.. include:: header.rst

.. _the-openmm-application-layer-introduction:

The OpenMM Application Layer: Introduction
##########################################

The first thing to understand about the OpenMM “application layer” is that it is
not exactly an application in the traditional sense: there is no program called
“OpenMM” that you run.  Rather, it is a collection of libraries written in the
Python programming language.  Those libraries can easily be chained together to
create Python programs that run simulations.  But don’t worry!  You don’t need
to know anything about Python programming (or programming at all) to use it.
Nearly all molecular simulation applications ask you to write some sort of
“script” that specifies the details of the simulation to run.  With OpenMM, that
script happens to be written in Python.  But it is no harder to write than those
for most other applications, and this guide will teach you everything you need
to know.  There is even a graphical interface that can write the script for you
based on a simple set of options (see section :ref:`the-script-builder-application`),
so you never need to type a single line of code!

On the other hand, if you don’t mind doing a little programming, this approach
gives you enormous power and flexibility.  Your script has complete access to
the entire OpenMM application programming interface (API), as well as the full
power of the Python language and libraries.  You have complete control over
every detail of the simulation, from defining the molecular system to analyzing
the results.


.. _installing-openmm:

Installing OpenMM
#################

Follow these instructions to install OpenMM.  There also is an online
troubleshooting guide that describes common problems and how to fix them
(http://wiki.simtk.org/openmm/FAQApp).

Installing on Mac OS X
**********************

OpenMM works on Mac OS X 10.7 or later.  GPU acceleration is currently only
supported on Nvidia GPUs, not on AMD or Intel GPUs.

\ **Important:** A serious bug was introduced in Mac OS X 10.7.5 that prevents
OpenMM’s OpenCL platform from working correctly.  At the time of this writing,
the bug is present in all versions from 10.7.5 onward.  The CUDA platform (see
below) is not affected by the bug, so if you have an affected version of OS X,
you should use it instead of the OpenCL platform.

1. Download the pre-compiled binary of OpenMM for Mac OS X, then double click
the .zip file to expand it.

2. If you have not already done so, install Apple’s Xcode developer tools from
the App Store.  They are required to use OpenMM.  (With Xcode 4.3 and later, you
must then launch Xcode, open the Preferences window, go to the Downloads tab,
and tell it to install the command line tools.  With Xcode 4.2 and earlier, the
command line tools are automatically installed when you install Xcode.)

3. (Optional) If you have an Nvidia GPU and want to use the CUDA platform,
download CUDA 5.5 from https://developer.nvidia.com/cuda-downloads.  Be sure to
install both the drivers and toolkit.

4. (Optional) If you plan to use the CPU platform, it is recommended that you
install FFTW, available from http://www.fftw.org.  When configuring it, be sure
to specify single precision and multiple threads (the |--|\ :code:`enable-float`
and |--|\ :code:`enable-threads` options).  OpenMM will still work without FFTW,
but the performance of particle mesh Ewald (PME) will be much worse.

5. Launch the Terminal application.  Change to the OpenMM directory by typing
::

    cd <openmm_directory>
    
where :code:`<openmm_directory>` is the path to the OpenMM folder.  Then run
the install script by typing
::

    sudo ./install.sh

It will prompt you for an install location and the path to the python
executable.  Unless you are certain you know what you are doing, accept the
defaults for both options.

6. (Optional) To use the CUDA platform on an Nvidia GPU, you must add the CUDA
libraries to your library path so your computer knows where to find them.  You
can do this by typing
::

    export DYLD_LIBRARY_PATH=/usr/local/cuda/lib

This will affect only the particular Terminal window you type it into.  If you
want to run OpenMM in another Terminal window, you must type the above command
in the new window.

If you plan to use the CUDA platform, OpenMM also needs to locate the CUDA
kernel compiler (nvcc).  By default it looks for it in the location
:file:`/usr/local/cuda/bin/nvcc`.  If you have installed the CUDA toolkit in a different
location, you can set OPENMM_CUDA_COMPILER to tell OpenMM where to find it.  For
example,
::

    export OPENMM_CUDA_COMPILER=/opt/CUDA/cuda-5.5/bin/nvcc

7. Verify your installation by running the “testInstallation.py” script found in
the “examples” folder of your OpenMM installation.  To run it, cd to the
examples folder and type
::

    python testInstallation.py

This script confirms that OpenMM is installed, checks whether GPU acceleration
is available (via the OpenCL and/or CUDA platforms), and verifies that all
platforms produce consistent results.

Important Note: Some Mac laptops have two GPUs, only one of which is capable of
running OpenMM.   If you have a laptop, open the System Preferences and go to
the Energy Saver panel.  There will be a checkbox labeled “Automatic graphics
switching”, which should be disabled.  Otherwise, trying to run OpenMM may
produce an error.  You will only see this option if your laptop has two GPUs

Installing on Linux
*******************

1. Download the pre-compiled binary of OpenMM for Linux, then double click the
.zip file to expand it.

2. Make sure you have Python 2.6 or higher (earlier versions will not work) and
a C++ compiler (typically gcc or clang) installed on your computer.  You can
check what version of Python is installed by typing :code:`python` |--|\ :code:`version`
into a console window.

3. (Optional) If you want to run OpenMM on a GPU, install CUDA and/or OpenCL.

  * If you have an Nvidia GPU, download CUDA 5.5 from
    https://developer.nvidia.com/cuda-downloads.  Be sure to install both the
    drivers and toolkit.  OpenCL is included with the CUDA drivers.
  * If you have an AMD GPU, download the latest version of the Catalyst driver
    from http://support.amd.com.

4. (Optional) If you plan to use the CPU platform, it is recommended that you
install FFTW.  It is probably available through your system’s package manager
such as :code:`yum` or :code:`apt-get`\ .  Alternatively, you can download
it from http://www.fftw.org.  When configuring it, be sure to specify single
precision and multiple threads (the |--|\ :code:`enable-float` and
|--|\ :code:`enable-threads` options).  OpenMM will still work without FFTW, but the
performance of particle mesh Ewald (PME) will be much worse.

5. In a console window, change to the OpenMM directory by typing
::

    cd <openmm_directory>
    
where :code:`<openmm_directory>` is the path to the OpenMM folder.  Then run
the install script by typing
::

    sudo ./install.sh

It will prompt you for an install location and the path to the python
executable.  Unless you are certain you know what you are doing, accept the
defaults for both options.

6. (Optional) To use the CUDA platform on an Nvidia GPU, you must add the CUDA
libraries to your library path so your computer knows where to find them.  You
can do this by typing
::

    export LD_LIBRARY_PATH=/usr/local/cuda/lib

This will affect only the particular console window you type it into.  If you
want to run OpenMM in another console window, you must type the above command in
the new window.

If you plan to use the CUDA platform, OpenMM also needs to locate the CUDA
kernel compiler (nvcc).  By default it looks for it in the location
:file:`/usr/local/cuda/bin/nvcc`.  If you have installed the CUDA toolkit in a different
location, you can set OPENMM_CUDA_COMPILER to tell OpenMM where to find it.  For
example,
::

    export OPENMM_CUDA_COMPILER=/opt/CUDA/cuda-5.5/bin/nvcc

7. Verify your installation by running the “testInstallation.py” script found in
the “examples” folder of your OpenMM installation.  To run it, cd to the
examples folder and type
::

    python testInstallation.py

This script confirms that OpenMM is installed, checks whether GPU acceleration
is available (via that OpenCL and/or CUDA platforms), and verifies that all
platforms produce consistent results.


Installing on Windows
*********************

1. Download the pre-compiled binary of OpenMM for Windows, then double click the
.zip file to expand it.  Move the files to :file:`C:\\Program Files\\OpenMM`.  (On 64 bit
Windows, use :file:`C:\\Program Files (x86)\\OpenMM`).

2. Make sure you have the 32-bit version of Python 3.3 (other versions will not
work) installed on your computer.  To do this, launch the Python program (either
the command line version or the GUI version).  The first line in the Python
window will indicate the version you have, as well as whether you have a 32-bit
or 64-bit version.

3. Double click the Python API Installer to install the Python components.  (On
some versions of Windows, a “Program Compatibility Assistant” window may appear
with the warning, “This program might not have installed correctly.”  This is
just Microsoft trying to scare you.  Click “This program installed correctly”
and ignore it.)

4. (Optional) If you want to run OpenMM on a GPU, install CUDA and/or OpenCL.

  * If you have an Nvidia GPU, download CUDA 5.5 from
    https://developer.nvidia.com/cuda-downloads.  Be sure to install both the
    drivers and toolkit. For 64-bit machines, you should install the 64-bit driver,
    but download the 32-bit version of the toolkit since the OpenMM binary is
    32-bit.  OpenCL is included with the CUDA drivers.
  * If you have an AMD GPU, download the latest version of the Catalyst driver
    from http://support.amd.com.


5. (Optional) If you plan to use the CPU platform, it is recommended that you
install FFTW.  Precompiled binaries are available from http://www.fftw.org.
Even on 64-bit machines you should use the 32-bit version since the OpenMM
binary is 32-bit.  OpenMM will still work without FFTW, but the performance of
particle mesh Ewald (PME) will be much worse.

