\(\renewcommand{\AA}{\text{Å}}\)

# 10.4.8. SPC and SPC/E water model

The SPC water model specifies a 3-site rigid water molecule with charges and Lennard-Jones parameters assigned to each of the three 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.

One suitable pair style with cutoff Coulomb would for instance be:

- pair_style lj/cut/coul/cut

These commands are examples for a long-range Coulomb model:

- pair_style lj/cut/coul/long

- pair_style lj/cut/coul/long/soft

- kspace_style pppm

- pair_style lj/long/coul/long

- kspace_style pppm/disp

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 (Berendsen2) 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. For simplicity and speed the example uses a cutoff Coulomb. Most production simulations require long-range Coulomb instead.

    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
    velocity all create 300.0 5463576
    fix integrate all nvt temp 300.0 300.0 100.0

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

(Berendsen2) Berendsen, Grigera, Straatsma, J Phys Chem, 91, 6269-6271 (1987).