Thermal quenching of classical and semiclassical scrambling.

Quantum scrambling often gives rise to short-time exponential growth in out-of-time-ordered correlators. The scrambling rate over an isolated saddle point at finite temperature is shown here to be reduced by a hierarchy of quenching processes. Two of these appear in the classical limit, where escape from the neighborhood of the saddle reduces the rate by a factor of two, and thermal fluctuations around the saddle reduce it further; a third process can be explained semiclassically as arising from quantum thermal fluctuations around the saddle, which are also responsible for imposing the Maldacena-Shenker-Stanford bound.

Quantum rates in dissipative systems with spatially varying friction.

We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics.

Path Integral Simulations of Condensed-Phase Vibrational Spectroscopy.

Recent theoretical and algorithmic developments have improved the accuracy with which path integral dynamics methods can include nuclear quantum effects in simulations of condensed-phase vibrational spectra. Such methods are now understood to be approximations to the delocalized classical Matsubara dynamics of smooth Feynman paths, which dominate the dynamics of systems such as liquid water at room temperature. Focusing mainly on simulations of liquid water and hexagonal ice, we explain how the recently developed quasicentroid molecular dynamics (QCMD), fast-QCMD, and temperature-elevated path integral coarse-graining simulations (Te PIGS) methods generate classical dynamics on potentials of mean force obtained by averaging over quantum thermal fluctuations.

Instantons and the quantum bound to chaos.

The rate at which information scrambles in a quantum system can be quantified using out-of-time-ordered correlators. A remarkable prediction is that the associated Lyapunov exponent [Formula: see text] that quantifies the scrambling rate in chaotic systems obeys a universal bound [Formula: see text]. Previous numerical and analytical studies have indicated that this bound has a quantum-statistical origin.

Comparison of Matsubara dynamics with exact quantum dynamics for an oscillator coupled to a dissipative bath.

We report the first numerical calculations in which converged Matsubara dynamics is compared directly with exact quantum dynamics with no artificial damping of the time-correlation functions (TCFs). The system treated is a Morse oscillator coupled to a harmonic bath. We show that, when the system-bath coupling is sufficiently strong, the Matsubara calculations can be converged by explicitly including up to M = 200 Matsubara modes, with the remaining modes included as a harmonic "tail" correction.

Improved torque estimator for condensed-phase quasicentroid molecular dynamics.

We describe improvements to the quasicentroid molecular dynamics (QCMD) path-integral method, which was developed recently for computing the infrared spectra of condensed-phase systems. The main development is an improved estimator for the intermolecular torque on the quasicentroid. When applied to qTIP4P/F liquid water and ice, the new estimator is found to remove an artificial 25 cm red shift from the libration bands, to increase slightly the intensity of the OH stretch band in the liquid, and to reduce small errors noted previously in the QCMD radial distribution functions.

Testing the quasicentroid molecular dynamics method on gas-phase ammonia.

Quasicentroid molecular dynamics (QCMD) is a path-integral method for approximating nuclear quantum effects in dynamics simulations, which has given promising results for gas- and condensed-phase water. In this work, by simulating the infrared spectrum of gas-phase ammonia, we test the feasibility of extending QCMD beyond water. Overall, QCMD works as well for ammonia as for water, reducing or eliminating blue shifts from the classical spectrum without introducing the artificial red shifts or broadening associated with other imaginary-time path-integral methods.

On the "Matsubara heating" of overtone intensities and Fermi splittings.

Classical molecular dynamics (MD) and imaginary-time path-integral dynamics methods underestimate the infrared absorption intensities of overtone and combination bands by typically an order of magnitude. Plé et al. [J.

Which quantum statistics-classical dynamics method is best for water?

There are a variety of methods for including nuclear quantum effects in dynamics simulations by combining quantum Boltzmann statistics with classical dynamics. Among them are thermostatted ring-polymer molecular dynamics (TRPMD), centroid molecular dynamics (CMD), quasi-centroid molecular dynamics (QCMD), and the linearised semi-classical initial value representation (LSC-IVR). Here we make a systematic comparison of these methods by calculating the infrared spectrum of water in the gas phase, and in the liquid and ice phases (using the q-TIP4P/F model potential).

Path Integral Energy Landscapes for Water Clusters.

