Cutoff truncation methods
for long-range interactions
Simple truncation
0
1
Rc
d > Rc
d < Rc
• If distance between particles > cutoff radius (Rc), interaction is neglected.
• Artificial discontinuity in the potential
• Leads to heating of the molecules at Rc
2
Rl Rc
Rc
Rl
Switching procedure
• Switching function to avoid discontinuity and heating.
• Starts at distance Rl until Rc.
• Creation of sudden changes in the force.
3
D
Reaction field
• If distance < Rc molecules interact
• Particles outside Rc are represented by a dielectric continuum
Dielectric continuum
Explicit solvent
Rc
4
Ion mobility
• Buildup of water before Rl
• Preferential orientation of water dipoles
• Caused by a sudden increase in the
Coulomb force near Rl
θ
5
Ion mobility
θ
• Buildup of water before Rl
• Preferential orientation of water dipoles
• Caused by a sudden increase in the
Coulomb force near Rl
6
Ion mobility
• Velocity autocorrelation functions
• Simulations with switching
function have more oscillations
• Initial decay enhanced
F−
Cl−
Br−
Increasing difference
Lower value of the
diffusion constant
7
Polarization and periodic conditions
• ST/NPBC: overpolarization for r < Rc;
underpolarization for r > Rc
• ST/PBC: polarization is lower in
general
• RF/NPBC: deviations around Rc
• RF/PBC: in general lower
ST: Simple truncation
RF: Reaction field
RIS = Rc
8
Solvation free energy
• Periodicity induced shift in solvation free energy
• PBC induce further reduction of solvation free energy
• If simulation box is big enough there is no difference
Ion size Shift
Rc Shift
Reaction field shift > Simple truncation shift
<
9
Ion-ion interaction
• Artifacts on the electrostatic
contribution to the potential
of mean force
• Around cutoff distance
• Very small changes when
PBC
• RF Works better
ST
RF
Same charge Opposite charge
10
Cutoff length
• 0.5 means random oriented water
molecules
• Phase transition towards a water
structure
Cutoff = 1.8 nm
Cutoff = 0.9 nm
11
Conclusions
• Standard truncation -> heating and ion-ion interaction artifacts around Rc
• Switching -> sudden force around Rl
• Reaction field and standard truncation -> solvation free energy changes
when using PBC
• Increasing the cutoff lenght is not always the solution
12