SM12: Solvation Model 12
************************

Continuum solvation can be done with the Minnesota Solvation Model 12
(SM12) [1]. Details on the implementation of SM12 in ADF can be found
in Ref. [2].

The SM12 model in ADF can use CM5, CHELPG, or RESP charges. The
calculation of SM12 analytical gradients with CHELPG or RESP charges
is implemented (ADF2026), which allows one to do geometry
optimizations, for example. The calculation of SM12 analytical
gradients with CM5 charges is not implemented.

The energetics of solvation is calculated using:

   \Delta G_S^\otimes = \Delta E_E + G_P + G_{CDS} + \Delta G_N +
   \Delta G_{conc}^\otimes

where the symbol \otimes denotes an arbitrary choice of standard
states, \Delta E_E is the change in the solute's internal electronic
energy in transferring from the gas phase to the liquid phase at the
same geometry, G_P is the polarization free energy of the
solute–solvent system when the solute is inserted, G_{CDS} is the
component of the free energy that is nominally associated with
cavitation, dispersion, and solvent structure, \Delta G_N is the
change in \Delta G_S^0 due to a change in nuclear coordinates, and
\Delta G_{conc}^\otimes accounts for the difference in concentrations,
if any, in the gas-phase standard state and the solution-phase one. In
case of 1 M concentration in both solution and gas, then \Delta
G_S^\otimes = 0 kcal/mol, which yields \Delta G_S^*. If the same
geometry is used in solution and gas phase calculation, then \Delta
G_N is zero.

SM12 makes use of the Generalized Born approximation to calculate the
bulk electrostatic contribution. This is comprised of several terms
that are together known as the ENP (Electronic, Nuclear, and
Polarization) term G_P. The SM12 model in ADF can use CM5 charges [3]
or charges which are derived from the electrostatic potential (ESP),
namely CHELPG or RESP. CM5 is a class 4 charge model, making use of
both empirical and density related terms. It is comprised of Hirshfeld
charges [4], a simple bond order calculation, atomic distances, and
atom-specific parameters [3]. The ESP charges are calculated in ADF
using atom-centered Lebedev grids, which is different from the way
they are calculated in Ref. [1]. The covalent radii utilized are based
on the atomic covalent radius from the Handbook of Chemistry and
Physics [5]. The Coulomb integral is described with the use of an
approximation from Still et al. [6]. Several parameters go into
describing this, which include: interatomic distance, an empirical
Born constant, and the Born area, which is calculated with the
Analytical Surface Area (ASA) algorithm [7]. The Born area is
calculated using Legendre-Gauss quadrature from the atomic radii to a
sphere that encapsulates the entire molecule.

The ASA algorithm is also used to calculate the solvent accessible
surface area (SASA), which is computed within the CDS (Cavitation,
Dispersion, Solvation) term of SM12. The CDS term depends on three
terms:

* SASA (ASA Algorithm)

* Atomic surface tension

* Macroscopic surface tension

Atomic surface tension is based on atom-atom distances and the
solvent. Macroscopic surface tension is solvent-specific. The SM12
implementation in ADF reports energies in an atom-specific way. You
can attribute exact CDS and polarization energies to each atom in your
solute. The parameters for SM12 are derived to explicitly incorporate
organic elements (N, C, O, F, Si, P, S, Cl, Br, I), with less emphasis
on non-organics. Also, while most solvents have a generic atomic
surface tension reliance for atoms, water has its own explicit set of
parameters to better describe it.

