.. default-domain:: py

.. _running-simulations:

Running Simulations
###################

.. _a-first-example:

A First Example
***************

Let’s begin with our first example of an OpenMM script. It loads a PDB file
called :file:`input.pdb` that defines a biomolecular system, parameterizes it using the Amber14 force field and TIP3P-FB water
model, energy minimizes it, simulates it for 10,000 steps with a Langevin
integrator, and saves a snapshot frame to a PDB file called :file:`output.pdb` every 1000 time
steps.

.. samepage::
    ::

        from openmm.app import *
        from openmm import *
        from openmm.unit import *
        from sys import stdout

        pdb = PDBFile('input.pdb')
        forcefield = ForceField('amber14-all.xml', 'amber14/tip3pfb.xml')
        system = forcefield.createSystem(pdb.topology, nonbondedMethod=PME,
                nonbondedCutoff=1*nanometer, constraints=HBonds)
        integrator = LangevinMiddleIntegrator(300*kelvin, 1/picosecond, 0.004*picoseconds)
        simulation = Simulation(pdb.topology, system, integrator)
        simulation.context.setPositions(pdb.positions)
        simulation.minimizeEnergy()
        simulation.reporters.append(PDBReporter('output.pdb', 1000))
        simulation.reporters.append(StateDataReporter(stdout, 1000, step=True,
                potentialEnergy=True, temperature=True))
        simulation.step(10000)

    .. caption::

        :autonumber:`Example,PDB example`

You can find this script in the :file:`examples` folder of your OpenMM installation.
It is called :file:`simulatePdb.py`.  To execute it from a command line, go to your
terminal/console/command prompt window (see Section :numref:`installing-openmm`
on setting up the window to use OpenMM).  Navigate to the :file:`examples` folder by typing
::

    cd <examples_directory>

where the typical directory is :file:`/usr/local/openmm/examples` on Linux
and Mac machines and  :file:`C:\\Program Files\\OpenMM\\examples` on Windows
machines.

Then type
::

    python simulatePdb.py

You can name your own scripts whatever you want.  Let’s go through the script line
by line and see how it works.
::

    from openmm.app import *
    from openmm import *
    from openmm.unit import *
    from sys import stdout

These lines are just telling the Python interpreter about some libraries we will
be using.  Don’t worry about exactly what they mean.  Just include them at the
start of your scripts.
::

    pdb = PDBFile('input.pdb')

This line loads the PDB file from disk.  (The :file:`input.pdb` file in the :file:`examples`
directory contains the villin headpiece in explicit solvent.)  More precisely,
it creates a :class:`PDBFile` object, passes the file name :file:`input.pdb` to it as an
argument, and assigns the object to a variable called :code:`pdb`\ .  The
:class:`PDBFile` object contains the information that was read from the file: the
molecular topology and atom positions.  Your file need not be called
:file:`input.pdb`.  Feel free to change this line to specify any file you want,
though it must contain all of the atoms needed by the force field.
(More information on how to add missing atoms and residues using OpenMM tools can be found in Chapter :numref:`model-building-and-editing`.)
Make sure you include the single quotes around the file name.  OpenMM also can load
files in the newer PDBx/mmCIF format: just change :class:`PDBFile` to :class:`PDBxFile`.
::

    forcefield = ForceField('amber14-all.xml', 'amber14/tip3pfb.xml')

This line specifies the force field to use for the simulation.  Force fields are
defined by XML files.  OpenMM includes XML files defining lots of standard force fields (see Section :numref:`force-fields`).
If you find you need to extend the repertoire of force fields available,
you can find more information on how to create these XML files in Chapter :numref:`creating-force-fields`.
In this case we load two of those files: :file:`amber14-all.xml`, which contains the
Amber14 force field, and :file:`amber14/tip3pfb.xml`, which contains the TIP3P-FB water model.  The
:class:`ForceField` object is assigned to a variable called :code:`forcefield`\ .
::

    system = forcefield.createSystem(pdb.topology, nonbondedMethod=PME,
            nonbondedCutoff=1*nanometer, constraints=HBonds)

This line combines the force field with the molecular topology loaded from the
PDB file to create a complete mathematical description of the system we want to
simulate.  (More precisely, we invoke the :class:`ForceField` object’s :meth:`.createSystem`
function.  It creates a :class:`System` object, which we assign to the variable
:code:`system`\ .)  It specifies some additional options about how to do that:
use particle mesh Ewald for the long range electrostatic interactions
(:code:`nonbondedMethod=PME`\ ), use a 1 nm cutoff for the direct space
interactions (\ :code:`nonbondedCutoff=1*nanometer`\ ), and constrain the length
of all bonds that involve a hydrogen atom (\ :code:`constraints=HBonds`\ ).
Note the way we specified the cutoff distance 1 nm using :code:`1*nanometer`:
This is an example of the powerful units tracking and automatic conversion facility
built into the OpenMM Python API that makes specifying unit-bearing quantities
convenient and less error-prone.  We could have equivalently specified
:code:`10*angstrom` instead of :code:`1*nanometer` and achieved the same result.
The units system will be described in more detail later, in Section :numref:`units-and-dimensional-analysis`.
::

    integrator = LangevinMiddleIntegrator(300*kelvin, 1/picosecond, 0.004*picoseconds)

This line creates the integrator to use for advancing the equations of motion.
It specifies a :class:`LangevinMiddleIntegrator`, which performs Langevin dynamics,
and assigns it to a variable called :code:`integrator`\ .  It also specifies
the values of three parameters that are specific to Langevin dynamics: the
simulation temperature (300 K), the friction coefficient (1 ps\ :sup:`-1`\ ), and
the step size (0.004 ps).  Lots of other integration methods are also available.
For example, if you wanted to simulate the system at constant energy rather than
constant temperature you would use a :code:`VerletIntegrator`\ .  The available
integration methods are listed in Section :numref:`integrators`.
::

    simulation = Simulation(pdb.topology, system, integrator)

This line combines the molecular topology, system, and integrator to begin a new
simulation.  It creates a :class:`Simulation` object and assigns it to a variable called
\ :code:`simulation`\ .  A :class:`Simulation` object manages all the processes
involved in running a simulation, such as advancing time and writing output.
::

    simulation.context.setPositions(pdb.positions)

This line specifies the initial atom positions for the simulation: in this case,
the positions that were loaded from the PDB file.
::

    simulation.minimizeEnergy()

This line tells OpenMM to perform a local energy minimization.  It is usually a
good idea to do this at the start of a simulation, since the coordinates in the
PDB file might produce very large forces.
::

    simulation.reporters.append(PDBReporter('output.pdb', 1000))

This line creates a “reporter” to generate output during the simulation, and
adds it to the :class:`Simulation` object’s list of reporters.  A :class:`PDBReporter` writes
structures to a PDB file.  We specify that the output file should be called
:file:`output.pdb`, and that a structure should be written every 1000 time steps.
::

    simulation.reporters.append(StateDataReporter(stdout, 1000, step=True,
            potentialEnergy=True, temperature=True))

It can be useful to get regular status reports as a simulation runs so you can
monitor its progress.  This line adds another reporter to print out some basic
information every 1000 time steps: the current step index, the potential energy
of the system, and the temperature.  We specify :code:`stdout` (not in
quotes) as the output file, which means to write the results to the console.  We
also could have given a file name (in quotes), just as we did for the
:class:`PDBReporter`, to write the information to a file.
::

    simulation.step(10000)

Finally, we run the simulation, integrating the equations of motion for 10,000
time steps.  Once it is finished, you can load the PDB file into any program you
want for analysis and visualization (VMD_, PyMol_, AmberTools_, etc.).

.. _VMD: http://www.ks.uiuc.edu/Research/vmd/
.. _PyMol: http://www.pymol.org
.. _AmberTools: http://ambermd.org

.. _using_amber_files:

Using AMBER Files
*****************

OpenMM can build a system in several different ways.  One option, as shown
above, is to start with a PDB file and then select a force field with which to
model it.  Alternatively, you can use AmberTools_ to model your system.  In that
case, you provide a :class:`prmtop` file and an :class:`inpcrd` file.  OpenMM loads the files and
creates a :class:`System` from them.  This is illustrated in the following script.  It can be
found in OpenMM’s :file:`examples` folder with the name :file:`simulateAmber.py`.

