Ab initio calculations of nonlinear optical rotation by several small chiral molecules and by uridine stereoisomers

Expressions for nonlinear optical rotation are presented based on the quantum theory of optical birefringence of Atkins and Barron [Proc. R. Soc. London, Ser. A 304, 303 (1968); 306, 119 (1968)]. As concrete examples, the ordinary and nonlinear optical rotations are calculated with density functional theory (DFT) methodology for some simple single-ring molecules, namely, oxaziridine, diaziridine, and their derivatives, and for two, somewhat more complicated, conformations of uridine. For the single-ring molecules, (1) the angles of the ordinary optical rotation are mostly positive and (2) the contributions of the nonlinear effect to the total optical rotation depend both on the nature of the substituted species and of the host atom located on the ring. For the two conformations of uridine, (1) the signs of nonlinear optical rotation differ even though their ordinary optical rotations have the same sign and (2) whether the molecular structures are geometrically optimized with Hartree-Fock or DFT methodologies has no significant effect on the calculated nonlinear optical rotation when gauge-including atomic orbitals were used, even though the basis sets are small. These studies are expected to be helpful for interpretation of experimental results on nonlinear optical rotation by molecules underway in our research group.