6. Before running OpenMM, you must add the OpenMM and FFTW libraries to your
PATH environment variable.  You may also need to add the Python executable to
your PATH.

  * To find out if the Python executable is already in your PATH, open a command
    prompt window by clicking on Start -> Programs -> Accessories -> Command Prompt.
    (On Windows 7, select Start -> All Programs -> Accessories -> Command Prompt).
    Type
    ::
    
        python

    If you get an error message, such as "‘python’ is not recognized as an
    internal or external command, operable program or batch file," then you need
    to add Python to your PATH.  To do so, locate it by typing
    ::

        dir C:\py*

    The files are typically located in a directory like :file:`C:\\Python33`.  Remember this
    location.  You will need to enter it, along with the location of the OpenMM
    libraries, later in this process.

  * Click on Start -> Control Panel -> System (On Windows 7, select Start ->
    Control Panel -> System and Security -> System)
  * Click on the “Advanced” tab or the “Advanced system settings” link
  * Click “Environment Variables”
  * Under “System variables,” select the line for “Path” and click “Edit…”
  * Add :file:`C:\\Program Files\\OpenMM\\lib` and :file:`C:\\Program Files\\OpenMM\\lib\\plugins`
    to the “Variable value”.  If you also need to add Python or FFTW to your
    PATH, enter their directory locations here.  Directory locations need to be
    separated by semi-colons (;).


    If you installed OpenMM somewhere other than the default location, you must also
    set OPENMM_PLUGIN_DIR to point to the plugins directory.  If this variable is
    not set, it will assume plugins are in the default location (:file:`C:\\Program
    Files\\OpenMM\\lib\\plugins` or :file:`C:\\Program Files (x86)\\OpenMM\\lib\\plugins`).

7. Verify your installation by running the “testInstallation.py” script found in
the “examples” folder of your OpenMM installation.  To run it, open a command
window, cd to the examples folder, and type
::

    python testInstallation.py

This script confirms that OpenMM is installed, checks whether GPU acceleration
is available (via that OpenCL and/or CUDA platforms), and verifies that all
platforms produce consistent results.



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 “input.pdb”, models it using the AMBER99SB force field and TIP3P water
model, energy minimizes it, simulates it for 10,000 steps with a Langevin
integrator, and saves a frame to a PDB file called “output.pdb” every 1000 time
steps.

.. samepage::
    ::

        from simtk.openmm.app import *
        from simtk.openmm import *
        from simtk.unit import *
        from sys import stdout
        
        pdb = PDBFile('input.pdb')
        forcefield = ForceField('amber99sb.xml', 'tip3p.xml')
        system = forcefield.createSystem(pdb.topology, nonbondedMethod=PME,
                nonbondedCutoff=1*nanometer, constraints=HBonds)
        integrator = LangevinIntegrator(300*kelvin, 1/picosecond, 0.002*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 “examples” folder of your OpenMM installation.
It is called “simulatePdb.py”.  To execute it from a command line, go to your
terminal/console/command prompt window (see Chapter :ref:`installing-openmm`
on setting up the window to use OpenMM).  Navigate to the “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, but their names should end with
“.py”. Let’s go through the script line by line and see how it works.
::

    from simtk.openmm.app import *
    from simtk.openmm import *
    from simtk.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 input.pdb file in the examples
directory contains the villin headpiece in explicit solvent.)  More precisely,
it creates a PDBFile object, passes the file name input.pdb to it as an
argument, and assigns the object to a variable called :code:`pdb`\ .  The
PDBFile object contains the information that was read from the file: the
molecular topology and atom positions.  Your file need not be called
“input.pdb”.  Feel free to change this line to specify any file you want.  Make
sure you include the single quotes around the file name.
::

    forcefield = ForceField('amber99sb.xml', 'tip3p.xml')

This line specifies the force field to use for the simulation.  Force fields are
defined by XML files.  Chapter :ref:`creating-force-fields` describes how to write these files,
if you are interested in that sort of thing, but you probably won’t need to.  OpenMM
includes XML files defining lots of standard force fields (see section :ref:`force-fields`).
In this case we load two of those files: amber99sb.xml, which contains the
AMBER99SB force field, and tip3p.xml, which contains the TIP3P water model.  The
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 ForceField object’s “createSystem”
function.  It creates a 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`\ ).
::

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

This line creates the integrator to use for advancing the equations of motion.
It specifies a LangevinIntegrator, which (surprise!) 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 (300K), the friction coefficient (1 ps\ :sup:`-1`\ ), and
the step size (0.002 ps).
::

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

This line combines the molecular topology, system, and integrator to begin a new
simulation.  It creates a Simulation object and assigns it to a variable called
\ :code:`simulation`\ .  A Simulation object coordinates 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 Simulation object’s list of reporters.  A PDBReporter writes
structures to a PDB file.  We specify that the output file should be called
“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
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.).

.. _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 prmtop file and an inpcrd file.  OpenMM loads the files and
creates a system from them.  This is shown in the following script.  It can be
found in OpenMM’s “examples” folder with the name “simulateAmber.py”.

.. samepage::
    ::

        from simtk.openmm.app import *
        from simtk.openmm import *
        from simtk.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 = LangevinIntegrator(300*kelvin, 1/picosecond, 0.002*picoseconds)
        simulation = Simulation(prmtop.topology, system, integrator)
        simulation.context.setPositions(inpcrd.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,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 AmberPrmtopFile and 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.
::

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

This line creates the system.  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 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 prmtop file and the atom positions
from the inpcrd file.  In the previous section, both of these came from a PDB
file, but AMBER puts the topology and positions in separate files.

.. _using_gromacs_files:

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

A third option for creating your system is to use the Gromacs setup tools.  They
produce a gro file containing the coordinates and a 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 “examples” folder
with the name “simulateGromacs.py”.

.. samepage::
    ::

        from simtk.openmm.app import *
        from simtk.openmm import *
        from simtk.unit import *
        from sys import stdout
        
        gro = GromacsGroFile('input.gro')
        top = GromacsTopFile('input.top', unitCellDimensions=gro.getUnitCellDimensions(),
                includeDir='/usr/local/gromacs/share/gromacs/top')
        system = top.createSystem(nonbondedMethod=PME, nonbondedCutoff=1*nanometer,
                constraints=HBonds)
        integrator = LangevinIntegrator(300*kelvin, 1/picosecond, 0.002*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
AmberInpcrdFile and AmberPrmtopFile with GromacsGroFile and GromacsTopFile.
Note that when we create the GromacsTopFile, we specify values for two extra
options.  First, we specify
:code:`unitCellDimensions=gro.getUnitCellDimensions()`\ .  Unlike OpenMM and
AMBER, which store the periodic unit cell dimensions with the topology, Gromacs
stores them with the coordinates.  To let GromacsTopFile create a Topology
object, we therefore need to tell it the unit cell dimensions that were loaded
from the 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 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 :numref:`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.

.. _the-script-builder-application:

The Script Builder Application
******************************

One option for writing your own scripts is to start with one of the examples
given above (the one in section :ref:`a-first-example` if you are starting from a PDB file, section
:ref:`using_amber_files` if you are starting from AMBER prmtop and inpcrd files, or section
:ref:`using_gromacs_files` if you are starting from Gromacs gro and top files), then customize it
to suit your needs.  Another option is to use the OpenMM Script Builder application.


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

   :autonumber:`Figure,script builder`:  The Script Builder application

This is a web application available at https://builder.openmm.org.  It provides
a graphical interface with simple choices for all the most common simulation
options, then automatically generates a script based on them.  As you change the
settings, the script is instantly updated to reflect them.  Once everything is
set the way you want, click the “Save Script” button to save it to disk, or
simply copy and paste it into a text editor.

.. _simulation-parameters:

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

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

Platforms
=========


When creating a Simulation, you can optionally tell it what Platform to use.
OpenMM includes four platforms: Reference, CPU, CUDA, and OpenCL.  For a
description of the differences between them, see Section :ref:`platforms`.  If you do not
specify a Platform, it will select one automatically.  Usually its choice will
be reasonable, but you may want to change it.

The following lines specify to use the CUDA Platform:
::

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

The Platform name should be :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 :ref:`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 = {'CudaDeviceIndex': '0,1', 'CudaPrecision': '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('amber99sb.xml', 'tip3p.xml')

For the main force field, OpenMM provides the following options:

.. tabularcolumns:: |l|L|

=================  ================================================================================
File               Force Field                                                                     
=================  ================================================================================
amber96.xml        AMBER96\ :cite:`Kollman1997`
amber99sb.xml      AMBER99\ :cite:`Wang2000` with modified backbone torsions\ :cite:`Hornak2006`
amber99sbildn.xml  AMBER99SB plus improved side chain torsions\ :cite:`Lindorff-Larsen2010`
amber99sbnmr.xml   AMBER99SB with modifications to fit NMR data\ :cite:`Li2010`
amber03.xml        AMBER03\ :cite:`Duan2003`
amber10.xml        AMBER10
amoeba2009.xml     AMOEBA 2009\ :cite:`Ren2002`.  This force field is deprecated.  It is 
                   recommended to use AMOEBA 2013 instead.
amoeba2013.xml     AMOEBA 2013\ :cite:`Shi2013`
=================  ================================================================================


The AMBER files do not include parameters for water molecules.  This allows you
to separately select which water model you want to use.  For simulations that
include explicit water molecules, you should also specify one of the following
files:

.. tabularcolumns:: |l|L|

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


For the AMOEBA force field, only one explicit water model is currently available
and the water parameters are included in the file :code:`amoeba2009.xml`\ .
Also the AMOEBA force field file only includes the parameters for amino acids
and ions; nucleic acids will be included in a future release.