.. samepage::
    ::

        from openmm.app import *
        from openmm import *
        from openmm.unit import *
        from sys import stdout

        prmtop = AmberPrmtopFile('input.prmtop')
        inpcrd = AmberInpcrdFile('input.inpcrd')
        system = prmtop.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
                constraints=HBonds)
        integrator = LangevinMiddleIntegrator(300*kelvin, 1/picosecond, 0.004*picoseconds)
        simulation = Simulation(prmtop.topology, system, integrator)
        simulation.context.setPositions(inpcrd.positions)
        if inpcrd.boxVectors is not None:
            simulation.context.setPeriodicBoxVectors(*inpcrd.boxVectors)
        simulation.minimizeEnergy()
        simulation.reporters.append(PDBReporter('output.pdb', 1000))
        simulation.reporters.append(StateDataReporter(stdout, 1000, step=True,
                potentialEnergy=True, temperature=True))
        simulation.step(10000)

    .. caption::

        :autonumber:`Example,AMBER example`

This script is very similar to the previous one.  There are just a few
significant differences:
::

    prmtop = AmberPrmtopFile('input.prmtop')
    inpcrd = AmberInpcrdFile('input.inpcrd')

In these lines, we load the prmtop file and inpcrd file.  More precisely, we
create :class:`AmberPrmtopFile` and :class:`AmberInpcrdFile` objects and assign them to the
variables :code:`prmtop` and :code:`inpcrd`\ , respectively.  As before,
you can change these lines to specify any files you want.  Be sure to include
the single quotes around the file names.

.. note::

    The :class:`AmberPrmtopFile` reader provided by OpenMM only supports "new-style"
    :file:`prmtop` files introduced in AMBER 7. The AMBER distribution still contains a number of
    example files that are in the "old-style" :file:`prmtop` format. These "old-style" files will
    not run in OpenMM.

Next, the :class:`System` object is created in a different way:
::

    system = prmtop.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
            constraints=HBonds)

In the previous section, we loaded the topology
from a PDB file and then had the force field create a system based on it.  In
this case, we don’t need a force field; the :file:`prmtop` file already contains the
force field parameters, so it can create the system
directly.
::

    simulation = Simulation(prmtop.topology, system, integrator)
    simulation.context.setPositions(inpcrd.positions)

Notice that we now get the topology from the :file:`prmtop` file and the atom positions
from the :file:`inpcrd` file.  In the previous section, both of these came from a PDB
file, but AMBER puts the topology and positions in separate files.  We also add the
following lines:
::

    if inpcrd.boxVectors is not None:
        simulation.context.setPeriodicBoxVectors(*inpcrd.boxVectors)

For periodic systems, the :file:`prmtop` file specifies the periodic box vectors, just
as a PDB file does.  When we call :meth:`createSystem`, it sets those as the default
periodic box vectors, to be used automatically for all simulations.  However, the
:file:`inpcrd` may *also* specify periodic box vectors,
and if so we want to use those ones instead.  For example, if the system has been
equilibrated with a barostat, the box vectors may have changed during equilibration.
We therefore check to see if the :file:`inpcrd` file contained box vectors.  If so,
we call :meth:`setPeriodicBoxVectors` to tell it to use those ones, overriding the
default ones provided by the :class:`System`.

.. _using_gromacs_files:

Using Gromacs Files
*******************

A third option for creating your system is to use the Gromacs setup tools.  They
produce a :file:`gro` file containing the coordinates and a :file:`top` file containing the
topology.  OpenMM can load these exactly as it did the AMBER files.  This is
shown in the following script.  It can be found in OpenMM’s :file:`examples` folder
with the name :file:`simulateGromacs.py`.

.. samepage::
    ::

        from openmm.app import *
        from openmm import *
        from openmm.unit import *
        from sys import stdout

        gro = GromacsGroFile('input.gro')
        top = GromacsTopFile('input.top', periodicBoxVectors=gro.getPeriodicBoxVectors(),
                includeDir='/usr/local/gromacs/share/gromacs/top')
        system = top.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
                constraints=HBonds)
        integrator = LangevinMiddleIntegrator(300*kelvin, 1/picosecond, 0.004*picoseconds)
        simulation = Simulation(top.topology, system, integrator)
        simulation.context.setPositions(gro.positions)
        simulation.minimizeEnergy()
        simulation.reporters.append(PDBReporter('output.pdb', 1000))
        simulation.reporters.append(StateDataReporter(stdout, 1000, step=True,
                potentialEnergy=True, temperature=True))
        simulation.step(10000)

    .. caption::

        :autonumber:`Example,Gromacs example`

This script is nearly identical to the previous one, just replacing
:class:`AmberInpcrdFile` and :class:`AmberPrmtopFile` with :class:`GromacsGroFile` and :class:`GromacsTopFile`.
Note that when we create the :class:`GromacsTopFile`, we specify values for two extra
options.  First, we specify
:code:`periodicBoxVectors=gro.getPeriodicBoxVectors()`\ .  Unlike OpenMM and
AMBER, which can store periodic unit cell information with the topology, Gromacs
only stores it with the coordinates.  To let :class:`GromacsTopFile` create a :class:`Topology`
object, we therefore need to tell it the periodic box vectors that were loaded
from the :file:`gro` file.  You only need to do this if you are simulating a periodic
system.  For implicit solvent simulations, it usually can be omitted.

Second, we specify :code:`includeDir='/usr/local/gromacs/share/gromacs/top'`\ .  Unlike AMBER,
which stores all the force field parameters directly in a :file:`prmtop` file, Gromacs just stores
references to force field definition files that are installed with the Gromacs
application.  OpenMM needs to know where to find these files, so the
:code:`includeDir` parameter specifies the directory containing them.  If you
omit this parameter, OpenMM will assume the default location :file:`/usr/local/gromacs/share/gromacs/top`,
which is often where they are installed on
Unix-like operating systems.  So in :autonumref:`Example,Gromacs example` we actually could have omitted
this parameter, but if the Gromacs files were installed in any other location,
we would need to include it.

.. _using-charmm-files:

Using CHARMM Files
******************

Yet another option is to load files created by the CHARMM setup tools, or other compatible
tools such as VMD.  Those include a :file:`psf` file containing topology information, and an
ordinary PDB file for the atomic coordinates.  (Coordinates can also be loaded from CHARMM
coordinate or restart files using the :class:`CharmmCrdFile` and :class:`CharmmRstFile` classes).  In addition,
you must provide a set of files containing the force
field definition to use.  This can involve several different files with varying formats and
filename extensions such as :file:`par`, :file:`prm`, :file:`top`, :file:`rtf`, :file:`inp`,
and :file:`str`.  To do this, load all the definition files into a :class:`CharmmParameterSet`
object, then include that object as the first parameter when you call :meth:`createSystem`
on the :class:`CharmmPsfFile`.

.. samepage::
    ::

        from openmm.app import *
        from openmm import *
        from openmm.unit import *
        from sys import stdout, exit, stderr

        psf = CharmmPsfFile('input.psf')
        pdb = PDBFile('input.pdb')
        params = CharmmParameterSet('charmm22.rtf', 'charmm22.prm')
        system = psf.createSystem(params, nonbondedMethod=NoCutoff,
                nonbondedCutoff=1*nanometer, constraints=HBonds)
        integrator = LangevinMiddleIntegrator(300*kelvin, 1/picosecond, 0.004*picoseconds)
        simulation = Simulation(psf.topology, system, integrator)
        simulation.context.setPositions(pdb.positions)
        simulation.minimizeEnergy()
        simulation.reporters.append(PDBReporter('output.pdb', 1000))
        simulation.reporters.append(StateDataReporter(stdout, 1000, step=True,
                potentialEnergy=True, temperature=True))
        simulation.step(10000)

    .. caption::

        :autonumber:`Example,CHARMM example`

Note that both the CHARMM and XPLOR versions of the :file:`psf` file format are supported.

.. _the-script-builder-application:

The OpenMM-Setup Application
****************************

One way to create your own scripts is to start with one of the examples given
above and customize it to suit your needs, but there's an even easier option.
OpenMM-Setup is a graphical application that walks you through the whole process
of loading your input files and setting options.  It then generates a complete
script, and can even run it for you.

