269 lines
11 KiB
ReStructuredText
269 lines
11 KiB
ReStructuredText
CHARMM, AMBER, COMPASS, and DREIDING force fields
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=================================================
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A compact summary of the concepts, definitions, and properties of
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force fields with explicit bonded interactions (like the ones discussed
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in this HowTo) is given in :ref:`(Gissinger) <Typelabel2>`.
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A force field has 2 parts: the formulas that define it and the
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coefficients used for a particular system. Here we only discuss
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formulas implemented in LAMMPS that correspond to formulas commonly used
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in the CHARMM, AMBER, COMPASS, and DREIDING force fields. Setting
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coefficients is done either from special sections in an input data file
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via the :doc:`read_data <read_data>` command or in the input script with
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commands like :doc:`pair_coeff <pair_coeff>` or :doc:`bond_coeff
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<bond_coeff>` and so on. See the :doc:`Tools <Tools>` doc page for
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additional tools that can use CHARMM, AMBER, or Materials Studio
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generated files to assign force field coefficients and convert their
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output into LAMMPS input. LAMMPS input scripts can also be generated by
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`charmm-gui.org <https://charmm-gui.org/>`_.
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CHARMM and AMBER
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----------------
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The `CHARMM force field
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<https://mackerell.umaryland.edu/charmm_ff.shtml>`_ :ref:`(MacKerell)
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<howto-MacKerell>` and `AMBER force field
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<https://ambermd.org/AmberModels.php>`_ :ref:`(Cornell) <howto-Cornell>`
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have potential energy function of the form
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.. math::
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V & = \sum_{bonds} E_b + \sum_{angles} \!E_a + \!\overbrace{\sum_{dihedral} \!\!E_d}^{\substack{
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\text{charmm} \\
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\text{charmmfsw}
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}} +\!\!\! \sum_{impropers} \!\!\!E_i \\[.6em]
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& \quad + \!\!\!\!\!\!\!\!\!\!\underbrace{~\sum_{pairs} \left(E_{LJ}+E_{coul}\right)}_{\substack{
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\text{lj/charmm/coul/charmm} \\
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\text{lj/charmm/coul/charmm/implicit} \\
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\text{lj/charmm/coul/long} \\
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\text{lj/charmm/coul/msm} \\
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\text{lj/charmmfsw/coul/charmmfsh} \\
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\text{lj/charmmfsw/coul/long}
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}} \!\!\!\!\!\!\!\!+ \!\!\sum_{special}\! E_s + \!\!\!\!\sum_{residues} \!\!\!{\scriptstyle\mathrm{CMAP}(\phi,\psi)}
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The terms are computed by bond styles (relationship between two atoms),
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angle styles (between 3 atoms) , dihedral/improper styles (between 4
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atoms), pair styles (non-covalently bonded pair interactions) and
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special bonds. The CMAP term (see :doc:`fix cmap <fix_cmap>` command for
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details) corrects for pairs of dihedral angles ("Correction MAP") to
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significantly improve the structural and dynamic properties of proteins
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in crystalline and solution environments :ref:`(Brooks)
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<howto-Brooks>`. The AMBER force field does not include the CMAP term.
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The interaction styles listed below compute force field formulas that
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are consistent with common options in CHARMM or AMBER. See each
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command's documentation for the formula it computes.
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* :doc:`bond_style <bond_harmonic>` harmonic
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* :doc:`angle_style <angle_charmm>` charmm
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* :doc:`dihedral_style <dihedral_charmm>` charmmfsh
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* :doc:`dihedral_style <dihedral_charmm>` charmm
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* :doc:`pair_style <pair_charmm>` lj/charmmfsw/coul/charmmfsh
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* :doc:`pair_style <pair_charmm>` lj/charmmfsw/coul/long
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* :doc:`pair_style <pair_charmm>` lj/charmm/coul/charmm
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* :doc:`pair_style <pair_charmm>` lj/charmm/coul/charmm/implicit
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* :doc:`pair_style <pair_charmm>` lj/charmm/coul/long
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* :doc:`special_bonds <special_bonds>` charmm
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* :doc:`special_bonds <special_bonds>` amber
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The pair styles compute Lennard Jones (LJ) and Coulombic interactions
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with additional switching or shifting functions that ramp the energy
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and/or force smoothly to zero between an inner :math:`(a)` and outer
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:math:`(b)` cutoff. The older styles with *charmm* (not *charmmfsw* or
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*charmmfsh*\ ) in their name compute the LJ and Coulombic interactions
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with an energy switching function (esw) :math:`S(r)` which ramps the energy
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smoothly to zero between the inner and outer cutoff. This can cause
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irregularities in pairwise forces (due to the discontinuous second
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derivative of energy at the boundaries of the switching region), which
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in some cases can result in complications in energy minimization and
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detectable artifacts in MD simulations.
