We present a time-dependent density-functional theory (TDDFT) with proper asymptotic long-range potential for nonperturbative treatment of multiphoton processes of many-electron molecular systems in intense laser fields. A time-dependent generalized pseudospectral method is extended for precision solution of the TDDFT equations for two-center diatomic systems. The procedure allows nonuniform optimal spatial grid discretization of the Hamiltonian in prolate spheroidal coordinates and a split-operator scheme in energy representation is used for the time propagation of the individual molecular spin orbital in space and time. The theory is applied to the first detailed all-electron study of multiphoton ionization and high-order harmonic generation (HHG) processes of ${\mathrm{N}}_2$ in intense laser fields. The results reveal unexpected and intriguing nonlinear optical response behaviors of the individual valence spin orbital to strong fields. In particular, it is found that the dominant contribution to the total HHG power spectrum of ${\mathrm{N}}_2$ is due to the constructive and destructive interferences of the induced dipoles of the two highest-occupied bonding $\left(3\mathrm{}{\sigma }_g\right)$ and antibonding $\left(2\mathrm{}{\sigma }_u\right)$ molecular orbitals in the presence of intense laser fields.

• Received 30 July 2001

DOI:https://doi.org/10.1103/PhysRevA.64.063404