Helical Chains of Diatomic Molecules as a Model for Solid-State Optical Rotation

Abstract

Optical rotation (OR) measurements are a common method for distinguishing chiral compounds, but it is not well understood how intra- and intermolecular interactions affect this electronic property. Theoretical comparisons with solution-phase measurements are hampered by the difficulty of modeling solvent effects and the isotropic averaging of the experimental observable. Solid-state OR experiments/calculations could alleviate these difficulties, but experimental measurements are challenging and computational efforts have been limited due to a lack of existing procedures. We report calculated OR tensor values for a series of helices of diatomic molecules that may serve as a benchmark in the development of general-purpose electronic structure methods to compute the optical rotation of solids, in particular, molecular crystals. We find that the OR tensors for small helix clusters show poor agreement with values converged with respect to the helix size, regardless of unit cell size. The dependence of the converged OR on the dihedral angle of homonuclear helices is well described by the Kirkwood polarizability model, indicating that nearest-neighbor interactions are very important, albeit not the only relevant interactions. Basis set comparisons suggest that the aug-cc-pVDZ basis is sufficient to obtain qualitatively accurate results.

Full optical rotation tensor at coupled cluster with single and double excitations level in the modified velocity gauge

“…Although the theory for the evaluation of the full OR tensor has been reported multiple times, 20,24,25 we review the basic equations here for completeness. The oriented Buckingham/Dunn optical activity tensorB is defined as 20,24,25B…”

“…Thus, only a few studies report the full OR tensor. [20][21][22][23][24] The simulations of the isotropic OR are less computationally demanding than those for the full OR tensor, but they are also more prone to numerical errors that make the comparison with experimental measurements more uncertain even when highly accurate methods are employed. 15 The former issue is due to the fact that forming the full OR tensor requires the evaluation of the mixed electric dipole-magnetic dipole and electric dipole-electric quadrupole polarizability tensors, while the isotropic OR only requires the former tensor.…”

Origin Invariant Optical Rotation in the Length Dipole Gauge without London Atomic Orbitals

“…Technically, the full OR tensor (the Buckingham/Dunn B tensor) includes contributions from the electric dipole-electric quadrupole polarizability tensor. 25,27,28 However, the latter does not contribute to [α] ω in Eq. 2 because the quadrupole operator is traceless, thus this tensor will be neglected here.…”

“…Nevertheless, such contribution cannot be ignored for spatially oriented systems. 28 Following the notation of Lazzeretti and coworkers, 18,29,30 the origin dependence of the β tensor can be expressed as:…”

Full Optical Rotation Tensor at CCSD Level in the Modified Velocity Gauge

“…Thus, only few studies report the full OR tensor. [20][21][22][23][24] The simulations of the isotropic OR are less computationally demanding than those for the full OR tensor, but they are also more prone to numerical errors that make the comparison with experimental measurements more uncertain even when highly accurate methods are employed. 15 The former issue is due to the fact that forming the full OR tensor requires the evaluation of the mixed electric dipole-magnetic dipole and electric dipole-electric quadrupole polarizability tensors, while the isotropic OR only requires the former tensor.…”