\(\renewcommand{\AA}{\text{Å}}\)
8.4.4. TIP4P water model
The four-point TIP4P rigid water model extends the traditional three-point TIP3P model by adding an additional site M, usually massless, where the charge associated with the oxygen atom is placed. This site M is located at a fixed distance away from the oxygen along the bisector of the HOH bond angle. A bond style of harmonic and an angle style of harmonic or charmm should also be used. In case of rigid bonds also bond style zero and angle style zero can be used.
There are two ways to implement TIP4P water in LAMMPS:
Use a specially written pair style that uses the TIP3P geometry without the point M. The point M location is then implicitly derived from the other atoms or each water molecule and used during the force computation. The forces on M are then projected on the oxygen and the two hydrogen atoms. This is computationally very efficient, but the charge distribution in space is only correct within the tip4p labeled styles. So all other computations using charges will “see” the negative charge incorrectly on the oxygen atom.
This can be done with the following pair styles for Coulomb with a cutoff:
or these commands for a long-range Coulomb treatment:
The bond lengths and bond angles should be held fixed using the fix shake or fix rattle command, unless a parameterization for a flexible TIP4P model is used. The parameter sets listed below are all for rigid TIP4P model variants and thus the bond and angle force constants are not used and can be set to any legal value; only equilibrium length and angle are used.
Use an explicit 4 point TIP4P geometry where the oxygen atom carries no charge and the M point no Lennard-Jones interactions. Since fix shake or fix rattle may not be applied to this kind of geometry, fix rigid or fix rigid/small or its thermostatted variants are required to maintain a rigid geometry. This avoids some of the issues with respect to analysis and non-tip4p styles, but it is a more costly force computation (more atoms in the same volume and thus more neighbors in the neighbor lists) and requires a much shorter timestep for stable integration of the rigid body motion. Since no bonds or angles are required, they do not need to be defined and atom style charge would be sufficient for a bulk TIP4P water system. In order to avoid that LAMMPS produces an error due to the massless M site a tiny non-zero mass needs to be assigned.
The table below lists the force field parameters (in real units) to for a selection of popular variants of the TIP4P model. There is the rigid TIP4P model with a cutoff (Jorgensen), the TIP4/Ice model (Abascal1), the TIP4P/2005 model (Abascal2) and a version of TIP4P parameters adjusted for use with a long-range Coulombic solver (e.g. Ewald or PPPM in LAMMPS). Note that for implicit TIP4P models the OM distance is specified in the pair_style command, not as part of the pair coefficients.
Parameter
TIP4P (original)
TIP4P/Ice
TIP4P/2005
TIP4P (Ewald)
O mass (amu)
15.9994
15.9994
15.9994
15.9994
H mass (amu)
1.008
1.008
1.008
1.008
O or M charge (\(e\))
-1.040
-1.1794
-1.1128
-1.04844
H charge (\(e\))
0.520
0.5897
0.5564
0.52422
LJ \(\epsilon\) of OO (kcal/mole)
0.1550
0.21084
0.1852
0.16275
LJ \(\sigma\) of OO (\(\AA\))
3.1536
3.1668
3.1589
3.16435
LJ \(\epsilon\) of HH, MM, OH, OM, HM (kcal/mole)
0.0
0.0
0.0
0.0
LJ \(\sigma\) of HH, MM, OH, OM, HM (\(\AA\))
1.0
1.0
1.0
1.0
\(r_0\) of OH bond (\(\AA\))
0.9572
0.9572
0.9572
0.9572
\(\theta_0\) of HOH angle
104.52\(^{\circ}\)
104.52\(^{\circ}\)
104.52\(^{\circ}\)
104.52\(^{\circ}\)
OM distance (\(\AA\))
0.15
0.1577
0.1546
0.1250
Note that the when using the TIP4P pair style, the neighbor list cutoff for Coulomb interactions is effectively extended by a distance 2 * (OM distance), to account for the offset distance of the fictitious charges on O atoms in water molecules. Thus it is typically best in an efficiency sense to use a LJ cutoff >= Coulomb cutoff + 2*(OM distance), to shrink the size of the neighbor list. This leads to slightly larger cost for the long-range calculation, so you can test the trade-off for your model. The OM distance and the LJ and Coulombic cutoffs are set in the pair_style lj/cut/tip4p/long command.
Below is the code for a LAMMPS input file using the implicit method and the TIP3P molecule file. Because the TIP4P charges are different from TIP3P they need to be reset (or the molecule file changed):
units real
atom_style full
region box block -5 5 -5 5 -5 5
create_box 2 box bond/types 1 angle/types 1 &
extra/bond/per/atom 2 extra/angle/per/atom 1 extra/special/per/atom 2
mass 1 15.9994
mass 2 1.008
pair_style lj/cut/tip4p/cut 1 2 1 1 0.15 8.0
pair_coeff 1 1 0.1550 3.1536
pair_coeff 2 2 0.0 1.0
bond_style zero
bond_coeff 1 0.9574
angle_style zero
angle_coeff 1 104.52
molecule water tip3p.mol # this uses the TIP3P geometry
create_atoms 0 random 33 34564 NULL mol water 25367 overlap 1.33
# must change charges for TIP4P
set type 1 charge -1.040
set type 2 charge 0.520
fix rigid all shake 0.001 10 10000 b 1 a 1
minimize 0.0 0.0 1000 10000
reset_timestep 0
timestep 1.0
velocity all create 300.0 5463576
fix integrate all nvt temp 300 300 100.0
thermo_style custom step temp press etotal pe
thermo 1000
run 20000
write_data tip4p-implicit.data nocoeff
Below is the code for a LAMMPS input file using the explicit method and a TIP4P molecule file. Because of using fix rigid/nvt/small no bonds need to be defined and thus no extra storage needs to be reserved for them, but we need to switch to atom style full or use fix property/atom mol so that fix rigid/nvt/small can identify rigid bodies by their molecule ID:
units real
atom_style charge
atom_modify map array
region box block -5 5 -5 5 -5 5
create_box 3 box
mass 1 15.9994
mass 2 1.008
mass 3 1.0e-100
pair_style lj/cut/coul/cut 8.0
pair_coeff 1 1 0.1550 3.1536
pair_coeff 2 2 0.0 1.0
pair_coeff 3 3 0.0 1.0
fix mol all property/atom mol
molecule water tip4p.mol
create_atoms 0 random 33 34564 NULL mol water 25367 overlap 1.33
timestep 0.5
fix integrate all rigid/nvt/small molecule temp 300.0 300.0 100.0
velocity all create 300.0 5463576
thermo_style custom step temp press etotal density pe ke
thermo 1000
run 20000
write_data tip4p-explicit.data nocoeff
# Water molecule. Explicit TIP4P geometry for use with fix rigid
4 atoms
Coords
1 0.00000 -0.06556 0.00000
2 0.75695 0.52032 0.00000
3 -0.75695 0.52032 0.00000
4 0.00000 0.08444 0.00000
Types
1 1 # O
2 2 # H
3 2 # H
4 3 # M
Charges
1 0.000
2 0.520
3 0.520
4 -1.040
Wikipedia also has a nice article on water models.
(Jorgensen) Jorgensen, Chandrasekhar, Madura, Impey, Klein, J Chem Phys, 79, 926 (1983).
- (Abascal1) Abascal, Sanz, Fernandez, Vega, J Chem Phys, 122, 234511 (2005)
- (Abascal2) Abascal, J Chem Phys, 123, 234505 (2005)