A simplifying treatment is developed for describing the molecular origins of electric dipole allowed sumfrequency generation (SFG) and second harmonic generation (SHG). The full sum-over-states expressions for the nonlinear polarizability simplify tremendously at or near resonance to straightforward formulas easily connected to intuitive molecular properties. For resonance enhancement at the sum or second harmonic frequency, the molecular nonlinear polarizability tensor is shown to be the direct product of the transition moment and the two-photon absorption (TPA) polarizability tensor. To our knowledge, this is the first rigorous mathematical demonstration indicating such a simple relationship directly connecting second harmonic generation with TPA, providing a link between the two fields of inquiry. Under resonance enhancement with one of the incident frequencies, the SFG and SHG nonlinear polarizability tensors similarly are given by the products of the transition moments and the anti-Stokes Raman polarizability tensors (a reasonably wellknown result for SFG). Under double-resonance conditions (i.e., resonant with one of the incident frequencies and the sum frequency), the two descriptions for the nonlinear polarizability become mathematically equivalent. Nonlinear optical character tables for both SHG and SFG under all resonance conditions have been compiled for chromophores of C s , C 2 , C 2V , and C 3V symmetries. Explicit evaluation of the corresponding orientational averages for each allowed transition in each character table assuming a uniaxial macroscopic orientation distribution reveals numerous relationships connecting the microscopic symmetry with the macroscopic nonlinear response. The approaches developed in this work are sufficiently general to allow their use in interpreting electronic, vibrational, and vibronic spectroscopic measurements by SHG and SFG.

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The past decade has witnessed the emergence of new measurement approaches and applications for chiral thin films and materials enabled by the observations of the high sensitivity of second-order nonlinear optical measurements to chirality. In thin films, the chiral response to second harmonic generation and sum frequency generation (SFG) from a single molecular monolayer is often comparable with the achiral response. The chiral specificity also allows for symmetry-allowed SFG in isotropic chiral media, confirming predictions made approximately 50 years ago. With these experimental demonstrations in hand, an important challenge is the construction of intuitive predictive models that allow the measured chiral response to be meaningfully related back to molecular and macromolecular structure. This review defines and considers three distinct mechanisms for chiral effects in uniaxially oriented assemblies: orientational chirality, intrinsic chirality, and isotropic chirality. The role of each is discussed in experimental and computational studies of bacteriorhodopsin films, binaphthol, and collagen. Collectively, these three model systems support a remarkably simple framework for quantitatively recovering the measured chiral-specific activity.

Recent observations of remarkably large chiroptical effects in second-harmonic generation (SHG) and sum-frequency generation (SFG) measurements suggest exciting possibilities for the development of new chiral-specific spectroscopies and novel chiral materials for nonlinear optics. Several fundamental studies designed to elucidate the molecular and macromolecular origins of the chiral responses are reviewed to provide a framework for development of this emerging field. In general, the chiral activity in SHG and SFG has the potential to arise from complex interactions between hosts of different competing effects. Fortunately, relatively simple electric dipole-allowed mechanisms routinely dominate the nonlinear optical chiral activities of most practical systemsexpressions can often be generated to link the. This substantial reduction in complexity allows for the development of simple models connecting the macroscopic nonlinear optical response to intuitive molecular and supramolecular properties.