Vibrational resonance in bichromatically excited diatomic molecules in a shifted molecular potential

For bichromatically excited diatomic molecules modeled in a shifted Tietz-Wei molecular potential, we demonstrate the occurrence of vibrational resonance (VR) when a saddle-node (SN) bifurcation takes place and its nonoccurrence in the absence of an SN bifurcation. We have examined the VR phenomenon and its connection with SN bifurcation for eight diatomic molecules, namely, ${\mathrm{H}}_2, {\mathrm{N}}_2, {\mathrm{Cl}}_2, {\mathrm{I}}_2, {\mathrm{O}}_2$, HF, CO, and NO, consisting of homogeneous, heterogenous, and halogen molecules. We demonstrate that each of them vibrates at a distinct resonant frequency but with a spread in frequency. The high-frequency amplitude at which VR occurs corresponds to the SN-bifurcation point. We validate our analytic results by numerical simulations and show that the homonuclear halogens respond only weakly to bichromatic fields, which may perhaps be linked to their absence of SN bifurcation.