From NWChem

COSMO Solvation Model

COSMO is the continuum solvation `COnductor-like Screening MOdel' of A. Klamt and G. Schüürmann to describe dielectric screening effects in solvents^[1]. This model has been enhanced by D.M. York and M. Karplus^[2] to create a smooth potential energy surface. The latter facilitates geometry optimization and dynamics and the implementation has been adapted to take advantage of those ideas.

The NWChem COSMO module implements algorithm for calculation of the energy for the following methods:

1. Restricted Hartree-Fock (RHF),
2. Restricted open-shell Hartree-Fock (ROHF),
3. Restricted Kohn-Sham DFT (DFT),
4. Unrestricted Kohn-Sham DFT (ODFT),

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

1. MP2,
2. CCSD,
3. CCSD+T(CCSD),
4. CCSD(T),

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 analytically, but frequencies are calculated by finite difference of the gradients. 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:

cosmo
  [off]
  [dielec  <real dielec default 78.4>]
  [parameters <filename>]
  [radius  <real atom1>
           <real atom2>
      . . .
           <real atomN>]
  [iscren  <integer iscren default 0>]
  [minbem  <integer minbem default 2>]
  [ificos  <integer ificos default 0>]
  [lineq   <integer lineq default 1>]
  [zeta <real zeta default 0.98>]
  [gamma_s <real gammas default 1.0>]
  [sw_tol <real swtol default 1.0e-4>]
  [do_gasphase <logical do_gasphase default True>]
end

followed by the task directive specifying the wavefunction and type of calculation, e.g., "task scf energy", "task mp2 energy", "task dft optimize", etc.

"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 "off" if COSMO is not needed in subsequent calculations.

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

"parameters" specifies COSMO radii parameters file that stores custom setting for COSMO parameters. The format for such file consists of the atom or element name followed by the radii. The program will first attempt to match based on atom name and only then the element name. Otherwise radius will be set based on default parameters. The file has to present in one of the three location ( in the order of preference) - directory specified by the environmental variable NWCHEM_COSMO_LIBRARY, permanent directory, and run directory. This directive is replacing previous facility of loading COSMO radii parameters through "set cosmo:map cosmo.par" directive. See example at the end of this section.

"Radius" is an array that specifies the radius of the spheres associated with each atom and that make up the molecule-shaped cavity. These values will override default radii setting including those specified in the COSMO parameter file (if any) Default values are Van der Waals radii. Values are in units of angstroms. The codes uses the following Van der Waals radii by default:

Default radii provided by Andreas Klamt (Cosmologic)

vdw radii: 1.17 (+/- 0.02) * Bondi radius^[3]

optimal vdw radii for H, C, N, O, F, S, Cl, Br, I^[4]

for heavy elements: 1.17*1.9

     data (vander(i),i=1,102)
    1 / 1.300,1.638,1.404,1.053,2.0475,2.00,
    2   1.830,1.720,1.720,1.8018,1.755,1.638,
    3   1.404,2.457,2.106,2.160,2.05,2.223,
    4   2.223,2.223,2.223,2.223,2.223,2.223,
    5   2.223,2.223,2.223,2.223,2.223,2.223,
    6   2.223,2.223,2.223,2.223,2.160,2.223,
    7   2.223,2.223,2.223,2.223,2.223,2.223,
    8   2.223,2.223,2.223,2.223,2.223,2.223,
    9   2.223,2.223,2.223,2.223,2.320,2.223,
    1   2.223,2.223,2.223,2.223,2.223,2.223,
    2   2.223,2.223,2.223,2.223,2.223,2.223,
    3   2.223,2.223,2.223,2.223,2.223,2.223,
    4   2.223,2.223,2.223,2.223,2.223,2.223,
    5   2.223,2.223,2.223,2.223,2.223,2.223,
    6   2.223,2.223,2.223,2.223,2.223,2.223,
    7   2.223,2.223,2.223,2.223,2.223,2.223,
    7   2.223,2.223,2.223,2.223,2.223,2.223/

For examples see Stefanovich et al.^[5] and Barone et al.^[6]

"Rsolv" is no longer used.

"Iscren' is a flag to define the dielectric charge scaling option. "iscren 1" implies the original scaling from Klamt and Schüürmann, mainly "(ε − 1) / (ε + 1 / 2)", where ε is the dielectric constant. "iscren 0" implies the modified scaling suggested by Stefanovich and Truong^[7], mainly "(ε − 1) / ε". Default is to use the modified scaling. For high dielectric the difference between the scaling is not significant.

