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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
<section id="tip4p-water-model">
<h1><span class="section-number">8.4.4. </span>TIP4P water model<a class="headerlink" href="#tip4p-water-model" title="Link to this heading"></a></h1>
<p>The four-point TIP4P rigid water model extends the traditional
<a class="reference internal" href="Howto_tip3p.html"><span class="doc">three-point TIP3P</span></a> model by adding an additional
site M, 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
<a class="reference internal" href="bond_harmonic.html"><span class="doc">harmonic</span></a> and an angle style of <a class="reference internal" href="angle_harmonic.html"><span class="doc">harmonic</span></a> or <a class="reference internal" href="angle_charmm.html"><span class="doc">charmm</span></a> should also be used.
In case of rigid bonds also bond style <a class="reference internal" href="bond_zero.html"><span class="doc">zero</span></a> and angle
style <a class="reference internal" href="angle_zero.html"><span class="doc">zero</span></a> can be used.</p>
<p>There are two ways to implement TIP4P water in LAMMPS:</p>
<ol class="arabic">
<li><p>Use a specially written pair style that uses the <a class="reference internal" href="Howto_tip3p.html#tip3p-molecule"><span class="std std-ref">TIP3P geometry</span></a> without the point M. The point M location is then
implicitly derived from the other atoms or each water molecule and
used during the force computation. The forces on M are then
projected on the oxygen and the two hydrogen atoms. This is
computationally very efficient, but the charge distribution in space
is only correct within the tip4p labeled styles. So all other
computations using charges will “see” the negative charge incorrectly
on the oxygen atom.</p>
<p>This can be done with the following pair styles for Coulomb with a cutoff:</p>
<ul class="simple">
<li><p><a class="reference internal" href="pair_coul.html"><span class="doc">pair_style tip4p/cut</span></a></p></li>
<li><p><a class="reference internal" href="pair_lj_cut_tip4p.html"><span class="doc">pair_style lj/cut/tip4p/cut</span></a></p></li>
</ul>
<p>or these commands for a long-range Coulomb treatment:</p>
<ul class="simple">
<li><p><a class="reference internal" href="pair_coul.html"><span class="doc">pair_style tip4p/long</span></a></p></li>
<li><p><a class="reference internal" href="pair_lj_cut_tip4p.html"><span class="doc">pair_style lj/cut/tip4p/long</span></a></p></li>
<li><p><a class="reference internal" href="pair_lj_long.html"><span class="doc">pair_style lj/long/tip4p/long</span></a></p></li>
<li><p><a class="reference internal" href="pair_fep_soft.html"><span class="doc">pair_style tip4p/long/soft</span></a></p></li>
<li><p><a class="reference internal" href="pair_fep_soft.html"><span class="doc">pair_style lj/cut/tip4p/long/soft</span></a></p></li>
<li><p><a class="reference internal" href="kspace_style.html"><span class="doc">kspace_style pppm/tip4p</span></a></p></li>
<li><p><a class="reference internal" href="kspace_style.html"><span class="doc">kspace_style pppm/disp/tip4p</span></a></p></li>
</ul>
<p>The bond lengths and bond angles should be held fixed using the
<a class="reference internal" href="fix_shake.html"><span class="doc">fix shake</span></a> or <a class="reference internal" href="fix_shake.html"><span class="doc">fix rattle</span></a> 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.</p>
</li>
<li><p>Use an <a class="reference internal" href="#tip4p-molecule"><span class="std std-ref">explicit 4 point TIP4P geometry</span></a> where
the oxygen atom carries no charge and the M point no Lennard-Jones
interactions. Since <a class="reference internal" href="fix_shake.html"><span class="doc">fix shake</span></a> or <a class="reference internal" href="fix_shake.html"><span class="doc">fix rattle</span></a> may not be applied to this kind of geometry, <a class="reference internal" href="fix_rigid.html"><span class="doc">fix
rigid or fix rigid/small</span></a> or its thermostatted variants
are required to maintain a rigid geometry. This avoids some of the
issues with respect to analysis and non-tip4p styles, but it is a
more costly force computation (more atoms in the same volume and thus
more neighbors in the neighbor lists) and requires a much shorter
timestep for stable integration of the rigid body motion. Since no
bonds or angles are required, they do not need to be defined and atom
style charge would be sufficient for a bulk TIP4P water system. In
order to avoid that LAMMPS produces an error due to the massless M
site a tiny non-zero mass needs to be assigned.</p></li>
</ol>
<p>The table below lists the force field parameters (in real <a class="reference internal" href="units.html"><span class="doc">units</span></a>) to for a selection of popular variants of the TIP4P model.
