating atoms is obtained in such a way that:		In ''EEM Cutoff Cover'', the subset of fragment generating atoms is obtained in such a way that:
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	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 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''.

	''EEM Cutoff Cover'' has also proven robust and sufficiently accurate (RMSD less than 0.003e compared to the ''EEM Cutoff ~~Cover~~'' of comparable cutoff radius), and is the method of choice for biomolecular complexes of tens of thousands of atoms and higher.		''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.

Crina: /* EEM */

2014-12-08T15:27:24Z

EEM

← Older revision		Revision as of 15:27, 8 December 2014
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	[[File:EEM equation.png]]		[[File:EEM equation.png]]

	In order solve this system of equations and calculate the atomic charges for all atoms, the following terms need to be known:		In order to solve this system of equations and calculate the atomic charges for all atoms, the following terms need to be known:
	* distances between all pairs of atoms		* distances between all pairs of atoms
	* total molecular charge		* total molecular charge

Crina: /* References */

2014-11-29T04:01:35Z

References

← Older revision		Revision as of 04:01, 29 November 2014
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	'''Return to the [[ChargeCalculator:UserManual \| Table of contents]].'''		'''Return to the [[ChargeCalculator:UserManual \| Table of contents]].'''

	==References==		=References=
	<references>		<references>
	<ref name="Ionescu_2013">Ionescu C-M, Geidl S, Svobodová Vareková R, Koca J. Rapid Calculation of Accurate Atomic Charges For Proteins via the Electronegativity Equalization Method. J. Chem. Inf. Model., 2013, 53 (10), pp 2548-2558. DOI: 10.1021/ci400448n</ref>		<ref name="Ionescu_2013">Ionescu C-M, Geidl S, Svobodová Vareková R, Koca J. Rapid Calculation of Accurate Atomic Charges For Proteins via the Electronegativity Equalization Method. J. Chem. Inf. Model., 2013, 53 (10), pp 2548-2558. DOI: 10.1021/ci400448n</ref>

Crina at 04:01, 29 November 2014

2014-11-29T04:01:20Z

← Older revision		Revision as of 04:01, 29 November 2014
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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.		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 classical EEM formalism, along with two additional modifications. We give a brief description of each below. Please refer to the literature ~~[[20,32-45]]~~ for a more in-depth description of EEM and ~~a few~~ examples of applications ~~[[44~~,~~46-50]]~~.		ACC implements one classical EEM formalism, along with two additional modifications. 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"/>).

	=EEM=		=EEM=
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	While in the ''EEM Cutoff'' method ACC generates one fragment for each atom in the molecule, this further approximation generates fragments only for a subset of atoms. The algorithm by which this subset of atoms is obtained ensures that each atom in the molecule will eventualy contribute to at least one fragment. In other words, the entire volume of the molecule is covered, and the method is thus termed ''EEM Cutoff Cover''.		While in the ''EEM Cutoff'' method ACC generates one fragment for each atom in the molecule, this further approximation generates fragments only for a subset of atoms. The algorithm by which this subset of atoms is obtained ensures that each atom in the molecule will eventualy contribute to at least one fragment. In other words, the entire volume of the molecule is covered, and the method is thus termed ''EEM Cutoff Cover''.

	In ''EEM Cutoff Cover', the subset of fragment generating atoms is obtained in such a way that:		In ''EEM Cutoff Cover'', the subset of fragment generating atoms is obtained in such a way that:
	* no two atoms in this subset are connected to each other		* no two atoms in this subset are connected to each other
	* each atom in the molecule has at least one neighbor (within two bonds) included in this subset.		* each atom in the molecule has at least one neighbor (within two bonds) included in this subset.
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	''EEM Cutoff Cover'' has also proven robust and sufficiently accurate (RMSD less than 0.003e compared to the ''EEM Cutoff Cover'' of comparable cutoff radius), and is the method of choice for biomolecular complexes of tens of thousands of atoms and higher.		''EEM Cutoff Cover'' has also proven robust and sufficiently accurate (RMSD less than 0.003e compared to the ''EEM Cutoff Cover'' of comparable cutoff radius), and is the method of choice for biomolecular complexes of tens of thousands of atoms and higher.