If you want to include an implicit solvation model, you can also specify one of
the following files:

.. tabularcolumns:: |l|L|

=================  =================================================================================================
File               Implicit Solvation Model                                                                      
=================  =================================================================================================
amber96_obc.xml    GBSA-OBC solvation model\ :cite:`Onufriev2004` for use with AMBER96 force field
amber99_obc.xml    GBSA-OBC solvation model for use with AMBER99 force fields
amber03_obc.xml    GBSA-OBC solvation model for use with AMBER03 force field
amber10_obc.xml    GBSA-OBC solvation model for use with AMBER10 force field
amoeba2009_gk.xml  Generalized Kirkwood solvation model\ :cite:`Schnieders2007` for use with AMOEBA 2009 force field
amoeba2013_gk.xml  Generalized Kirkwood solvation model for use with AMOEBA 2013 force field
=================  =================================================================================================


For example, to use the GBSA-OBC solvation model with the Amber99SB force field,
you would type:
::

    forcefield = ForceField('amber99sb.xml', 'amber99_obc.xml')

If you are running a vacuum simulation, you do not need to specify a water
model.  The following line specifies the AMBER10 force field and no water model.
If you try to use it with a PDB file that contains explicit water, it will
produce an error since no water parameters are defined:
::

    forcefield = ForceField('amber10.xml')

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 most of the implicit solvent models used by AMBER.  Here are the
allowed values for :code:`implicitSolvent`\ :

.. tabularcolumns:: |l|L|

=====  ==================================================================================================================================
Value  Meaning                                                                                                                                                                                                          
=====  ==================================================================================================================================
None   No implicit solvent is used.                                                                                                                                                                                     
HCT    Hawkins-Cramer-Truhlar GBSA model\ :cite:`Hawkins1995` (corresponds to igb=1 in AMBER)                                                                                                                         
OBC1   Onufriev-Bashford-Case GBSA model\ :cite:`Onufriev2004` using the GB\ :sup:`OBC`\ I parameters (corresponds to igb=2 in AMBER).                                                                                
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 :ref:`force-fields`.
GBn    GBn solvation model\ :cite:`Mongan2007` (corresponds to igb=7 in AMBER).                                                                                                                                       
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=2.0,
            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 screening parameter:
::

    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                                                                                                                                                                                                                                    
=================  ===========================================================================================================================================================================================================================================
NoCutoff           No cutoff is applied.                                                                                                                                                                                                                      
CutoffNonPeriodic  The reaction field method is used to eliminate all interactions beyond a cutoff distance.  Not valid for AMOEBA.                                                                                                                           
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.
Ewald              Periodic boundary conditions are applied.  Ewald summation is used to compute long range interactions.  (This option is rarely used, since PME is much faster for all but the smallest systems.)  Not valid for AMOEBA.                    
PME                Periodic boundary conditions are applied.  The Particle Mesh Ewald method is used to compute long range interactions.                                                                                                                      
=================  ===========================================================================================================================================================================================================================================


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` or :code:`PME`\ , 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.


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
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

OpenMM allows the setting of several other parameters particular to the AMOEBA
force field.  The :code:`mutualInducedTargetEpsilon` option allows you to
specify the accuracy to which the induced dipoles are calculated at each time
step; the default value is 0.00001.  The :code:`polarization` setting
determines whether the calculation of the induced dipoles is continued until the
dipoles are self-consistent to within the tolerance specified by
:code:`mutualInducedTargetEpsilon` or whether a quick estimate of the induced
dipoles is used instead.  The first option corresponds to the
:code:`polarization='mutual'` setting and is the default; the quick estimate
option is given by :code:`polarization='direct'` and in this case,
:code:`mutualInducedTargetEpsilon` is ignored, if provided.  Simulations using
:code:`polarization='direct'` will be significantly faster than those with
:code:`polarization='mutual'`\ , but less accurate.  Examples using the two
options are given below:
::

    system = forcefield.createSystem(nonbondedMethod=PME,
        nonbondedCutoff=1*nanometer,ewaldErrorTolerance=0.00001,
        vdwCutoff=1.2*nanometer, mutualInducedTargetEpsilon=0.01)

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


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

For implicit solvent simulations using the AMOEBA force field, the
'amoeba2009_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 a 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                                                                                                                                      
========  =============================================================================================================================================
None      No constraints are applied.  This is the default value.                                                                                      
HBonds    The lengths of all bonds that involve a hydrogen atom are constrained.                                                                       
AllBonds  The lengths of all bonds are constrained.                                                                                                    
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.  With :code:`HBonds` constraints, this can be increased
to about 2 fs.  With :code:`HAngles`\ , it can be further increased to 3.5 or
4 fs.

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.

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


When creating the system (either from a force field or a 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 allows a
further increase in integration step size.

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.

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

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

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

The three parameter values in this line are the simulation temperature (300K),
the friction coefficient (1 ps\ :sup:`-1`\ ), and the step size (0.002 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:`0.002*picoseconds` or :code:`2*femtoseconds`\ .  They are exactly
equivalent.

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 (300K),
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.

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, add a single line to the script as shown below.  (The lines in grey
are just for context.)
::

    ...
    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 (300K) 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 = LangevinIntegrator(300*kelvin, 1/picosecond, 0.002*picoseconds)
    ...

The parameters of the Monte Carlo barostat are the pressure (1 bar) and
temperature (300K).  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))

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=10*kilojoule/mole)

If you do not specify this parameter, a default tolerance of 1 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, OpenMM 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 two formats: PDB and DCD.
Both of these are widely supported formats, so you should be able to read them
into most analysis and visualization programs.

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 PDBReporter are the output filename and how often (in
number of time steps) output structures should be written.  To use DCD format,
just replace “PDBReporter” with “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 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=' '))


Model Building and Editing
##########################

Sometimes you have a PDB file that needs some work before you can simulate it.
Maybe it doesn’t contain hydrogen atoms (which is common for structures
determined by x-ray crystallography), so you need to add them.  Or perhaps you
want to simulate the system in explicit water, but the PDB file doesn’t contain
water molecules.  Or maybe it does contain water molecules, but they contain the
wrong number of interaction sites for the water model you want to use.  OpenMM’s
Modeller class can fix problems such as these.

To use it, create a Modeller object, providing the initial Topology and atom
positions.  You then can invoke various modelling functions on it.  Each one
modifies the system in some way, creating a new Topology and list of positions.
When you are all done, you can retrieve them from the Modeller and use them as
the starting point for your simulation:

.. samepage::
    ::

        ...
        pdb = PDBFile('input.pdb')
        modeller = Modeller(pdb.topology, pdb.positions)
        # ... Call some modelling functions here ...
        system = forcefield.createSystem(modeller.topology, nonbondedMethod=PME)
        simulation = Simulation(modeller.topology, system, integrator)
        simulation.context.setPositions(modeller.positions)

    .. caption::

        :autonumber:`Example,Modeller outline`

Now let’s consider the particular functions you can call.

Adding Hydrogens
****************

Call the addHydrogens function to add missing hydrogen atoms:
::

    modeller.addHydrogens(forcefield)

The force field is needed to determine the positions for the hydrogen atoms.  If
the system already contains some hydrogens but is missing others, that is fine.
The Modeller will recognize the existing ones and figure out which ones need to
be added.

Some residues can exist in different protonation states depending on the pH and
on details of the local environment.  By default it assumes pH 7, but you can
specify a different value:
::

    modeller.addHydrogens(forcefield, pH=5.0)

For each residue, it selects the protonation state that is most common at the
specified pH.  In the case of Cysteine residues, it also checks whether the
residue participates in a disulfide bond when selecting the state to use.
Histidine has two different protonation states that are equally likely at
neutral pH.  It therefore selects which one to use based on which will form a
better hydrogen bond.

If you want more control, it is possible to specify exactly which protonation
state to use for particular residues.  For details, consult the API
documentation for the Modeller class.

Adding Solvent
**************

Call addSolvent to create a box of solvent (water and ions) around the model:
::

    modeller.addSolvent(forcefield)

This constructs a box of water around the solute, ensuring that no water
molecule comes closer to any solute atom than the sum of their van der Waals
radii.  It also determines the charge of the solute, and adds enough positive or
negative ions to make the system neutral.