.. figure:: ../../images/OpenMMSetup.png
   :align: center
   :width: 100%

   :autonumber:`Figure,openmm setup`:  The OpenMM-Setup application

To install OpenMM-Setup, open a command line terminal and type the following command
::

    conda install -c conda-forge openmm-setup

You can then launch it by typing the command
::

    openmm-setup

It will automatically open a window in your web browser displaying the user interface.

OpenMM-Setup is far more than just a script generator.  It can fix problems in
your input files, add missing atoms, build membranes and water boxes, and much
more.  It is a very easy way to quickly do all necessary preparation and setup.
We highly recommend it to all users of OpenMM, from novices to experts.

.. _simulation-parameters:

Simulation Parameters
*********************

Now let’s consider lots of ways you might want to customize your script.

Platforms
=========

When creating a :class:`Simulation`, you can optionally tell it what :class:`Platform` to use.
OpenMM includes four platforms: :class:`Reference`, :class:`CPU`, :class:`CUDA`, and :class:`OpenCL`.  For a
description of the differences between them, see Section :numref:`platforms`.  There are three ways in which
the :class:`Platform` can be chosen:

1. By default, OpenMM will try to select the fastest available :class:`Platform`.  Usually its choice will
be reasonable, but sometimes you may want to change it.

2. Alternatively, you can set the :envvar:`OPENMM_DEFAULT_PLATFORM` environment variable to the name
of the :class:`Platform` to use.  This overrides the default logic.

3. Finally, you can explicitly specify a :class:`Platform` object in your script when you create the
:class:`Simulation`.  The following lines specify to use the :class:`CUDA` platform:
::

    platform = Platform.getPlatformByName('CUDA')
    simulation = Simulation(prmtop.topology, system, integrator, platform)

The platform name should be one of :code:`OpenCL`, :code:`CUDA`, :code:`CPU`, or
:code:`Reference`.

You also can specify platform-specific properties that customize how
calculations should be done.  See Chapter :numref:`platform-specific-properties` for details of the
properties that each Platform supports.  For example, the following lines specify to parallelize
work across two different GPUs (CUDA devices 0 and 1), doing all computations in
double precision:
::

    platform = Platform.getPlatformByName('CUDA')
    properties = {'DeviceIndex': '0,1', 'Precision': 'double'}
    simulation = Simulation(prmtop.topology, system, integrator, platform, properties)

.. _force-fields:

Force Fields
============

When you create a force field, you specify one or more XML files from which to
load the force field definition.  Most often, there will be one file to define
the main force field, and possibly a second file to define the water model
(either implicit or explicit).  For example:
::

    forcefield = ForceField('amber14-all.xml', 'amber14/tip3pfb.xml')

In some cases, one XML file may load several others.  For example, :file:`amber14-all.xml`
is really just a shortcut for loading several different files that together make up
the AMBER14 force field.  If you need finer grained control over which parameters
are loaded, you can instead specify the component files individually.

Be aware that some force fields and water models include "extra particles", such
as lone pairs or Drude particles.  Examples include the CHARMM polarizable force
field and all of the 4 and 5 site water models.  To use these force fields, you
must first add the extra particles to the :class:`Topology`.  See section
:numref:`adding-or-removing-extra-particles` for details.

The force fields described below are the ones that are bundled with OpenMM.
Additional force fields are available online at https://github.com/choderalab/openmm-forcefields.

Amber14
-------

The Amber14\ :cite:`Maier2015` force field is made up of various files that define
parameters for proteins, DNA, RNA, lipids, water, and ions.

.. tabularcolumns:: |l|L|

===================================  ============================================
File                                 Parameters
===================================  ============================================
:file:`amber14/protein.ff14SB.xml`   Protein (recommended)
:file:`amber14/protein.ff15ipq.xml`  Protein (alternative)
:file:`amber14/DNA.OL15.xml`         DNA (recommended)
:file:`amber14/DNA.bsc1.xml`         DNA (alternative)
:file:`amber14/RNA.OL3.xml`          RNA
:file:`amber14/lipid17.xml`          Lipid
:file:`amber14/GLYCAM_06j-1.xml`     Carbohydrates and glycosylated proteins\ :cite:`Kirschner2007`
:file:`amber14/tip3p.xml`            TIP3P water model\ :cite:`Jorgensen1983` and ions
:file:`amber14/tip3pfb.xml`          TIP3P-FB water model\ :cite:`Wang2014` and ions
:file:`amber14/tip4pew.xml`          TIP4P-Ew water model\ :cite:`Horn2004` and ions
:file:`amber14/tip4pfb.xml`          TIP4P-FB water model\ :cite:`Wang2014` and ions
:file:`amber14/spce.xml`             SPC/E water model\ :cite:`Berendsen1987` and ions
===================================  ============================================

As a convenience, the file :file:`amber14-all.xml` can be used as a shortcut to include
:file:`amber14/protein.ff14SB.xml`, :file:`amber14/DNA.OL15.xml`, :file:`amber14/RNA.OL3.xml`,
and :file:`amber14/lipid17.xml`.  In most cases, you can simply include that file,
plus one of the water models, such as :file:`amber14/tip3pfb.xml` for the TIP3P-FB
water model and ions\ :cite:`Wang2014`:
::

    forcefield = ForceField('amber14-all.xml', 'amber14/tip3pfb.xml')

GLYCAM is not included by default, since it is quite large.  If your system contains
carbohydrates, include that file as well:
::

    forcefield = ForceField('amber14-all.xml', 'amber14/tip3pfb.xml', 'amber14/GLYCAM_06j-1.xml')

Be aware that GLYCAM works somewhat differently from most force fields.  It uses
its own nonstandard `naming convention <http://legacy.glycam.org/docs/forcefield/glycam-naming-2/index.html>`_
for carbohydrates, and requires your input file to follow it.  If any residues have
names different from what it expects, GLYCAM will be unable to assign parameters
to them.

.. tip:: The solvent model XML files included under the :file:`amber14/` directory
         include both water *and* ions compatible with that water model, so if you
         mistakenly specify :file:`tip3p.xml` instead of :file:`amber14/tip3p.xml`,
         you run the risk of having :class:`ForceField` throw an exception since
         :file:`tip3p.xml` will be missing parameters for ions in your system.

The converted parameter sets come from the `AmberTools 17 release <http://ambermd.org/AmberTools.php>`_
and were converted using the `openmm-forcefields <https://github.com/choderalab/openmm-forcefields>`_ package and `ParmEd <https://github.com/parmed/parmed>`_.

CHARMM36
--------

The CHARMM36\ :cite:`Best2012` force field provides parameters for proteins, DNA,
RNA, lipids, carbohydrates, water, ions, and various small molecules (see `here <http://mackerell.umaryland.edu/charmm_ff.shtml#refs>`_
for full references).

.. tabularcolumns:: |l|L|

=================================  ============================================
File                               Parameters
=================================  ============================================
:file:`charmm36.xml`               Protein, DNA, RNA, lipids, carbohydrates, and small molecules
:file:`charmm36/water.xml`         Default CHARMM water model (a modified version of TIP3P\ :cite:`Jorgensen1983`) and ions
:file:`charmm36/spce.xml`          SPC/E water model\ :cite:`Berendsen1987` and ions
:file:`charmm36/tip3p-pme-b.xml`   TIP3P-PME-B water model\ :cite:`Price2004` and ions
:file:`charmm36/tip3p-pme-f.xml`   TIP3P-PME-F water model\ :cite:`Price2004` and ions
:file:`charmm36/tip4pew.xml`       TIP4P-Ew water model\ :cite:`Horn2004` and ions
:file:`charmm36/tip4p2005.xml`     TIP4P-2005 water model\ :cite:`Abascal2005` and ions
:file:`charmm36/tip5p.xml`         TIP5P water model\ :cite:`Mahoney2000` and ions
:file:`charmm36/tip5pew.xml`       TIP5P-Ew water model\ :cite:`Rick2004` and ions
=================================  ============================================

The file :file:`charmm36.xml` bundles everything but the water and ions into a single
file.  In most cases, you can simply include that file, plus one of the water models,
such as :file:`charmm36/water.xml`, which specifies the default CHARMM water model
(a modified version of TIP3P\ :cite:`Jorgensen1983`) and ions:
::

    forcefield = ForceField('charmm36.xml', 'charmm36/water.xml')

.. warning:: Drude polarizable sites and lone pairs are not yet supported
             by `ParmEd <https://github.com/parmed/parmed>`_ and the CHARMM36 forcefields
             that depend on these features are not included in this port.
             To use the CHARMM 2019 polarizable force field\ :cite:`Lopes2013`,
             include the single file :file:`charmm_polar_2019.xml`.

