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% $Id: cosmo.tex 19708 2010-10-29 18:04:21Z d3y133 $
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% $Id: cosmo.tex 19708 2010-10-29 18:04:21Z d3y133 $
\label{sec:cosmo}

COSMO is the continuum solvation `COnductor-like Screening MOdel'
of A. Klamt and G. Sch\"{u}\"{u}rmann to describe dielectric screening
effects in solvents.

\begin{enumerate}
\item A. Klamt and G. Sch\"{u}\"{u}rmann, J.~Chem.~Soc.~Perkin Trans.~2, 1993
799 (1993).
\end{enumerate}

The NWChem COSMO module implements algorithm for calculation of the
energy for the following methods:
\begin{enumerate}
\item Restricted Hartree-Fock (RHF),
\item Restricted open-shell Hartree-Fock (ROHF),
\item Restricted Kohn-Sham DFT (DFT),
\item Unrestricted Kohn-Sham DFT (ODFT),
\end{enumerate}
by determining the solvent reaction field self-consistently
with the solute charge distribution from the respective methods.
Note that COSMO for unrestricted Hartree-Fock (UHF) method
can also be performed by invoking the DFT module with appropriate
keywords.

Correlation energy of solvent molecules may also be evaluated at 
\begin{enumerate}
\item MP2,
\item CCSD,
\item CCSD+T(CCSD),
\item CCSD(T),
\end{enumerate}
levels of theory.  It is cautioned,
however, that these correlated COSMO calculations determine
the solvent reaction field using the HF charge distribution of
the solute rather than the charge distribution of the correlation
theory and are not entirely self consistent in that respect.  
In other words, these calculations assume that the correlation
effect and solvation effect are largely additive, and the combination
effect thereof is neglected. 
COSMO for MCSCF has not been implemented yet. 

In the current implementation the code
calculates the gas-phase energy of the system followed by the
solution-phase energy, and returns the electrostatic contribution
to the solvation free energy. 
At the present gradients are calculated by finite
difference of the energy.  Known problems include that the code does not 
work with spherical basis functions.
The code does not calculate the
non-electrostatic contributions to the free energy, except for
the cavitation/dispersion contribution to the solvation free energy,
which is computed and printed.
It should be noted that one must in general take into account 
the standard state correction besides the electrostatic
and cavitation/dispersion contribution to the solvation free energy,
when a comparison to experimental data is made.

Invoking the COSMO solvation model is done by specifying the input
COSMO input block with the input options as:
\begin{verbatim}
cosmo
   [off]
   [dielec  <real dielec default 78.4>]
   [radius  <real atom1>
            <real atom2>
       . . .
            <real atomN>]
   [rsolv   <real rsolv default 0.00>]
   [iscren  <integer iscren default 0>]
   [minbem  <integer minbem default 2>]
   [maxbem  <integer maxbem default 3>]
   [ificos  <integer ificos default 0>]
   [lineq   <integer lineq default 1>]
end
\end{verbatim}
followed by the task directive specifying the wavefunction and
type of calculation, e.g., \verb+task scf energy+, \verb+task mp2 energy+,
\verb+task dft optimize+, etc.

\verb+off+ can be used to turn off COSMO in a compound (multiple task)
run. By default, once the COSMO solvation model has been defined it will
be used in subsequent calculations. Add the keyword \verb+off+ if COSMO
is not needed in subsequent calculations.

\verb+Dielec+ is the value of the dielectric constant of the medium, 
with a default value of 78.4 (the dielectric constant for water).

\verb+Radius+ is an array that specifies the radius of the spheres
associated with each atom and that make up the molecule-shaped cavity.
Default values are Van der Waals radii. Values are in units of angstroms.
The codes uses the following Van der Waals radii by default:
\begin{verbatim}
      data vdwr(103) /
     1   0.80,0.49,0.00,0.00,0.00,1.65,1.55,1.50,1.50,0.00,
     2   2.30,1.70,2.05,2.10,1.85,1.80,1.80,0.00,2.80,2.75,
     3   0.00,0.00,1.20,0.00,0.00,0.00,2.70,0.00,0.00,0.00,
     4   0.00,0.00,0.00,1.90,1.90,0.00,0.00,0.00,0.00,1.55,
     5   0.00,1.64,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,
     6   0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,
     7   0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,
     8   0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,
     9   0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,
     1   0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,0.00,1.65,
     2   0.00,0.00,0.00/
\end{verbatim}
with 0.0 values replaced by 1.80. Other radii can be used as well.
See for examples:

\begin{enumerate}
\item E. V. Stefanovich and T. N. Truong, Chem.~Phys.~Lett. 244, 65 (1995).
\item V. Barone, M. Cossi, and J. Tomasi, J.~Chem.~Phys. 107, 3210 (1997).
\end{enumerate}

\verb+Rsolv+ is a parameter used to define the solvent accessible
surface. See the original reference of Klamt and Schuurmann for a
description. The default value is 0.00 (in angstroms).

\verb+Iscren+ is a flag to define the dielectric charge scaling option.
``{\tt iscren 1}'' implies the original scaling from Klamt and Sch\"{u}\"{u}rmann,
mainly ``$(\epsilon-1)/(\epsilon+1/2)$'', where $\epsilon$ is the dielectric constant.
``{\tt iscren 0}'' implies the modified scaling suggested by Stefanovich and
Truong, mainly ``$(\epsilon-1)/\epsilon$''. Default is to use the modified scaling.
For high dielectric the difference between the scaling is not 
significant.

The next three parameters define the tesselation of the unit sphere.
The approach follows the original proposal by Klamt and Sch\"{u}\"{u}rmann.
A very fine tesselation is generated from \verb+maxbem+ refining 
passes starting from either an octahedron or an icosahedron. The
boundary elements created with the fine tesselation are condensed
down to a coarser tesselation based on \verb+minbem+. The induced
point charges from the polarization of the medium are assigned to
the centers of the coarser tesselation. Default values are
``{\tt minbem 2}'' and ``{\tt maxbem 3}''. The flag \verb+ificos+ serves to
select the original tesselation, ``{\tt ificos 0}'' for an octahedron
(default) and ``{\tt ificos 1}'' for an icoshedron. Starting from an icosahedron
yields a somewhat finer tesselation that converges somewhat faster.
Solvation energies are not really sensitive to this choice for
sufficiently fine tesselations.

The \verb+lineq+ parameter serves to select the numerical algorithm to solve
the linear equations yielding the effective charges that represent
the polarization of the medium. ``{\tt lineq 0}'' selects an iterative method 
(default), ``{\tt lineq 1}'' selects a dense matrix linear equation solver.
For large molecules where the number of effective charges is large,
the codes selects the iterative method.

The following example is for a water molecule in `water', using
the HF/6-31G** level of theory:

\begin{verbatim}
start
echo
 title "h2o"
geometry
o                  .0000000000         .0000000000        -.0486020332
h                  .7545655371         .0000000000         .5243010666
h                 -.7545655371         .0000000000         .5243010666
end
basis segment cartesian
  o library 6-31g**
  h library 6-31g**
end
cosmo
  dielec 78.0
  radius 1.40
         1.16
         1.16
  rsolv  0.50
  lineq  0
end
task scf energy
\end{verbatim}
