12.2.9 Langevin Dipoles Model

Q-Chem provides the option to calculate molecular properties in aqueous solution and the magnitudes of the hydration free energies by the Langevin dipoles (LD) solvation model developed by Jan Florián and Arieh Warshel^{266, 267} at the University of Southern California. In this model, a solute molecule is surrounded by a sphere of point dipoles, with centers on a cubic lattice. Each of these “Langevin” dipoles changes its size and orientation in the electrostatic field of the solute and the other Langevin dipoles. The electrostatic field from the solute is determined rigorously by the integration of its charge density, whereas for dipole–dipole interactions, a 12 Å cutoff is used. The Q-Chem/ChemSol 1.0 implementation of the LD model is fully self-consistent in that the molecular quantum mechanical calculation takes into account solute–solvent interactions. Further details on the implementation and parameterization of this model can be found in the literature.^{266, 267}

The results of ChemSol calculations are printed in the standard output file. Below is a part of the output for a calculation on the methoxide anion (corresponding to the sample input given later on, and the sample file in the $QC/samples directory).

The total hydration free energy, $\mathrm{\Delta }G$(ILD) is calculated as a sum of several contributions. Note that the electrostatic part of $\mathrm{\Delta }G$ is calculated by using the linear-response approximation²⁶⁶ and contains contributions from the polarization of the solute charge distribution due to its interaction with the solvent. This results from the self-consistent implementation of the Langevin dipoles model within Q-Chem.

To perform an LD calculation in Q-Chem, specify normal job-control variables for a Hartree-Fock or DFT calculation, and set SOLVENT_METHOD = CHEM_SOL in the $rem section. Additional fine-tuning is accomplished using a set of keywords in a $chem_sol input section. The remainder of this section summarizes these keywords.

Accurate calculations of hydration free energies require a judicious choice of the solute–solvent boundary in terms of atom-type dependent parameters. The default atomic van der Waals radii available in Q-Chem were chosen to provide reasonable hydration free energies for most solutes and basis sets. These parameters basically coincide with the ChemSol 2.0 radii given in Ref. 267. The only difference between the Q-Chem and ChemSol 2.0 atomic radii stems from the fact that Q-Chem parameter set uses radii for carbon and oxygen that are independent of the atom’s hybridization state. User-defined atomic radii can be specified by declaring the option ReadRadii in the $chem_sol input section, and then placing the radii in the $van_der_waals section. Two different (and mutually exclusive) formats can be used, as shown below.

$van_der_waals
1
atomic_number   vdW_radius
...
$end

$van_der_waals
2
sequential_atom_number   vdW_radius
...
$end

The purpose of the second format is to permit the user to customize the radius of specific atoms, in the order that they appear in the $molecule section, rather than simply by atomic numbers as in format 1. The radii of atoms that are not listed in the $van_der_waals input will be assigned default values. The atomic radii that were used in the calculation are printed in the ChemSol part of the output file in the column denoted rp. All radii should be given in Ångstroms.