When called as shown above, addSolvent expects that periodic box dimensions were
specified in the PDB file, and it uses them as the size for the water box.  If
your PDB file does not specify a box size, or if you want to use a different
size, you can specify one:
::

    modeller.addSolvent(forcefield, boxSize=Vec3(5.0, 3.5, 3.5)*nanometers)

This requests a 5 nm by 3.5 nm by 3.5 nm box.  Another option is to specify a
padding distance:
::

    modeller.addSolvent(forcefield, padding=1.0*nanometers)

This determines the largest size of the solute along any axis (x, y, or z).  It
then creates a cubic box of width (solute size)+2*(padding).  The above line
guarantees that no part of the solute comes closer than 1 nm to any edge of the
box.

By default, addSolvent creates TIP3P water molecules, but it also supports other
water models:
::

    modeller.addSolvent(forcefield, model='tip5p')

Allowed values for the :code:`model` option are 'tip3p', 'spce', 'tip4pew',
and 'tip5p'.  Be sure to include the single quotes around the value.

Another option is to add extra ion pairs to give a desired total ionic strength.
For example:
::

    modeller.addSolvent(forcefield, ionicStrength=0.1*molar)

This solvates the system with a salt solution whose ionic strength is 0.1 molar.
Note that when computing the ionic strength, it does *not* consider the ions
that were added to neutralize the solute.  It assumes those are bound to the
solute and do not contribute to the bulk ionic strength.

By default, Na\ :sup:`+` and Cl\ :sup:`-` ions are used, but you can specify
different ones using the :code:`positiveIon` and :code:`negativeIon`
options.  For example, this creates a potassium chloride solution:
::

    modeller.addSolvent(forcefield, ionicStrength=0.1*molar, positiveIon='K+')

Allowed values for :code:`positiveIon` are 'Cs+', 'K+', 'Li+', 'Na+', and
'Rb+'.  Allowed values for :code:`negativeIon` are 'Cl-', 'Br-', 'F-', and
'I-'.  Be sure to include the single quotes around the value.  Also be aware
some force fields do not include parameters for all of these ion types, so you
need to use types that are supported by your chosen force field.

Adding or Removing Extra Particles
**********************************

“Extra particles” are particles that do not represent ordinary atoms.  This
includes the virtual interaction sites used in many water models, Drude
particles, etc.  If you are using a force field that involves extra particles,
you must add them to the Topology.  To do this, call:
::

    modeller.addExtraParticles(forcefield)

This looks at the force field to determine what extra particles are needed, then
modifies each residue to include them.  This function can remove extra particles
as well as adding them.

Removing Water
**************

Call deleteWater to remove all water molecules from the system:
::

    modeller.deleteWater()

This is useful, for example, if you want to simulate it with implicit solvent.
Be aware, though, that this only removes water molecules, not ions or other
small molecules that might be considered “solvent”.

Saving The Results
******************

Once you have finished editing your model, you can immediately use the resulting
Topology and atom positions as the input to a Simulation.  If you plan to
simulate it many times, though, it is usually better to save the result to a new
PDB file, then use that as the input for the simulations.  This avoids the cost
of repeating the modeling operations at the start of every simulation, and also
ensures that all your simulations are really starting from exactly the same
structure.

The following example loads a PDB file, adds missing hydrogens, builds a solvent
box around it, performs an energy minimization, and saves the result to a new
PDB file.

.. samepage::
    ::

        from simtk.openmm.app import *
        from simtk.openmm import *
        from simtk.unit import *
        
        print('Loading...')
        pdb = PDBFile('input.pdb')
        forcefield = ForceField('amber99sb.xml', 'tip3p.xml')
        modeller = Modeller(pdb.topology, pdb.positions)
        print('Adding hydrogens...')
        modeller.addHydrogens(forcefield)
        print('Adding solvent...')
        modeller.addSolvent(forcefield, model='tip3p', padding=1*nanometer)
        print('Minimizing...')
        system = forcefield.createSystem(modeller.topology, nonbondedMethod=PME)
        integrator = VerletIntegrator(0.001*picoseconds)
        simulation = Simulation(modeller.topology, system, integrator)
        simulation.context.setPositions(modeller.positions)
        simulation.minimizeEnergy(maxIterations=100)
        print('Saving...')
        positions = simulation.context.getState(getPositions=True).getPositions()
        PDBFile.writeFile(simulation.topology, positions, open('output.pdb', 'w'))
        print('Done')

    .. caption::

        :autonumber:`Example,Modeller complete`


Advanced Simulation Examples
############################

In the previous chapter, we looked at some basic scripts for running simulations
and saw lots of ways to customize them.  If that is all you want to do—run
straightforward molecular simulations—you already know everything you need to
know.  Just use the example scripts and customize them in the ways described in
section :ref:`simulation-parameters`.

OpenMM can do far more than that.  Your script has the full OpenMM API at its
disposal, along with all the power of the Python language and libraries.  In
this chapter, we will consider some examples that illustrate more advanced
techniques.  Remember that these are still only examples; it would be impossible
to give an exhaustive list of everything OpenMM can do.  Hopefully they will
give you a sense of what is possible, and inspire you to experiment further on
your own.

Starting in this section, we will assume some knowledge of programming, as well
as familiarity with the OpenMM API.  Consult the OpenMM Users Guide and API
documentation if you are uncertain about how something works.   You can also use
the Python “help” command.  For example,
::

    help(Simulation)

will print detailed documentation on the Simulation class.

Simulated Annealing
*******************

Here is a very simple example of how to do simulated annealing.  The following
lines linearly reduce the temperature from 300K to 0K in 100 increments,
executing 1000 time steps at each temperature:

.. samepage::
    ::

        ...
        simulation.context.setPositions(pdb.positions)
        simulation.minimizeEnergy()
        for i in range(100):
            integrator.setTemperature(3*(100-i)*kelvin)
            simulation.step(1000)

    .. caption::

        :autonumber:`Example,simulated annealing`

This code needs very little explanation.  The loop is executed 100 times.  Each
time through, it adjusts the temperature of the LangevinIntegrator and then
calls :code:`step(1000)` to take 1000 time steps.

Applying an External Force to Particles: a Spherical Container
**************************************************************

In this example, we will simulate a non-periodic system contained inside a
spherical container with radius 2 nm.  We implement the container by applying a
harmonic potential to every particle:

.. math::
    \begin{array}{lll}
    E(r) = & 0          & r\le2\\
           & 100(r-2)^2 & r>2
    \end{array}

where *r* is the distance of the particle from the origin, measured in nm.
We can easily do this using OpenMM’s CustomExternalForce class.  This class
applies a force to some or all of the particles in the system, where the energy
is an arbitrary function of each particle’s (\ *x*\ , *y*\ , *z*\ )
coordinates.  Here is the code to do it:

.. samepage::
    ::

        ...
        system = forcefield.createSystem(pdb.topology, nonbondedMethod=CutoffNonPeriodic,
                nonbondedCutoff=1*nanometer, constraints=None)
        force = CustomExternalForce('100*max(0, r-2)^2; r=sqrt(x*x+y*y+z*z)')
        system.addForce(force)
        for i in range(system.getNumParticles()):
            force.addParticle(i, [])
        integrator = LangevinIntegrator(300*kelvin, 91/picosecond, 0.002*picoseconds)
        ...

    .. caption::

        :autonumber:`Example,spherical container`

The first thing it does is create a CustomExternalForce object and add it to the
System.  The argument to CustomExternalForce is a mathematical expression
specifying the energy of each particle.  This can be any function of *x*\ ,
*y*\ , and *z* you want.  It also can depend on global or per-particle
parameters.  A wide variety of restraints, steering forces, shearing forces,
etc. can be implemented with this method.

Next it must specify which particles to apply the force to.  In this case, we
want it to affect every particle in the system, so we loop over them and call
:code:`addParticle()` once for each one.  The two arguments are the index of
the particle to affect, and the list of per-particle parameter values (an empty
list in this case).  If we had per-particle parameters, such as to make the
force stronger for some particles than for others, this is where we would
specify them.

Notice that we do all of this immediately after creating the System.  That is
not an arbitrary choice.

.. warning::

    If you add new forces to a System, you must do so before creating the Simulation.
    Once you create a Simulation, modifying the System will have no effect on that Simulation.

Extracting and Reporting Forces (and other data)
************************************************

OpenMM provides reporters for two output formats: PDB and DCD.  Both of those
formats store only positions, not velocities, forces, or other data.  In this
section, we create a new reporter that outputs forces.  This illustrates two
important things: how to write a reporter, and how to query the simulation for
forces or other data.

Here is the definition of the ForceReporter class:

.. samepage::
    ::
    
        class ForceReporter(object):
            def __init__(self, file, reportInterval):
                self._out = open(file, 'w')
                self._reportInterval = reportInterval
        
            def __del__(self):
                self._out.close()
            
            def describeNextReport(self, simulation):
                steps = self._reportInterval - simulation.currentStep%self._reportInterval
                return (steps, False, False, True, False)
            
            def report(self, simulation, state):
                forces = state.getForces().value_in_unit(kilojoules/mole/nanometer)
                for f in forces:
                    print >>self._out, f[0], f[1], f[2]

    .. caption::

        :autonumber:`Example,ForceReporter`

The constructor and destructor are straightforward.  The arguments to the
constructor are the output filename and the interval (in time steps) at which it
should generate reports.  It opens the output file for writing and records the
reporting interval.  The destructor closes the file.

