Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo

We demonstrate computation of total dynamic multipole polarizabilities using path-integral Monte Carlo method (PIMC). The PIMC approach enables accurate thermal and nonadiabatic mixing of electronic, rotational, and vibrational degrees of freedom. Therefore, we can study the thermal effects, or lack thereof, in the full multipole spectra of the chosen one- and two-electron systems: H, Ps, He, Ps₂, H₂, and HD⁺. We first compute multipole-multipole correlation functions up to octupole order in imaginary time. The real-domain spectral function is then obtained by analytical continuation with the maximum entropy method. In general, sharpness of the active spectra is limited, but the obtained off-resonant polarizabilities are in good agreement with the existing literature. Several weak and strong thermal effects are observed. Furthermore, the polarizabilities of Ps₂ and some higher multipole and higher frequency data have not been published before. In addition, we compute isotropic dispersion coefficients C₆, C₈, and C₁₀ between pairs of species using the simplified Casimir-Polder formulas.