.. tip:: The solvent model XML files included under the :file:`charmm36/` directory
         include both water *and* ions compatible with that water model, so if you
         mistakenly specify :file:`tip3p.xml` instead of :file:`charmm36/water.xml`,
         you run the risk of having :class:`ForceField` raise an exception due to
         missing parameters for ions in your system.

.. tip:: CHARMM makes extensive use of patches, which are automatically combined with
         residue templates to create an expanded library of patched residue templates
         by :class:`ForceField`. That means that patched residues, such as ``ACE`` and
         ``NME`` patched termini, must occur as a single residue in order for :class:`ForceField`
         to correctly match the residue template and apply parameters. Since these
         patched residues are not standard PDB residues, :class:`Modeller` does not know
         how to add hydrogens to these nonstandard residues, and your input topologies
         must already contain appropriate hydrogens. This can often cause problems when
         trying to read in PDB files from sources such as `CHARMM-GUI <http://charmm-gui.org/>`_
         that do not generate PDB files that comply with the `PDB standard <http://www.wwpdb.org/documentation/file-format>`_.
         If you're using files from `CHARMM-GUI <http://charmm-gui.org/>`_, it's easiest to load
         the PSF file directly, as discussed in Section :numref:`using-charmm-files`.

.. tip:: Trying to read in PDB files from sources such as `CHARMM-GUI <http://charmm-gui.org/>`_
         that do not generate PDB files that comply with the `PDB standard <http://www.wwpdb.org/documentation/file-format>`_
         and omit ``CONECT`` records specifying bonds between residues (such as cysteines)
         or include ``CONECT`` records specifying non-chemical ``H-H`` bonds in waters
         can cause issues with the detection and parameter assignment for disulfide bonds.
         Make sure the files you read in comply with the appropriate standards regarding
         additional bonds and nonstandard residue definitions. If you're using files from
         `CHARMM-GUI <http://charmm-gui.org/>`_, it's easiest to load
         the PSF file directly, as discussed in Section :numref:`using-charmm-files`.

The converted parameter sets come from the `CHARMM36 July 2017 update <http://mackerell.umaryland.edu/charmm_ff.shtml>`_
and were converted using the `openmm-forcefields <https://github.com/choderalab/openmm-forcefields>`_ package and `parmed <https://github.com/parmed/parmed>`_.

Implicit Solvent
----------------

The Amber and CHARMM force fields described above can be used with any of the Generalized
Born implicit solvent models from AMBER.  To use them, include an extra file when
creating the ForceField.  For example,
::

    forcefield = ForceField('amber14-all.xml', 'implicit/gbn2.xml')

.. tabularcolumns:: |l|L|

==========================  ==================================================================================================================================
File                        Implicit Solvent Model
==========================  ==================================================================================================================================
:file:`implicit/hct.xml`    Hawkins-Cramer-Truhlar GBSA model\ :cite:`Hawkins1995` (corresponds to igb=1 in AMBER)
:file:`implicit/obc1.xml`   Onufriev-Bashford-Case GBSA model\ :cite:`Onufriev2004` using the GB\ :sup:`OBC`\ I parameters (corresponds to igb=2 in AMBER).
:file:`implicit/obc2.xml`   Onufriev-Bashford-Case GBSA model\ :cite:`Onufriev2004` using the GB\ :sup:`OBC`\ II parameters (corresponds to igb=5 in AMBER).
:file:`implicit/gbn.xml`    GBn solvation model\ :cite:`Mongan2007` (corresponds to igb=7 in AMBER).
:file:`implicit/gbn2.xml`   GBn2 solvation model\ :cite:`Nguyen2013` (corresponds to igb=8 in AMBER).
==========================  ==================================================================================================================================

The only nonbonded methods that are supported with implicit solvent are :code:`NoCutoff` (the default),
:code:`CutoffNonPeriodic`, and :code:`CutoffPeriodic.`  If you choose to use a nonbonded cutoff with
implicit solvent, it is usually best to set the cutoff distance larger than is typical with explicit solvent.
A cutoff of 2 nm gives good results in most cases.  Periodic boundary conditions are not usually used
with implicit solvent.  In fact, the lack of need for periodicity and the artifacts it creates is one
of the advantages of implicit solvent.  The option is still offered, since it could be useful in some
unusual situations.

You can further control the solvation model in a few ways.  First, you can
specify the dielectric constants to use for the solute and solvent:
::

    system = forcefield.createSystem(topology, soluteDielectric=1.0, solventDielectric=80.0)

If they are not specified, the solute and solvent dielectric constants default to 1.0 and
78.5, respectively.

You also can model the effect of a non-zero salt concentration by specifying the
Debye-Huckel screening parameter\ :cite:`Srinivasan1999`:
::

    system = forcefield.createSystem(topology, implicitSolventKappa=1.0/nanometer)

The screening parameter can be calculated as

.. math::
  \kappa = 367.434915 \sqrt{\frac{I}{\epsilon T}}

where :math:`I` is the ionic strength in moles/liter, :math:`\epsilon` is the solvent
dielectric constant, and :math:`T` is the temperature in Kelvin.

AMOEBA
------

The AMOEBA polarizable force field provides parameters for proteins, nucleic acids, water, and ions.

.. tabularcolumns:: |l|L|

=============================  ================================================================================
File                           Parameters
=============================  ================================================================================
:file:`amoeba2018.xml`         AMOEBA 2018\ :cite:`Shi2013`
:file:`amoeba2018_gk.xml`      Generalized Kirkwood solvation model\ :cite:`Schnieders2007` for use with AMOEBA 2018 force field
:file:`amoeba2013.xml`         AMOEBA 2013.  This force field is deprecated.  It is
                               recommended to use AMOEBA 2018 instead.
:file:`amoeba2013_gk.xml`      Generalized Kirkwood solvation model for use with AMOEBA 2013 force field
:file:`amoeba2009.xml`         AMOEBA 2009\ :cite:`Ren2002`.  This force field is deprecated.  It is
                               recommended to use AMOEBA 2018 instead.
:file:`amoeba2009_gk.xml`      Generalized Kirkwood solvation model for use with AMOEBA 2009 force field
=============================  ================================================================================

For explicit solvent simulations, just include the single file :file:`amoeba2018.xml`.
AMOEBA also supports implicit solvent using a Generalized Kirkwood model.  To enable
it, also include :file:`amoeba2018_gk.xml`.

The older AMOEBA 2009 and 2013 force fields are provided only for backward compatibility, and are not
recommended for most simulations.

CHARMM Polarizable Force Field
------------------------------

To use the CHARMM 2019 polarizable force field\ :cite:`Lopes2013`, include the
single file :file:`charmm_polar_2019.xml`.  It includes parameters for proteins, lipids,
water, and ions.  When using this force field, remember to add extra particles to
the :class:`Topology` as described in section :numref:`adding-or-removing-extra-particles`.
This force field also requires that you use one of the special integrators that
supports Drude particles.  The options are DrudeLangevinIntegrator, DrudeNoseHooverIntegrator,
and DrudeSCFIntegrator.

Older Force Fields
------------------

OpenMM includes several older force fields as well.  For most simulations, the
newer force fields described above are preferred over any of these, but they are
still useful for reproducing older results.

.. tabularcolumns:: |l|L|

=============================  ================================================================================
File                           Force Field
=============================  ================================================================================
:code:`amber96.xml`            Amber96\ :cite:`Kollman1997`
:code:`amber99sb.xml`          Amber99\ :cite:`Wang2000` with modified backbone torsions\ :cite:`Hornak2006`
:code:`amber99sbildn.xml`      Amber99SB plus improved side chain torsions\ :cite:`Lindorff-Larsen2010`
:code:`amber99sbnmr.xml`       Amber99SB with modifications to fit NMR data\ :cite:`Li2010`
:code:`amber03.xml`            Amber03\ :cite:`Duan2003`
:code:`amber10.xml`            Amber10 (documented in the AmberTools_ manual as `ff10`)
:code:`charmm_polar_2013.xml`  2013 version of the CHARMM polarizable force field\ :cite:`Lopes2013`
=============================  ================================================================================

Several of these force fields support implicit solvent.  To enable it, also
include the corresponding OBC file.