There is the rigid TIP4P model with a cutoff <a class="reference internal" href="#jorgensen5"><span class="std std-ref">(Jorgensen)</span></a>, the TIP4/Ice model <a class="reference internal" href="#abascal1"><span class="std std-ref">(Abascal1)</span></a>, the
TIP4P/2005 model <a class="reference internal" href="#abascal2"><span class="std std-ref">(Abascal2)</span></a> and a version of TIP4P
parameters adjusted for use with a long-range Coulombic solver
(e.g. Ewald or PPPM in LAMMPS). Note that for implicit TIP4P models the
OM distance is specified in the <a class="reference internal" href="pair_style.html"><span class="doc">pair_style</span></a> command,
not as part of the pair coefficients.</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 36.0%" />
<col style="width: 19.0%" />
<col style="width: 13.0%" />
<col style="width: 15.0%" />
<col style="width: 17.0%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Parameter</p></th>
<th class="head"><p>TIP4P (original)</p></th>
<th class="head"><p>TIP4P/Ice</p></th>
<th class="head"><p>TIP4P/2005</p></th>
<th class="head"><p>TIP4P (Ewald)</p></th>
</tr>
</thead>
<tbody>
<tr class="row-even"><td><p>O mass (amu)</p></td>
<td><p>15.9994</p></td>
<td><p>15.9994</p></td>
<td><p>15.9994</p></td>
<td><p>15.9994</p></td>
</tr>
<tr class="row-odd"><td><p>H mass (amu)</p></td>
<td><p>1.008</p></td>
<td><p>1.008</p></td>
<td><p>1.008</p></td>
<td><p>1.008</p></td>
</tr>
<tr class="row-even"><td><p>O or M charge (<span class="math notranslate nohighlight">\(e\)</span>)</p></td>
<td><p>-1.040</p></td>
<td><p>-1.1794</p></td>
<td><p>-1.1128</p></td>
<td><p>-1.04844</p></td>
</tr>
<tr class="row-odd"><td><p>H charge (<span class="math notranslate nohighlight">\(e\)</span>)</p></td>
<td><p>0.520</p></td>
<td><p>0.5897</p></td>
<td><p>0.5564</p></td>
<td><p>0.52422</p></td>
</tr>
<tr class="row-even"><td><p>LJ <span class="math notranslate nohighlight">\(\epsilon\)</span> of OO (kcal/mole)</p></td>
<td><p>0.1550</p></td>
<td><p>0.21084</p></td>
<td><p>0.1852</p></td>
<td><p>0.16275</p></td>
</tr>
<tr class="row-odd"><td><p>LJ <span class="math notranslate nohighlight">\(\sigma\)</span> of OO (<span class="math notranslate nohighlight">\(\AA\)</span>)</p></td>
<td><p>3.1536</p></td>
<td><p>3.1668</p></td>
<td><p>3.1589</p></td>
<td><p>3.16435</p></td>
</tr>
<tr class="row-even"><td><p>LJ <span class="math notranslate nohighlight">\(\epsilon\)</span> of HH, MM, OH, OM, HM (kcal/mole)</p></td>
<td><p>0.0</p></td>
<td><p>0.0</p></td>
<td><p>0.0</p></td>
<td><p>0.0</p></td>
</tr>
<tr class="row-odd"><td><p>LJ <span class="math notranslate nohighlight">\(\sigma\)</span> of HH, MM, OH, OM, HM (<span class="math notranslate nohighlight">\(\AA\)</span>)</p></td>
<td><p>1.0</p></td>
<td><p>1.0</p></td>
<td><p>1.0</p></td>
<td><p>1.0</p></td>
</tr>
<tr class="row-even"><td><p><span class="math notranslate nohighlight">\(r_0\)</span> of OH bond (<span class="math notranslate nohighlight">\(\AA\)</span>)</p></td>
<td><p>0.9572</p></td>
<td><p>0.9572</p></td>
<td><p>0.9572</p></td>
<td><p>0.9572</p></td>
</tr>
<tr class="row-odd"><td><p><span class="math notranslate nohighlight">\(\theta_0\)</span> of HOH angle</p></td>
<td><p>104.52<span class="math notranslate nohighlight">\(^{\circ}\)</span></p></td>
<td><p>104.52<span class="math notranslate nohighlight">\(^{\circ}\)</span></p></td>
<td><p>104.52<span class="math notranslate nohighlight">\(^{\circ}\)</span></p></td>
<td><p>104.52<span class="math notranslate nohighlight">\(^{\circ}\)</span></p></td>
</tr>
<tr class="row-even"><td><p>OM distance (<span class="math notranslate nohighlight">\(\AA\)</span>)</p></td>
<td><p>0.15</p></td>
<td><p>0.1577</p></td>
<td><p>0.1546</p></td>
<td><p>0.1250</p></td>
</tr>
</tbody>
</table>
<p>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 &gt;= 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 <a class="reference internal" href="pair_lj_cut_tip4p.html"><span class="doc">pair_style lj/cut/tip4p/long</span></a> command.</p>
<p>Below is the code for a LAMMPS input file using the implicit method and
the <a class="reference internal" href="Howto_tip3p.html#tip3p-molecule"><span class="std std-ref">TIP3P molecule file</span></a>. Because the TIP4P
