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Update 4.3ADMPQeqForce.md
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WangXinyan940 committed Nov 8, 2023
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Expand Up @@ -7,6 +7,7 @@ ADMPQeqForce provides a support to coulombic energy calculation for constant pot
### 1.1 General Energy Equations

First, assume the coulombic energy of the total system is:

```math
E_{coul}(q_i) = E_{pc}\left(q_i\right) + E_{sr}(q_i) + E_{corr} + E_{on-site}({q_i}; \chi_i, J_i)
```
Expand All @@ -18,6 +19,7 @@ The total coulombic energy is composed of the followling four parts.
#### 1.1.1 Point Charge Part

Here, the first term $`E_{pc}`$ is electrostatic energy of point-charge systems, which is typically done in Ewald/PME method. For isolated molecule/clusters, it can also be computed using cutoff scheme:

```math
E_{pc}\left(q_i\right) = \sum_{i<j}\frac{q_i q_j}{r_{ij}}
```
Expand All @@ -32,7 +34,7 @@ The second term is the short-range damping term, which can be different for diff
```math
E_{sr}\left(q_i\right) = \sum_{i<j} f(r_{ij})\frac{q_i q_j}{r_{ij}} \\
f(r) = - \exp\left[-\left(\frac{J_{ij}r}{K}\right)^2\right]\left(1-\frac{J_{ij}r}{K}+\left(\frac{J_{ij}r}{K}\right)^2\right) \\
J_{ij} = \sqrt{J_i J_j} \\
J_{ij} = \sqrt{J_i J_j}
```
* Another typical example is the Tang-Toennies damping:

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