Density Functional Restricted-Unrestricted/Molecular Mechanics Theory for Hyperfine Coupling Constants of Molecules in Solution

A density functional restricted-unrestricted approach, capable of evaluating hyperfine coupling constants with the inclusion of spin polarization effects in a spin-restricted Kohn-Sham method, has been extended to incorporate environmental effects. This is accomplished by means of a hybrid quantum mechanics/molecular mechanics formalism which allows for a granular representation of the polarization and electrostatic interactions with the classically described medium. By this technique, it is possible to trace the physical origin of hyperfine coupling constants in terms of spin polarization and spin density contributions and disentangle the dependence of these contributions on molecular geometry and solvent environment, something that increases the prospects for optimal design of spin labels for particular applications. A demonstration is given for the nitrogen isotropic hyperfine coupling constant in di-tert-butyl nitroxide solvated in water. The results indicate that the direct spin density contribution is about 5 times smaller than the spin polarization contribution to the nitrogen isotropic hyperfine coupling constant and that the latter contribution is solely responsible for the solvent shift of the constant. The developed approach is found capable of achieving satisfactory accuracy in prediction of the hyperfine coupling constants of solvated di-tert-butyl nitroxide and other similar nitroxides without the inclusion of solvent molecules in the quantum region provided polarizable force fields are used for the description of these molecules.