previous paragraphs; here we report them more explicitly and with
a brief explanation:
l Use a soft-core potential for decoupling/annihilating the LJ
interactions (seeNote 2)[55–58]. Simple scaling schemes for
the LJ parameters result in unequal phase space overlap between
lambda windows, as well as large forces and numerical instabil-
ities due to a singularity atrij¼0, whereiandjare two particles
andrthe distance between them. Soft-core potentials resolve
the instabilities observed during the decoupling of the van der
Waals parameters by modifying the LJ equation so that the
interaction energy is finite for any configuration.
l Decouple charges and LJ separately (as shown inNote 1).
Imagine two atoms with opposite partial charges and little
repulsion. Even if the charges are small, in the limit ofrij¼0,
the potential energy of the interaction goes to infinity. This
results in large forces and simulation crashes [59, 60]. Thus, a
simple way to resolve this issue is to make sure the LJ parameters
are decoupled after the charges, or coupled before them, so that
when charges are present the repulsive part of the LJ interactions
is present too. Another way around this problem is to use a soft-Fig. 4Thermodynamic integration plot for the decoupling of a ligand from solution. More specifically, it shows
theh∂U/∂λiprofile for the decoupling of n-phenylglycinonitrile [54], the ligand used as an example in the
tutorial that accompanies this chapter and available on thealchemistry.orgwebsite. It is possible to notice the
separate decoupling of coulombic and vdW interactions, as well as the fact that the coulombic transformation
is smoother than the vdW one
Absolute Alchemical Free Energy 215