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Nuclear quantum effects enter the mainstream

Abstract

Atomistic simulations of chemical, biological and materials systems have become increasingly precise and predictive owing to the development of accurate and efficient techniques that describe the quantum mechanical behaviour of electrons. Nevertheless, the overwhelming majority of such simulations still assumes that the nuclei behave as classical particles. Historically, this approximation could sometimes be justified owing to the complexity and computational overhead. However, neglecting nuclear quantum effects has become one of the largest sources of error, especially when systems containing light atoms are treated using current state-of-the-art descriptions of chemical interactions. Over the past decade, this realization has spurred a series of methodological advances that have dramatically reduced the cost of including these important physical effects in the structure and dynamics of chemical systems. Here, we discuss how these developments are now allowing nuclear quantum effects to become a mainstream feature of molecular simulations. These advances have led to new insights into phenomena that are relevant to different areas of science — from biochemistry to condensed matter — and open the door to many exciting future opportunities.

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Figure 1: A summary of accelerated path integral molecular dynamics techniques.
Figure 2: Competing quantum effects in biomolecules.
Figure 3: Classical vs quantum proton momentum distribution.
Figure 4: Hydrogen–hydrogen radial distribution functions for different phases of solid hydrogen.

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Acknowledgements

M.C. was supported by the European Research Council under the European Union's Horizon 2020 research and innovation programme (Grant Agreement No. 677013-HBMAP), and the Swiss National Science Foundation (Project No. 200021-159896). T.E.M. was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0014437 and the National Science Foundation under Grant No. CHE-1652960. T.E.M. also acknowledges support from a Cottrell Scholarship from the Research Corporation for Science Advancement and the Camille Dreyfus Teacher-Scholar Awards Program.

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Glossary

Zero-point energy

(ZPE). The minimum amount of energy a quantum particle must possess, even at 0 K.

Tunnelling

The ability of quantum particles to pass through a barrier rather than traverse over it, as required in classical mechanics.

Exchange effects

The effects arising from the exchange of indistinguishable particles in quantum mechanics. These are generally substantial for electrons but are often small for nuclei, except at low temperatures (although ortho-hydrogen and para-hydrogen still exhibit some differences even at room temperature).

Centroid

The centre of the imaginary time path that is obtained by taking the mean position of the replicas that comprise it.

Estimators

Formulae to compute an observed property from simulation data.

Ergodicity

The assumption that as a particle evolves in time, it will visit all states with the appropriate frequency associated with the required distribution (e.g. Boltzmann).

Normal-mode or staging representation

Methods of decoupling the spring terms in the imaginary time path integral Hamiltonian.

Quantum thermostat

A method that includes quantum effects by applying a non-equilibrium Langevin equation to a classical molecular dynamics simulation.

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Markland, T., Ceriotti, M. Nuclear quantum effects enter the mainstream. Nat Rev Chem 2, 0109 (2018). https://doi.org/10.1038/s41570-017-0109

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