Equilibrium solvation in quadrupolar solvents

Abstract

We present a microscopic theory of equilibrium solvation in solvents with zero dipole moment and non-zero quadrupole moment (quadrupolar solvents). The theory is formulated in terms of autocorrelation functions of the quadrupolar polarization (structure factors). It can be therefore applied to an arbitrary dense quadrupolar solvent for which the structure factors are defined. We formulate a simple analytical perturbation treatment for the structure factors. The solute is described by coordinates, radii, and partial charges of constituent atoms. The theory is tested on Monte Carlo simulations of solvation in model quadrupolar solvents. It is also applied to the calculation of the activation barrier of electron transfer reactions in a cleft-shaped donor-acceptor complex dissolved in benzene with the structure factors of quadrupolar polarization obtained from Molecular Dynamics simulations.

Comment on “A spherical cavity model for quadrupolar dielectrics” [J. Chem. Phys. 144, 114502 (2016)]

“…1 (18) holds true with the new formulae presented here; note that it is actually incorrect with the old ones due to an arithmetic mistake. This means that the revised Onsager model following from the new boundary condition (6) leads to the correct continuum single particle limit of the perturbation theory of Milischuk and Matyushov, 8 while the old one 1 stemming from Eq. (2) does not.…”

“…1, we used the condition for continuity of the normal displacement field (D r ) at the surface of the spherical cavity, Eq. 1 (8) …”

Quadrupolar solvatochromism: 4-amino-phthalimide in toluene

“…6 Therefore we will use the following expressions for the structure factors of toluene: S 0 ͑k͒ = 1 − 12y q I ͑2͒ ͑k, * ͒, S 1 ͑k͒ = 2 + 16y q I ͑2͒ ͑k, * ͒, ͑9͒ S 2 ͑k͒ = 2 − 4y q I ͑2͒ ͑k, * ͒. 2͒ can be calculated either from computer experiment or from analytical models.…”

“…Integral equation ͓reference interaction site model ͑RISM͔͒, 1 continuum, [2][3][4] and perturbation 5,6 approaches have been suggested. 5,6 The first approach 5 approximates the solute by a spherical dipole and gives the solvation chemical potential in a dipolar-quadrupolar solvent as a Padé expansion in the solute-solvent potential. In short, the RISM implementation approximates both the solute and the solvent by a set of coarse-grained spheres characterized by charges and Lennard-Jones ͑LJ͒ potentials.…”

“…They differ by the details of the solute and solvent structure incorporated in the modeling and by complexity of calculations. 6 This much more realistic description of the solute allows us to use the results of quantum calculations to parametrize the atomic charges. The interaction energy is taken in the form of a site-site potential, and the theory solves a set of integral equations for the site-site pair distribution functions.…”