To provide an insight into the microscopic second and third-order nonlinear optical (NLO) behavior of chlorophyll a and crocin, we have computed the electric dipole moments (μ), dispersion-free first hyperpolarizabilities (β), frequency-dependent first and second (γ) hyperpolarizabilities at 1064 nm wavelength area using time-dependent Hartree-Fock (TDHF) method. According to ab-initio calculation results, the examined compounds exhibit first and second hyperpolarizabilities with non-zero values, implying second and third-order NLO phenomena.