$$\renewcommand{\AA}{\text{Å}}$$

# 8.4.6. SPC water model¶

The SPC water model specifies a 3-site rigid water molecule with charges and Lennard-Jones parameters assigned to each of the 3 atoms. In LAMMPS the fix shake command can be used to hold the two O-H bonds and the H-O-H angle rigid. A bond style of harmonic and an angle style of harmonic or charmm should also be used.

These are the additional parameters (in real units) to set for O and H atoms and the water molecule to run a rigid SPC model.

O mass = 15.9994
H mass = 1.008
O charge = -0.820
H charge = 0.410
LJ $$\epsilon$$ of OO = 0.1553
LJ $$\sigma$$ of OO = 3.166
LJ $$\epsilon$$, $$\sigma$$ of OH, HH = 0.0
$$r_0$$ of OH bond = 1.0
$$\theta_0$$ of HOH angle = 109.47$$^{\circ}$$

Note that as originally proposed, the SPC model was run with a 9 Angstrom cutoff for both LJ and Coulomb terms. It can also be used with long-range electrostatic solvers (e.g. Ewald or PPPM in LAMMPS) without changing any of the parameters above, although it becomes a different model in that mode of usage.

The SPC/E (extended) water model is the same, except the partial charge assignments change:

O charge = -0.8476
H charge = 0.4238

See the (Berendsen) reference for more details on both the SPC and SPC/E models.

Below is the code for a LAMMPS input file and a molecule file (spce.mol) of SPC/E water for use with the molecule command demonstrating how to set up a small bulk water system for SPC/E with rigid bonds.

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/coul/cut 10.0
pair_coeff 1 1 0.1553 3.166
pair_coeff 1 2 0.0    1.0
pair_coeff 2 2 0.0    1.0

bond_style zero
bond_coeff 1 1.0

angle_style zero
angle_coeff 1 109.47

molecule water spce.mol
create_atoms 0 random 33 34564 NULL mol water 25367 overlap 1.33

timestep 1.0
fix rigid     all shake 0.0001 10 10000 b 1 a 1
minimize 0.0 0.0 1000 10000
run 0 post no
reset_timestep 0
velocity all create 300.0 5463576
fix integrate all nvt temp 300.0 300.0 1.0

thermo_style custom step temp press etotal density pe ke
thermo 1000
run 20000 upto
write_data tip4p.data nocoeff

# Water molecule. SPC/E geometry

3 atoms
2 bonds
1 angles

Coords

1    0.00000  -0.06461   0.00000
2    0.81649   0.51275   0.00000
3   -0.81649   0.51275   0.00000

Types

1        1   # O
2        2   # H
3        2   # H

Charges

1       -0.8476
2        0.4238
3        0.4238

Bonds

1   1      1      2
2   1      1      3

Angles

1   1      2      1      3

Shake Flags

1 1
2 1
3 1

Shake Atoms

1 1 2 3
2 1 2 3
3 1 2 3

Shake Bond Types

1 1 1 1
2 1 1 1
3 1 1 1

Special Bond Counts

1 2 0 0
2 1 1 0
3 1 1 0

Special Bonds

1 2 3
2 1 3
3 1 2


Wikipedia also has a nice article on water models.

(Berendsen) Berendsen, Grigera, Straatsma, J Phys Chem, 91, 6269-6271 (1987).