charges are different from TIP3P they need to be reset (or the molecule
file changed):</p>
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">units</span><span class="w"> </span><span class="n">real</span>
<span class="k">atom_style</span><span class="w"> </span><span class="n">full</span>
<span class="k">region </span><span class="nv nv-Identifier">box</span><span class="w"> </span><span class="n">block</span><span class="w"> </span><span class="o">-</span><span class="m">5</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">-</span><span class="m">5</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">-</span><span class="m">5</span><span class="w"> </span><span class="m">5</span>
<span class="k">create_box </span><span class="nv nv-Identifier">2</span><span class="w"> </span><span class="nv nv-Identifier">box</span><span class="w"> </span><span class="n">bond</span><span class="o">/</span><span class="n">types</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">angle</span><span class="o">/</span><span class="n">types</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">&amp;</span>
<span class="w"> </span><span class="n">extra</span><span class="o">/</span><span class="n">bond</span><span class="o">/</span><span class="n">per</span><span class="o">/</span><span class="n">atom</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="n">extra</span><span class="o">/</span><span class="n">angle</span><span class="o">/</span><span class="n">per</span><span class="o">/</span><span class="n">atom</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">extra</span><span class="o">/</span><span class="n">special</span><span class="o">/</span><span class="n">per</span><span class="o">/</span><span class="n">atom</span><span class="w"> </span><span class="m">2</span>
<span class="k">mass</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">15.9994</span>
<span class="k">mass</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">1.008</span>
<span class="k">pair_style</span><span class="w"> </span><span class="n">lj</span><span class="o">/</span><span class="n">cut</span><span class="o">/</span><span class="n">tip4p</span><span class="o">/</span><span class="n">cut</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">0.15</span><span class="w"> </span><span class="m">8.0</span>
<span class="k">pair_coeff</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">0.1550</span><span class="w"> </span><span class="m">3.1536</span>
<span class="k">pair_coeff</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">0.0</span><span class="w"> </span><span class="m">1.0</span>
<span class="k">bond_style</span><span class="w"> </span><span class="n">zero</span>
<span class="k">bond_coeff</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">0.9574</span>
<span class="k">angle_style</span><span class="w"> </span><span class="n">zero</span>
<span class="k">angle_coeff</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">104.52</span>
<span class="k">molecule</span><span class="w"> </span><span class="n">water</span><span class="w"> </span><span class="n">tip3p.mol</span><span class="w"> </span><span class="c"># this uses the TIP3P geometry</span>
<span class="k">create_atoms</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="n">random</span><span class="w"> </span><span class="m">33</span><span class="w"> </span><span class="m">34564</span><span class="w"> </span><span class="n">NULL</span><span class="w"> </span><span class="n">mol</span><span class="w"> </span><span class="n">water</span><span class="w"> </span><span class="m">25367</span><span class="w"> </span><span class="n">overlap</span><span class="w"> </span><span class="m">1.33</span>
<span class="c"># must change charges for TIP4P</span>
<span class="k">set</span><span class="w"> </span><span class="n">type</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">charge</span><span class="w"> </span><span class="o">-</span><span class="m">1.040</span>
<span class="k">set</span><span class="w"> </span><span class="n">type</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="n">charge</span><span class="w"> </span><span class="m">0.520</span>