We then have two methods that every reporter must implement:
:code:`describeNextReport()` and :code:`report()`\ .  A Simulation object
periodically calls :code:`describeNextReport()` on each of its reporters to
find out when that reporter will next generate a report, and what information
will be needed to generate it.  The return value should be a five element tuple,
whose elements are as follows:

* The number of time steps until the next report.  We calculate this as
  *(report interval)*\ -\ *(current step)*\ %\ *(report interval)*\ .  For
  example, if we want a report every 100 steps and the simulation is currently on
  step 530, we will return 100-(530%100) = 70.
* Whether the next report will need particle positions.
* Whether the next report will need particle velocities.
* Whether the next report will need forces.
* Whether the next report will need energies.


When the time comes for the next scheduled report, the Simulation calls
:code:`report()` to generate the report.  The arguments are the Simulation
object, and a State that is guaranteed to contain all the information that was
requested by :code:`describeNextReport()`\ .  A State object contains a
snapshot of information about the simulation, such as forces or particle
positions.  We call :code:`getForces()` to retrieve the forces and convert
them to the units we want to output (kJ/mole/nm).  Then we loop over each value
and write it to the file.  To keep the example simple, we just print the values
in text format, one line per particle.  In a real program, you might choose a
different output format.

Now that we have defined this class, we can use it exactly like any other
reporter.  For example,
::

    simulation.reporters.append(ForceReporter('forces.txt', 100))

will output forces to a file called “forces.txt” every 100 time steps.

Computing Energies
******************

This example illustrates a different sort of analysis.  Instead of running a
simulation, assume we have already identified a set of structures we are
interested in.  These structures are saved in a set of PDB files.  We want to
loop over all the files in a directory, load them in one at a time, and compute
the potential energy of each one.  Assume we have already created our System and
Simulation.  The following lines perform the analysis:

.. samepage::
    ::

        import os
        for file in os.listdir('structures'):
            pdb = PDBFile(os.path.join('structures', file))
            simulation.context.setPositions(pdb.positions)
            state = simulation.context.getState(getEnergy=True)
            print file, state.getPotentialEnergy()

    .. caption::

        :autonumber:`Example,computing energies`

We use Python’s :code:`listdir()` function to list all the files in the
directory.  We create a PDBFile object for each one and call
:code:`setPositions()` on the Context to specify the particle positions loaded
from the PDB file.  We then compute the energy by calling :code:`getState()`
with the option :code:`getEnergy=True`\ , and print it to the console along
with the name of the file.


.. _creating-force-fields:

Creating Force Fields
#####################

OpenMM uses a simple XML file format to describe force fields.  It includes many
common force fields, but you can also create your own.  A force field can use
all the standard OpenMM force classes, as well as the very flexible custom force
classes.  You can even extend the ForceField class to add support for completely
new forces, such as ones defined in plugins.  This makes it a powerful tool for
force field development.

Basic Concepts
**************

Let’s start by considering how OpenMM defines a force field.  There are a small
number of basic concepts to understand.

Atom Types and Atom Classes
===========================

Force field parameters are assigned to atoms based on their “atom types”.  Atom
types should be the most specific identification of an atom that will ever be
needed.  Two atoms should have the same type only if the force field will always
treat them identically in every way.

Multiple atom types can be grouped together into “atom classes”.  In general,
two types should be in the same class if the force field usually (but not
necessarily always) treats them identically.  For example, the :math:`\alpha`\ -carbon of an
alanine residue will probably have a different atom type than the :math:`\alpha`\ -carbon of a
leucine residue, but both of them will probably have the same atom class.

All force field parameters can be specified either by atom type or atom class.
Classes exist as a convenience to make force field definitions more compact.  If
necessary, you could define everything in terms of atom types, but when many
types all share the same parameters, it is convenient to only have to specify
them once.

Residue Templates
=================

Types are assigned to atoms by matching residues to templates.  A template
specifies a list of atoms, the type of each one, and the bonds between them.
For each residue in the PDB file, the force field searches its list of templates
for one that has an identical set of atoms with identical bonds between them.
When matching templates, neither the order of the atoms nor their names matter;
it only cares about their elements and the set of bonds between them.  (The PDB
file reader does care about names, of course, since it needs to figure out which
atom each line of the file corresponds to.)

Forces
======

Once a force field has defined its atom types and residue templates, it must
define its force field parameters.  This generally involves one block of XML for
each Force object that will be added to the System.  The details are different
for each Force, but it generally consists of a set of rules for adding
interactions based on bonds and atom types or classes.  For example, when adding
a HarmonicBondForce, the force field will loop over every pair of bonded atoms,
check their types and classes, and see if they match any of its rules.  If so,
it will call :code:`addBond()` on the HarmonicBondForce.  If none of them
match, it simply ignores that pair and continues.

Writing the XML File
********************

The root element of the XML file must be a :code:`<ForceField>` tag:

.. code-block:: xml

    <ForceField>
    ...
    </ForceField>

The :code:`<ForceField>` tag contains the following children:

* An :code:`<AtomTypes>` tag containing the atom type definitions
* A :code:`<Residues>` tag containing the residue template definitions
* Zero or more tags defining specific forces


The order of these tags does not matter.  They are described in details below.

<AtomTypes>
===========

The atom type definitions look like this:

.. code-block:: xml

    <AtomTypes>
     <Type name="0" class="N" element="N" mass="14.00672"/>
     <Type name="1" class="H" element="H" mass="1.007947"/>
     <Type name="2" class="CT" element="C" mass="12.01078"/>
     ...
    </AtomTypes>

There is one :code:`<Type>` tag for each atom type.  It specifies the name
of the type, the name of the class it belongs to, the symbol for its element,
and its mass in amu.  The names are arbitrary strings: they need not be numbers,
as in this example.  The only requirement is that all types have unique names.
The classes are also arbitrary strings, and in general will not be unique.  Two
types belong to the same class if they list the same value for the
:code:`class` attribute.

<Residues>
==========

The residue template definitions look like this:

.. code-block:: xml

    <Residues>
     <Residue name="ACE">
      <Atom name="HH31" type="710"/>
      <Atom name="CH3" type="711"/>
      <Atom name="HH32" type="710"/>
      <Atom name="HH33" type="710"/>
      <Atom name="C" type="712"/>
      <Atom name="O" type="713"/>
      <Bond from="0" to="1"/>
      <Bond from="1" to="2"/>
      <Bond from="1" to="3"/>
      <Bond from="1" to="4"/>
      <Bond from="4" to="5"/>
      <ExternalBond from="4"/>
     </Residue>
     <Residue name="ALA">
      ...
     </Residue>
     ...
    </Residues>

There is one :code:`<Residue>` tag for each residue template.  That in turn
contains the following tags:

* An :code:`<Atom>` tag for each atom in the residue.  This specifies the
  name of the atom and its atom type.
* A :code:`<Bond>` tag for each pair of atoms that are bonded to each
  other.  The :code:`to` and :code:`from` attributes are the indices of
  the two bonded atoms (starting from 0) in the order they were listed.  For
  example, :code:`<Bond from="1" to="3"/>` describes a bond between atom CH3
  and atom HH33.
* An :code:`<ExternalBond>` tag for each atom that will be bonded to an
  atom of a different residue.


The :code:`<Residue>` tag may also contain :code:`<VirtualSite>` tags,
as in the following example:

.. code-block:: xml

    <Residue name="HOH">
     <Atom name="O" type="tip4pew-O"/>
     <Atom name="H1" type="tip4pew-H"/>
     <Atom name="H2" type="tip4pew-H"/>
     <Atom name="M" type="tip4pew-M"/>
     <VirtualSite type="average3" index="3" atom1="0" atom2="1" atom3="2"
         weight1="0.786646558" weight2="0.106676721" weight3="0.106676721"/>
     <Bond from="0" to="1"/>
     <Bond from="0" to="2"/>
    </Residue>

Each :code:`<VirtualSite>` tag indicates an atom in the residue that should
be represented with a virtual site.  The :code:`type` attribute may equal
:code:`"average2"`\ , :code:`"average3"`\ , or :code:`"outOfPlane"`\ , which
correspond to the TwoParticleAverageSite, ThreeParticleAverageSite, and
OutOfPlaneSite classes respectively.  The :code:`index` attribute gives the
index (starting from 0) of the atom to represent with a virtual site.  The atoms
it is calculated based on are specified by :code:`atom1`\ , :code:`atom2`\ ,
and (for virtual site classes that involve three atoms) :code:`atom3`\ .  The
remaining attributes are specific to the virtual site class, and specify the
parameters for calculating the site position.  For a TwoParticleAverageSite,
they are :code:`weight1` and :code:`weight2`\ .  For a
ThreeParticleAverageSite, they are :code:`weight1`\ , :code:`weight2`\ , and
\ :code:`weight3`\ . For an OutOfPlaneSite, they are :code:`weight12`\ ,
:code:`weight13`\ , and :code:`weightCross`\ .


