LAUSR

Imaginary time path-integral (PI) simulations that account for nuclear quantum effects (NQE) beyond the harmonic approximation are increasingly employed together with modern electronic-structure calculations. Existing PI methods are applicable to molecules, liquids, and solids, however the computational cost of such simulations increases dramatically with decreasing temperature. To address this challenge, here we propose to combine high-order PI factorization with perturbation theory (PT). Already for conventional second-order PI simulations, the PT ansatz increases the accuracy twofold compared to fourth-order schemes with the same settings. In turn, applying PT to high-order path-integrals (HOPI) further improves the efficiency of simulations for molecular and condensed matter systems especially at low temperatures. We present results for bulk liquid water, aspirin molecule, and CH5+ molecule. Perturbed HOPI simulations remain both efficient and accurate down to 20 K and provide a convenient method to estimate the convergence of quantum-mechanical observables.