<span class="k">fix </span><span class="nv nv-Identifier">rigid</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">shake</span><span class="w"> </span><span class="m">0.001</span><span class="w"> </span><span class="m">10</span><span class="w"> </span><span class="m">10000</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="m">1</span>
<span class="k">minimize</span><span class="w"> </span><span class="m">0.0</span><span class="w"> </span><span class="m">0.0</span><span class="w"> </span><span class="m">1000</span><span class="w"> </span><span class="m">10000</span>
<span class="k">reset_timestep</span><span class="w"> </span><span class="m">0</span>
<span class="k">timestep</span><span class="w"> </span><span class="m">1.0</span>
<span class="k">velocity </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">create</span><span class="w"> </span><span class="m">300.0</span><span class="w"> </span><span class="m">5463576</span>
<span class="k">fix </span><span class="nv nv-Identifier">integrate</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">nvt</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="m">300</span><span class="w"> </span><span class="m">300</span><span class="w"> </span><span class="m">100.0</span>
<span class="k">thermo_style</span><span class="w"> </span><span class="n">custom</span><span class="w"> </span><span class="n">step</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="n">press</span><span class="w"> </span><span class="n">etotal</span><span class="w"> </span><span class="n">pe</span>
<span class="k">thermo</span><span class="w"> </span><span class="m">1000</span>
<span class="k">run</span><span class="w"> </span><span class="m">20000</span>
<span class="k">write_data </span><span class="nv nv-Identifier">tip4p-implicit.data</span><span class="w"> </span><span class="n">nocoeff</span>
</pre></div>
</div>
<p>Below is the code for a LAMMPS input file using the explicit method and
a TIP4P molecule file. Because of using <a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid/small</span></a> no bonds need to be defined and thus no extra storage needs
to be reserved for them, but we need to either switch to atom style full
or use <a class="reference internal" href="fix_property_atom.html"><span class="doc">fix property/atom mol</span></a> so that fix
rigid/small can identify rigid bodies by their molecule ID. Also a
<a class="reference internal" href="neigh_modify.html"><span class="doc">neigh_modify exclude</span></a> command is added to exclude
computing intramolecular non-bonded interactions, since those are
removed by the rigid fix anyway:</p>
<div class="highlight-LAMMPS notranslate"><div class="highlight"><pre><span></span><span class="k">units</span><span class="w"> </span><span class="n">real</span>
<span class="k">atom_style</span><span class="w"> </span><span class="n">charge</span>
<span class="k">atom_modify</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="n">array</span>
<span class="k">region </span><span class="nv nv-Identifier">box</span><span class="w"> </span><span class="n">block</span><span class="w"> </span><span class="o">-</span><span class="m">5</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">-</span><span class="m">5</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">-</span><span class="m">5</span><span class="w"> </span><span class="m">5</span>
<span class="k">create_box </span><span class="nv nv-Identifier">3</span><span class="w"> </span><span class="nv nv-Identifier">box</span>
<span class="k">mass</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">15.9994</span>
<span class="k">mass</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">1.008</span>
<span class="k">mass</span><span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="m">1.0e-100</span>
<span class="k">pair_style</span><span class="w"> </span><span class="n">lj</span><span class="o">/</span><span class="n">cut</span><span class="o">/</span><span class="n">coul</span><span class="o">/</span><span class="n">cut</span><span class="w"> </span><span class="m">8.0</span>
<span class="k">pair_coeff</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="m">0.1550</span><span class="w"> </span><span class="m">3.1536</span>
