Optical Activity in Crystalline Solids: Theoretical Formulations of Vibrational Circular Dichroism

Theoretical descriptions of vibrational circular dichroism (VCD) in solids unite vibrational spectroscopy, structural chirality and periodicity. Unlike isolated molecules, crystalline systems require the explicit consideration of long-range order, including supramolecular chirality and collective vibrational motion. Electronic structure and linear response theory, adapted for the solid state, provide the necessary computational framework. In practice, plane-wave basis sets and pseudopotentials facilitate efficient electronic-structure calculations using Kohn-Sham density functional theory (KS-DFT) under periodic boundary conditions (PBCs). A distinctive feature of solid-state VCD is the separation of local terms, which capture intramolecular contributions, from non-local terms, which describe intermolecular couplings. This can be achieved by analysing the response functions using maximally localised Wannier functions (MLWFs). Decomposing the electric and magnetic dipole operators enables the spectra to be interpreted in terms of both molecular and supramolecular chirality. Vibrational modes can be computed either statically, through harmonic normal-mode analysis (NMA), or dynamically, by molecular dynamics (MD) simulations, which capture anharmonicity and finite-temperature effects. In molecular crystals, Davydov (factor group) splitting determines the IR/VCD-active vibrational manifold due to intermolecular coupling. Among the available response formalisms, nuclear velocity perturbation theory (NVPT) has proven particularly valuable, as the current-based formulation of this theory naturally integrates with periodic density functional theory (DFT), thereby removing origin dependence at the linear response level. By linking collective vibrational dynamics, periodic electronic structure, and a well-defined magnetic gauge, these approaches establish a robust foundation of vibrational chiroptical spectroscopy, transitioning from isolated molecules to crystalline environments.