TIP4P water model
=================

The four-point TIP4P rigid water model extends the traditional
three-point TIP3P model by adding an additional site, 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.

A TIP4P model is run with LAMMPS using either these commands
for a cutoff model:

* :doc:`pair_style tip4p/cut <pair_lj_cut_tip4p>`
* :doc:`pair_style lj/cut/tip4p/cut <pair_lj_cut_tip4p>`

or these commands for a long-range model:

* :doc:`pair_style tip4p/long <pair_coul>`
* :doc:`pair_style lj/cut/tip4p/long <pair_lj_cut_tip4p>`
* :doc:`pair_style lj/long/tip4p/long <pair_lj_long>`
* :doc:`pair_style tip4p/long/soft <pair_fep_soft>`
* :doc:`pair_style lj/cut/tip4p/long/soft <pair_fep_soft>`
* :doc:`kspace_style pppm/tip4p <kspace_style>`
* :doc:`kspace_style pppm/disp/tip4p <kspace_style>`

The bond lengths and bond angles should be held fixed using the
:doc:`fix shake <fix_shake>` or :doc:`fix rattle <fix_shake>` 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.

These are the additional parameters (in real units) to set for O and H
atoms and the water molecule to run a rigid TIP4P model with a cutoff
:ref:`(Jorgensen) <Jorgensen5>`.  Note that the OM distance is specified in
the :doc:`pair_style <pair_style>` command, not as part of the pair
coefficients.

| O mass = 15.9994
| H mass = 1.008
| O charge = -1.040
| H charge = 0.520
| :math:`r_0` of OH bond = 0.9572
| :math:`\theta` of HOH angle = 104.52\ :math:`^{\circ}`
| OM distance = 0.15
| LJ :math:`\epsilon` of O-O = 0.1550
| LJ :math:`\sigma` of O-O = 3.1536
| LJ :math:`\epsilon`, :math:`\sigma` of OH, HH = 0.0
| Coulomb cutoff = 8.5
|

For the TIP4/Ice model (J Chem Phys, 122, 234511 (2005);
https://doi.org/10.1063/1.1931662) these values can be used:

| O mass = 15.9994
| H mass =  1.008
| O charge = -1.1794
| H charge =  0.5897
| :math:`r_0` of OH bond = 0.9572
| :math:`\theta` of HOH angle = 104.52\ :math:`^{\circ}`
| OM distance = 0.1577
| LJ :math:`\epsilon` of O-O = 0.21084
| LJ :math:`\sigma` of O-O = 3.1668
| LJ :math:`\epsilon`, :math:`\sigma` of OH, HH = 0.0
| Coulomb cutoff = 8.5
|

For the TIP4P/2005 model (J Chem Phys, 123, 234505 (2005);
https://doi.org/10.1063/1.2121687), these values can be used:

| O mass = 15.9994
| H mass =  1.008
| O charge = -1.1128
| H charge = 0.5564
| :math:`r_0` of OH bond = 0.9572
| :math:`\theta` of HOH angle = 104.52\ :math:`^{\circ}`
| OM distance = 0.1546
| LJ :math:`\epsilon` of O-O = 0.1852
| LJ :math:`\sigma` of O-O = 3.1589
| LJ :math:`\epsilon`, :math:`\sigma` of OH, HH = 0.0
| Coulomb cutoff = 8.5
|

These are the parameters to use for TIP4P with a long-range Coulombic
solver (e.g. Ewald or PPPM in LAMMPS):

| O mass = 15.9994
| H mass = 1.008
| O charge = -1.0484
| H charge = 0.5242
| :math:`r_0` of OH bond = 0.9572
| :math:`\theta` of HOH angle = 104.52\ :math:`^{\circ}`
| OM distance = 0.1250
| LJ :math:`\epsilon` of O-O = 0.16275
| LJ :math:`\sigma` of O-O = 3.16435
| LJ :math:`\epsilon`, :math:`\sigma` of OH, HH = 0.0
|

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 :doc:`pair_style lj/cut/tip4p/long
<pair_lj_cut_tip4p>` command.

Wikipedia also has a nice article on `water models <https://en.wikipedia.org/wiki/Water_model>`_.

----------

.. _Jorgensen5:

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