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Currently the most likely mechanism of the magnetic compass sense in migratory songbirds relies on the coherent spin dynamics of pairs of photochemically formed radicals in the retina. Spin-conserving electron transfer reactions are thought to result in radical pairs whose near-degenerate electronic singlet and triplet states interconvert coherently as a result of hyperfine, exchange, and dipolar couplings and, crucially for a compass sensor, Zeeman interactions with the geomagnetic field. In this way, the yields of the reaction products can be influenced by magnetic interactions a million times smaller than kBT. The question we ask here is whether one can only account for the coherent spin dynamics using quantum mechanics. We find that semiclassical approximations to the spin dynamics of radical pairs only provide a satisfactory description of the anisotropic product yields when there is no electron spin-spin coupling, a situation unlikely to be consistent with a magnetic sensing function. Although these methods perform reasonably well for shorter-lived radical pairs with stronger electron-spin coupling, the accurate simulation of anisotropic magnetic field effects relevant to magnetoreception seems to require full quantum mechanical calculations.

We shall use this introduction to the Faraday Discussion on quantum effects in complex systems to review the recent progress that has been made in using imaginary time path integral methods to calculate chemical reaction rates. As a result of this progress, it is now routinely possible to calculate accurate rate constants including quantum mechanical zero point energy and tunnelling effects for arbitrarily complex (anharmonic and multi-dimensional) systems. This is true in the adiabatic (Born-Oppenheimer) limit, in the non-adiabatic (Fermi Golden Rule) limit, and everywhere between these two limits in the normal Marcus regime. Quantum mechanical effects on reaction rates can be enormous, even at room temperature, and the problem of including these effects in simulations of a wide variety of chemical reactions in complex systems has now effectively been solved.

Magnetic field effects on radical pair reactions arise due to the interplay of coherent electron spin dynamics and spin relaxation effects, a rigorous treatment of which requires the solution of the Liouville-von Neumann equation. However, it is often found that simple incoherent kinetic models of the radical pair singlet-triplet intersystem crossing provide an acceptable description of experimental measurements. In this paper, we outline the theoretical basis for this incoherent kinetic description, elucidating its connection to exact quantum mechanics. We show, in particular, how the finite lifetime of the radical pair spin states, as well as any additional spin-state dephasing, leads to incoherent intersystem crossing. We arrive at simple expressions for the radical pair spin state interconversion rates to which the functional form proposed recently by Steiner et al. [J. Phys. Chem. C 122, 11701 (2018)] can be regarded as an approximation. We also test the kinetic master equation against exact quantum dynamical simulations for a model radical pair and for a series of PTZ •+ -Ph n -PDI •- molecular wires.

Photodetachment spectroscopy of the FH2(-) and FD2(-) anions allows for the direct observation of reactive resonances in the benchmark reaction F + H2 → HF + H. Using cooled anion precursors and a high-resolution electron spectrometer, we observe several narrow peaks not seen in previous experiments. Theoretical calculations, based on a highly accurate F + H2 potential energy surface, convincingly assign these peaks to resonances associated with quasibound states in the HF + H and DF + D product arrangements and with a quasibound state in the transition state region of the F + H2 reaction. The calculations also reveal quasibound states in the reactant arrangement, which have yet to be resolved experimentally., (Copyright © 2015, American Association for the Advancement of Science.)

We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable., (© 2011 American Institute of Physics)

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

The approximate quantum mechanical ring polymer molecular dynamics (RPMD) and linearized semiclassical initial value representation (LSC-IVR) methods are compared and contrasted in a study of the dynamics of the flexible q-TIP4P/F water model at room temperature. For this water model, a RPMD simulation gives a diffusion coefficient that is only a few percent larger than the classical diffusion coefficient, whereas a LSC-IVR simulation gives a diffusion coefficient that is three times larger. We attribute this discrepancy to the unphysical leakage of initially quantized zero point energy (ZPE) from the intramolecular to the intermolecular modes of the liquid as the LSC-IVR simulation progresses. In spite of this problem, which is avoided by construction in RPMD, the LSC-IVR may still provide a useful approximation to certain short-time dynamical properties which are not so strongly affected by the ZPE leakage. We illustrate this with an application to the liquid water dipole absorption spectrum, for which the RPMD approximation breaks down at frequencies in the O-H stretching region owing to contamination from the internal modes of the ring polymer. The LSC-IVR does not suffer from this difficulty and it appears to provide quite a promising way to calculate condensed phase vibrational spectra.

