# 11.2.1 Kirkwood-Onsager Model

The simplest implicit solvation model available in Q-Chem is the Kirkwood-Onsager model,Kirkwood:1934, Onsager:1936, Kirkwood:1939 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

 $a=(3V_{m}/4\pi N_{A})^{1/3}$ (11.1)

where $V_{m}$ is the solute’s molar volume, usually obtained from experiment (molecular weight or densityWeast:1989), and $N_{A}$ is Avogadro’s number. It is also common to add 0.5 Å to the value of $a$ in Eq. (11.1) in order to account for the first solvation shell.Wong:1991 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,Born:1920 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. (11.1).

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 11.1  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 11.2  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