  Path integral Monte Carlo with Green's function analysis allows the sampling
of quantum mechanical properties of molecules at finite temperature. While a
high-precision computation of the energy of the Born-Oppenheimer surface from
path integral Monte Carlo is quite costly, we can extract many properties
without explicitly calculating the electronic energies. We demonstrate how
physically relevant quantities, such as bond-length, vibrational spectra, and
polarizabilities of molecules may be sampled directly from the path integral
simulation using Matsubura (temperature) Green's functions (imaginary-time
correlation functions). These calculations on the hydrogen molecule are a
proof-of-concept, designed to motivate new work on fixed-node path-integral
calculations for molecules.
