updated documentation and ev_tally

\begin{eqnarray*}

  E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\

  V_{ij} & = & e^{-\lambda(r_{ij} -z_0}) \left[ C + f(\rho_{ij}) + f(\rho_{ji}) - A \left( \frac{r_{ij}}{z_0}\right)^{-6}\right] \\

  \rho_{ij}^2 & = & x_{ij}^2 + y_{ij}^2 \\

  f(\rho) & = &  e^{-(\rho/\delta)^2} \sum_{n=0}^2 C_{2n} { \rho/\delta }^{2n}

  V_{ij} & = & e^{-\lambda(r_{ij} -z_0}) \left[ C + f(\rho_{ij}) + f(\rho_{ji}) \right] - A \left( \frac{r_{ij}}{z_0}\right)^{-6} + A \left( \frac{\textrm{cutoff}}{z_0}\right)^{-6} \\

  \rho_{ij}^2 = \rho_{ji}^2 & = &  x_{ij}^2 + y_{ij}^2 ~\hspace{2cm} (\mathbf{n_i}\equiv\hat \mathbf{z})\\

  f(\rho) & = &  e^{-(\rho/\delta)^2} \sum_{n=0}^2 C_{2n} \left( \rho/\delta \right) ^{2n}

\end{eqnarray*}

\end{document}

[Syntax:]

pair_style kolmogorov/crespi/z cutoff :pre

pair_style hybrid/overlay kolmogorov/crespi/z cutoff :pre

[Examples:]

[Description:]

The {kolmogorov/crespi/z} style computes the Kolmogorov-Crespi interaction potential as 

described in "(KC)"_#KC. An important simplification is made, which is to 

take all normals along the z-axis. 

The {kolmogorov/crespi/z} style computes the Kolmogorov-Crespi interaction 

potential as described in "(KC05)"_#KC05. An important simplification is made, 

which is to take all normals along the z-axis. 

:c,image(Eqs/pair_kolmogorov_crespi_z.jpg)

It is important to have a suffiently large cutoff to ensure smooth forces. 

Energies are shifted so that they go continously to zero at the cutoff assuming 

that the exponential part of {Vij} (first term) decays sufficiently fast.

This shift is achieved by the last term in the equation for {Vij} above.

This potential is intended for interactions between two layers of graphene. 

Therefore, to avoid interaction between layers in multi-layered materials, 

each layer should have a separate atom type and interactions should only 

be computed between atom types of neighbouring layers.

The parameter file (e.g. CC.KC), is intended for use with metal 

"units"_units.html, with energies in meV.

"units"_units.html, with energies in meV. An additional parameter, {S}, 

is available to facilitate scaling of energies in accordance with 

"(vanWijk)"_#vanWijk.

This potential must be used in combination with hybrid/overlay.

Other interactions can be set to zero using pair_style {none}.

"pair_coeff"_pair_coeff.html

"pair_none"_pair_none.html

"pair_style hybrid/overlay"_pair_hybrid.html

[Default:] none

:line

:link(KC)

[(KC)] Kolmogorov, Crespi, Phys. Rev. B 71, 235415 (2005)

:link(KC05) 

[(KC05)] A. N. Kolmogorov, V. H. Crespi, Phys. Rev. B 71, 235415 (2005)

:link(vanWijk) 

[(vanWijk)] M. M. van Wijk, A. Schuring, M. I. Katsnelson, and A. Fasolino, 

Physical Review Letters, 113, 135504 (2014)

#

# Cite as A.N. Kolmogorov & V. H. Crespi, 

# Registry-dependent interlayer potential for graphitic systems

# Physical Review B 71, 2354150 (2005)

# Physical Review B 71, 235415 (2005)

# 

#      z0     C0     C2      C4       C    delta  lambda      A     S

C  C  3.34  15.71  12.29   4.933   3.030   0.578   3.629   10.238  1.0

        }

        if (eflag) {

          evdwl = -p.A*p.z06/r6+ exp1*sumCff+offset[itype][jtype];

          evdwl = -p.A*p.z06/r6+ exp1*sumCff - offset[itype][jtype];

        }

        if (evflag){

          ev_tally(i,j,nlocal,newton_pair,evdwl,0.0,fpair,delx,dely,delz);

          ev_tally_xyz(i,j,nlocal,newton_pair,evdwl,0,

                       fsum,fsum,fpair,delx,dely,delz);

        }

      }

    }

  if (offset_flag) {

    int iparam_ij = elem2param[map[i]][map[j]];

    offset[i][j] = params[iparam_ij].A*pow(params[iparam_ij].z0/cut[i][j],6);

    Param& p = params[iparam_ij];

    offset[i][j] = -p.A*pow(p.z0/cut[i][j],6);

  } else offset[i][j] = 0.0;

  offset[j][i] = offset[i][j];