Here, we develop the normal-mode sampling algorithm, an importance sampling method specifically designed for path-integral quantum Monte Carlo simulations of flexible molecular systems. This work is motivated by the desire to include vibrational degrees of freedom in numerical studies of confined molecular lattices.

We first introduce a novel density matrix factorization that arises from decomposing our system Hamiltonian into its harmonic and anharmonic terms. The normal-mode sampling algorithm is then constructed using this factorization.

Finally, we validate our normal-mode sampling algorithm in the context of path-integral quantum Monte Carlo simulations of several flexible molecular systems, namely the water monomer, dimer, and a few equilibrium geometries of the hexamer. For each of these systems, we calculate the ground-state energy and various structural properties, benchmarking our results against exact diagonalization, path integral molecular dynamics, and diffusion Monte Carlo studies from the literature.

We also propose applying this methodology to study quantum phase transitions in one-dimensional chains and higher-dimensional lattices of water molecules.