LennardJonesAlpha

class LennardJonesAlpha : public feasst::LennardJones

This Lennard-Jones potential, $U_{LJ}$ is a generalization of the one described in LennardJones.

$U_{LJ}=4ϵ[{\left(\frac{\sigma +{\mathrm{\Delta }}_{\sigma }}{r+{\mathrm{\Delta }}_{\sigma }}\right)}^{2\alpha }-{\left(\frac{\sigma +{\mathrm{\Delta }}_{\sigma }}{r+{\mathrm{\Delta }}_{\sigma }}\right)}^{\alpha }]$,

In this class, the $\alpha$ parameter may be varied (default: 6). In addition, the delta_sigma parameter may be set as a site-specific ModelParam in the fstprt file (default: 0).

Note that $U_{LJ}$ crosses zero when $r=\sigma$.

Consider an alternative interpretation for ${\mathrm{\Delta }}_{\sigma }={\sigma }_r-\sigma$

$U_{LJ}=4ϵ[{\left(\frac{{\sigma }_r}{r-\sigma +{\sigma }_r}\right)}^{2\alpha }-{\left(\frac{{\sigma }_r}{r-\sigma +{\sigma }_r}\right)}^{\alpha }]$

Thus, ${\sigma }_r=\sigma +{\mathrm{\Delta }}_{\sigma }$ determines the well width and shape of the potential, while $\sigma$ determines the excluded volume by shifting the potential right or left.

The Ashbaugh-Hatch model described in https://dx.doi.org/10.1021/ja802124e is also available with the site-specific “lambda” ModelParam in the fstprt file. The lambda parameter decouples the attractive and repulsive portions of the LJ potential to allow for a modified well-depth or a repulsive shoulder, as shown in Fig. 1 of https://doi.org/10.1039/C7SM01005B and also described in https://dx.doi.org/10.1021/ja802124e.

$U^{\lambda }=\{\begin{array}{lr}{U}_{LJ}+ϵ(1-{\lambda }_{ij})& r\le r_m\\ {\lambda }_{ij}{U}_{LJ}& r>r_m\end{array}$

where $r_m=(\sigma +{\mathrm{\Delta }}_{\sigma })2^{1/\alpha }-{\mathrm{\Delta }}_{\sigma }$ is the minimum. The lambda parameter is a site-specific ModelParam in the fstprt file, just like epsilon or sigma.

References: [1]

[1]

Henry S. Ashbaugh and Harold W. Hatch. Natively Unfolded Protein Stability as a Coil-to-Globule Transition in Charge/Hydropathy Space. Journal of the American Chemical Society, 130(29):9536–9542, July 2008. doi:10.1021/ja802124e.

Subclassed by feasst::LennardJonesCutShift, feasst::LennardJonesForceShift

Arguments

• alpha: set the value of $\alpha$ (default: 6).

class DeltaSigma : public feasst::ModelParam

class Lambda : public feasst::ModelParam

The lambda parameter has the default mixing rule: ${\lambda }_{ij}=\sqrt{{\lambda }_i{\lambda }_j}$

class EnergyAtCutOff : public feasst::ModelParam

class EnergyDerivAtCutOff : public feasst::ModelParam