\(\renewcommand{\AA}{\text{Å}}\)

# 10.4.5. TIP3P water model

The TIP3P water model as implemented in CHARMM (MacKerell) specifies a 3-site rigid water molecule with charges and Lennard-Jones parameters assigned to each of the three atoms.

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

And these pair styles are compatible with the CHARMM force field:

- pair_style lj/charmm/coul/charmm

- pair_style lj/charmm/coul/long

- pair_style lj/charmmfsw/coul/long

In LAMMPS the fix shake or fix rattle 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. In case of rigid bonds also bond style zero and angle style zero can be used.

The table below lists the force field parameters (in real units) to for the water molecule atoms to run a rigid or flexible TIP3P-CHARMM model with a cutoff, the original 1983 TIP3P model (Jorgensen), or a TIP3P model with parameters optimized for a long-range Coulomb solver (e.g. Ewald or PPPM in LAMMPS) (Price). The K values can be used if a flexible TIP3P model (without fix shake) is desired, for rigid bonds/angles they are ignored.

Parameter | TIP3P-CHARMM | TIP3P (original) | TIP3P (Ewald)
--- | --- | --- | ---
O mass (amu) | 15.9994 | 15.9994 | 15.9994
H mass (amu) | 1.008 | 1.008 | 1.008
O charge (\(e\)) | -0.834 | -0.834 | -0.834
H charge (\(e\)) | 0.417 | 0.417 | 0.417
LJ \(\epsilon\) of OO (kcal/mole) | 0.1521 | 0.1521 | 0.1020
LJ \(\sigma\) of OO (\(\AA\)) | 3.1507 | 3.1507 | 3.188
LJ \(\epsilon\) of HH (kcal/mole) | 0.0460 | 0.0 | 0.0
LJ \(\sigma\) of HH (\(\AA\)) | 0.4 | 1.0 | 1.0
LJ \(\epsilon\) of OH (kcal/mole) | 0.0836 | 0.0 | 0.0
LJ \(\sigma\) of OH (\(\AA\)) | 1.7753 | 1.0 | 1.0
K of OH bond (kcal/mole/\(\AA^2\)) | 450 | 450 | 450
\(r_0\) of OH bond (\(\AA\)) | 0.9572 | 0.9572 | 0.9572
K of HOH angle (kcal/mole) | 55.0 | 55.0 | 55.0
\(\theta_0\) of HOH angle | 104.52\(^{\circ}\) | 104.52\(^{\circ}\) | 104.52\(^{\circ}\)

Below is the code for a LAMMPS input file and a molecule file (`tip3p.mol`) of TIP3P water for use with the molecule command demonstrating how to set up a small bulk water system for TIP3P 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 8.0
    pair_coeff 1 1 0.1521 3.1507
    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
    create_atoms 0 random 33 34564 NULL mol water 25367 overlap 1.33

    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 tip3p.data nocoeff

    # Water molecule. TIP3P geometry

    3 atoms
    2 bonds
    1 angles

    Coords

    1    0.00000  -0.06556   0.00000
    2    0.75695   0.52032   0.00000
    3   -0.75695   0.52032   0.00000

    Types

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

    Charges

    1       -0.834
    2        0.417
    3        0.417

    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.

(MacKerell) MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field, Fischer, Gao, Guo, Ha, et al, J Phys Chem, 102, 3586 (1998).

(Jorgensen) Jorgensen, Chandrasekhar, Madura, Impey, Klein, J Chem Phys, 79, 926 (1983).

(Price) Price and Brooks, J Chem Phys, 121, 10096 (2004).