Nuclear quantum effects are often neglected for systems without hydrogen atoms. However some planar boron rotors turn out to exhibit remarkable nuclear quantum effects. Recent experiment on infrared spectroscopy of B13+ shows unexpected spectral broadening which still awaits physical explanation. Here we present quantitative investigations of the vibrational energy levels of B11− up to full dimension. A harmonic-bath averaged Hamiltonian suitable for planar boron rotors is constructed and used to predict typical types of vibrational states of B11−. Band structures caused by internal rotations are found for all the investigated vibrational states. The experimental phenomenon of spectral broadening is thus due to the band structures of the corresponding vibrational levels. The detailed information of the relevant vibrational states reported in the present work may provide valuable references for future investigations of high resolution spectroscopy of B11−.
