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2018-04-25 16:24:25
The following is my notes about the GROMACS Soft-Core Potential for Free Energy Calculation
The soft-core potential between two states A and B is defined as
Vsc(r)=(1−λ)VA(rA)+λVB(rB)=(1−λ)VA(r)+λVB(r)if ασ=0rA=(ασ6Aλp+r6)1/6rB=(ασ6B(1−λ)p+r6)1/6
When α=0 or σ=0, the soft-core potential degenerates to the original potential. α is usually about 0.5 and p=1 or p=2. The recommended combination is α=0.5,p=1.
For LJ potential,
V=C12r12−C6r6Vsc=C12[1−λ(ασ6λp+r6)2+λ(ασ6(1−λ)6+r6)2]−C6[1−λασ6λp+r6+λασ6(1−λ)6+r6]
Some special cases
Vsc=0⇒V(rA)=0V(rB)=0rA=rB⇒λ=0.5
If A state is totally decoupled, which means VA=0, in this case
Vsc(r)=λVB(rB)=λ{C12(ασ6(1−λ)p+r6)2−C6ασ6(1−λ)p+r6}
Define
s6=ασ6rsc=(r6+(1−λ)ps6)1/6minrsc=rwhen λ=1maxrsc=(r6+s6)1/6when λ=0
rsc/r=(1+(1−λ)p(s/r)6)1/6
maxrsc/r=(1+(s/r)6)1/6
% <![CDATA[
\alg
V_{sc}(r, s, \l) &= \lambda \left\\{ {C_{12} \over \left(r^6+(1-\lambda)^p s^6\right)^2} -{C_6 \over r^6+(1-\lambda)^p s^6} \right\\} \\
&=4\e \lambda \left\\{ {\s^{12} \over \left(r^6+(1-\lambda)^p s^6\right)^2} -{\s^6 \over r^6+(1-\lambda)^p s^6} \right\\}
\ealg %]]>
In GMX, α,σ,p is corresponding to sc_alpha
, sc_sigma
, sc_power
, respectively. The manual said
sc-alpha
: (0
) the soft-core alpha parameter, a value of 0 results in linear interpolation of the LJ and Coulomb interactions
sc-r-power
: (6
) the power of the radial term in the soft-core equation. Possible values are 6 and 48. 6 is more standard, and is the default. When 48 is used, then sc-alpha should generally be much lower (between 0.001 and 0.003).
sc-power
: (0
) the power for lambda in the soft-core function, only the values 1 and 2 are supported
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 sc-sigma
The description of sc-sigma
is not correct, actually
σ={σ∗=(C12/C6)1/6sc_sigma if C6×C12=0
See the discussion
GROMACS DOES support table potential for free energy calculations
GROMACS calculates the interaction only If r_sc
less than rvdw
The r_sc
for any distance should be in the range of the table files, otherwise GROMACS will use a unkown value
If DispCorr
is used, be sure C6
is the correct value
If sc-alpha
is not zero, be sure the σ GROMACS used is the correct value
If DispCorr
not used, put total interaction in dispersion or repulsion column will force GROMACS to use sc-sigma
If DispCorr
is used and sc-alpha
is not zero, be sure C6
and C12
are both correct