<HarmonicBondForce>
===================

To add a HarmonicBondForce to the System, include a tag that looks like this:

.. code-block:: xml

    <HarmonicBondForce>
     <Bond class1="C" class2="C" length="0.1525" k="259408.0"/>
     <Bond class1="C" class2="CA" length="0.1409" k="392459.2"/>
     <Bond class1="C" class2="CB" length="0.1419" k="374049.6"/>
     ...
    </HarmonicBondForce>

Every :code:`<Bond>` tag defines a rule for creating harmonic bond
interactions between atoms.  Each tag may identify the atoms either by type
(using the attributes :code:`type1` and :code:`type2`\ ) or by class
(using the attributes :code:`class1` and :code:`class2`\ ).  For every
pair of bonded atoms, the force field searches for a rule whose atom types or
atom classes match the two atoms.  If it finds one, it calls
:code:`addBond()` on the HarmonicBondForce with the specified parameters.
Otherwise, it ignores that pair and continues.  :code:`length` is the
equilibrium bond length in nm, and :code:`k` is the spring constant in
kJ/mol/nm\ :sup:`2`\ .

<HarmonicAngleForce>
====================

To add a HarmonicAngleForce to the System, include a tag that looks like this:

.. code-block:: xml

    <HarmonicAngleForce>
     <Angle class1="C" class2="C" class3="O" angle="2.094" k="669.44"/>
     <Angle class1="C" class2="C" class3="OH" angle="2.094" k="669.44"/>
     <Angle class1="CA" class2="C" class3="CA" angle="2.094" k="527.184"/>
     ...
    </HarmonicAngleForce>

Every :code:`<Angle>` tag defines a rule for creating harmonic angle
interactions between triplets of atoms.  Each tag may identify the atoms either
by type (using the attributes :code:`type1`\ , :code:`type2`\ , ...) or by
class (using the attributes :code:`class1`\ , :code:`class2`\ , ...).  The
force field identifies every set of three atoms in the system where the first is
bonded to the second, and the second to the third.  For each one, it searches
for a rule whose atom types or atom classes match the three atoms.  If it finds
one, it calls :code:`addAngle()` on the HarmonicAngleForce with the
specified parameters.  Otherwise, it ignores that set and continues.
:code:`angle` is the equilibrium angle in radians, and :code:`k` is the
spring constant in kJ/mol/radian\ :sup:`2`\ .

<PeriodicTorsionForce>
======================

To add a PeriodicTorsionForce to the System, include a tag that looks like this:

.. code-block:: xml

    <PeriodicTorsionForce>
     <Proper class1="HC" class2="CT" class3="CT" class4="CT" periodicity1="3" phase1="0.0"
         k1="0.66944"/>
     <Proper class1="HC" class2="CT" class3="CT" class4="HC" periodicity1="3" phase1="0.0"
         k1="0.6276"/>
     ...
     <Improper class1="N" class2="C" class3="CT" class4="O" periodicity1="2"
         phase1="3.14159265359" k1="4.6024"/>
     <Improper class1="N" class2="C" class3="CT" class4="H" periodicity1="2"
         phase1="3.14159265359" k1="4.6024"/>
     ...
    </PeriodicTorsionForce>

Every child tag defines a rule for creating periodic torsion interactions
between sets of four atoms.  Each tag may identify the atoms either by type
(using the attributes :code:`type1`\ , :code:`type2`\ , ...) or by class
(using the attributes :code:`class1`\ , :code:`class2`\ , ...).

The force field recognizes two different types of torsions: proper and improper.
A proper torsion involves four atoms that are bonded in sequence: 1 to 2, 2 to
3, and 3 to 4.  An improper torsion involves a central atom and three others
that are bonded to it: atoms 2, 3, and 4 are all bonded to atom 1.  The force
field begins by identifying every set of atoms in the system of each of these
types. For each one, it searches for a rule whose atom types or atom classes
match the four atoms.  If it finds one, it calls :code:`addTorsion()` on the
PeriodicTorsionForce with the specified parameters.  Otherwise, it ignores that
set and continues.  :code:`periodicity1` is the periodicity of the torsion,
\ :code:`phase1` is the phase offset in radians, and :code:`k1` is the
force constant in kJ/mol.

Each torsion definition can specify multiple periodic torsion terms to add to
its atoms.  To add a second one, just add three more attributes:
:code:`periodicity2`\ , :code:`phase2`\ , and :code:`k2`\ .  You can have as
many terms as you want.  Here is an example of a rule that adds three torsion
terms to its atoms:

.. code-block:: xml

    <Proper class1="CT" class2="CT" class3="CT" class4="CT"
        periodicity1="3" phase1="0.0" k1="0.75312"
        periodicity2="2" phase2="3.14159265359" k2="1.046"
        periodicity3="1" phase3="3.14159265359" k3="0.8368"/>

You can also use wildcards when defining torsions.  To do this, simply leave the
type or class name for an atom empty.  That will cause it to match any atom.
For example, the following definition will match any sequence of atoms where the
second atom has class OS and the third has class P:

.. code-block:: xml

    <Proper class1="" class2="OS" class3="P" class4="" periodicity1="3" phase1="0.0" k1="1.046"/>

<RBTorsionForce>
================

To add an RBTorsionForce to the System, include a tag that looks like this:

.. code-block:: xml

    <RBTorsionForce>
     <Proper class1="CT" class2="CT" class3="OS" class4="CT" c0="2.439272" c1="4.807416"
         c2="-0.8368" c3="-6.409888" c4="0" c5="0" />
     <Proper class1="C" class2="N" class3="CT" class4="C" c0="10.46" c1="-3.34720"
         c2="-7.1128" c3="0" c4="0" c5="0" />
     ...
     <Improper class1="N" class2="C" class3="CT" class4="O" c0="0.8368" c1="0"
         c2="-2.76144" c3="0" c4="3.3472" c5="0" />
     <Improper class1="N" class2="C" class3="CT" class4="H" c0="29.288" c1="-8.368"
         c2="-20.92" c3="0" c4="0" c5="0" />
     ...
    </RBTorsionForce>

Every child tag defines a rule for creating Ryckaert-Bellemans torsion
interactions between sets of four atoms.  Each tag may identify the atoms either
by type (using the attributes :code:`type1`\ , :code:`type2`\ , ...) or by
class (using the attributes :code:`class1`\ , :code:`class2`\ , ...).

The force field recognizes two different types of torsions: proper and improper.
A proper torsion involves four atoms that are bonded in sequence: 1 to 2, 2 to
3, and 3 to 4.  An improper torsion involves a central atom and three others
that are bonded to it: atoms 2, 3, and 4 are all bonded to atom 1.  The force
field begins by identifying every set of atoms in the system of each of these
types. For each one, it searches for a rule whose atom types or atom classes
match the four atoms.  If it finds one, it calls :code:`addTorsion()` on the
RBTorsionForce with the specified parameters.  Otherwise, it ignores that set
and continues.  The attributes :code:`c0` through :code:`c5` are the
coefficients of the terms in the Ryckaert-Bellemans force expression.

You can also use wildcards when defining torsions.  To do this, simply leave the
type or class name for an atom empty.  That will cause it to match any atom.
For example, the following definition will match any sequence of atoms where the
second atom has class OS and the third has class P:

.. code-block:: xml

    <Proper class1="" class2="OS" class3="P" class4="" c0="2.439272" c1="4.807416"
        c2="-0.8368" c3="-6.409888" c4="0" c5="0" />

<CMAPTorsionForce>
==================

To add a CMAPTorsionForce to the System, include a tag that looks like this:

.. code-block:: xml

    <CMAPTorsionForce>
     <Map>
      0.0 0.809 0.951 0.309
      -0.587 -1.0 -0.587 0.309
      0.951 0.809 0.0 -0.809
      -0.951 -0.309 0.587 1.0
     </Map>
     <Torsion map="0" class1="CT" class2="CT" class3="C" class4="N" class5="CT"/>
     <Torsion map="0" class1="N" class2="CT" class3="C" class4="N" class5="CT"/>
     ...
    </CMAPTorsionForce>

Each :code:`<Map>` tag defines an energy correction map.  Its content is the
list of energy values in kJ/mole, listed in the correct order for
CMAPTorsionForce’s :code:`addMap()` method and separated by white space.
See the API documentation for details.  The size of the map is determined from
the number of energy values.

Each :code:`<Torsion>` tag defines a rule for creating CMAP torsion
interactions between sets of five atoms.  The tag may identify the atoms either
by type (using the attributes :code:`type1`\ , :code:`type2`\ , ...) or by
class (using the attributes :code:`class1`\ , :code:`class2`\ , ...).  The
force field identifies every set of five atoms that are bonded in sequence: 1 to
2, 2 to 3, 3 to 4, and 4 to 5.  For each one, it searches for a rule whose atom
types or atom classes match the five atoms.  If it finds one, it calls
:code:`addTorsion()` on the CMAPTorsionForce with the specified parameters.
Otherwise, it ignores that set and continues.  The first torsion is defined by
the sequence of atoms 1-2-3-4, and the second one by atoms 2-3-4-5.
:code:`map` is the index of the map to use, starting from 0, in the order they
are listed in the file.

