2009/08/21 by Mark G. Kuzyk, Kuzyk, Mark G. · 1 citation
Chemistry · Engineering · Materials Science · Physics and Astronomy · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Molecular spectroscopy and chirality #Nonlinear Optical Materials Research #Nonlinear Optical Materials Studies #Optics (physics.optics) #physics.chem-ph #physics.optics
paper · pdf · doi:10.48550/arxiv.0908.3200
16 pages, three figures
arxiv created 2009/08/21 · openalex publication_date 2009/08/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Schrödinger equation has the property that when changing the length scale by r → εr and the energy scale by E → E / ε2, the shape of the wavefunction remains unchanged. The same re-scaling leaves the intrinsic hyperpolarizability (as well as higher-order hyperpolarizabilities) unchanged. As such, the intrinsic hyperpolarizability is the best quantity for comparing molecules since it re-normalizes for trivial differences that are due to molecular size and energy gap. Similarly, the intrinsic hyperpolarizability is invariant to changes in the number of electrons. In this paper, we review the concept of scale invariance and how it can be applied to better understand the nonlinear optical response, which can be used to develop new paradigms for it's optimization.