.. tabularcolumns:: |l|L|

=========================  =================================================================================================
File                       Implicit Solvation Model
=========================  =================================================================================================
:code:`amber96_obc.xml`    GBSA-OBC solvation model\ :cite:`Onufriev2004` for use with Amber96 force field
:code:`amber99_obc.xml`    GBSA-OBC solvation model for use with Amber99 force field and its variants
:code:`amber03_obc.xml`    GBSA-OBC solvation model for use with Amber03 force field
:code:`amber10_obc.xml`    GBSA-OBC solvation model for use with Amber10 force field
=========================  =================================================================================================

Note that the GBSA-OBC parameters in these files are those used in TINKER.\ :cite:`Tinker`
They are designed for use with Amber force fields, but they are different from
the parameters found in the AMBER application.

Water Models
------------

The following files define popular water models.  They can be used with force fields
that do not provide their own water models.  When using Amber14 or CHARMM36, use
the water files included with those force fields instead, since they also include
ion parameters.

.. tabularcolumns:: |l|L|

===================  ============================================
File                 Water Model
===================  ============================================
:code:`tip3p.xml`    TIP3P water model\ :cite:`Jorgensen1983`
:code:`tip3pfb.xml`  TIP3P-FB water model\ :cite:`Wang2014`
:code:`tip4pew.xml`  TIP4P-Ew water model\ :cite:`Horn2004`
:code:`tip4pfb.xml`  TIP4P-FB water model\ :cite:`Wang2014`
:code:`tip5p.xml`    TIP5P water model\ :cite:`Mahoney2000`
:code:`spce.xml`     SPC/E water model\ :cite:`Berendsen1987`
:code:`swm4ndp.xml`  SWM4-NDP water model\ :cite:`Lamoureux2006`
===================  ============================================

Small molecule parameters
=========================

The OpenMM force fields above include pregenerated templates for biopolymers
and solvents. If your system instead contain small molecules, it is often
necessary to generate these parameters on the fly.


There are two options for doing this within the OpenMM ``app`` ecosystem:

Small molecule residue template generators
------------------------------------------

One approach is to use residue template generators for small molecules from the
openmmforcefields_  conda package.
You can install this via conda with:

.. code-block:: bash

    $ conda install -c conda-forge openmmforcefields

You can then add a small molecule residue template generator using the Open Force
Field Initiative small molecule force fields using the following example:

::

    # Create an OpenFF Molecule object for benzene from SMILES
    from openff.toolkit.topology import Molecule
    molecule = Molecule.from_smiles('c1ccccc1')
    # Create the SMIRNOFF template generator with the default installed force field (openff-1.0.0)
    from openmmforcefields.generators import SMIRNOFFTemplateGenerator
    smirnoff = SMIRNOFFTemplateGenerator(molecules=molecule)
    # Create an OpenMM ForceField object with AMBER ff14SB and TIP3P with compatible ions
    from openmm.app import ForceField
    forcefield = ForceField('amber/protein.ff14SB.xml', 'amber/tip3p_standard.xml', 'amber/tip3p_HFE_multivalent.xml')
    # Register the SMIRNOFF template generator
    forcefield.registerTemplateGenerator(smirnoff.generator)

Alternatively, you can use the older `AMBER GAFF small molecule force field <http://ambermd.org/antechamber/gaff.html>`_:

::

    # Create an OpenFF Molecule object for benzene from SMILES
    from openff.toolkit.topology import Molecule
    molecule = Molecule.from_smiles('c1ccccc1')
    # Create the GAFF template generator
    from openmmforcefields.generators import GAFFTemplateGenerator
    gaff = GAFFTemplateGenerator(molecules=molecule)
    # Create an OpenMM ForceField object with AMBER ff14SB and TIP3P with compatible ions
    from openmm.app import ForceField
    forcefield = ForceField('amber/protein.ff14SB.xml', 'amber/tip3p_standard.xml', 'amber/tip3p_HFE_multivalent.xml')
    # Register the GAFF template generator
    forcefield.registerTemplateGenerator(gaff.generator)
    # You can now parameterize an OpenMM Topology object that contains the specified molecule.
    # forcefield will load the appropriate GAFF parameters when needed, and antechamber
    # will be used to generate small molecule parameters on the fly.
    from openmm.app import PDBFile
    pdbfile = PDBFile('t4-lysozyme-L99A-with-benzene.pdb')
    system = forcefield.createSystem(pdbfile.topology)

More documentation can be found on the openmmforcefields_ page.

Managing force fields with ``SystemGenerator``
----------------------------------------------

As an alternative to explicitly registering template generators, the openmmforcefields_
package provides a ``SystemGenerator`` facility to simplify biopolymer and
small molecule force field management. To use this, you can simply specify the
small molecule force field you want to use:

::

    # Define the keyword arguments to feed to ForceField
    from openmm import unit, app
    forcefield_kwargs = { 'constraints' : app.HBonds, 'rigidWater' : True, 'removeCMMotion' : False, 'hydrogenMass' : 4*unit.amu }
    # Initialize a SystemGenerator using GAFF
    from openmmforcefields.generators import SystemGenerator
    system_generator = SystemGenerator(forcefields=['amber/ff14SB.xml', 'amber/tip3p_standard.xml'], small_molecule_forcefield='gaff-2.11', forcefield_kwargs=forcefield_kwargs, cache='db.json')
    # Create an OpenMM System from an OpenMM Topology object
    system = system_generator.create_system(openmm_topology)
    # Alternatively, create an OpenMM System from an OpenMM Topology object and a list of OpenFF Molecule objects
    molecules = Molecule.from_file('molecules.sdf', file_format='sdf')
    system = system_generator.create_system(openmm_topology, molecules=molecules)

The ``SystemGenerator`` will match any instances of the molecules found in ``molecules.sdf`` to those that appear in ``topology``.
Note that the protonation and tautomeric states must match exactly between the ``molecules`` read and those appearing in the Topology.
See the openmmforcefields_ documentation for more details.

.. _openmmforcefields: http://github.com/openmm/openmmforcefields

AMBER Implicit Solvent
======================


When creating a system from a prmtop file you do not specify force field files,
so you need a different way to tell it to use implicit solvent.  This is done
with the :code:`implicitSolvent` parameter:
::

    system = prmtop.createSystem(implicitSolvent=OBC2)

OpenMM supports all of the Generalized Born models used by AMBER.  Here are the
allowed values for :code:`implicitSolvent`\ :

.. tabularcolumns:: |l|L|

=============  ==================================================================================================================================
Value          Meaning
=============  ==================================================================================================================================
:code:`None`   No implicit solvent is used.
:code:`HCT`    Hawkins-Cramer-Truhlar GBSA model\ :cite:`Hawkins1995` (corresponds to igb=1 in AMBER)
:code:`OBC1`   Onufriev-Bashford-Case GBSA model\ :cite:`Onufriev2004` using the GB\ :sup:`OBC`\ I parameters (corresponds to igb=2 in AMBER).
:code:`OBC2`   Onufriev-Bashford-Case GBSA model\ :cite:`Onufriev2004` using the GB\ :sup:`OBC`\ II parameters (corresponds to igb=5 in AMBER).
               This is the same model used by the GBSA-OBC files described in Section :numref:`force-fields`.
:code:`GBn`    GBn solvation model\ :cite:`Mongan2007` (corresponds to igb=7 in AMBER).
:code:`GBn2`   GBn2 solvation model\ :cite:`Nguyen2013` (corresponds to igb=8 in AMBER).
=============  ==================================================================================================================================


You can further control the solvation model in a few ways.  First, you can
specify the dielectric constants to use for the solute and solvent:
::

    system = prmtop.createSystem(implicitSolvent=OBC2, soluteDielectric=1.0,
            solventDielectric=80.0)

If they are not specified, the solute and solvent dielectrics default to 1.0 and
78.5, respectively.  These values were chosen for consistency with AMBER, and
are slightly different from those used elsewhere in OpenMM: when building a
system from a force field, the solvent dielectric defaults to 78.3.

