The frequency and temperature dependence of dipole-quadrupole polarizability of tetrahedral P-4 and adamantane molecules have been studied using first-principle all-electron density functional theory calculation. The recently developed time-dependent auxiliary density functional theory is extended for the calculation of dynamic dipole-quadrupole polarizabilities. Temperature effects are incorporated by Born-Oppenheimer molecular dynamics (BOMD) simulations recorded up to 100 ps. The dynamic dipole-quadrupole polarizabilities are calculated along these trajectories. The frequency and temperature effects can be significant for the accurate calculation of dipole-quadrupole polarizability. We have also identified the main reason for the observed discrepancy between experiment and theory in the case of adamantane. (c) 2012 Elsevier B.V. All rights reserved.