Coulomb distance cutoffs

For coupling purposes the QM particles are separated into two sets — those which are near the QM center and those located close to the QM/MM border. For QM atoms close to the center the intermolecular distances to MM particles are typically larger than the non-Coulombic cutoff distances and, therefore, these atoms only require a Coulombic term to account for the coupling between the QM and the MM particles. A correction term compensating for the Coulombic cutoff such as Ewald summation or a reaction field is typically applied. Atoms close to the interface region have small intermolecular distances and consequently, non-Coulombic interactions have to be included in addition to the Coulombic forces to achieve a proper coupling. 

The size assigned to the core and layer regions is an important consideration for such simulations. The size of the solute determines the minimum radius of the core region, but it is often necessary to include the first hydration layer as well, for instance when hydrated ions are studied. The distance of all particles included in the QM core to the QM/MM interface should exceed the non-Coulombic cutoff distance of all involved interactions. In the case of water the minimum size of the layer region is 2.5-3.0 A. 

The computational requirements of the calculations are dependent on the accuracy of the force field. These can, for example, be dramatically altered by changing the cutoff distance for coulombic interactions [80] or using Ewald or Fast Multipole methods to compute long range electrostatic interactions. 

Coulomb interactions show critically poor convergence properties as a function of distance (i.e., 1/r interactions). Interaction cutoffs have shown prone to artifacts and motivated the development of long-range electrostatic methods, such as Ewald summation (see, e.g.. Reference [25] and references therein). A number of Ewald summation methods have been extended to MTPs (e.g., [43, 54, 120]), providing a rigorous treatment of electrostatics in MD simulations. 

Except for the Coulombic contributions, which are computed by an Ewald-type summation, as described in Section 2.3, a potential cutoff distance is imposed to avoid unnecessary computing time calculating negligible contributions by short-range interactions from most of the V 2N N— 1) atom pairs in the system. In the commonly used nearest-image convention, if the cutoff obeys the condition re < VtJL, Then atom pair interactions included are between atom i in the central box and either atomj in the same box or one of its imagesf in an adjacent one, depending on whichever distance x/ - Xy or x/ - f is least (see Fig. 5.4). 

The electrostatic (coulomb) interactions take a special place in any force field expression. One major difference between the coulombic and all other interactions is the slow decay of the energy term with distance due to the 1/r dependence. This results in practical issues when calculating these energy contributions, as much longer cutoff distances are required to ensure that the energy term is represented accurately in the total energy. An alternative method that calculates coulombic interactions in reciprocal space (Ewald summation) is preferable to direct space calculations due to faster convergence. 

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