Continuum solvation (CPCM, SMD)

The conductor-like polarizable continuum model, CPCM, is implemented in ORCA and is an efficient, albeit crude, way of accounting for solvent effects in quantum chemical calculations. The solvent is represented as a dielectric polarizable continuum and the solute is placed in a cavity of approximately molecular shape. The solvent reaction field is described by polarization charges on the surface of the cavity and is now described by Gaussians rather than regular pointcharges. The cavity is created by a vdW surface by default but there are also other options described in the manual. See ORCA manual for details on the CPCM continuum solvation model.

The SMD solvation model has been implemented into ORCA as well and uses the CPCM algorithm but uses different radii to create the cavity and calculates a different non-electrostatic contribution (the cavity-dispersion-solvent structure (CDS) term). See article by Cramer,Truhlar et al. The manual discusses the SMD implementation.

Simple use of CPCM

Most of the time it is sufficient to simply use the CPCM Simpleinput keyword with the name of the solvent in parentheses. Table 1 contains the list of solvent keywords.

Table 1. List of available solvents keywords, the dielectric constants of solvents and refractive index.

! CPCM(solvent)

To specify a CPCM calculation with water used as solvent one simply choooses:

! CPCM(Water)

To choose an infinite dielectric constant (crude model for a polar crystal environment) one simply chooses the CPCM keyword alone:

! CPCM

To choose a solvent manually by its dielectric constant requires use of the %cpcm block. Below a hypothetical ε=4 solvent is chosen. This is a common way of crudely model a protein environment.

! CPCM
%cpcm
epsilon 4
end

Other CPCM options:

! CPCM

%cpcm
epsilon 80.0 # Dielectric constant
refrac 1.0 # Refractive index
rsolv 1.3 # Solvent probe radius
rmin 0.5 #Minimal GEPOL sphere radius
fepstype cpcm # Epsilon function type: cpcm, cosmo
surfacetype vdw_gaussian # GEPOL surface: gepol_ses, gepol_sas, gepol_ses_gaussian
ndiv 5 # Maximum depth for recursive sphere generation
radius[N] 1.3 # Atomic radius for atomic number N in Angstrom
end

The refractive index can be specified (refrac keyword within %cpcm block). Note that the refractive index is only needed for excited state calculations.

Note: For the accurate calculation of solvation free energies etc. it might be important to consider the outlying charge correction which is calculated in every CPCM calculation but is not added to the total energy (due to its non-variational nature and inconsistency with geometry optimization). The correction is usually small, however.

Example CPCM ORCA output:

CPCM Solvation Model Properties:
Surface-charge : -0.00486063
Charge-correction : 0.00000685 Eh 0.00019 eV
Free-energy (cav+disp) : 0.00265352 Eh 0.07221 eV
Corrected G(solv) : -129.58433447 Eh -3526.16901 eV

Using CPCM for optimizations and frequencies

• Using CPCM in DFT optimizations is straightforward. Note that if one is interested in computing free energies of solvation that gas phase vs. CPCM geometries tend to be rather similar so often a single-point CPCM calculation on a gasphase optimized geometry may be sufficient. There are exceptions to this, however, e.g. anions and zwitterions whose geometries may behave completely different in the vacuum vs. polarizable continuum.

• Numerical frequencies with CPCM are available (and more recently analytical).
  

The SMD solvation model

The SMD solvation model is also available in ORCA. It uses the CPCM model inside ORCA to calculate the electrostatic solvation energy but with different atomic radii for creating the cavity and also calculates a non-electrostatic contribution.

To use SMD, CPCM is specified as usual but SMD invoked in the %cpcm block. The SMD solvent is then specified using the SMDSolvent keyword, see list of all solvents in manual.

! CPCM
%cpcm
smd true
SMDsolvent "DMF"
end
%cpcm
smd true
SMDsolvent "WATER"
end