The nonlinear coefficients, n4, of the time-dependent refractive index for argon are calculated in the non-resonant optical regime. Second-order polynomial fitting of DC-Kerr, γ((2))(-ω; ω, 0, 0), electric field induced second harmonic generation (ESHG), γ((2))(-2ω; ω, ω, 0), and static second-order hyperpolarizability, γ((2))(0; 0, 0, 0), is performed using an auxiliary electric field approach...