   SOLVATION SM12
     {SM12SolvationPotential <CM5|CHELPG|RESP>}
     {SOLV NAME=solvent}
     {CUST {NAME=solvent}}
     {REF 1.33}
     {ACID 0.82}
     {BASE 0.35}
     {TENS 103.62}
     {EPS 78.36}
     {ARO 0.0}
     {HALO 0.0}
     {RADSOLV 0.4}
     {CHGAL 2.474}
     {BORNC 3.70}
     {PRINTSM12}
     {SM12printSCRF}
     {SM12espgridorder 19}
     {SM12espgridspacing 0.5}
   End

Presence of the SOLVATION SM12 block key triggers the solvent
calculation and does not require additional data. Curly brackets are
not part of the key. If no other keywords are present the default is
Water. If SM12 gradients are wanted one needs to specify CHELPG or
RESP for the SM12SolvationPotential keyword as these are not
implemented in case of CM5. With subkeys you can customize various
aspects of the model, for instance to specify the type of solute. None
of the subkeys is obligatory. Follows a description of the subkeys

"SM12SolvationPotential <CM5|CHELPG|RESP>"
   Which partial charges to use in SM12. Default CM5. CHELPG or RESP
   is needed for analytical gradients.

"SOLV NAME=solvent"
   Defines which solvent to be used. Each solvent has parameters set
   for each of the variables defined below. All of which can be found
   in the SM12 ref. [1]. Any variable can be changed with the
   inclusion of its key. "solvent" can be one of the following:

