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Real-time simulations of laser-driven electron dynamics contain informationabout molecular optical properties through all orders in response theory. Theseproperties can be extracted by assuming convergence of the power seriesexpansion of induced electric and magnetic multipole moments. However, theaccuracy relative to analytical results from response theory quicklydeteriorates for higher-order responses due to the presence of high-frequencyoscillations in the induced multipole moment in the time domain. This problemhas been ascribed to missing higher-order corrections. We here demonstrate thatthe deviations are caused by nonadiabatic effects arising from the finite-timeramping from zero to full strength of the external laser field. Three differentapproaches, two using a ramped wave and one using a pulsed wave, for extractingelectrical properties from real-time time-dependent electronic-structuresimulations are investigated. The standard linear ramp is compared to aquadratic ramp, which is found to yield highly accurate results forpolarizabilities, and first and second hyperpolarizabilities, at roughly halfthe computational cost. Results for the third hyperpolarizability are presentedalong with a simple, computable measure of reliability.

Adiabatic extraction of nonlinear optical properties from real-time time-dependent electronic-structure theory