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.. grid:: 1 1 2 2
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.. grid-item::
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.. math::
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LJ(r) &= 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
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\left(\frac{\sigma}{r}\right)^6 \right]\\[.6em]
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C(r) &= \frac{C q_i q_j}{ \epsilon r}\\[.6em]
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S(r) &= \frac{ \left(b^2 - r^2\right)^2 \left(b^2 + 2r^2 - 3{a^2}\right)}
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{ \left(b^2 - a^2\right)^3 }\\[.6em]
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E_{LJ}(r) &= \begin{cases}
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LJ(r), & r \leq a \\
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LJ(r) S(r), & a < r \leq b \\
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0, &r > b
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\end{cases} \\[.6em]
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E_{coul}(r) &= \begin{cases}
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C(r), & r \leq a \\
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C(r) S(r), & a < r \leq b \\
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0, & r > b
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\end{cases}
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.. grid-item::
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.. image:: img/howto_charmm_ELJ.png
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:align: center
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The newer styles with *charmmfsw* or *charmmfsh* in their name replace
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energy switching with force switching (fsw) for LJ interactions and
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force shifting (fsh) functions for Coulombic interactions
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:ref:`(Steinbach) <howto-Steinbach>`
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.. grid:: 1 1 2 2
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.. grid-item::
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.. math::
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E_{LJ}(r) = & \begin{cases}
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4 \epsilon \sigma^6 \left(\frac{\displaystyle\sigma
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^6-r^6}{\displaystyle r^{12}}-\frac{\displaystyle\sigma ^6}{\displaystyle a^6
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b^6}+\frac{\displaystyle 1}{\displaystyle a^3 b^3}\right) & r\leq a \\
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\frac{\displaystyle 4 \epsilon \sigma^6 \left(\sigma ^6
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\left(b^6-r^6\right)^2-b^3 r^6 \left(a^3+b^3\right)
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\left(b^3-r^3\right)^2\right)}{\displaystyle b^6 r^{12}
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\left(b^6-a^6\right)} & a<r \leq b\\
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0, & r>b
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\end{cases}\\[.6em]
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E_{coul}(r) & = \begin{cases}
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C(r) \frac{\displaystyle (b-r)^2}{\displaystyle r b^2}, & r \leq b \\
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0, & r > b
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\end{cases}
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.. grid-item::
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.. image:: img/howto_charmmfsw_ELJ.png
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:align: center
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These styles are used by LAMMPS input scripts generated by
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https://charmm-gui.org/ :ref:`(Brooks) <howto-Brooks>`.
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.. note::
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For CHARMM, newer *charmmfsw* or *charmmfsh* styles were released in
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March 2017. We recommend they be used instead of the older *charmm*
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styles. See discussion of the differences on the :doc:`pair charmm
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<pair_charmm>` and :doc:`dihedral charmm <dihedral_charmm>` doc
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pages.
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.. note::
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The TIP3P water model is strongly recommended for use with the CHARMM
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force field. In fact, `"using the SPC model with CHARMM parameters is
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a bad idea"
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<https://matsci.org/t/using-spc-water-with-charmm-ff/24715>`_ and `"to
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enable TIP4P style water in CHARMM, you would have to write a new pair
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style"
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<https://matsci.org/t/hybrid-pair-styles-for-charmm-and-tip4p-ew/32609>`_
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. LAMMPS input scripts generated by Solution Builder on https://charmm-gui.org
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use TIP3P molecules for solvation. Any other water model can and
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probably will lead to false conclusions.
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COMPASS
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-------
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COMPASS is a general force field for atomistic simulation of common
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organic molecules, inorganic small molecules, and polymers which was
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developed using ab initio and empirical parameterization techniques
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:ref:`(Sun) <howto-Sun>`. See the :doc:`Tools <Tools>` page for the
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msi2lmp tool for creating LAMMPS template input and data files from
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BIOVIA's Materials Studio files. Please note that the msi2lmp tool is
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very old and largely unmaintained, so it does not support all features
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of Materials Studio provided force field files, especially additions
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during the last decade. You should watch the output carefully and
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compare results, where possible. See :ref:`(Sun) <howto-Sun>` for a
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description of the COMPASS force field.
