Modern chemistry emerged from the quest to describe the three-dimensional structure of molecules: van't Hoff's tetravalent carbon placed symmetry and dissymmetry at the heart of chemistry. In this Account, we explore how modern theory, synthesis, and spectroscopy can be used in concert to elucidate the symmetry and dissymmetry of molecules and their assemblies. Chiroptical spectroscopy, including optical rotatory dispersion (ORD), electronic circular dichroism (ECD), vibrational circular dichroism (VCD), and Raman optical activity (ROA), measures the response of dissymmetric structures to electromagnetic radiation. This response can in turn reveal the arrangement of atoms in space, but deciphering the molecular information encoded in chiroptical spectra requires an effective theoretical approach. Although important correlations between ECD and molecular stereochemistry have existed for some time, a battery of accurate new theoretical methods that link a much wider range of chiroptical spectroscopies to structure have emerged over the past decade. The promise of this field is considerable: theory and spectroscopy can assist in assigning the relative and absolute configurations of complex products, revealing the structure of noncovalent aggregates, defining metrics for molecular diversity based on polarization response, and designing chirally imprinted nanomaterials. The physical organic chemistry of chirality is fascinating in its own right: defining atomic and group contributions to optical rotation (OR) is now possible. Although the common expectation is that chiroptical response is determined solely by a chiral solute's electronic structure in a given environment, chiral imprinting effects on the surrounding medium and molecular assembly can, in fact, dominate the chiroptical signatures. The theoretical interpretation of chiroptical markers is challenging because the optical properties are subtle, resulting from the strong electric dipole and the weaker electric quadrupole and magnetic dipole perturbations by the electromagnetic field. Moreover, OR arises from a combination of nearly canceling contributions to the electronic response. Indeed, the challenge posed by the chiroptical properties delayed the advent of even qualitatively accurate descriptions for some chiroptical signatures until the past decade when, for example, prediction of the observed sign of experimental OR became accessible to theory. The computation of chiroptical signatures, in close coordination with synthesis and spectroscopy, provides a powerful framework to diagnose and interpret the dissymmetry of chemical structures and molecular assemblies. Chiroptical theory now produces new schemes to elucidate structure, to describe the specific molecular sources of chiroptical signatures, and to assist in our understanding of how dissymmetry is templated and propagated in the condensed phase.
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