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.

A perturbation theory approach was developed for predicting the vibrational and electronic second-order nonlinear optical (NLO) polarizabilities of materials and macromolecules comprised of many coupled chromophores, with an emphasis on common protein secondary structural motifs. The polarization-dependent NLO properties of electronic and vibrational transitions in assemblies of amide chromophores comprising the polypeptide backbones of proteins were found to be accurately recovered in quantum chemical calculations by treating the coupling between adjacent oscillators perturbatively. A novel diagrammatic approach was developed to provide an intuitive visual means of interpreting the results of the perturbation theory calculations. Using this approach, the chiral and achiral polarization-dependent electronic SHG, isotropic SFG, and vibrational SFG nonlinear optical activities of protein structures were predicted and interpreted within the context of simple orientational models.

Second harmonic generation (SHG) and angle-resolved absorbance with photoacoustic detection were combined to evaluate both the mean orientation angle and the width of the angular distribution for two surface-bound molecular systems. Assuming a Gaussian distribution function, a physisorbed stilbene dye on fused silica exhibited a narrow distribution centered at 73 degrees with a root-mean-square (rms) width of less than approximately 8 degrees. In contrast, a covalently bound azo dye resulted in a broad orientation distribution (rms width of approximately 30 degrees) centered at 60 degrees. It was also demonstrated that the combination of nonlinear (SHG) and linear (absorbance) spectroscopic techniques provides valuable insight into molecular orientation that a combination of two linear techniques (such as fluorescence and absorbance) is unable to provide.

Second-order nonlinear optical imaging of chiral crystals (SONICC) is an emerging technique for crystal imaging and characterization. We provide a brief overview of the origin of second harmonic generation signals in SONICC and discuss recent studies using SONICC for biological applications. Given that they provide near-complete suppression of any background, SONICC images can be used to determine the presence or absence of protein crystals through both manual inspection and automated analysis. Because SONICC creates high-resolution images, nucleation and growth kinetics can also be observed. SONICC can detect metastable, homochiral crystalline forms of amino acids crystallizing from racemic solutions, which confirms Ostwald’s rule of stages for crystal growth. SONICC’s selectivity, based on order, and sensitivity, based on background suppression, make it a promising technique for numerous fields concerned with chiral crystal formation.