The simplest implicit solvation model available in Q-Chem is the multipolar expansion model,569, 782, 461 which has also been called the Kirkwood-Onsager model or sometimes the generalized Kirkwood model.461 In this approach, the solute is placed inside of a spherical cavity of radius that is surrounded by a homogeneous dielectric medium whose dielectric constant is , and these constitute the only parameters of the model. The term Onsager model is sometimes synonymous with a point-dipole approximation for the solute’s charge density, but Q-Chem’s version uses a single-center multipole expansion of the density (which can be extended to arbitrarily high order), in order to obtain an essentially exact description of the solute’s electrostatic potential. The model then consists of using Kirkwood’s analytic expressions for the solvation energy of each spherical harmonic function, in a spherical cavity inside of a dielectric continuum.461
Regarding the cavity radius , Onsager’s original suggestion is based on the molar volume of the pure solute,
where is Avogadro’s constant. This was later shown to be a poor choice in the context of modern quantum chemistry calculations.461 It is also common to add 0.5 Å to the value of in Eq. (11.1) in order to account for the first solvation shell,1232 or to set equal to 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 (the cavity diameter) equal to the largest solute–solvent internuclear distance, plus the van der Waals radii of the relevant atoms. Clearly, there is quite a bit of arbitrariness in this choice and solvation energies are quite sensitive to the value of ,461 and the PCMs that are described in Section 11.2.3 have largely made the multipolar expansion method obsolete, since the PCMs employ the exact electron density and can be used (if desired) with a spherical cavity, although the more typical choice is a molecule-shaped van der Waals cavity.
The Kirkwood-Onsager SCRF is requested by setting SOLVENT_METHOD = KIRKWOOD in the $rem section. Some additional options can be specified in the $solvent section, as described below, of which only CavityRadius is required. 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. For coupled-cluster calculations using this model, one may set CC_SAVEAMPL = TRUE to retain the CC amplitudes from the gas-phase calculation, which will save some time in the subsequent solution-phase calculation.
Note: For CCSD calculations the Kirkwood-Onsager model works only with CCMAN2 = FALSE.
The following job-control options belong in the $solvent section, not the $rem section. As with other parts of the Q-Chem input file, this input section is not case-sensitive.
$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
$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 KIRKWOOD SCF_GUESS READ ! read vacuum solution as a guess $end $solvent CavityRadius 2.5 $end