Application of computational techniques to nonlinear optical spectroscopy provides significant insights in the prediction and explanation of the experimental behaviour of various systems. The determination of the second harmonic generation (SHG) hyperpolarizabilities of chromophores with varying degrees of charge transfer by computational means is an important test of the capability of these approaches. In this study, we computationally investigate the hyperpolarizabilities of the three nitroaniline isomers, para-nitroaniline (pNA), ortho-nitroaniline (oNA), meta-nitroaniline (mNA) by density functional theory (B3LYP, LC-BLYP, ωB97, and ωB97XD) with reference to gas phase CCSD/aug-cc-pVDZ results and experimental measurements conducted in the presence of solvent.(1) In particular, the emphasis is on understanding the trend in measured hyperpolarizabilities (pNA>oNA>mNA) as well as the effect of excitation wavelength. For the range separated functionals (LC-BLYP, ωB97, and ωB97XD) optimal gap tuning of the range separation parameter is performed such that Koopman’s theorem is satisfied. (2) The resultant hyperpolarizabilities from the tuned functionals are compared to the untuned functionals. The effect of the excitation wavelength is apparent on the computed hyperpolarizabilities of the isomers, as the hyperpolarizability trend is broken at the static limit and for excitation wavelengths near the electronic resonances (~250 nm). The need for optimal gap tuning of range separated hybrid functionals becomes more apparent at the highest wavelength (1907 nm) and the static limit for reproduction of the experimental trend and CCSD/aug-cc-pVDZ results respectively. Additionally, the excitation wavelength is also found to influence optimal gap tuning of range separated functionals where at 1907 nm and the static limit, the behaviour is pathological while at 1064 nm it reverts to the typical behaviour associated with optimal gap tuning.(3)

1. Levine, B. F.; Bethea, C. G. Molecular Hyperpolarizabilities Determined from Conjugated and Nonconjugated Organic Liquids. Appl. Phys. Lett. 1974, 24 (9), 445–447.
2. Kronik, L.; Stein, T.; Refaely-Abramson, S.; Baer, R. Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals. J. Chem. Theory Comput. 2012, 8 (5), 1515–1531.
3. Garza, A. J.; Osman, O. I.; Asiri, A. M.; Scuseria, G. E. Can Gap Tuning Schemes of Long-Range Corrected Hybrid Functionals Improve the Description of Hyperpolarizabilities. J. Phys. Chem. B 2015, 119 (3), 1202–1212.

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