Updated documentation for dispersion PME

docs-source/usersguide/application.rst

@@ -916,8 +916,9 @@ Value                      Meaning
 :code:`NoCutoff`           No cutoff is applied.
 :code:`CutoffNonPeriodic`  The reaction field method is used to eliminate all interactions beyond a cutoff distance.  Not valid for AMOEBA.
 :code:`CutoffPeriodic`     The reaction field method is used to eliminate all interactions beyond a cutoff distance.  Periodic boundary conditions are applied, so each atom interacts only with the nearest periodic copy of every other atom.  Not valid for AMOEBA.
-:code:`Ewald`              Periodic boundary conditions are applied.  Ewald summation is used to compute long range interactions.  (This option is rarely used, since PME is much faster for all but the smallest systems.)  Not valid for AMOEBA.
-:code:`PME`                Periodic boundary conditions are applied.  The Particle Mesh Ewald method is used to compute long range interactions.
+:code:`Ewald`              Periodic boundary conditions are applied.  Ewald summation is used to compute long range Coulomb interactions.  (This option is rarely used, since PME is much faster for all but the smallest systems.)  Not valid for AMOEBA.
+:code:`PME`                Periodic boundary conditions are applied.  The Particle Mesh Ewald method is used to compute long range Coulomb interactions.
+:code:`LJPME`              Periodic boundary conditions are applied.  The Particle Mesh Ewald method is used to compute long range interactions for both Coulomb and Lennard-Jones.
 =========================  ===========================================================================================================================================================================================================================================
 
 
@@ -926,7 +927,7 @@ 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
+When using :code:`Ewald`, :code:`PME`, or :code:`LJPME`\ , you can optionally specify an
 error tolerance for the force computation.  For example:
 ::
 

docs-source/usersguide/references.bib

@@ -517,3 +517,15 @@
    year = {2014},
    type = {Journal Article}
 }
+
+@article{Wennberg2015
+   author = {Wennberg, Christian L. and Murtola, Teemu and Páll, Szilárd and Abraham, Mark J. and Hess, Berk and Lindahl, Erik},
+   title = {Direct-Space Corrections Enable Fast and Accurate {Lorentz–Berthelot} Combination Rule {Lennard-Jones} Lattice Summation},
+   journal = {Journal of Chemical Theory and Computation},
+   volume = {11},
+   number = {12},
+   pages = {5737-5746},
+   year = {2015},
+   type = {Journal Article}
+}
+

docs-source/usersguide/theory.rst

@@ -412,7 +412,7 @@ and the number of nodes in the mesh along each dimension as
 
 
 .. math::
-   n_\mathit{mesh}=\frac{2\alpha d}{{3d}^{1/5}}
+   n_\mathit{mesh}=\frac{2\alpha d}{{3\delta}^{1/5}}
 
 
 where *d* is the width of the periodic box along that dimension.  Alternatively,
@@ -432,6 +432,38 @@ to numerical round-off error than Ewald summation.  For Platforms that do
 calculations in single precision, making :math:`\delta` too small (typically below about
 5·10\ :sup:`-5`\ ) can actually cause the error to increase.
 
+Lennard-Jones Interaction With Particle Mesh Ewald
+==================================================
+
+The PME algorithm can also be used for Lennard-Jones interactions.  Usually this
+is not necessary, since Lennard-Jones forces are short ranged, but there are
+situations (such as membrane simulations) where neglecting interactions beyond
+the cutoff can measurably affect results.
+
+For computational efficiency, certain approximations are made\ :cite:`Wennberg2015`.
+Interactions beyond the cutoff distance include only the attractive :math:`1/r^6`
+term, not the repulsive :math:`1/r^{12}` term.  Since the latter is much smaller
+than the former at long distances, this usually has negligible effect.  Also,
+the interaction between particles farther apart than the cutoff distance is
+computed using geometric combination rules:
+
+.. math::
+   \sigma=\sqrt{\sigma_1 \sigma_2}
+
+The effect of this approximation is also quite small, and it is still far more
+accurate than ignoring the interactions altogether (which is what would happen
+with PME).
+
+The formula used to compute the number of nodes along each dimension of the mesh
+is slightly different from the one used for Coulomb interactions:
+
+.. math::
+   n_\mathit{mesh}=\frac{\alpha d}{{3\delta}^{1/20}}
+
+As before, this is an empirical formula.  It will usually produce an average
+relative error in the forces less than or similar to :math:`\delta`\ , but that
+is not guaranteed.
+
 .. _gbsaobcforce:
 
 GBSAOBCForce