Calculating the static and dynamic hyperpolarizabilities of methyl oxirane with the Numerical Liouville Approach - Sanders, Reese (My University, 2026)
Since its conception, nonlinear optics has proved to be a crucial tool for physicists across the discipline. Ultrafast researchers employ nonlinear optics to produce high harmonic pulses, and biophysicists apply nonlinear imaging techniques to image organic systems without the need for tagging the system. In this thesis, we investigate the fundamental nonlinear properties known as the hyperpolarizabilities for hydrogen fluoride and methyl oxirane. To calculate these, we numerically solve the Liouville equation for the case of the molecule in an oscillating field. From these solutions we extract the induced dipole, whose Fourier transform we fit to the appropriate nonlinear contributions to derive the hyperpolarizabilities. Using hydrogen fluoride, we validated our methods for the polarizability and first hyper polarizability. Our calculations for the polarizability differed from the literature by 3.37% to 6.56% while the first hyperpolarizability varied by 2.6.% to 17.06%. Our investigation into the the second hyperpolarizability revealed a strong dependence on the number of states for multiple basis sets. With methyl oxirane, we calculated the average polarizability to be 2.867 a.u., the parallel component of the first hyperpolarizability to be -240.5 a.u., and approximated the average second hyperpolarizability to be -1319 a.u. While future projects should continue to explore the inclusion of many more states, our preliminary results for methyl oxirane show that second harmonic generation studies may be particularly useful for experimental studies of the molecule.
Keywords: Molecular hyperpolarizability; Nonlinear optics; Quantum chemistry; Methyl oxirane; Physics