12.2 Chemical Solvent Models 12.2 Chemical Solvent Models 12.2.2 Polarizable Continuum Models

12.2.1 Kirkwood-Onsager Model

The simplest implicit solvation model available in Q-Chem is the Kirkwood-Onsager model,^{470, 692, 471} wherein the solute is placed inside of a spherical cavity that is surrounded by a homogeneous dielectric medium. This model is characterized by two parameters: the cavity radius, $a$ , and the solvent dielectric constant, $\varepsilon$ . The former is typically calculated according to

a=(3V_{m}/4\pi N_{A})^{1/3}

(12.1)

where $V_{m}$ is the solute’s molar volume, usually obtained from experiment (molecular weight or density⁹⁷¹), and $N_{A}$ is Avogadro’s number. It is also common to add 0.5 Å to the value of $a$ in Eq. (12.1) in order to account for the first solvation shell.¹⁰¹³ Alternatively, $a$ is sometimes selected as the maximum distance between the solute center of mass and the solute atoms, plus the relevant van der Waals radii. A third option is to set $2a$ (the cavity diameter) equal to the largest solute–solvent internuclear distance, plus the van der Waals radii of the relevant atoms. Unfortunately, solvation energies are typically quite sensitive to the choice of $a$ (and to the construction of the solute cavity, more generally).

Unlike older versions of the Kirkwood-Onsager model, in which the solute’s electron distribution was described entirely in terms of its dipole moment, Q-Chem’s version can use multipoles of arbitrarily high order, including the Born (monopole) term for charged solutes,¹¹⁰ in order to describe the solute’s electrostatic potential. The solute–continuum electrostatic interaction energy is then computed using analytic expressions for the interaction of the point multipoles with a dielectric continuum.

Energies and analytic gradients for the Kirkwood-Onsager solvent model are available for Hartree-Fock, DFT, and CCSD calculations. It is often advisable to perform a gas-phase calculation of the solute molecule first, which can serve as the initial guess for a subsequent Kirkwood-Onsager implicit solvent calculation.

The Kirkwood-Onsager SCRF is requested by setting SOLVENT_METHOD = ONSAGER in the $rem section (along with normal job control variables for an energy or gradient calculation), and furthermore specifying several additional options in a $solvent input section, as described below. Of these, the keyword CavityRadius is required. The $rem variable CC_SAVEAMPL may save some time for CCSD calculations using the Kirkwood-Onsager model.

Note: SCRF and CCSD combo works only in CCMAN (with CCMAN2 = FALSE).

Note: The following three job control variables belong only in the $solvent section. Do not place them in the $rem section. As with other parts of the Q-Chem input file, this input section is not case-sensitive.

CavityRadius
       Sets the radius of the spherical solute cavity.
INPUT SECTION: $solvent
TYPE:
       FLOAT
DEFAULT:
       No default.
OPTIONS:
       $a$ Desired cavity radius, in Ångstroms.
RECOMMENDATION:
       Use Eq. (12.1).

Dielectric
       Sets the dielectric constant of the solvent continuum.
INPUT SECTION: $solvent
TYPE:
       FLOAT
DEFAULT:
       78.39
OPTIONS:
       $\varepsilon$ Use a (dimensionless) value of $\varepsilon$ .
RECOMMENDATION:
       As per required solvent; the default corresponds to water at 25 ${}^{\circ}$ C.

MultipoleOrder
       Determines the order to which the multipole expansion of the solute charge density is carried out.
INPUT SECTION: $solvent
TYPE:
       INTEGER
DEFAULT:
       15
OPTIONS:
       $\ell$ Include up to $\ell$ th order multipoles.
RECOMMENDATION:
       Use the default. The multipole expansion is usually converged by order $\ell$ = 15.

Example 12.1 Onsager model applied at the Hartree-Fock level to H ${}_{2}$ O in acetonitrile

$molecule
   0 1
   O       0.00000000     0.00000000     0.11722303
   H      -0.75908339     0.00000000    -0.46889211
   H       0.75908339     0.00000000    -0.46889211
$end

$rem
   METHOD            HF
   BASIS             6-31g**
   SOLVENT_METHOD    Onsager
$end

$solvent
   CavityRadius      1.8    !   1.8 Angstrom Solute Radius
   Dielectric        35.9   !   Acetonitrile
   MultipoleOrder    15     !   this is the default value
$end

Example 12.2 Kirkwood-Onsager SCRF applied to hydrogen fluoride in water, performing a gas-phase calculation first.

$molecule
   0 1
   H       0.000000     0.000000    -0.862674
   F       0.000000     0.000000     0.043813
 $end

$rem
   METHOD          HF
   BASIS           6-31G*
$end

@@@

$molecule
  read
$end

$rem
   JOBTYPE           FORCE
   METHOD            HF
   BASIS             6-31G*
   SOLVENT_METHOD    ONSAGER
   SCF_GUESS         READ  ! read vacuum solution as a guess
$end

$solvent
   CavityRadius    2.5
$end

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12.2.1 Kirkwood-Onsager Model