Quantum Dynamics with Electronic Friction

i-PI 3.0: A flexible and efficient framework for advanced atomistic simulations

Atomic-scale simulations have progressed tremendously over the past decade, largely thanks to the availability of machine-learning interatomic potentials. These potentials combine the accuracy of electronic structure calculations with the ability to reach extensive length and time scales. The i-PI package facilitates integrating the latest developments in this field with advanced modeling techniques thanks to a modular software architecture based on inter-process communication through a socket interface. The choice of Python for implementation facilitates rapid prototyping but can add computational overhead. In this new release, we carefully benchmarked and optimized i-PI for several common simulation scenarios, making such overhead negligible when i-PI is used to model systems up to tens of thousands of atoms using widely adopted machine learning interatomic potentials, such as Behler-Parinello, DeePMD, and MACE neural networks. We also present the implementation of several new features, including an efficient algorithm to model bosonic and fermionic exchange, a framework for uncertainty quantification to be used in conjunction with machine-learning potentials, a communication infrastructure that allows for deeper integration with electronic-driven simulations, and an approach to simulate coupled photon-nuclear dynamics in optical or plasmonic cavities.

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. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates.

Dynamics of the Molecular Geometric Phase

The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wave function and a recently proposed quantum hydrodynamical description of its dynamics. An instantaneous, gauge-invariant phase is introduced for arbitrary paths in nuclear configuration space in terms of hydrodynamical variables, and shown to reduce to the adiabatic geometric phase when the state is adiabatic and the path is closed. The evolution of the closed-path phase over time is shown to adhere to a Maxwell-Faraday induction law, with nonconservative forces arising from the electron dynamics that play the role of electromotive forces. We identify the pivotal forces that are able to change the value of the phase, thereby challenging any topological argument. Nonetheless, negligible changes in the phase occur when the local dynamics along the probe loop is approximately adiabatic. That is, the geometric phase effects that arise in an adiabatic limiting situation remain suitable to effectively describe certain dynamic observables.

A Discrete-Variable Local Diabatic Representation of Conical Intersection Dynamics

Conical intersections (CIs) are ubiquitous in polyatomic molecules and are responsible for a wide range of phenomena in photochemistry and photophysics. Modeling the conical intersection dynamics with adiabatic electronic states is hindered by the divergence of the first- and second-order derivative couplings at CIs due to electronic degeneracy. We introduce and implement a novel diabatic representation for exact correlated electron-nuclear wave packet dynamics through conical intersections. It directly employs the adiabatic electronic states but avoids the singular first- and second-order derivative couplings and is robust to different gauge choices of the electronic wave function phases. The reference nuclear geometries defining the adiabatic electronic states are determined by a discrete-variable representation of the nuclear coordinates. The nonadiabatic effects are accounted for by the electronic overlap matrix instead of derivative couplings as in the adiabatic representation. Illustrated by a two-mode conical intersection model, this representation captures all nonadiabatic effects, including electronic transitions, electronic coherence, and geometric phases. Thus, this representation provides a singularity-free framework for modeling ab initio conical intersection wave packet dynamics.

Assessing Mixed Quantum-Classical Molecular Dynamics Methods for Nonadiabatic Dynamics of Molecules on Metal Surfaces

Mixed quantum-classical (MQC) methods for simulating the dynamics of molecules at metal surfaces have the potential to accurately and efficiently provide mechanistic insight into reactive processes. Here, we introduce simple two-dimensional models for the scattering of diatomic molecules at metal surfaces based on recently published electronic structure data. We apply several MQC methods to investigate their ability to capture how nonadiabatic effects influence molecule-metal energy transfer during the scattering process. Specifically, we compare molecular dynamics with electronic friction, Ehrenfest dynamics, independent electron surface hopping, and the broadened classical master equation approach. In the case of independent electron surface hopping, we implement a simple decoherence correction approach and assess its impact on vibrationally inelastic scattering. Our results show that simple, low-dimensional models can be used to qualitatively capture experimentally observed vibrational energy transfer and provide insight into the relative performance of different MQC schemes. We observe that all approaches predict similar kinetic energy dependence but return different vibrational energy distributions. Finally, by varying the molecule-metal coupling, we can assess the coupling regime in which some MQC methods become unsuitable.

Classical Quantum Friction at Water-Carbon Interfaces

Friction at water-carbon interfaces remains a major puzzle with theories and simulations unable to explain experimental trends in nanoscale waterflow. A recent theoretical framework─quantum friction (QF)─proposes to resolve these experimental observations by considering nonadiabatic coupling between dielectric fluctuations in water and graphitic surfaces. Here, using a classical model that enables fine-tuning of the solid's dielectric spectrum, we provide evidence from simulations in general support of QF. In particular, as features in the solid's dielectric spectrum begin to overlap with water's librational and Debye modes, we find an increase in friction in line with that proposed by QF. At the microscopic level, we find that this contribution to friction manifests more distinctly in the dynamics of the solid's charge density than that of water. Our findings suggest that experimental signatures of QF may be more pronounced in the solid's response rather than liquid water's.