Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison toab initiomolecular dynamics

Abstract

We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems.

A Two-State Picture of Water and the Funnel of Life

“…2c) 36 . In another approach, VandeVondele and coworkers 31 135 and quantum ring-polymer contraction 136 .…”

Accelerated path-integral simulations using ring-polymer interpolation

“…However, in favourable cases, this work also found that using n c = 1 contracted ringpolymer beads for evaluation of the full DFT PES also gave reasonably good reproduction of quantum properties, suggesting that this reference PES RPC scheme enables quantum simulations at near-classical cost. A similar conclusion was reached by Kühne and coworkers, 51 although in this case the reference PES was selected to be a simple fixed-charge empirical model, similar to q-TIP4P/F, 16 which was force-matched to a DFTB PES in a preliminary step; this approach enables the reference PES calculations to simultaneously exploit the original and electrostatic RPC schemes.…”

“…16 Unfortunately, both the original RPC scheme and its electrostatic variant cannot be applied directly to more general PESs such as those arising in DFT or other ab initio calculations, the reason being that both schemes rely on the ability to decompose the PES into independent contributions which can be identified as either "high" or "low" frequency (or short-range and long-range); such a separation is not straightforward in ab initio-based PESs. As a result, Markland and Marsalek 20 and, independently, Kühne and coworkers, 51 have proposed a RPC-like scheme which relies on the availability of a "reference" PES which is broadly similar to the PES under direct investigation but much less computationallyexpensive to evaluate. Here, the reference PES is evaluated on the entire n-bead ring-polymer while the "full" PES of interest is evaluated on a contracted ring-polymer with a smaller number of beads n c ; the underlying assumption at play is that the reference PES faithfully captures the rapidly-varying part of the full PES, such that the slowly-varying remainder between the reference and full PES can be evaluated using a reduced number of beads.…”

“…and, independently, Kühne and coworkers, 51 proposed a scheme based on using a reference PES, V ref (r). In particular, one rewrites the potential energy contribution to the ring-polymer Hamiltonian as…”

Proton transfer in guanine–cytosine base pair analogues studied by NMR spectroscopy and PIMD simulations

“…Recently, different methods have been suggested to decrease the computational cost of the PIMD simulations without compromising the quality of the calculations. [57][58][59] Here, we employ the PI + GLE method which is based on the generalized Langevin equation (GLE) thermostat combined with PIMD. 59 With this choice, it is enough to use only 4 beads to get converged nuclear densities in a sufficient quality for electronic spectroscopy.…”