<span class="k">pair_coeff</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="m">0.0</span><span class="w"> </span><span class="m">1.0</span>
<span class="k">pair_coeff</span><span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="m">3</span><span class="w"> </span><span class="m">0.0</span><span class="w"> </span><span class="m">1.0</span>
<span class="k">fix </span><span class="nv nv-Identifier">mol</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">property</span><span class="o">/</span><span class="n">atom</span><span class="w"> </span><span class="n">mol</span><span class="w"> </span><span class="n">ghost</span><span class="w"> </span><span class="n">yes</span>
<span class="k">molecule</span><span class="w"> </span><span class="n">water</span><span class="w"> </span><span class="n">tip4p.mol</span>
<span class="k">create_atoms</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="n">random</span><span class="w"> </span><span class="m">33</span><span class="w"> </span><span class="m">34564</span><span class="w"> </span><span class="n">NULL</span><span class="w"> </span><span class="n">mol</span><span class="w"> </span><span class="n">water</span><span class="w"> </span><span class="m">25367</span><span class="w"> </span><span class="n">overlap</span><span class="w"> </span><span class="m">1.33</span>
<span class="k">neigh_modify</span><span class="w"> </span><span class="n">exclude</span><span class="w"> </span><span class="n">molecule</span><span class="o">/</span><span class="n">intra</span><span class="w"> </span><span class="n">all</span>
<span class="k">timestep</span><span class="w"> </span><span class="m">0.5</span>
<span class="k">fix </span><span class="nv nv-Identifier">integrate</span><span class="w"> </span><span class="nv nv-Identifier">all</span><span class="w"> </span><span class="n">rigid</span><span class="o">/</span><span class="n">small</span><span class="w"> </span><span class="n">molecule</span><span class="w"> </span><span class="n">langevin</span><span class="w"> </span><span class="m">300.0</span><span class="w"> </span><span class="m">300.0</span><span class="w"> </span><span class="m">100.0</span><span class="w"> </span><span class="m">2345634</span>
<span class="k">thermo_style</span><span class="w"> </span><span class="n">custom</span><span class="w"> </span><span class="n">step</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="n">press</span><span class="w"> </span><span class="n">etotal</span><span class="w"> </span><span class="n">density</span><span class="w"> </span><span class="n">pe</span><span class="w"> </span><span class="n">ke</span>
<span class="k">thermo</span><span class="w"> </span><span class="m">2000</span>
<span class="k">run</span><span class="w"> </span><span class="m">40000</span>
<span class="k">write_data </span><span class="nv nv-Identifier">tip4p-explicit.data</span><span class="w"> </span><span class="n">nocoeff</span>
</pre></div>
</div>
<div class="highlight-none notranslate" id="tip4p-molecule"><div class="highlight"><pre><span></span># Water molecule. Explicit TIP4P geometry for use with fix rigid
4 atoms
Coords
1 0.00000 -0.06556 0.00000
2 0.75695 0.52032 0.00000
3 -0.75695 0.52032 0.00000
4 0.00000 0.08444 0.00000
Types
1 1 # O
2 2 # H
3 2 # H
4 3 # M
Charges
1 0.000
2 0.520
3 0.520
4 -1.040
</pre></div>
</div>
<p>Wikipedia also has a nice article on <a class="reference external" href="https://en.wikipedia.org/wiki/Water_model">water models</a>.</p>
<hr class="docutils" />
<p id="jorgensen5"><strong>(Jorgensen)</strong> Jorgensen, Chandrasekhar, Madura, Impey, Klein, J Chem
Phys, 79, 926 (1983).</p>
<dl class="simple" id="abascal1">
<dt><strong>(Abascal1)</strong> Abascal, Sanz, Fernandez, Vega, J Chem Phys, 122, 234511 (2005)</dt><dd><p><a class="reference external" href="https://doi.org/10.1063/1.1931662">https://doi.org/10.1063/1.1931662</a></p>
</dd>
</dl>
<dl class="simple" id="abascal2">
<dt><strong>(Abascal2)</strong> Abascal, J Chem Phys, 123, 234505 (2005)</dt><dd><p><a class="reference external" href="https://doi.org/10.1063/1.2121687">https://doi.org/10.1063/1.2121687</a></p>
</dd>
</dl>
</section>
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