The Gapsys *et al.* soft-core is formulated to act on the level of van der Waals and electrostatic forces:
the non-bonded interactions are linearized at a point defined as, :math:`r_{scLJ}` or :math:`r_{scQ}`, respectively.
The linearization point depends on the state of the system as controlled by the :math:`\lambda` parameter and
-two parameters :math:`\alpha_Q` and :math:`\alpha_{LJ}`.
+two parameters :math:`\alpha_Q` (set with ``sc-scale-linpoint-Q-gapsys``) and :math:`\alpha_{LJ}` (set with ``sc-scale-linpoint-LJ-gapsys``).
The dependence on :math:`\lambda` guarantees that the end-states are properly represented by their hard-core potentials.
:numref:`Fig. %s <fig-gapsyssc>` illustrates the behaviour of the linearization point, forces and integrated potential energies with respect
-to the parameters :math:`\alpha_Q` and :math:`\alpha_{LJ}`.
+to the parameters :math:`\alpha_Q` and :math:`\alpha_{LJ}`. The optimal choices of the parameter values have been systematically explored in :ref:`185 <refGapsys2012>`. These recommended values are set by default when ``sc-function=gapsys`` is selected: ``sc-scale-linpoint-Q-gapsys=0.3`` and ``sc-scale-linpoint-LJ-gapsys=0.85``.
.. _fig-gapsyssc:
The parameter :math:`\alpha_{LJ}` is a unitless scaling factor in the range :math:`[0,1)`.
It scales the position of the point from which the van der Waals force will be linearized.
The linearization of the force is allowed in the range :math:`[0,F_{min}^{LJ})`,
-where setting :math:`\alpha_{LJ}=0` results in a standard hard-core interaction.
+where setting :math:`\alpha_{LJ}=0` results in a standard hard-core van der Waals interaction.
Setting :math:`\alpha_{LJ}` closer to 1 brings the force linearization point towards
the minimum in the Lennard-Jones force curve (:math:`F_{min}^{LJ}`).
This construct allows retaining the repulsion between two particles with non-zero C12 parameter at any :math:`\lambda` value.
It scales the position of the point from which the Coulombic force will be linearized.
Even though in theory :math:`\alpha_{Q}` can be set to an arbitrarily large value,
algorithmically the linearization point for the force is bound in the range :math:`[0,F_{rcoul}^{Q})`,
-where setting :math:`\alpha_{Q}=0` results in a standard hard-core interaction.
+where setting :math:`\alpha_{Q}=0` results in a standard hard-core Coulombic interaction.
Setting :math:`\alpha_{Q}` to a larger value softens the Coulombic force.
In all the notations below, for simplicity, the distance between two atoms :math:`i` and :math:`j` is noted as :math:`r`, i.e. :math:`r=r_{ij}`.
:label: eqvdwforces
where the switching point between the soft and hard-core Lennard-Jones forces
-:math:`r_{scLJ} = \alpha_{LJ}(\frac{26}{7}\frac{C_{ij}^{(12)}}{C_{ij}^{(6)}}\lambda)^{\frac{1}{6}}` for state A, and
-:math:`r_{scLJ} = \alpha_{LJ}(\frac{26}{7}\frac{C_{ij}^{(12)}}{C_{ij}^{(6)}}(1-\lambda))^{\frac{1}{6}}` for state B.
+:math:`r_{scLJ} = \alpha_{LJ}(\frac{26}{7}\sigma^6\lambda)^{\frac{1}{6}}` for state A, and
+:math:`r_{scLJ} = \alpha_{LJ}(\frac{26}{7}\sigma^6(1-\lambda))^{\frac{1}{6}}` for state B.
+In analogy to the Beutler *et al.* soft core version, :math:`\sigma` is the radius of the interaction, which is :math:`(C_{12}/C_6)^{1/6}`
+or an input parameter (set with ``sc-sigma-LJ-gapsys``) when C6 or C12 is zero. The default value for this parameter is ``sc-sigma-LJ-gapsys=0.3``.
Explicit expression:
written out. For normal BAR such as with :ref:`gmx bar`, a value of
1 is sufficient, while for MBAR -1 should be used.
+.. mdp:: sc-function
+
+ (beutler)
+
+ .. mdp-value:: beutler
+
+ Beutler *et al.* soft-core function
+
+ .. mdp-value:: gapsys
+
+ Gapsys *et al.* soft-core function
+
.. mdp:: sc-alpha
(0)
- the soft-core alpha parameter, a value of 0 results in linear
- interpolation of the LJ and Coulomb interactions
+ for `sc-function=beutler` the soft-core alpha parameter,
+ a value of 0 results in linear interpolation of the
+ LJ and Coulomb interactions.
+ Used only with `sc-function=beutler`
.. mdp:: sc-r-power
(6)
power 6 for the radial term in the soft-core equation.
+ Used only with `sc-function=beutler`
.. mdp:: sc-coul
states are used, not with :mdp:`couple-lambda0` /
:mdp:`couple-lambda1`, and you can still turn off soft-core
interactions by setting :mdp:`sc-alpha` to 0.
+ Used only with `sc-function=beutler`
.. mdp:: sc-power
(0)
the power for lambda in the soft-core function, only the values 1
- and 2 are supported
+ and 2 are supported. Used only with `sc-function=beutler`
.. mdp:: sc-sigma
(0.3) [nm]
- the soft-core sigma for particles which have a C6 or C12 parameter
- equal to zero or a sigma smaller than :mdp:`sc-sigma`
+ for `sc-function=beutler` the soft-core sigma for particles
+ which have a C6 or C12 parameter equal to zero or a sigma smaller
+ than :mdp:`sc-sigma`.
+ Used only with `sc-function=beutler`
+
+.. mdp:: sc-linpoint-LJ-gapsys
+
+ (0.85)
+ for `sc-function=gapsys` it is the unitless alphaLJ parameter.
+ It controls the softness of the van der Waals interactions
+ by scaling the point for linearizing the vdw force.
+ Setting it to 0 will result in the standard hard-core
+ van der Waals interactions.
+ Used only with `sc-function=gapsys`
+
+.. mdp:: sc-linpoint-Q-gapsys
+
+ (0.3) [nm/e^2]
+ For `sc-function=gapsys` the alphaQ parameter
+ with the unit of [nm/e^2] and default value of 0.3. It controls
+ the softness of the Coulombic interactions. Setting it to 0 will
+ result in the standard hard-core Coulombic interactions.
+ Used only with `sc-function=gapsys`
+
+.. mdp:: sc-sigma-LJ-gapsys
+
+ (0.3) [nm]
+ for `sc-function=gapsys` the soft-core sigma for particles
+ which have a C6 or C12 parameter equal to zero.
+ Used only with `sc-function=gapsys`
.. mdp:: couple-moltype
biod.pnpi.spb.ru / alexxy / gromacs.git / commitdiff