# 8.4.4. 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
$$\theta$$ 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.

Wikipedia also has a nice article on water models.

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