Effect of nuclear vibration on high-order-harmonic generation of alignedH2+molecules

High-order-harmonic generation (HHG) spectra have been calculated for ${{\mathrm{H}}_2}^{+}$ molecules aligned parallel to the polarization of the laser field. We make use of the Jacobi coordinates and neglect the rotation of the nuclei. The remaining time-dependent Schrödinger equation is three dimensional in spatial coordinates, one of them being the internuclear separation and the other two describing the electronic motion. The problem is solved using the accurate and efficient time-dependent generalized pseudospectral method in prolate spheroidal coordinates for the electronic coordinates and Fourier grid method for the internuclear separation. Laser pulses with a carrier wavelength of 800 nm, a duration of ten optical cycles, and a peak intensity of $2\times {10}^{14}$ ${\text{W/cm}}^2$ have been used in the calculations. Our HHG spectra, which incorporate the effect of nuclear vibration, generally exhibit a significant deviation from those calculated for the fixed internuclear separations. The low-energy regions of the spectra, however, resemble those for the nuclei fixed at larger separations, while the high-energy regions are closer to those for the nuclei fixed at smaller internuclear distances. The dynamics of the nuclear vibrational wave packet is also obtained and analyzed.