SM12: Solvation Model 12¶

Continuum solvation can be done with the Minnesota’s Solvation Model 12 (SM12) [399]. Details on the implementation of SM12 in ADF can be found in Ref. [439]. The energetics of solvation is calculated using:

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 uses CM5 charges [378]. CM5 is a class 4 charge model, making use of both empirical and density related terms. It is comprised of Hirshfeld charges [125], a simple bond order calculation, atomic distances, and atom specific parameters [378]. The covalent radii utilized are based on the atomic covalent radius from the Handbook of Chemistry and Physics [402]. The Coulomb integral is described with the use of an approximation from Still et al. [400]. Several parameters go into describing this, which include: inter atomic distance, an empirical Born constant, and the Born area, which is calculated with the Analytical Surface Area (ASA) algorithm [401]. 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
  {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}
End

Presence of the SOLVATION SM12 key block key triggers the solvent calculation and does not require additional data. If no other keywords are present the default is water. 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

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. [399]. 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 un-specified 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.

BORNC

Empirical Born constant, see Ref. [399]

PRINTSM12

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