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Merged Marcin Kirsz requested to merge main into develop
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*
* The ZBL (Ziegler-Biersack-Littmark) potential is an empirical potential used to model short-range interactions between atoms.
*
* The constant term \( \frac{4 \pi \varepsilon_0 e^2}{1} \) is set to 1 and will be fitted as needed.
* The constant term \f$ \frac{4 \pi \varepsilon_0 e^2}{1} \f$ is set to 1 and will be fitted as needed.
*
* The simplified expression for the ZBL potential is given by:
*
* \f[
* V(r) = \frac{Z_1 Z_2 }{r} \phi\left(\frac{r}{a}\right)
* V(r) = \frac{Z_1 Z_2}{r} \phi\left(\frac{r}{a}\right)
* \f]
*
* where \( a \) is the screening length, expressed as:
* where \f$ a \f$ is the screening length, expressed as:
* \f[
* a = \frac{s_0 \cdot a_0}{Z_1^{p_0} + Z_2^{p_1}}
* \f]
*
* Here, \( a_0 \), \( s_0 \), \( p_0 \), and \( p_1 \) are adjustable hyperparameters.
* Here, \f$ a_0 \f$, \f$ s_0 \f$, \f$ p_0 \f$, and \f$ p_1 \f$ are adjustable hyperparameters.
* Setting any of these to -1 uses the default values:
*
* - \( a_0 = 0.52917721067 \) Å
* - \( s_0 = 0.88534 \)
* - \( p_0 = 0.23 \)
* - \( p_1 = 0.23 \)
* - \f$ a_0 = 0.52917721067 \, \text{Å} \f$
* - \f$ s_0 = 0.88534 \f$
* - \f$ p_0 = 0.23 \f$
* - \f$ p_1 = 0.23 \f$
*
*
* The screening function \(\phi\) is defined as:
* The screening function \f$ \phi \f$ is defined as:
* \f[
* \phi(x) = 0.1818 e^{-3.2x} + 0.5099 e^{-0.9423x} + 0.2802 e^{-0.4029x} + 0.02817 e^{-0.2016x}
* \f]
*
* Required Config Key: \ref INIT2B \ref TYPE2B
*
* - TYPE2B D2_ZBL \( a_0 \) \( s_0 \) \( p_0 \) \( p_1 \)
* - TYPE2B D2_ZBL \f$ a_0 \f$ \f$ s_0 \f$ \f$ p_0 \f$ \f$ p_1 \f$
*
* Examples:
*
* - TYPE2B D2_ZBL 0.53 0.90 0.23 0.23 # Custom parameters
* - TYPE2B D2_ZBL -1 -1 -1 -1 # Default values
* - TYPE2B D2_ZBL 0.53 -1 -1 -1 # Mix of default and custom
* - TYPE2B D2_ZBL 0.53 0.90 0.23 0.23 Kr Kr # Custom parameters
* - TYPE2B D2_ZBL -1 -1 -1 -1 Kr Kr # Default values
* - TYPE2B D2_ZBL 0.53 -1 -1 -1 Kr Kr # Mix of default and custom
*
*/
class D2_ZBL : public D2_Base {
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