You also can model the effect of a non-zero salt concentration by specifying the
Debye-Huckel screening parameter\ :cite:`Srinivasan1999`:
::

    system = prmtop.createSystem(implicitSolvent=OBC2, implicitSolventKappa=1.0/nanometer)


Nonbonded Interactions
======================


When creating the system (either from a force field or a prmtop file), you can
specify options about how nonbonded interactions should be treated:
::

    system = prmtop.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer)

The :code:`nonbondedMethod` parameter can have any of the following values:

.. tabularcolumns:: |l|L|

=========================  ===========================================================================================================================================================================================================================================
Value                      Meaning
=========================  ===========================================================================================================================================================================================================================================
:code:`NoCutoff`           No cutoff is applied.
:code:`CutoffNonPeriodic`  The reaction field method is used to eliminate all interactions beyond a cutoff distance.  Not valid for AMOEBA.
:code:`CutoffPeriodic`     The reaction field method is used to eliminate all interactions beyond a cutoff distance.  Periodic boundary conditions are applied, so each atom interacts only with the nearest periodic copy of every other atom.  Not valid for AMOEBA.
:code:`Ewald`              Periodic boundary conditions are applied.  Ewald summation is used to compute long range Coulomb interactions.  (This option is rarely used, since PME is much faster for all but the smallest systems.)  Not valid for AMOEBA.
:code:`PME`                Periodic boundary conditions are applied.  The Particle Mesh Ewald method is used to compute long range Coulomb interactions.
:code:`LJPME`              Periodic boundary conditions are applied.  The Particle Mesh Ewald method is used to compute long range interactions for both Coulomb and Lennard-Jones.
=========================  ===========================================================================================================================================================================================================================================


When using any method other than :code:`NoCutoff`\ , you should also specify a
cutoff distance.  Be sure to specify units, as shown in the examples above. For
example, :code:`nonbondedCutoff=1.5*nanometers` or
:code:`nonbondedCutoff=12*angstroms` are legal values.

When using :code:`Ewald`, :code:`PME`, or :code:`LJPME`\ , you can optionally specify an
error tolerance for the force computation.  For example:
::

    system = prmtop.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
            ewaldErrorTolerance=0.00001)

The error tolerance is roughly equal to the fractional error in the forces due
to truncating the Ewald summation.  If you do not specify it, a default value of
0.0005 is used.

Another optional parameter when using a cutoff is :code:`switchDistance`.  This
causes Lennard-Jones interactions to smoothly go to zero over some finite range,
rather than being sharply truncated at the cutoff distance.  This can improve
energy conservation.  To use it, specify a distance at which the interactions
should start being reduced.  For example:
::

    system = prmtop.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
            switchDistance=0.9*nanometer)


Nonbonded Forces for AMOEBA
---------------------------

For the AMOEBA force field, the valid values for the :code:`nonbondedMethod`
are :code:`NoCutoff` and :code:`PME`\ .  The other nonbonded methods,
:code:`CutoffNonPeriodic`\ , :code:`CutoffPeriodic`\ , and :code:`Ewald`
are unavailable for this force field.

For implicit solvent runs using AMOEBA, only the :code:`nonbondedMethod`
option :code:`NoCutoff` is available.

Lennard-Jones Interaction Cutoff Value
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

In addition, for the AMOEBA force field a cutoff for the Lennard-Jones
interaction independent of the value used for the electrostatic interactions may
be specified using the keyword :code:`vdwCutoff`\ .
::

    system = forcefield.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
            ewaldErrorTolerance=0.00001, vdwCutoff=1.2*nanometer)

If :code:`vdwCutoff` is not specified, then the value of
:code:`nonbondedCutoff` is used for the Lennard-Jones interactions.

Specifying the Polarization Method
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

When using the AMOEBA force field, OpenMM allows the induced dipoles to be
calculated in any of three different ways.  The slowest but potentially most
accurate method is to iterate the calculation until the dipoles converge to a
specified tolerance.  To select this, specify :code:`polarization='mutual'`.
Use the :code:`mutualInducedTargetEpsilon` option to select the tolerance; for
most situations, a value of 0.00001 works well.  Alternatively you can specify
:code:`polarization='extrapolated'`.  This uses an analytic approximation
:cite:`Simmonett2015` to estimate what the fully converged dipoles will be without
actually continuing the calculation to convergence.  In many cases this can be
significantly faster with only a small loss in accuracy.  Finally, you can
specify :code:`polarization='direct'` to use the direct polarization
approximation, in which induced dipoles depend only on the fixed multipoles, not
on other induced dipoles.  This is even faster, but it produces very different
forces from mutual polarization, so it should only be used with force fields
that have been specifically parameterized for use with this approximation.

Here are examples of using each method:
::

    system = forcefield.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
        vdwCutoff=1.2*nanometer, polarization='mutual', mutualInducedTargetEpsilon=0.00001)

    system = forcefield.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
        vdwCutoff=1.2*nanometer, polarization='extrapolated')

    system = forcefield.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
        vdwCutoff=1.2*nanometer, polarization='direct')


Implicit Solvent and Solute Dielectrics
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

For implicit solvent simulations using the AMOEBA force field, the
:file:`amoeba2013_gk.xml` file should be included in the initialization of the force
field:
::

    forcefield = ForceField('amoeba2009.xml', 'amoeba2009_gk.xml')

Only the :code:`nonbondedMethod` option :code:`NoCutoff` is available
for implicit solvent runs using AMOEBA.  In addition, the solvent and solute
dielectric values can be specified for implicit solvent simulations:
::

    system=forcefield.createSystem(nonbondedMethod=NoCutoff, soluteDielectric=2.0,
            solventDielectric=80.0)

The default values are 1.0 for the solute dielectric and 78.3 for the solvent
dielectric.

Constraints
===========


When creating the system (either from a force field or an AMBER :file:`prmtop` file), you can
optionally tell OpenMM to constrain certain bond lengths and angles.  For
example,
::

    system = prmtop.createSystem(nonbondedMethod=NoCutoff, constraints=HBonds)

The :code:`constraints` parameter can have any of the following values:

.. tabularcolumns:: |l|L|

================  =============================================================================================================================================
Value             Meaning
================  =============================================================================================================================================
:code:`None`      No constraints are applied.  This is the default value.
:code:`HBonds`    The lengths of all bonds that involve a hydrogen atom are constrained.
:code:`AllBonds`  The lengths of all bonds are constrained.
:code:`HAngles`   The lengths of all bonds are constrained.  In addition, all angles of the form H-X-H or H-O-X (where X is an arbitrary atom) are constrained.
================  =============================================================================================================================================


The main reason to use constraints is that it allows one to use a larger
integration time step.  With no constraints, one is typically limited to a time
step of about 1 fs for typical biomolecular force fields like AMBER or CHARMM.
With :code:`HBonds` constraints, this can be increased to about 2 fs for Verlet
dynamics, or about 4 fs for Langevin dynamics.  With :code:`HAngles`\ , it can
sometimes be increased even further.

Regardless of the value of this parameter, OpenMM makes water molecules
completely rigid, constraining both their bond lengths and angles.  You can
disable this behavior with the :code:`rigidWater` parameter:
::

    system = prmtop.createSystem(nonbondedMethod=NoCutoff, constraints=None, rigidWater=False)

Be aware that flexible water may require you to further reduce the integration
step size, typically to about 0.5 fs.

.. note::

   The AMOEBA forcefield is designed to be used without constraints, so by
   default OpenMM makes AMOEBA water flexible.  You can still force it to be
   rigid by specifying :code:`rigidWater=True`.

Heavy Hydrogens
===============


When creating the system (either from a force field or an AMBER :file:`prmtop` file), you can
optionally tell OpenMM to increase the mass of hydrogen atoms.  For example,
::

    system = prmtop.createSystem(hydrogenMass=4*amu)

This applies only to hydrogens that are bonded to heavy atoms, and any mass
added to the hydrogen is subtracted from the heavy atom.  This keeps their total
mass constant while slowing down the fast motions of hydrogens.  When combined
with constraints (typically :code:`constraints=AllBonds`\ ), this often allows a
further increase in integration step size.

