Classical molecular dynamics simulations of electronically non-adiabatic processes
Professor William H Miller ForMemRS, University of California, Berkeley, USA
A recently described symmetrical quasi-classical (SQC) windowing methodology for classical trajectory simulations has been applied to the Meyer-Miller (MM) model for the electronic degrees of freedom in electronically non-adiabatic dynamics. The approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard molecular dynamics), providing “quantization” of the electronic states through the symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). It is able to provide the full electronic density matrix from the one ensemble of trajectories, and the SQC windowing methodology correctly describes detailed balance (unlike the traditional Ehrenfest approach). Calculations can be (equivalently) carried out in the adiabatic or a diabatic representation of the electronic states, and most recently it has been shown that a modification of the canonical equations of motion in the adiabatic representation eliminates (without approximation) the need for second-derivative coupling terms.
When instantons get wet: path-integral rate theory for the condensed-phase
Dr Jeremy O Richardson, ETH Zurich, Switzerland
Instanton theory results from a rigorous semiclassical derivation for the rate of a chemical reaction. However, due to a number of harmonic approximations, it is not applicable to study reactions in liquids, where many transition-states exist close to each other such that they cannot be treated independently. Ring-polymer molecular dynamics avoids this problem by effectively sampling the instantons without making the harmonic approximation. A similar instanton theory can also be derived for the rate of the fundamental process of electron transfer, in which the electron dynamics are coupled strongly to the nuclear degrees of freedom such that the Born-Oppenheimer approximation cannot be made. Again, however, this instanton theory cannot be applied to atomlistic models of liquids and a new ring-polymer sampling scheme is be required. It will be shown that starting from a physically motivated ansatz, it is possible to derive new ring-polymer sampling schemes which dominately sample the instanton configurations and thus give excellent approximations to the rate of electron transfer.
Quantum statistics with classical dynamics: applications to liquid water and ice
Professor Stuart C Althorpe, University of Cambridge, UK
In water and ice, the nuclear motion takes place on a single Born-Oppenheimer surface, under conditions of thermal equilibrium. The nuclei exhibit quantum properties, which a growing body of evidence suggests are caused almost entirely by the quantum Boltzmann statistics, with the dynamics of the nuclei being classical. Here we summarise a recently developed theory which explains how such a classical dynamics can arise as a result of certain properties of the quantum statistics. This dynamics involves the motion of smooth delocalised loops of the hydrogen atoms which, despite being classical, conserve the quantum Boltzmann distribution. Exact implementation of this dynamics is not possible because of a phase problem, but its approximate implementation can be done using a ‘planetary’ model (originally developed heuristically by others), in which each hydrogen nucleus is represented by two particles, one (the ‘centroid’) describing its position, the other (the ‘planet’) describing the extent of delocalisation. We report recent simulations of the infrared spectrum of liquid water and ice, obtained using the planetary model. Despite the approximations made, the model is capable of reproducing the line shapes of the bend and stretch peaks, which are found to be motionally narrowed by the dynamics of the centroid.
Quantum nonadiabatic dynamics from classical trajectories
Professor Nandini Ananth, Cornell University, USA
Simulating energy transfer pathways in reactions at metal surfaces requires methods that describe electronically nonadiabatic processes, capture quantum coherence effects, and remain computationally feasible for high dimensional systems. Quantum-limit semiclassical methods meet almost all these criteria, but the computational costs scale poorly with system size limiting their applications. The recently derived Mixed Quantum-Classical Initial Value Representation (MQCIVR) provides a uniform semiclassical framework for the calculation of real-time correlation functions where a subset of system modes are treated in the quantum limit while the rest are treated in the classical limit. This is achieved by selectively filtering amplitude of the semiclassical integrand in regions of highly oscillatory phase, leading to improved numerical convergence without significant loss of accuracy. This method is applied to several model systems and its ability to systematically tune individual system modes between quantum-limit and classical-limit semiclassical behaviour clearly demonstrated. MQC-IVR is further extended to electronically nonadiabatic processes for the study of inelastic scattering at a metal surface.