The next two parameters define the tesselation of the unit sphere. The approach still follows the original proposal by Klamt and Schüürmann to some degree. Basically a tesselation is generated from "minbem" refining passes starting from either an octahedron or an icosahedron. Each level of refinement partitions the triangles of the current tesselation into four triangles. This procedure is repeated recursively until the desired granularity of the tesselation is reached. The induced point charges from the polarization of the medium are assigned to the centers of the tesselation. The default value is "minbem 2". The flag +ificos+ serves to select the original tesselation, "ificos 0" for an octahedron (default) and "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 old "maxbem" directive is no longer used.

The "lineq" parameter serves to select the numerical algorithm to solve the linear equations yielding the effective charges that represent the polarization of the medium. "lineq 0" selects an iterative method (default), "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.

"zeta" sets the width of the Gaussian charge distributions that were suggested by York and Karplus to avoid singularities when two surface charges coincide. The default value is "zeta 0.98" this value was chosen to ensure that the results of the current implementation are as close as possible to those of the original Klamt and Schuurmann based implementation.

"gamma_s" modifies the width of the smooth switching function that eliminates surface charges when their positions move into the sphere of a neighboring atom. "gamma_s 0.0" leads to a heavyside or abrupt switching function, whereas "gamma_s 1.0" maximizes the width of the switching function. The default value is "gamma_s 1.0".

"sw_tol" specifies the cutoff of the switching function below which a surface charge at a particular point is eliminated. The values of the switching function lie in the domain from 0 to 1. This value should not be set too small as that leads to instabilities in the linear system solvers. The default value is "sw_tol 1.0e-4".

"do_gasphase" is a flag to control whether the calculation of the solvation energy is preceded by a gas phase calculation. The default is to always perform a gas phase calculation first and then calculate the solvation starting from the converged gas phase electron density. However, in geometry optimizations this approach can double the cost. In such a case setting "do_gasphase false" suppresses the gas phase calculations and only the solvated system calculations are performed. This option needs to be used with care as in some cases starting the COSMO solvation from an unconverged electron density can generate unphysical charges that lock the calculation into strange electron distributions.

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

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
 lineq  0
end
task scf energy

Alternatively, instead of listing COSMO radii parameters in the input, the former can be loaded using an external file through the "parameters" directive

start
echo
 title "h2o"
geometry
 ow                  .0000000000         .0000000000        -.0486020332
 hw                  .7545655371         .0000000000         .5243010666
 h                  -.7545655371         .0000000000         .5243010666
end
basis segment cartesian
 * library 6-31g**
end

cosmo
 dielec 78.0
 lineq  0
 parameters water.par
end

task scf energy

where "water.par" may the following form:

O 1.40
H 1.16

This will set radii of all oxygen atoms to 1.4 and all hydrogen atoms to 1.16. More fine grained control may be achieved using specific atom names. For example, the following parameter file

O    1.40
H    1.16
HW  1.06

will set a different radii of 1.06 to hydrogen atoms named HW. Note that, as per general rule in NWChem, all names are case insensitive.

and placed in one of the these locations - directory specified by the environmental variable NWCHEM_COSMO_LIBRARY, permanent directory, or run directory.

References

1. ↑ Klamt, A; Schuurmann, G (1993). "COSMO: A new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient". Journal of the Chemical Society, Perkin Transactions 2: 799-805. doi:10.1039/P29930000799. 
2. ↑ York, D.M.; Karplus, M. (1999). "A smooth solvation potential based on the conductor-like screening model". Journal of physical chemistry A 103: 11060-11079. doi:10.1021/jp992097l. 
3. ↑ A. Bondi (1964). "van der Waals volums and radii". Journal of Physical Chemistry 68: 441-451. doi:10.1021/j100785a001. 
4. ↑ A. Klamt, V. Jonas (1998). "Refinement and parametrization of COSMO-RS". Journal of physical chemistry A 102: 5074-5085. doi:10.1021/jp980017s. 
5. ↑ E. V. Stefanovich, T. N. Truong (1995). "Optimized atomic radii for quantum dielectric continuum solvation models". Chemical Physics Letters 244: 65-74. doi:10.1016/0009-2614(95)00898-E. 
6. ↑ V. Barone, M. Cossi (1997). "A new definition of cavities for the computation of solvation free energies by the polarizable continuum model". Journal of Chemical Physics 107: 3210-3221. doi:10.1063/1.474671. 
7. ↑ E. V. Stefanovich, T. N. Truong (1995). "Optimized atomic radii for quantum dielectric continuum solvation models". Chemical Physics Letters 244: 65-74. doi:10.1016/0009-2614(95)00898-E.