.. _integrators:

Integrators
===========


OpenMM offers a choice of several different integration methods.  You select
which one to use by creating an integrator object of the appropriate type.
Detailed descriptions of all these integrators can be found in Chapter
:numref:`integrators-theory`.  In addition to these built in integrators, lots of
others are available as part of the `OpenMMTools <https://openmmtools.readthedocs.io>`_ package.

Langevin Middle Integrator
--------------------------

In the examples of the previous sections, we used Langevin integration:
::

    integrator = LangevinMiddleIntegrator(300*kelvin, 1/picosecond, 0.004*picoseconds)

The three parameter values in this line are the simulation temperature (300 K),
the friction coefficient (1 ps\ :sup:`-1`\ ), and the step size (0.004 ps).  You
are free to change these to whatever values you want.  Be sure to specify units
on all values.  For example, the step size could be written either as
:code:`0.004*picoseconds` or :code:`4*femtoseconds`\ .  They are exactly
equivalent.  Note that :code:`LangevinMiddleIntegrator` is a leapfrog
integrator, so the velocities are offset by half a time step from the positions.

Langevin Integrator
-------------------

:code:`LangevinIntegrator` is very similar to :code:`LangevinMiddleIntegrator`,
but it uses a different discretization of the Langevin equation.
:code:`LangevinMiddleIntegrator` tends to produce more accurate configurational
sampling, and therefore is preferred for most applications.  Also note that
:code:`LangevinIntegrator`\ , like :code:`LangevinMiddleIntegrator`\ , is a leapfrog
integrator, so the velocities are offset by half a time step from the positions.

Nosé-Hoover Integrator
----------------------

The :code:`NoseHooverIntegrator` uses the same "middle" leapfrog propagation
algorithm as :code:`LangevinMiddleIntegrator`, but replaces the stochastic
temperature control with a velocity scaling algorithm that produces more
accurate transport properties :cite:`Basconi2013`.  This velocity scaling
results from propagating a chain of extra variables, which slightly reduces the
computational efficiency with respect to :code:`LangevinMiddleIntegrator`.  The
thermostated integrator is minimally created with syntax analogous to the
:code:`LangevinMiddleIntegrator` example above::

    NoseHooverIntegrator integrator(300*kelvin, 1/picosecond,
                                    0.004*picoseconds);

The first argument specifies the target temperature.  The second specifies the
frequency of interaction with the heat bath: a lower value interacts minimally,
yielding the microcanonical ensemble in the limit of a zero frequency, while a
larger frequency will perturb the system greater, keeping it closer to the
target temperature.  The third argument is the integration timestep that, like
the other arguments, must be specified with units.  For initial equilibration
to the target temperature, a larger interaction frequency is recommended,
*e.g.* 25 ps\ :sup:`-1`.

This integrator supports lots of other options, including the ability to couple
different parts of the system to thermostats at different temperatures. See the
API documentation for details.

Leapfrog Verlet Integrator
--------------------------

A leapfrog Verlet integrator can be used for running constant energy dynamics.
The command for this is:
::

    integrator = VerletIntegrator(0.002*picoseconds)

The only option is the step size.

Brownian Integrator
-------------------

Brownian (diffusive) dynamics can be used by specifying the following:
::

    integrator = BrownianIntegrator(300*kelvin, 1/picosecond, 0.002*picoseconds)

The parameters are the same as for Langevin dynamics: temperature (300 K),
friction coefficient (1 ps\ :sup:`-1`\ ), and step size (0.002 ps).

Variable Time Step Langevin Integrator
--------------------------------------

A variable time step Langevin integrator continuously adjusts its step size to
keep the integration error below a specified tolerance.  In some cases, this can
allow you to use a larger average step size than would be possible with a fixed
step size integrator.  It also is very useful in cases where you do not know in
advance what step size will be stable, such as when first equilibrating a
system.  You create this integrator with the following command:
::

    integrator = VariableLangevinIntegrator(300*kelvin, 1/picosecond, 0.001)

In place of a step size, you specify an integration error tolerance (0.001 in
this example).  It is best not to think of this value as having any absolute
meaning.  Just think of it as an adjustable parameter that affects the step size
and integration accuracy.  Smaller values will produce a smaller average step
size.  You should try different values to find the largest one that produces a
trajectory sufficiently accurate for your purposes.

Variable Time Step Leapfrog Verlet Integrator
---------------------------------------------

A variable time step leapfrog Verlet integrator works similarly to the variable
time step Langevin integrator in that it continuously adjusts its step size to
keep the integration error below a specified tolerance.  The command for this
integrator is:
::

    integrator = VariableVerletIntegrator(0.001)

The parameter is the integration error tolerance (0.001), whose meaning is the
same as for the Langevin integrator.

Multiple Time Step Integrator
-----------------------------

The :class:`MTSIntegrator` class implements the rRESPA multiple time step
algorithm\ :cite:`Tuckerman1992`.  This allows some forces in the system to be evaluated more
frequently than others.  For details on how to use it, consult the API
documentation.

Multiple Time Step Langevin Integrator
--------------------------------------

:class:`MTSLangevinIntegrator` is similar to :class:`MTSIntegrator`, but it uses
the Langevin method to perform constant temperature dynamics.  For details on
how to use it, consult the API documentation.

Compound Integrator
-------------------

The :class:`CompoundIntegrator` class is useful for cases where you want to use
multiple integration algorithms within a single simulation.  It allows you to
create multiple integrators, then switch back and forth between them.  For
details on how to use it, consult the API documentation.

Temperature Coupling
====================


If you want to run a simulation at constant temperature, using a Langevin
integrator (as shown in the examples above) is usually the best way to do it.
OpenMM does provide an alternative, however: you can use a Verlet integrator,
then add an Andersen thermostat to your system to provide temperature coupling.

To do this, we can add an :class:`AndersenThermostat` object to the :class:`System` as shown below.
::

    ...
    system = prmtop.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
            constraints=HBonds)
    system.addForce(AndersenThermostat(300*kelvin, 1/picosecond))
    integrator = VerletIntegrator(0.002*picoseconds)
    ...

The two parameters of the Andersen thermostat are the temperature (300 K) and
collision frequency (1 ps\ :sup:`-1`\ ).

Pressure Coupling
=================


All the examples so far have been constant volume simulations.  If you want to
run at constant pressure instead, add a Monte Carlo barostat to your system.
You do this exactly the same way you added the Andersen thermostat in the
previous section:
::

    ...
    system = prmtop.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
            constraints=HBonds)
    system.addForce(MonteCarloBarostat(1*bar, 300*kelvin))
    integrator = LangevinMiddleIntegrator(300*kelvin, 1/picosecond, 0.004*picoseconds)
    ...

The parameters of the Monte Carlo barostat are the pressure (1 bar) and
temperature (300 K).  The barostat assumes the simulation is being run at
constant temperature, but it does not itself do anything to regulate the
temperature.

.. warning::

    It is therefore critical that you always use it along with a Langevin integrator or
    Andersen thermostat, and that you specify the same temperature for both the barostat
    and the integrator or thermostat.  Otherwise, you will get incorrect results.

There also is an anisotropic barostat that scales each axis of the periodic box
independently, allowing it to change shape.  When using the anisotropic
barostat, you can specify a different pressure for each axis.  The following
line applies a pressure of 1 bar along the X and Y axes, but a pressure of 2 bar
along the Z axis:
::

    system.addForce(MonteCarloAnisotropicBarostat((1, 1, 2)*bar, 300*kelvin))

Another feature of the anisotropic barostat is that it can be applied to only
certain axes of the periodic box, keeping the size of the other axes fixed.
This is done by passing three additional parameters that specify whether the
barostat should be applied to each axis.  The following line specifies that the
X and Z axes of the periodic box should not be scaled, so only the Y axis can
change size.
::

    system.addForce(MonteCarloAnisotropicBarostat((1, 1, 1)*bar, 300*kelvin,
            False, True, False))

There is a third barostat designed specifically for simulations of membranes.
It assumes the membrane lies in the XY plane, and treats the X and Y axes of the
box differently from the Z axis.  It also applies a uniform surface tension in
the plane of the membrane.  The following line adds a membrane barostat that
applies a pressure of 1 bar and a surface tension of 200 bar*nm.  It specifies
that the X and Y axes are treated isotropically while the Z axis is free to
change independently.
::

    system.addForce(MonteCarloMembraneBarostat(1*bar, 200*bar*nanometer,
        MonteCarloMembraneBarostat.XYIsotropic, MonteCarloMembraneBarostat.ZFree, 300*kelvin))

See the API documentation for details about the allowed parameter values and
their meanings.


