Nuclear quantum effectsΒΆ

Most atomistic simulations treat nuclei as classical particles, that sample a Boltzmann distribution. This approximation breaks down for light nuclei (hydrogen above all) and high-frequency vibrations, requiring more sophisticated statistical sampling to compute accurate statistical and dynamical properties.

Path integral molecular dynamics
This example shows how to run a path integral molecular dynamics simulation using i-PI, analyze the output and visualize the trajectory in chemiscope. It uses LAMMPS as the driver to simulate the q-TIP4P/f water model.
Path integral molecular dynamics
Path integral metadynamics
This example shows how to run a free-energy sampling calculation that combines path integral molecular dynamics to model nuclear quantum effects and metadynamics to accelerate sampling of the high-free-energy regions.
Path integral metadynamics
Quantum heat capacity of water
This example shows how to estimate the heat capacity of liquid water from a path integral molecular dynamics simulation. The dynamics are run with i-PI, and LAMMPS is used as the driver to simulate the q-TIP4P/f water model.
Quantum heat capacity of water
Multiple time stepping and ring-polymer contraction
This notebook provides an introduction to multiple time stepping and ring polymer contraction, two closely-related techniques, that are geared towards reducing the cost of calculations by separating slowly-varying (and computationally-expensive) components of the potential energy from the fast-varying (and hopefully cheaper) ones.
Multiple time stepping and ring-polymer contraction
Ring Polymer Instanton Rate Theory: Tunneling Rates
This notebook introduces the calculation of tunneling rates using ring-polymer instanton rate theory. A comprehensive presentation of the instanton formalism can be found in the review article by J. Richardson, Int. Rev. Phys. Chem., 37, 171, 2018, while the implementation within i-PI is described in V. Kapil et al., Comp. Phys. Commun., 236, 214, 2020. Additional practical details are available in Yair Litman's doctoral thesis.
Ring Polymer Instanton Rate Theory: Tunneling Rates
Path integral molecular dynamics of bosons and fermions
This example shows how to run path integral molecular dynamics (PIMD) simulations of indistinguishable particles -- bosons and fermions -- with i-PI, and how to analyze the output. It is a modernized version of the "Bosonic and Fermionic PIMD" module of the PIQM 2023 tutorial, updated to i-PI 3.x.
Path integral molecular dynamics of bosons and fermions
Computing the pKw of water with a machine-learning potential
The autoionization of water, \mathrm{2H_2O \rightleftharpoons H_3O^+ + OH^-}, is the prototypical acid-base equilibrium, and its equilibrium constant K_\mathrm{w}=[\mathrm{H_3O^+}][\mathrm{OH^-}]/(c^\circ)^2 (\mathrm{p}K_\mathrm{w}=-\log_{10}K_\mathrm{w}=13.93 at 300 K) sets the scale of every \mathrm{p}K_\mathrm{a} and \mathrm{p}K_\mathrm{b}. Computing it from first principles is a stringent test of a simulation protocol, because it combines several ingredients that are each worth one or more pK units if neglected: a reactive potential, collective variables that follow the proton as it hops between molecules, enhanced sampling of a free energy of about 32\,k_\mathrm{B}T, a well-defined relation between the free-energy profile and the equilibrium constant, the long-range Coulomb interaction of the products in a small periodic box, and the quantum nature of the nuclei.
Computing the pKw of water with a machine-learning potential