A quantum simulation of an imaginary time path integral typically requires around n times more computational effort than the corresponding classical simulation, where n is the number of ring polymer beads (or imaginary time slices) used in the calculation. However, this estimate neglects the fact that the potential energies of many systems can be decomposed into a sum of rapidly varying short-range and slowly varying long-range contributions. For such systems, the computational effort of the path integral simulation can be reduced considerably by evaluating the long-range forces on a contracted ring polymer with fewer beads than are needed to evaluate the short-range forces. This idea is developed and then illustrated with an application to a flexible model of liquid water in which the intramolecular forces are evaluated with 32 beads, the oxygen-oxygen Lennard-Jones forces with seven, and the intermolecular electrostatic forces with just five. The resulting static and dynamic properties are within a few percent of those of a full 32-bead calculation, and yet they are obtained with a computational effort less than six times (rather than 32 times) that of a classical simulation. We hope that this development will encourage future studies of quantum mechanical fluctuations in liquid water and aqueous solutions and in many other systems with similar interaction potentials.

The Feynman-Kleinert linearized path integral molecular dynamics (FK-LPI), ring polymer molecular dynamics (RPMD), and centroid molecular dynamics (CMD) methods are applied to the simulation of normal liquid helium. Comparisons of the simulation results at the T = 4 K and rho = 0.01873 A-3 state point are presented. The calculated quantum correlation functions for the three methods show significant differences, both in the short time and in the intermediate regions of the spectrum. Our simulation results are also compared to the recent results of other approximate quantum simulation methods. We find that FK-LPI qualitatively agrees with other approximate quantum simulation results while CMD and RPMD predict a qualitatively different impulsive rebound in the velocity autocorrelation function. Frequency space analysis reveals that RPMD exhibits a broad high-frequency tail similar to that from quantum mode coupling theory and numerical analytic continuation approaches, while FK-LPI provides a somewhat more rapid decay at high frequency than any of these three methods. CMD manifests a high-frequency component that is greatly reduced compared with the other methods.

The degree of electronic and nuclear coupling in the Cl + H2 reaction has become a vexing problem in chemical dynamics. We report slow electron velocity-map imaging (SEVI) spectra of ClH2- and ClD2-. These spectra probe the reactant valley of the neutral reaction potential energy surface, where nonadiabatic transitions responsible for reactivity of the Cl excited spin-orbit state with H2 would occur. The SEVI spectra reveal progressions in low-frequency Cl.H2 bending and stretching modes, and are compared to simulations with and without nonadiabatic couplings between the Cl spin-orbit states. Although nonadiabatic effects are small, their inclusion improves agreement with experiment. This comparison validates the theoretical treatment, especially of the nonadiabatic effects, in this critical region of the Cl + H2 reaction, and suggests strongly that these effects are minor.

The statistical model of atom-diatom insertion reactions is combined with coupled-states capture theory and used to calculate product multiplet-resolved integral cross sections for the title reaction. This involves an ab initio determination of the four electronic potential energy surfaces that correlate with the products ((1,3)A(') and (1,3)A(")), and an accurate description of the electronic and spin-orbit couplings between them. The dependence of the resulting cross sections on the final-state rotational quantum number shows a statistical behavior similar to that observed in earlier studies of the reaction in which only the lowest ((1)A(')) potential was retained. In addition, however, the present calculations provide information on the branching between the OH((2)Pi) multiplet levels. Although the two spin-orbit manifolds are predicted to be equally populated, we find a strong propensity for the formation of the Pi(A(')) Lambda-doublet states. These two predictions confirm the experimental results of Butler, Wiesenfeld, Gericke, Brouard, and their co-workers. The nonstatistical population of the OH Lambda-doublet levels is a consequence of the bond breaking in the intermediate H(2)O complex and is preserved through the multiple curve crossings as the products separate. This exit-channel coupling is correctly described by the present theory.