Derivation and Implementation of the Optical Rotation Tensor for Chiral Crystals

12 October 2022, Version 1
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

This work reports the derivation and implementation of the electric dipole-magnetic dipole and electric dipole- electric quadrupole polarizability tensors at density functional theory level with periodic boundary conditions (DFT-PBC). These tensors are combined to evaluate the Buckingham/Dunn tensor that describes the optical rotation (OR) in oriented chiral systems. We detail several aspects of the derivation of the equations, and present test calculations that verify the correctness of the tensors formulation and of their implementation. The results show that the full OR tensor is completely origin invariant as for molecules and that PBC calculations match molecular cluster calculations on 1D chains. A preliminary investigation on the choice of density functional, basis set, and gauge indicates a similar dependence as for molecules: the functional is the primary factor that determines the OR magnitude, followed by the basis set and to a much smaller extent the choice of gauge. However, diffuse functions may be problematic for PBC calculations even if they are necessary for the molecular case. A comparison with experimental data of OR for the tartaric acid crystal shows reasonable agreement given the level of theory employed. The development presented in this work offers the opportunity to simulate the OR of chiral crystalline materials with general purpose DFT-PBC methods, which in turn may help to understand the role of intermolecular interactions on this sensitive electronic property.

Supplementary materials

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Supporting Information for: Derivation and Implementation of the Optical Rotation Tensor for Chiral Crystals
Description
The Supporting Information includes: the geometry for the unit cell of the 1D H2O2 chain, Table S1; the MVG and LG(OI) tensors for the 39 and 37-unit molecular chains of H2O2 molecules as well as the tensors for the PBC calculations, Tables S2-S4; the specific rotation for the periodic 1D H2O2 chain computed with the SVWN5 and HSE06 functionals and the aTZ, QZ, and aQZ basis sets, Table S5; the geometry of the unit cell of tartaric acid, Table S6; the MVG and LG(OI) α tensors, refractive indices along the α principal axes, and OR tensors for the tartaric acid crystal, Tables S7-S10.
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