COMB3 Potential Notes¶
This potential class is part of the third generation charge-optimized-many-body (COMB) potential [1]. The total potential energy consists of an electrostatic part \(E^{ES}\) and a short-ranged term \(E^{SR}\). Additional terms, such as van-der-Waals interactions or angle correction terms, can be added later on.
As in the first and second generation COMB potentials, variable charges \(q_i\) are used. They are determined by minimizing \(E^{total}\) in each time step with respect to the charges. Additionally, induced dipoles \(\bf{\Delta}_i\) may be calculated for each particle, if polarization effects are allowed. The electrostatic part \(E^{ES}\) consists of four different terms: The self-energy term \(E^{self}\), the interactions between the variable charges \(E^{qq}\), the interactions between variable and fixed charges \(E^{qZ}\), and the polarization term \(E^{pol}\).
These four terms are defined as follows:
All long-range interactions that occur in \(E^{ES}\) are computed using the Wolf-summation [2]. The dipoles are calculated by minimizing \(E^{pol}\) with respect to the \(\Delta_i\), which corresponds to solving a set of linear equations.
The short-range interactions are given by
which are defined by the following equations:
A COMB3 potential is initiated by setting up a comb3particle
object for each particle type.
This will automatically activate all electrostatic interactions that act on the given particle type.
Note, that the constructor parameter p corresponds to the polarizability \(P_i\) in \(E^{pol}\).
The short-range interactions are activated by specifying the corresponding pair parameters in comb3pairpotential
.
Here, the parameters b0, b1, and b2 correspond to \(B_{ij}^0\), \(B_{ij}^1\), and \(B_{ij}^2\), respectively, while the constructor arguments di can be used to set \(b_{ij}^i\) (i=0,…,6).
Note, that these pair interactions are non-symmetric, meaning that both particle-type combinations have to be specified, e.g. Titanium-Nitrogen and Nitrogen-Titanium in the above example.
One can also add a comb3fieldcorrection
term \(E^{field}\) of the form
Similar to comb3pairpotential
these interactions are non-symmetric and need to be specified for both particle-pair-combinations.