<P>In the H-AdResS scheme, the description of the interactions within a system of particles is given in terms
of a global Hamiltonian function H, which has the following form <A HREF = "#Potestio2013_1">(Potestio2013_1)</A>, <A HREF = "#Potestio2013_2">(Potestio2013_2)</A>, <A HREF = "#Heidari2016">(Heidari2016)</A>:
<P>The <I>lj/cut/hars/at</I> styles compute the standard 12/6 Lennard-Jones potential for the atoms located in atomistic (high resolution) and hybrid region.
The general formula is given by
</P>
<CENTER><IMG SRC = "Eqs/HADRESS_AT_pair_lj.png">
</CENTER>
<P>rc is the cutoff.
</P>
<P>Style <I>lj/cut/coul/dsf/hars/at</I> computes the standard 12/6 Lennard-Jones and Coulomb interactions for atoms of atomistic (high resolution) and hybrid region.
The Coulombic term is computed via the damped shifted force model introduced by <A HREF = "#Fennell">Fennell et al.</A>, given by:
<P>The <I>lj/cut/hars/cg</I> styles compute the standard 12/6 Lennard-Jones potential for the atoms located in the low resolution (coarse-grained) and hybrid region.
The general formula is given by
</P>
<CENTER><IMG SRC = "Eqs/HADRESS_CG_pair_lj.png">
</CENTER>
<P>rc is the cutoff.
As mentioned above, the interactions in the coarse-grained region are computed based on the center of mass of the particles.
</P>
<P>Important Note: For dual resolution simulations, it is required to use hybrid/overlay to include
both resolution pair-styles.
</P>
<P>For all of dual resolution pair styles, the following coefficients must
be defined for each pair of atoms types via the
<A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples below
<P>All of the <I>lj/cut</I> pair styles support the
<A HREF = "pair_modify.html">pair_modify</A> shift option for the energy of the
Lennard-Jones portion of the pair interaction.
</P>
<P>All of the <I>lj/cut</I> pair styles write their information to <A HREF = "restart.html">binary
restart files</A>, so pair_style and pair_coeff commands do
not need to be specified in an input script that reads a restart file.
</P>
<P>The pair styles do not support the use of the rRESPA hierarchy.
</P>
<P>Each pair styles creates a file named as "Mean_Comp_Energy_XX.txt", where the file name's suffix "XX", is replaced by "AT" and "CG" for atomistic and coarse-grained pairwise interactions respectively.
In these files the averaged compensation energy as function of the resolution (λ) is printed. Each file is created at <I>T<sub>p</sub><sup>Start</sup></I> and is updated every <I>dT<sub>p</sub></I>.
The updating process of the files is finished at time step <I>T<sub>p</sub><sup>End</sup></I>.
For those equilibrated simulations starting at time step larger than <I>T<sub>p</sub><sup>End</sup></I>, the file "Mean_Comp_Energy_XX.txt" is loaded in each pair styles. For more information,
see <A HREF = "fix_lambdah_calc.html">fix_lambdah_calc</A>.
</P>
<HR>
<P><B>Restrictions:</B>
</P>
<P>In HAdResS, it is required to include both high resolution (atomistic)
and low resolution (coarse-grained) force fields together through
</P>
<PRE> pair_style hybrid/overlay
</PRE>
<P>An example of such setup is given above.
</P>
<P>To employ the H-AdResS scheme, the full/hars atom style as well as <A HREF = "fix_lambdah_calc.html">(fix_lambdah_calc)</A> have to be used:
<P><B>(Potestio2013_1)</B> R. Potestio, S. Fritsch, P. Espanol, R. Delgado-Buscalioni, K. Kremer, R. Everaers, and D. Donadio, <I>Hamiltonian Adaptive Resolution Simulation for Molecular Liquids</I>, <A HREF = "http://dx.doi.org/10.1103/PhysRevLett.110.108301">Phys. Rev. Lett. [110],
108301 (2013)</A>
</P>
<A NAME = "Potestio2013_2"></A>
<P><B>(Potestio2013_2)</B> R. Potestio, S. Fritsch, P. Espanol, R. Delgado-Buscalioni, K. Kremer, R. Everaers, and D. Donadio, <I>Monte Carlo Adaptive Resolution Simulation of Multicomponent Molecular Liquids</I>, <A HREF = "http://dx.doi.org/10.1103/PhysRevLett.111.060601">Phys. Rev. Lett. [111],
060601 (2013)</A>
</P>
<A NAME = "Heidari2016"></A>
<P><B>(Heidari2016)</B> M. Heidari, R. Cortes-Huerto, D. Donadio and R. Potestio, <I>Accurate and general treatment of electrostatic interaction in Hamiltonian adaptive resolution simulations</I>, "EPJST (2016)"
</P>
<A NAME = "Fennell"></A>
<P><B>(Fennell)</B> C. J. Fennell, J. D. Gezelter, J Chem Phys, 124,