Sign inversion of nonlinear optical response of nitrogen upon ionization

We report hyperpolarizability calculations for the nitrogen radical cation at neutral and relaxed geometries in the static and dynamic non-resonant regime, using multi-configurational self-consistent field (MCSCF) response theory. The results were compared with those computed using density functional theory (DFT). The open-shell electronic system of nitrogen radical cation was found to exhibit negative second-order optical nonlinearity. The drastic change in the magnitude and sign of the hyperpolarizability coefficient $\gamma^{(2)}$ from the neutral nitrogen molecule to radical cation indicates an enhanced role of excitations in the polarization response of ion as compared with the neutral molecule. The second-order optical properties of nitrogen radical cation have been also calculated as a function of bond length starting with the neutral molecular geometry (S$_{\mathrm{0}}$ minimum) and stretching the N-N triple bond, reaching the ionic D$_{\mathrm{0}}$ relaxed geometry, and all the way toward dissociation limit. The results obtained provide the potential for controlling optical properties of laser filament wake channels.