Coupling Interaction with \(\lambda\)
In this section, the scaling nonbonded and long-range correction energies with \(\lambda\) is discussed in detailed.
VDW
Soft-core
In free energy calculation, the VDW
interaction between solute and solvent is scaled with \(\lambda\), non-linearly (soft-core scheme), to avoid
end-point catastrophe and numerical issue
the scaled solute-solvent distance, \(r_{sc}\) is defined as:
where, \(\alpha\) and \(p\) are the soft-core parameters defined by user (ScaleAlpha
, ScalePower
) and \(\sigma\) is the diameter of atom.
To improve numerical convergence of the calculation, a minimum interaction diameter \(\sigma_{min}\) should be defined by user (MinSigma
) for any atom with a diameter
less than \(\sigma_{min}\), e.g. hydrogen atoms attached to oxygen in water or alcohols.
To calculate the solvation free energy with thermodynamic integration (TI) method, the derivative of energy with respect to lambda (\(\frac{dE_{\lambda}(\texttt{VDW})}{d\lambda_{\texttt{VDW}}}\)) is required:
Electrostatic
Hard-core
In free energy calculation, the Coulombic
interaction between solute and solvent can be scaled with \(\lambda\), linearly (hard-core scheme),
by setting the ScaleCoulomb
to false.
where, \(r\) is the distance between solute and solvent, without any modification.
To calculate the solvation free energy with thermodynamic integration (TI) method, the derivative of energy with respect to lambda (\(\frac{dE_{\lambda}(\texttt{Elect})}{d\lambda_{\texttt{Elect}}}\)) is required:
Warning
To avoid end-point catastrophe and numerical issue, it’s suggested to turn on the VDW
interaction completely, before turning
on the Coulombic
interaction.
Soft-core
In free energy calculation, the Coulombic
interaction between solute and solvent can be scaled with \(\lambda\), non-linearly (soft-core scheme), to avoid
end-point catastrophe and numerical issue. This option can be activated by setting the ScaleCoulomb
to true.
the scaled solute-solvent distance, \(r_{sc}\) is defined as:
where, \(\alpha\) and \(p\) are the soft-core parameters defined by user (ScaleAlpha
, ScalePower
) and \(\sigma\) is the diameter of atom.
To improve numerical convergence of the calculation, a minimum interaction diameter \(\sigma_{min}\) should be defined by user (MinSigma
) for any atom with a diameter
less than \(\sigma_{min}\), e.g. hydrogen atoms attached to oxygen in water or alcohols.
To calculate the solvation free energy with thermodynamic integration (TI) method, the derivative of energy with respect to lambda (\(\frac{dE_{\lambda}(\texttt{Elect})}{d\lambda_{\texttt{Elect}}}\)) is required:
Warning
Using soft-core scheme to scale the coulombic interaction non-linearly, would result in inaccurate results if Ewald
method is activated.
Using Ewald Summation Method, we suggest to use hard-core scheme, to scale the coulombic interaction linearly with \(\lambda\).
Long-range Correction (VDW)
The effect of long-range corrections on predicted free energies were determined for VDW
interactions via a linear coupling with \(\lambda\).
where, \(\Delta E_{\texttt{LRC(VDW)}}\) is the the change in the long-range correction energy, due to adding a fully interacting solute
to the solvent for VDW
interaction.
To calculate the solvation free energy with thermodynamic integration (TI) method, the derivative of energy with respect to lambda (\(\frac{dE_{\lambda}(\texttt{LRC-VDW})}{\lambda_{\texttt{VDW}}}\)) is required:
Long-range Correction (Electrostatic)
Using Ewald Summation Method, the effect of long-range corrections on predicted free energies were determined for Coulombic
interactions
via a linear coupling with \(\lambda\).
where, \(\Delta E_{reciprocal}\), \(\Delta E_{self}\), and \(\Delta E_{correction}\) are the the change in the reciprocal, self,
and correction energy term in Ewald
method, due to adding a fully interacting solute to the solvent.
To calculate the solvation free energy with thermodynamic integration (TI) method, the derivative of energy with respect to lambda (\(\frac{dE_{\lambda}(\texttt{LRC-Elect})}{\lambda_{\texttt{Elect}}}\)) is required: