Timothy J. Hele

Timothy J. Hele
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Timothy J. Hele

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Physics - Chemical Physics (13)
Quantum Physics (5)
Physics - Statistical Mechanics (4)

Publications Authored By Timothy J. Hele

Thermal quantum time-correlation functions are of fundamental importance in quantum dynamics, allowing experimentally-measurable properties such as reaction rates, diffusion constants and vibrational spectra to be computed from first principles. Since the exact quantum solution scales exponentially with system size, there has been considerable effort in formulating reliable linear-scaling methods involving exact quantum statistics and approximate quantum dynamics modelled with classical-like trajectories. Here we review recent progress in the field with the development of methods including Centroid Molecular Dynamics (CMD), Ring Polymer Molecular Dynamics (RPMD) and Thermostatted RPMD (TRPMD). Read More

Clathrate hydrates hold considerable promise as safe and economical materials for hydrogen storage. Here we present a quantum mechanical study of H$_2$ and D$_2$ diffusion through a hexagonal face shared by two large cages of clathrate hydrates over a wide range of temperatures. Path integral molecular dynamics simulations are used to compute the free-energy profiles for the diffusion of H$_2$ and D$_2$ as a function of temperature. Read More

We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting expression is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact propagator lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated error term for each method. Read More

We obtain thermostatted ring polymer molecular dynamics (TRPMD) from exact quantum dynamics via Matsubara dynamics, a recently-derived form of linearization which conserves the quantum Boltzmann distribution. Performing a contour integral in the complex quantum Boltzmann distribution of Matsubara dynamics, replacement of the imaginary Liouvillian which results with a Fokker-Planck term gives TRPMD. We thereby provide error terms between TRPMD and quantum dynamics and predict the systems in which they are likely to be small. Read More

We apply Thermostatted Ring Polymer Molecular Dynamics (TRPMD), a recently-proposed approximate quantum dynamics method, to the computation of thermal reaction rates. Its short-time Transition-State Theory (TST) limit is identical to rigorous Quantum Transition-State Theory, and we find that its long-time limit is independent of the location of the dividing surface. TRPMD rate theory is then applied to one-dimensional model systems, the atom-diatom bimolecular reactions H+H$_2$, D+MuH and F+H$_2$, and the prototypical polyatomic reaction H+CH$_4$. Read More

We recently obtained a quantum-Boltzmann-conserving classical dynamics by making a single change to the derivation of the `Classical Wigner' approximation. Here, we show that the further approximation of this `Matsubara dynamics' gives rise to two popular heuristic methods for treating quantum Boltzmann time-correlation functions: centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD). We show that CMD is a mean-field approximation to Matsubara dynamics, obtained by discarding (classical) fluctuations around the centroid, and that RPMD is the result of discarding a term in the Matsubara Liouvillian which shifts the frequencies of these fluctuations. Read More

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or classical Wigner approximation) results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e. Read More

This dissertation unifies one of the central methods of classical rate calculation, `Transition-State Theory' (TST), with quantum mechanics, thereby deriving a rigorous `Quantum Transition-State Theory' (QTST). The resulting QTST is identical to ring polymer molecular dynamics transition-state theory (RPMD-TST), which was previously considered a heuristic method, and whose results we thereby validate. The key step in deriving a QTST is alignment of the flux and side dividing surfaces in path-integral space to obtain a quantum flux-side time-correlation function with a non-zero $t\to 0_+$ limit. Read More

In this thesis I generalize Ring Polymer Molecular Dynamics (RPMD) rate theory to electronically non-adiabatic systems, followed by application to two one-dimensional curve crossing models and a multidimensional spin-boson model. Read More

It was shown recently that there exists a true quantum transition-state theory (QTST) corresponding to the t->0+ limit of a (new form of) quantum flux-side time-correlation function. Remarkably, this QTST is identical to ring-polymer molecular dynamics (RPMD) TST. Here we provide evidence which suggests very strongly that this QTST (= RPMD-TST) is unique, in the sense that the t->0+ limit of any other flux-side time-correlation function gives either non-positive-definite quantum statistics or zero. Read More

Surprisingly, there exists a quantum flux-side time-correlation function which has a non-zero short-time (t->0+) limit, and thus yields a rigorous quantum generalization of classical transition-state theory (TST). In this Part I of two articles, we introduce the new time-correlation function, and derive its short-time limit. The new ingredient is a generalized Kubo transform which allows the flux and side dividing surfaces to be the same function of path-integral space. Read More