   * ACETICACID

   * ACETONITRILE

   * ACETOPHENONE

   * ANILINE

   * ANISOLE

   * BENZENE

   * BENZONITRILE

   * BENZYLALCOHOL

   * BROMOBENZENE

   * BROMOETHANE

   * BROMOFORM

   * BROMOOCTANE

   * N-BUTANOL

   * SEC-BUTANOL

   * BUTANONE

   * BUTYLACETATE

   * N-BUTYLBENZENE

   * SEC-BUTYLBENZENE

   * T-BUTYLBENZENE

   * CARBONDISULFIDE

   * CARBONTETRACHLORIDE

   * CHLOROBENZENE

   * CHLOROFORM

   * CHLOROHEXANE

   * M-CRESOL

   * CYCLOHEXANE

   * CYCLOHEXANONE

   * DECALIN

   * DECANE

   * DECANOL

   * 1-2-DIBROMOETHANE

   * DIBUTYLETHER

   * O-DICHLOROBENZENE

   * 1-2-DICHLOROETHANE

   * DIETHYLETHER

   * DIISOPROPYLETHER

   * N-N-DIMETHYLACETAMIDE

   * N-N-DIMETHYLFORMAMIDE

   * 2-6-DIMETHYLPYRIDINE

   * DIMETHYLSULFOXIDE

   * DODECANE

   * ETHANOL

   * ETHOXYBENZENE

   * ETHYLACETATE

   * ETHYLBENZENE

   * FLUOROBENZENE

   * 1-FLUORO-N-OCTANE

   * HEPTANE

   * HEPTANOL

   * HEXADECANE

   * HEXADECYLIODIDE

   * HEXANE

   * HEXANOL

   * IODOBENZENE

   * ISOBUTANOL

   * ISOOCTANE

   * ISOPROPANOL

   * ISOPROPYLBENZENE

   * P-ISOPROPYLTOLUENE

   * MESITYLENE

   * METHANOL

   * METHOXYETHANOL

   * METHYLENECHLORIDE

   * N-METHYLFORMAMIDE

   * 2-METHYLPYRIDINE

   * 4-METHYL-2-PENTANONE

   * NITROBENZENE

   * NITROETHANE

   * NITROMETHANE

   * O-NITROTOLUENE

   * NONANE

   * NONANOL

   * OCTANE

   * OCTANOL

   * PENTADECANE

   * PENTANE

   * PENTANOL

   * PERFLUOROBENZENE

   * PHENYLETHER

   * PROPANOL

   * PYRIDINE

   * TETRACHLOROETHENE

   * TETRAHYDROFURAN

   * TETRAHYDROTHIOPHENEDIOXIDE

   * TETRALIN

   * TOLUENE

   * TRIBUTYLPHOSPHATE

   * TRIETHYLAMINE

   * 1-2-4-TRIMETHYLBENZENE

   * UNDECANE

   * WATER

   * XYLENE

   * 1-2-DIBROMOETHANE_WATER

   * 1-2-DICHLOROETHANE_WATER

   * BENZENE_WATER

   * CARBONTETRACHLORIDE_WATER

   * CHLOROBENZENE_WATER

   * CHLOROFORM_WATER

   * CYCLOHEXANE_WATER

   * DIBUTYLETHER_WATER

   * DIETHYLETHER_WATER

   * ETHYLACETATE_WATER

   * HEPTANE_WATER

   * HEXANE_WATER

   * NITROBENZENE_WATER

   * OCTANOL_WATER

"CUST {NAME=solvent}"
   A solvent with user specified parameters can be used. A user-
   specified name of the solvent "solvent" can be provided, but should
   not match one of the solvent names listed above. Any unspecified
   parameters will be set to zero, with the exception of the
   dielectric constant, which will be set to the dielectric constant
   of water.

"REF"
   Index of refraction at 293K (n).

"ACID"
   Abrahams hydrogen bond acidity (\alpha).

"BASE"
   Abrahams hydrogen bond basicity (\beta).

"TENS"
   Macroscopic surface tension of the solvent at the air interface
   (cal mol^-1 Å^-2)(\gamma).

"EPS"
   Dielectric constant. If not specified it will be set to the default
   of water. (\epsilon).

"ARO"
   Square root of the fraction of non-hydrogen atoms in the solvent
   molecule that are aromatic carbon atoms (carbon aromaticity)
   (\phi).

"HALO"
   Square of the fraction of non-hydrogen atoms in the solvent
   molecule that are halogens (electronegative halogenicity)(\psi).

"RADSOLV"
   Solvent radius, this is added to the van der Waals radius used for
   the cavity calculation.

"CHGAL"
   CM5 alpha parameter for Pauling bond order.

"BORNC"
   Empirical Born constant, see Ref. [1].

"PRINTSM12"
   Print more information on the SM12 calculation: CDS atom terms, ENP
   charges.

"SM12printSCRF"
   Print more information on the SCRF (self-consistent reaction field)
   during the SM12 calculation.

"SM12espgridorder"
   ESP Lebedeev Grid order for SM12 CHELPG and RESP. Accepted values
   are 19 (default), 23, 29, 31, and 41.

"SM12espgridspacing"
   ESP Lebedeev Grid spacing for SM12 CHELPG and RESP in Angstrom.
   Reasonable choices are 0.1, 0.2, 0.3, or 0.5 (default) Angstrom.

[1] A.V. Marenich, C.J. Cramer, and D.G. Truhlar, *Generalized Born
    Solvation Model SM12*, Journal of Chemical Theory and Computation
    9, 609 (2013)

[2] C.A. Peeples and G. Schreckenbach, *Implementation of the SM12
    Solvation Model into ADF and Comparison with COSMO*, Journal of
    Chemical Theory and Computation 12, 4033 (2016)

[3] A.V. Marenich, S.V. Jerome, C.J. Cramer, D.G. Truhlar, *Charge
    Model 5: An Extension of Hirshfeld Population Analysis for the
    Accurate Description of Molecular Interactions in Gaseous and
    Condensed Phases*, Journal of Chemical Theory and Computation 8,
    527 (2012)

[4] F.L. Hirshfeld, *Bonded-atom fragments for describing molecular
    charge densities*, Theoretica Chimica Acta 44, 129 (1977)

[5] M. Mantina, R. Valero, C.J. Cramer, D.G. Truhlar, in *CRC Handbook
    of Chemistry and Physics*, 91st ed. (2010-2011), ISBN13
    9781439820773, W.M. Haynes, Ed., CRC Press: Boca Raton, FL, 2010.

[6] W.C. Still, A. Tempczyk, R.C. Hawley, and T. Hendrickson,
    *Semianalytical treatment of solvation for molecular mechanics and
    dynamics*, Journal of the American Chemical Society 112, 6127
    (1990)

[7] D.A. Liotard, G.D. Hawkins, G.C. Lynch, C.J. Cramer, and D.G.
    Truhlar, *Improved Methods for Semiempirical Solvation Models*,
    Journal of Computational Chemistry 16, 422 (1995)