Energy Minimization
===================


As seen in the examples, performing a local energy minimization takes a single
line in the script:
::

    simulation.minimizeEnergy()

In most cases, that is all you need.  There are two optional parameters you can
specify if you want further control over the minimization.  First, you can
specify a tolerance for when the energy should be considered to have converged:
::

    simulation.minimizeEnergy(tolerance=5*kilojoule/mole)

If you do not specify this parameter, a default tolerance of 10 kJ/mole is used.

Second, you can specify a maximum number of iterations:
::

    simulation.minimizeEnergy(maxIterations=100)

The minimizer will exit once the specified number of iterations is reached, even
if the energy has not yet converged.  If you do not specify this parameter, the
minimizer will continue until convergence is reached, no matter how many
iterations it takes.

These options are independent.  You can specify both if you want:
::

    simulation.minimizeEnergy(tolerance=0.1*kilojoule/mole, maxIterations=500)

Removing Center of Mass Motion
==============================


By default, :class:`System` objects created with the OpenMM application tools add
a :class:`CMMotionRemover` that removes all center of mass motion at every time step so the
system as a whole does not drift with time.  This is almost always what you
want.  In rare situations, you may want to allow the system to drift with time.
You can do this by specifying the :code:`removeCMMotion` parameter when you
create the System:
::

    system = forcefield.createSystem(pdb.topology, nonbondedMethod=NoCutoff,
            removeCMMotion=False)

Writing Trajectories
====================


OpenMM can save simulation trajectories to disk in three formats: PDB_,
`PDBx/mmCIF`_, and DCD_.  All of these are widely supported formats, so you
should be able to read them into most analysis and visualization programs.

.. _PDB: http://www.wwpdb.org/documentation/format33/v3.3.html
.. _PDBx/mmCIF: http://mmcif.wwpdb.org
.. _DCD: http://www.ks.uiuc.edu/Research/vmd/plugins/molfile/dcdplugin.html

To save a trajectory, just add a “reporter” to the simulation, as shown in the
example scripts above:
::

    simulation.reporters.append(PDBReporter('output.pdb', 1000))

The two parameters of the :class:`PDBReporter` are the output filename and how often (in
number of time steps) output structures should be written.  To use PDBx/mmCIF or
DCD format, just replace :class:`PDBReporter` with :class:`PDBxReporter` or
:class:`DCDReporter`.  The parameters represent the same values:
::

    simulation.reporters.append(DCDReporter('output.dcd', 1000))

Recording Other Data
====================


In addition to saving a trajectory, you may want to record other information
over the course of a simulation, such as the potential energy or temperature.
OpenMM provides a reporter for this purpose also.  Create a :class:`StateDataReporter`
and add it to the simulation:
::

    simulation.reporters.append(StateDataReporter('data.csv', 1000, time=True,
            kineticEnergy=True, potentialEnergy=True))

The first two parameters are the output filename and how often (in number of
time steps) values should be written.  The remaining arguments specify what
values should be written at each report.  The available options are
:code:`step` (the index of the current time step), :code:`time`\ ,
:code:`progress` (what percentage of the simulation has completed),
:code:`remainingTime` (an estimate of how long it will take the simulation to
complete), :code:`potentialEnergy`\ , :code:`kineticEnergy`\ ,
:code:`totalEnergy`\ , :code:`temperature`\ , :code:`volume` (the volume
of the periodic box), :code:`density` (the total system mass divided by the
volume of the periodic box), and :code:`speed` (an estimate of how quickly
the simulation is running).  If you include either the :code:`progress` or
:code:`remainingTime` option, you must also include the :code:`totalSteps`
parameter to specify the total number of time steps that will be included in the
simulation.  One line is written to the file for each report containing the
requested values.  By default the values are written in comma-separated-value
(CSV) format.  You can use the :code:`separator` parameter to choose a
different separator.  For example, the following line will cause values to be
separated by spaces instead of commas:
::

    simulation.reporters.append(StateDataReporter('data.txt', 1000, progress=True,
            temperature=True, totalSteps=10000, separator=' '))


Saving Simulation Progress and Results
==========================================

There are three built-in ways to save the results of your simulation in OpenMM
(additional methods can be written yourself or imported through other packages
like mdtraj or parmed). If you are simply interested in saving the structure,
you can write it out as a PDB file using :code:`PDBFile.writeFile()`.  You can
see an example of this in the modeller section :numref:`saving-the-results`.

If you are hoping to save more information than just positions, you can use
:code:`simulation.saveState()`. This will save the entire state of the
simulation, including positions, velocities, box dimensions and much more in an
XML file. This same file can be loaded back into OpenMM and used to continue
the simulation. Importantly, because this file is a text file, it can be
transfered between different platforms and different versions of OpenMM. A
potential downside to this approach is that state files are often quite large,
and may not fit all use cases. Here's an example of how to use it:
::

    simulation.saveState('output.xml')

To load the simulation back in:
::

    simulation.loadState('output.xml')

There is a third way to save your simulation, known as a checkpoint file, which
will save the entire simulation as a binary file. It will allow you to exactly
continue a simulation if the need arises (though whether the simulation is
deterministic depends on platform and methods, see
:numref:`platform-specific-properties-determinism`). There are important caveats
to this approach, however. This binary can only be used to restart simulations
on machines with the same hardware and the same OpenMM version as the one that
saved it. Therefore, it should only be used when it's clear that won't be an
issue.
::

    simulation.saveCheckpoint('state.chk')

And can be loaded back in like this:
::

    simulation.loadCheckpoint('state.chk')

Finally, OpenMM comes with a built-in reporter for saving checkpoints, the
:class:`CheckpointReporter`, which can be helpful in restarting simulations
that failed unexpectedly or due to outside reasons (e.g. server crash). To save
a checkpoint file every 5,000 steps, for example:
::

    simulation.reporters.append(CheckpointReporter('checkpnt.chk', 5000))

Note that the checkpoint reporter will overwrite the last checkpoint file.


Enhanced Sampling Methods
=========================

In many situations, the goal of a simulation is to sample the range of configurations
accessible to a system.  It does not matter whether the simulation represents a
single, physically realistic trajectory, only whether it produces a correct distribution
of states.  In this case, a variety of methods can be used to sample configuration
space much more quickly and efficiently than a single physical trajectory would.
These are known as enhanced sampling methods.  OpenMM offers several that you
can choose from.  They are briefly described here.  Consult the API documentation
for more detailed descriptions and example code.

Simulated Tempering
-------------------

Simulated tempering\ :cite:`Marinari1992` involves making frequent changes to the
temperature of a simulation.  At high temperatures, it can quickly cross energy barriers
and explore a wide range of configurations.  At lower temperatures, it more thoroughly
explores each local region of configuration space.  This is a powerful method to
speed up sampling when you do not know in advance what motions you want to sample.
Simply specify the range of temperatures to simulate and the algorithm handles
everything for you mostly automatically.

Metadynamics
------------

Metadynamics\ :cite:`Barducci2008` is used when you do know in advance what
motions you want to sample.  You specify one or more collective variables, and the
algorithm adds a biasing potential to make the simulation explore a wide range of
values for those variables.  It does this by periodically adding "bumps" to the biasing
potential at the current values of the collective variables.  This encourages the simulation
to move away from regions it has already explored and sample a wide range of values.
At the end of the simulation, the biasing potential can be used to calculate the
free energy of the system as a function of the collective variables.

Accelerated Molecular Dynamics (aMD)
------------------------------------

aMD\ :cite:`Hamelberg2007` is another method that can be used when you do not know in
advance what motions you want to accelerate.  It alters the potential energy surface
by adding a "boost" potential whenever the potential energy is below a threshold.
This makes local minima shallower and allows more frequent transitions between them.
The boost can be applied to the total potential energy, to just a subset of interactions
(typically the dihedral torsions), or both.  There are separate integrator classes
for each of these options: :class:`AMDIntegrator`, :class:`AMDForceGroupIntegrator`,
and :class:`DualAMDIntegrator`.