You can also use wildcards when defining torsions.  To do this, simply leave the
type or class name for an atom empty.  That will cause it to match any atom.
For example, the following definition will match any sequence of five atoms
where the middle three have classes CT, C, and N respectively:

.. code-block:: xml

    <Torsion map="0" class1="" class2="CT" class3="C" class4="N" class5=""/>

<NonbondedForce>
================

To add a NonbondedForce to the System, include a tag that looks like this:

.. code-block:: xml

    <NonbondedForce coulomb14scale="0.833333" lj14scale="0.5">
     <Atom type="0" charge="-0.4157" sigma="0.32499" epsilon="0.71128"/>
     <Atom type="1" charge="0.2719" sigma="0.10690" epsilon="0.06568"/>
     <Atom type="2" charge="0.0337" sigma="0.33996" epsilon="0.45772"/>
     ...
    </NonbondedForce>

The :code:`<NonbondedForce>` tag has two attributes
:code:`coulomb14scale` and :code:`lj14scale` that specify the scale
factors between pairs of atoms separated by three bonds.  After setting the
nonbonded parameters for all atoms, the force field calls
:code:`createExceptionsFromBonds()` on the NonbondedForce, passing in these
scale factors as arguments.

Each :code:`<Atom>` tag specifies the nonbonded parameters for one atom type
(specified with the :code:`type` attribute) or atom class (specified with
the :code:`class` attribute).  It is fine to mix these two methods, having
some tags specify a type and others specify a class.  However you do it, you
must make sure that a unique set of parameters is defined for every atom type.
:code:`charge` is measured in units of the proton charge, :code:`sigma`
is in nm, and :code:`epsilon` is in kJ/mole.

<GBSAOBCForce>
==============

To add a GBSAOBCForce to the System, include a tag that looks like this:

.. code-block:: xml

    <GBSAOBCForce>
     <Atom type="0" charge="-0.4157" radius="0.1706" scale="0.79"/>
     <Atom type="1" charge="0.2719" radius="0.115" scale="0.85"/>
     <Atom type="2" charge="0.0337" radius="0.19" scale="0.72"/>
     ...
    </GBSAOBCForce>

Each :code:`<Atom>` tag specifies the OBC parameters for one atom type
(specified with the :code:`type` attribute) or atom class (specified with
the :code:`class` attribute).  It is fine to mix these two methods, having
some tags specify a type and others specify a class.  However you do it, you
must make sure that a unique set of parameters is defined for every atom type.
:code:`charge` is measured in units of the proton charge, :code:`radius`
is the GBSA radius in nm, and :code:`scale` is the OBC scaling factor.

<CustomBondForce>
=================

To add a CustomBondForce to the System, include a tag that looks like this:

.. code-block:: xml

    <CustomBondForce energy="scale*k*(r-r0)^2">
     <GlobalParameter name="scale" defaultValue="0.5"/>
     <PerBondParameter name="k"/>
     <PerBondParameter name="r0"/>
     <Bond class1="OW" class2="HW" r0="0.09572" k="462750.4"/>
     <Bond class1="HW" class2="HW" r0="0.15136" k="462750.4"/>
     <Bond class1="C" class2="C" r0="0.1525" k="259408.0"/>
     ...
    </CustomBondForce>

The energy expression for the CustomBondForce is specified by the
:code:`energy` attribute.  This is a mathematical expression that gives the
energy of each bond as a function of its length *r*\ .  It also may depend on
an arbitrary list of global or per-bond parameters.  Use a
:code:`<GlobalParameter>` tag to define a global parameter, and a
:code:`<PerBondParameter>` tag to define a per-bond parameter.

Every :code:`<Bond>` tag defines a rule for creating custom bond
interactions between atoms.  Each tag may identify the atoms either by type
(using the attributes :code:`type1` and :code:`type2`\ ) or by class
(using the attributes :code:`class1` and :code:`class2`\ ).  For every
pair of bonded atoms, the force field searches for a rule whose atom types or
atom classes match the two atoms.  If it finds one, it calls
:code:`addBond()` on the CustomBondForce.  Otherwise, it ignores that pair and
continues.  The remaining attributes are the values to use for the per-bond
parameters.  All per-bond parameters must be specified for every
:code:`<Bond>` tag, and the attribute name must match the name of the
parameter.  For instance, if there is a per-bond parameter with the name “k”,
then every :code:`<Bond>` tag must include an attribute called :code:`k`\ .

<CustomAngleForce>
==================

To add a CustomAngleForce to the System, include a tag that looks like this:

.. code-block:: xml

    <CustomAngleForce energy="scale*k*(theta-theta0)^2">
     <GlobalParameter name="scale" defaultValue="0.5"/>
     <PerAngleParameter name="k"/>
     <PerAngleParameter name=" theta0"/>
     <Angle class1="HW" class2="OW" class3="HW" theta0="1.824218" k="836.8"/>
     <Angle class1="HW" class2="HW" class3="OW" theta0="2.229483" k="0.0"/>
     <Angle class1="C" class2="C" class3="O" theta0="2.094395" k="669.44"/>
     ...
    </CustomAngleForce>

The energy expression for the CustomAngleForce is specified by the
:code:`energy` attribute.  This is a mathematical expression that gives the
energy of each angle as a function of the angle *theta*\ .  It also may depend
on an arbitrary list of global or per-angle parameters.  Use a
:code:`<GlobalParameter>` tag to define a global parameter, and a
:code:`<PerAngleParameter>` tag to define a per-angle parameter.

Every :code:`<Angle>` tag defines a rule for creating custom angle
interactions between triplets of atoms.  Each tag may identify the atoms either
by type (using the attributes :code:`type1`\ , :code:`type2`\ , ...) or by
class (using the attributes :code:`class1`\ , :code:`class2`\ , ...).  The
force field identifies every set of three atoms in the system where the first is
bonded to the second, and the second to the third.  For each one, it searches
for a rule whose atom types or atom classes match the three atoms.  If it finds
one, it calls :code:`addAngle()` on the CustomAngleForce.  Otherwise, it
ignores that set and continues. The remaining attributes are the values to use
for the per-angle parameters. All per-angle parameters must be specified for
every :code:`<Angle>` tag, and the attribute name must match the name of the
parameter.  For instance, if there is a per-angle parameter with the name “k”,
then every :code:`<Angle>` tag must include an attribute called :code:`k`\ .

<CustomTorsionForce>
====================

To add a CustomTorsionForce to the System, include a tag that looks like this:

.. code-block:: xml

    <CustomTorsionForce energy="scale*k*(1+cos(per*theta-phase))">
     <GlobalParameter name="scale" defaultValue="1"/>
     <PerTorsionParameter name="k"/>
     <PerTorsionParameter name="per"/>
     <PerTorsionParameter name="phase"/>
     <Proper class1="HC" class2="CT" class3="CT" class4="CT" per="3" phase="0.0" k="0.66944"/>
     <Proper class1="HC" class2="CT" class3="CT" class4="HC" per="3" phase="0.0" k="0.6276"/>
     ...
     <Improper class1="N" class2="C" class3="CT" class4="O" per="2" phase="3.14159265359"
         k="4.6024"/>
     <Improper class1="N" class2="C" class3="CT" class4="H" per="2" phase="3.14159265359"
         k="4.6024"/>
     ...
    </CustomTorsionForce>

The energy expression for the CustomTorsionForce is specified by the
:code:`energy` attribute.  This is a mathematical expression that gives the
energy of each torsion as a function of the angle *theta*\ .  It also may
depend on an arbitrary list of global or per-torsion parameters.  Use a
:code:`<GlobalParameter>` tag to define a global parameter, and a
:code:`<PerTorsionParameter>` tag to define a per-torsion parameter.

Every child tag defines a rule for creating custom torsion interactions between
sets of four atoms.  Each tag may identify the atoms either by type (using the
attributes :code:`type1`\ , :code:`type2`\ , ...) or by class (using the
attributes :code:`class1`\ , :code:`class2`\ , ...).

The force field recognizes two different types of torsions: proper and improper.
A proper torsion involves four atoms that are bonded in sequence: 1 to 2, 2 to
3, and 3 to 4.  An improper torsion involves a central atom and three others
that are bonded to it: atoms 2, 3, and 4 are all bonded to atom 1.  The force
field begins by identifying every set of atoms in the system of each of these
types. For each one, it searches for a rule whose atom types or atom classes
match the four atoms.  If it finds one, it calls :code:`addTorsion()` on the
CustomTorsionForce with the specified parameters.  Otherwise, it ignores that
set and continues. The remaining attributes are the values to use for the per-
torsion parameters.  Every :code:`<Torsion>` tag must include one attribute
for every per-torsion parameter, and the attribute name must match the name of
the parameter.