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These interaction styles listed below compute force field formulas that
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are consistent with the COMPASS force field. See each command's
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documentation for the formula it computes.
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* :doc:`bond_style <bond_class2>` class2
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* :doc:`angle_style <angle_class2>` class2
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* :doc:`dihedral_style <dihedral_class2>` class2
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* :doc:`improper_style <improper_class2>` class2
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* :doc:`pair_style <pair_class2>` lj/class2
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* :doc:`pair_style <pair_class2>` lj/class2/coul/cut
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* :doc:`pair_style <pair_class2>` lj/class2/coul/long
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* :doc:`special_bonds <special_bonds>` lj/coul 0 0 1
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DREIDING
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--------
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DREIDING is a generic force field developed by the `Goddard group
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<http://www.wag.caltech.edu>`_ at Caltech and is useful for predicting
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structures and dynamics of organic, biological and main-group inorganic
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molecules. The philosophy in DREIDING is to use general force constants
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and geometry parameters based on simple hybridization considerations,
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rather than individual force constants and geometric parameters that
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depend on the particular combinations of atoms involved in the bond,
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angle, or torsion terms. DREIDING has an :doc:`explicit hydrogen bond
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term <pair_hbond_dreiding>` to describe interactions involving a
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hydrogen atom on very electronegative atoms (N, O, F). Unlike CHARMM
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or AMBER, the DREIDING force field has not been parameterized for
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considering solvents (like water).
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See :ref:`(Mayo) <howto-Mayo>` for a description of the DREIDING force field
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The interaction styles listed below compute force field formulas that
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are consistent with the DREIDING force field. See each command's
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documentation for the formula it computes.
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* :doc:`bond_style <bond_harmonic>` harmonic
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* :doc:`bond_style <bond_morse>` morse
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* :doc:`angle_style <angle_cosine_squared>` cosine/squared
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* :doc:`angle_style <angle_harmonic>` harmonic
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* :doc:`angle_style <angle_cosine>` cosine
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* :doc:`angle_style <angle_cosine_periodic>` cosine/periodic
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* :doc:`dihedral_style <dihedral_charmm>` charmm
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* :doc:`improper_style <improper_umbrella>` umbrella
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* :doc:`pair_style <pair_buck>` buck
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* :doc:`pair_style <pair_buck>` buck/coul/cut
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* :doc:`pair_style <pair_buck>` buck/coul/long
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* :doc:`pair_style <pair_lj>` lj/cut
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* :doc:`pair_style <pair_lj_cut_coul>` lj/cut/coul/cut
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* :doc:`pair_style <pair_lj_cut_coul>` lj/cut/coul/long
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* :doc:`pair_style <pair_hbond_dreiding>` hbond/dreiding/lj
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* :doc:`pair_style <pair_hbond_dreiding>` hbond/dreiding/morse
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* :doc:`special_bonds <special_bonds>` dreiding
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----------
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.. _Typelabel2:
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**(Gissinger)** J. R. Gissinger, I. Nikiforov, Y. Afshar, B. Waters, M. Choi, D. S. Karls, A. Stukowski, W. Im, H. Heinz, A. Kohlmeyer, and E. B. Tadmor, J Phys Chem B, 128, 3282-3297 (2024).
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.. _howto-MacKerell:
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**(MacKerell)** MacKerell, Bashford, Bellott, Dunbrack, Evanseck, Field, Fischer, Gao, Guo, Ha, et al (1998). J Phys Chem, 102, 3586 . https://doi.org/10.1021/jp973084f
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.. _howto-Cornell:
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**(Cornell)** Cornell, Cieplak, Bayly, Gould, Merz, Ferguson, Spellmeyer, Fox, Caldwell, Kollman (1995). JACS 117, 5179-5197. https://doi.org/10.1021/ja00124a002
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.. _howto-Steinbach:
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**(Steinbach)** Steinbach, Brooks (1994). J Comput Chem, 15, 667. https://doi.org/10.1002/jcc.540150702
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.. _howto-Brooks:
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**(Brooks)** Brooks, et al (2009). J Comput Chem, 30, 1545. https://onlinelibrary.wiley.com/doi/10.1002/jcc.21287
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.. _howto-Sun:
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**(Sun)** Sun (1998). J. Phys. Chem. B, 102, 7338-7364. https://doi.org/10.1021/jp980939v
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.. _howto-Mayo:
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**(Mayo)** Mayo, Olfason, Goddard III (1990). J Phys Chem, 94, 8897-8909. https://doi.org/10.1021/j100389a010
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