	'''Return to the [[ChargeCalculator:UserManual \| Table of contents]].'''		'''Return to the [[ChargeCalculator:UserManual \| Table of contents]].'''

			==References==
			<references>
			<ref name="Ionescu_2013">Ionescu C-M, Geidl S, Svobodová Vareková R, Koca J. Rapid Calculation of Accurate Atomic Charges For Proteins via the Electronegativity Equalization Method. J. Chem. Inf. Model., 2013, 53 (10), pp 2548-2558. DOI: 10.1021/ci400448n</ref>

			<ref name="Svobodova_2013">Svobodová Vareková R, Geidl S, Ionescu C-M, Skrehota O, Bouchal T, Sehnal D, Abagyan R, Koca J. Predicting pKa values from EEM atomic charges. J. Cheminf. 2013, 5, 18.</ref>
			</references>

Crina: /* EEM Cutoff Cover */

2014-11-29T00:57:17Z

EEM Cutoff Cover

← Older revision		Revision as of 00:57, 29 November 2014
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	''EEM Cutoff Cover'' has also proven robust and sufficiently accurate (RMSD less than 0.003e compared to the ''EEM Cutoff Cover'' of comparable cutoff radius), and is the method of choice for biomolecular complexes of tens of thousands of atoms and higher.		''EEM Cutoff Cover'' has also proven robust and sufficiently accurate (RMSD less than 0.003e compared to the ''EEM Cutoff Cover'' of comparable cutoff radius), and is the method of choice for biomolecular complexes of tens of thousands of atoms and higher.

			'''Return to the [[ChargeCalculator:UserManual \| Table of contents]].'''

Crina at 00:53, 29 November 2014

2014-11-29T00:53:51Z

← Older revision		Revision as of 00:53, 29 November 2014
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	=EEM Cutoff Cover=		=EEM Cutoff Cover=

	To further enhance the time and memory efficiency of EEM, ACC implements an additional approximation with specific focus on large biomolecular complexes with hundreds of thousands of atoms. This additional approximation is applied to the ''EEM Cutoff'' method		To further enhance the time and memory efficiency of EEM, ACC implements an additional approximation with specific focus on large biomolecular complexes with hundreds of thousands of atoms. This additional approximation is applied to the ''EEM Cutoff'' method in order to reduce the number of EEM matrices that will be solved.

			While in the ''EEM Cutoff'' method ACC generates one fragment for each atom in the molecule, this further approximation generates fragments only for a subset of atoms. The algorithm by which this subset of atoms is obtained ensures that each atom in the molecule will eventualy contribute to at least one fragment. In other words, the entire volume of the molecule is covered, and the method is thus termed ''EEM Cutoff Cover''.

	~~The atom selection algorithm~~ is ~~ensures~~ that the ~~entire volume~~ of the ~~molecule is covered~~, and the ~~method is thus termed~~ ''EEM Cutoff Cover''.		In ''EEM Cutoff Cover', the subset of fragment generating atoms is obtained in such a way that:
			* no two atoms in this subset are connected to each other
			* 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''.

			''EEM Cutoff Cover'' has also proven robust and sufficiently accurate (RMSD less than 0.003e compared to the ''EEM Cutoff Cover'' of comparable cutoff radius), and is the method of choice for biomolecular complexes of tens of thousands of atoms and higher.

Crina: /* EEM Cutoff Cover */

2014-11-29T00:16:10Z

EEM Cutoff Cover

← Older revision		Revision as of 00:16, 29 November 2014
Line 34:		Line 34:
	=EEM Cutoff Cover=		=EEM Cutoff Cover=

	To further enhance the time and memory efficiency of EEM		To further enhance the time and memory efficiency of EEM, ACC implements an additional approximation with specific focus on large biomolecular complexes with hundreds of thousands of atoms. This additional approximation is applied to the ''EEM Cutoff'' method


			The atom selection algorithm is ensures that the entire volume of the molecule is covered, and the method is thus termed ''EEM Cutoff Cover''.