Computing optical rotation via an N-body approach

Properties of four chiral compounds—(S)-methyloxirane, (S)-methylthiirane, (S)-2-chloropropionitrile, and (M)-dimethylallene—centered in a solvation shell of six to seven water molecules have been computed using time-dependent density functional theory at several wavelengths using a many-body expansion. Interaction energies, total system dipole moments, and dynamic dipole polarizabilities converge rapidly and smoothly, exhibiting only minor oscillations with higher-body contributions. At three-body truncation of the expansion, errors in such properties as compared to the full cluster typically fall to less than 1 % (and much smaller in most cases). Specific optical rotations, however, are found to converge much more slowly and erratically, requiring five-body contributions to obtain errors less than 5 % in three of four test cases, and six-body terms for (S)-methylthiirane. The source of this behavior is found to be the wide variation of both magnitude and sign of the specific rotation with changes in the configuration of individual solute/solvent clusters. Thus, unlike simpler properties such as energies or dipole moments, where each fragment makes a small, same-sign contribution to the total property, specific rotations typically involve much larger contributions that partly cancel in the many-body expansion. Thus, the computational costs of molecular dynamics simulations of explicit solvation, for example, will be only partially alleviated by such expansions.