The energy landscapes for a discretized path integral representation of the water dimer, trimer and pentamer are characterized in terms of the localized (classical) and delocalized minima and transition states. The transition states are finite-temperature approximations to the exact instanton path, and they are typically used to calculate the tunneling splittings or reaction rates. The features of the path integral landscape are explored, thus elucidating procedures that could usefully be automated when searching for instantons in larger systems.

Mean-field Matsubara dynamics: Analysis of path-integral curvature effects in rovibrational spectra.

It was shown recently that smooth and continuous "Matsubara" phase-space loops follow a quantum-Boltzmann-conserving classical dynamics when decoupled from non-smooth distributions, which was suggested as the reason that many dynamical observables appear to involve a mixture of classical dynamics and quantum Boltzmann statistics. Here we derive a mean-field version of this "Matsubara dynamics" which sufficiently mitigates its serious phase problem to permit numerical tests on a two-dimensional "champagne-bottle" model of a rotating OH bond. The Matsubara-dynamics rovibrational spectra are found to converge toward close agreement with the exact quantum results at all temperatures tested (200-800 K), the only significant discrepancies being a temperature-independent 22 cm blue-shift in the position of the vibrational peak and a slight broadening in its line shape.

Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice.

Matsubara dynamics is the quantum-Boltzmann-conserving classical dynamics which remains when real-time coherences are taken out of the exact quantum Liouvillian [T. J. H.

Non-equilibrium dynamics from RPMD and CMD.

We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions.

Quantum Tunneling Rates of Gas-Phase Reactions from On-the-Fly Instanton Calculations.

The instanton method obtains approximate tunneling rates from the minimum-action path (known as the instanton) linking reactants to the products at a given temperature. An efficient way to find the instanton is to search for saddle-points on the ring-polymer potential surface, which is obtained by expressing the quantum Boltzmann operator as a discrete path-integral. Here we report a practical implementation of this ring-polymer form of instanton theory into the Molpro electronic-structure package, which allows the rates to be computed on-the-fly, without the need for a fitted analytic potential-energy surface.

Rovibrational transitions of the methane-water dimer from intermolecular quantum dynamical computations.

Rovibrational quantum nuclear motion computations, with J = 0, 1, and 2, are reported for the intermolecular degrees of freedom of the methane-water dimer, where J is the quantum number describing the overall rotation of the complex. The computations provide the first explanation of the far-infrared spectrum of this complex published in J. Chem.

An alternative derivation of ring-polymer molecular dynamics transition-state theory.

In a previous article [T. J. H.

Calculating splittings between energy levels of different symmetry using path-integral methods.

It is well known that path-integral methods can be used to calculate the energy splitting between the ground and the first excited state. Here we show that this approach can be generalized to give the splitting patterns between all the lowest energy levels from different symmetry blocks that lie below the first-excited totally symmetric state. We demonstrate this property numerically for some two-dimensional models.

Quantum tunneling splittings from path-integral molecular dynamics.

We illustrate how path-integral molecular dynamics can be used to calculate ground-state tunnelling splittings in molecules or clusters. The method obtains the splittings from ratios of density matrix elements between the degenerate wells connected by the tunnelling. We propose a simple thermodynamic integration scheme for evaluating these elements.

Concerted hydrogen-bond breaking by quantum tunneling in the water hexamer prism.

The nature of the intermolecular forces between water molecules is the same in small hydrogen-bonded clusters as in the bulk. The rotational spectra of the clusters therefore give insight into the intermolecular forces present in liquid water and ice. The water hexamer is the smallest water cluster to support low-energy structures with branched three-dimensional hydrogen-bond networks, rather than cyclic two-dimensional topologies.

Locating Instantons in Calculations of Tunneling Splittings: The Test Case of Malonaldehyde.

The recently developed ring-polymer instanton (RPI) method [J. Chem. Phys.

Which Is Better at Predicting Quantum-Tunneling Rates: Quantum Transition-State Theory or Free-Energy Instanton Theory?

Quantum transition-state theory (QTST) and free-energy instanton theory (FEIT) are two closely related methods for estimating the quantum rate coefficient from the free-energy at the reaction barrier. In calculations on one-dimensional models, FEIT typically gives closer agreement than QTST with the exact quantum results at all temperatures below the crossover to deep tunneling, suggesting that FEIT is a better approximation than QTST in this regime. Here we show that this simple trend does not hold for systems of greater dimensionality.