You can also use wildcards when defining torsions.  To do this, simply leave the
type or class name for an atom empty.  That will cause it to match any atom.
For example, the following definition will match any sequence of atoms where the
second atom has class OS and the third has class P:

.. code-block:: xml

    <Proper class1="" class2="OS" class3="P" class4="" per="3" phase="0.0" k="0.66944"/>

<CustomGBForce>
===============

To add a CustomGBForce to the System, include a tag that looks like this:

.. code-block:: xml

    <CustomGBForce>
     <GlobalParameter name="solventDielectric" defaultValue="78.3"/>
     <GlobalParameter name="soluteDielectric" defaultValue="1"/>
     <PerParticleParameter name="charge"/>
     <PerParticleParameter name="radius"/>
     <PerParticleParameter name="scale"/>
     <ComputedValue name="I" type="ParticlePairNoExclusions">
        step(r+sr2-or1)*0.5*(1/L-1/U+0.25*(1/U^2-1/L^2)*(r-sr2*sr2/r)+0.5*log(L/U)/r+C);
        U=r+sr2; C=2*(1/or1-1/L)*step(sr2-r-or1); L=max(or1, D); D=abs(r-sr2); sr2 =
        scale2*or2; or1 = radius1-0.009; or2 = radius2-0.009
     </ComputedValue>
     <ComputedValue name="B" type="SingleParticle">
      1/(1/or-tanh(1*psi-0.8*psi^2+4.85*psi^3)/radius); psi=I*or; or=radius-0.009
     </ComputedValue>
     <EnergyTerm type="SingleParticle">
      28.3919551*(radius+0.14)^2*(radius/B)^6-0.5*138.935456*
              (1/soluteDielectric-1/solventDielectric)*charge^2/B
     </EnergyTerm>
     <EnergyTerm type="ParticlePair">
      -138.935456*(1/soluteDielectric-1/solventDielectric)*charge1*charge2/f;
              f=sqrt(r^2+B1*B2*exp(-r^2/(4*B1*B2)))
     </EnergyTerm>
     <Atom type="0" charge="-0.4157" radius="0.1706" scale="0.79"/>
     <Atom type="1" charge="0.2719" radius="0.115" scale="0.85"/>
     <Atom type="2" charge="0.0337" radius="0.19" scale="0.72"/>
     ...
    </CustomGBForce>

The above (rather complicated) example defines a generalized Born model that is
equivalent to GBSAOBCForce.  The definition consists of a set of computed values
(defined by :code:`<ComputedValue>` tags) and energy terms (defined by
:code:`<EnergyTerm>` tags), each of which is evaluated according to a
mathematical expression.  See the API documentation for details.

The expressions may depend on an arbitrary list of global or per-atom
parameters.  Use a :code:`<GlobalParameter>` tag to define a global
parameter, and a :code:`<PerAtomParameter>` tag to define a per-atom
parameter.

Each :code:`<Atom>` tag specifies the parameters for one atom type
(specified with the :code:`type` attribute) or atom class (specified with
the :code:`class` attribute).  It is fine to mix these two methods, having
some tags specify a type and others specify a class.  However you do it, you
must make sure that a unique set of parameters is defined for every atom type.
The remaining attributes are the values to use for the per-atom parameters. All
per-atom parameters must be specified for every :code:`<Atom>` tag, and the
attribute name must match the name of the parameter.  For instance, if there is
a per-atom parameter with the name “radius”, then every :code:`<Atom>` tag
must include an attribute called :code:`radius`\ .

CustomGBForce also allows you to define tabulated functions.  To define a
function, include a :code:`<Function>` tag inside the
:code:`<CustomGBForce>` tag:

.. code-block:: xml

    <Function name="myfn" min="-5" max="5">
    0.983674857694 -0.980096396266 -0.975743130031 -0.970451936613 -0.964027580076
    -0.956237458128 -0.946806012846 -0.935409070603 -0.921668554406 -0.905148253645
    -0.885351648202 -0.861723159313 -0.833654607012 -0.800499021761 -0.761594155956
    -0.716297870199 -0.664036770268 -0.604367777117 -0.537049566998 -0.46211715726
    -0.379948962255 -0.291312612452 -0.197375320225 -0.099667994625 0.0
    0.099667994625 0.197375320225 0.291312612452 0.379948962255 0.46211715726
    0.537049566998 0.604367777117 0.664036770268 0.716297870199 0.761594155956
    0.800499021761 0.833654607012 0.861723159313 0.885351648202 0.905148253645
    0.921668554406 0.935409070603 0.946806012846 0.956237458128 0.964027580076
    0.970451936613 0.975743130031 0.980096396266 0.983674857694 0.986614298151
    0.989027402201
    </Function>

The tag’s attributes define the name of the function and the range of values for
which it is defined.  The tabulated values are listed inside the body of the
tag, with successive values separated by white space.  Again, see the API
documentation for more details.

Writing Custom Expressions
==========================

The custom forces described in this chapter involve user defined algebraic
expressions.  These expressions are specified as character strings, and may
involve a variety of standard operators and mathematical functions.

The following operators are supported: + (add), - (subtract), * (multiply), /
(divide), and ^ (power).  Parentheses “(“and “)” may be used for grouping.

The following standard functions are supported: sqrt, exp, log, sin, cos, sec,
csc, tan, cot, asin, acos, atan, sinh, cosh, tanh, erf, erfc, min, max, abs,
step. step(x) = 0 if x < 0, 1 otherwise.  Some custom forces allow additional
functions to be defined from tabulated values.

Numbers may be given in either decimal or exponential form.  All of the
following are valid numbers: 5, -3.1, 1e6, and 3.12e-2.

The variables that may appear in expressions are specified in the API
documentation for each force class.  In addition, an expression may be followed
by definitions for intermediate values that appear in the expression.  A
semicolon “;” is used as a delimiter between value definitions.  For example,
the expression
::

    a^2+a*b+b^2; a=a1+a2; b=b1+b2

is exactly equivalent to
::

    (a1+a2)^2+(a1+a2)*(b1+b2)+(b1+b2)^2

The definition of an intermediate value may itself involve other intermediate
values.  All uses of a value must appear *before* that value’s definition.


Using Multiple Files
********************

If multiple XML files are specified when a ForceField is created, their
definitions are combined as follows.

* A file may refer to atom types and classes that it defines, as well as those
  defined in previous files.  It may not refer to ones defined in later files.
  This means that the order in which files are listed when calling the ForceField
  constructor is potentially significant.
* Forces that involve per-atom parameters (such as NonbondedForce or
  GBSAOBCForce) require parameter values to be defined for every atom type.  It
  does not matter which file those types are defined in.  For example, files that
  define explicit water models generally define a small number of atom types, as
  well as nonbonded parameters for those types.  In contrast, files that define
  implicit solvent models do not define any new atom types, but provide parameters
  for all the atom types that were defined in the main force field file.
* For other forces, the files are effectively independent.  For example, if two
  files each include a :code:`<HarmonicBondForce>` tag, bonds will be created
  based on the rules in the first file, and then more bonds will be created based
  on the rules in the second file.  This means you could potentially end up with
  multiple bonds between a single pair of atoms.


Extending ForceField
********************

The ForceField class is designed to be modular and extensible.  This means you
can add support for entirely new force types, such as ones implemented with
plugins.

For every force class, there is a “generator” class that parses the
corresponding XML tag, then creates Force objects and adds them to the System.
ForceField maintains a map of tag names to generator classes.  When a ForceField
is created, it scans through the XML files, looks up the generator class for
each tag, and asks that class to create a generator object based on it.  Then,
when you call :code:`createSystem()`\ ,  it loops over each of its generators
and asks each one to create its Force object.  Adding a new Force type therefore
is simply a matter of creating a new generator class and adding it to
ForceField’s map.

The generator class must define two methods.  First, it needs a static method
with the following signature to parse the XML tag and create the generator:
::

    @staticmethod
    def parseElement(element, forcefield):

:code:`element` is the XML tag (an xml.etree.ElementTree.Element object) and
:code:`forcefield` is the ForceField being created.  This method should
create a generator and add it to the ForceField:

generator = MyForceGenerator()
forcefield._forces.append(generator)

It then should parse the information contained in the XML tag and configure the
generator based on it.

Second, it must define a method with the following signature:
::

    def createForce(self, system, data, nonbondedMethod, nonbondedCutoff, args):

When :code:`createSystem()` is called on the ForceField, it first creates
the System object, then loops over each of its generators and calls
:code:`createForce()` on each one.  This method should create the Force object
and add it to the System.  :code:`data` is a ForceField._SystemData object
containing information about the System being created (atom types, bonds,
angles, etc.), :code:`system` is the System object, and the remaining
arguments are values that were passed to :code:`createSystem()`\ .  To get a
better idea of how this works, look at the existing generator classes in
forcefield.py.

The generator class may optionally also define a method with the following
signature:
::

    def postprocessSystem(self, system, data, args):

If this method exists, it will be called after all Forces have been created.
This gives generators a chance to make additional changes to the System.

Finally, you need to register your class by adding it to ForceField’s map:
::

    forcefield.parsers['MyForce'] = MyForceGenerator.parseElement

The key is the XML tag name, and the value is the static method to use for
parsing it.

Now you can simply create a ForceField object as usual.  If an XML file contains
a :code:`<MyForce>` tag, it will be recognized and processed correctly.

