Divide-and-Conquer Method for Instanton Rate Theory

Ring-polymer instanton theory has been developed to simulate the quantum dynamics of molecular systems at low temperatures. Chemical reaction rates can be obtained by locating the dominant tunneling pathway and analyzing fluctuations around it. In the standard method, calculating the fluctuation terms involves the diagonalization of a large matrix, which can be unfeasible for large systems with a high number of ring-polymer beads. Here we present a method for computing the instanton fluctuations with a large reduction in computational scaling. This method is applied to three reactions described by fitted, analytic and on-the-fly ab initio potential-energy surfaces and is shown to be numerically stable for the calculation of thermal reaction rates even at very low temperature

Semiclassical instanton formulation of Marcus-Levich-Jortner theory

Marcus-Levich-Jortner (MLJ) theory is one of the most commonly used methods for including nuclear quantum effects into the calculation of electron-transfer rates and for interpreting experimental data. It divides the molecular problem into a subsystem treated quantum-mechanically by Fermi's golden rule and a solvent bath treated by classical Marcus theory. As an extension of this idea, we here present a "reduced" semiclassical instanton theory, which is a multiscale method for simulating quantum tunnelling of the subsystem in molecular detail in the presence of a harmonic bath. We demonstrate that instanton theory is typically significantly more accurate than the cumulant expansion or the semiclassical Franck-Condon sum, which can give orders-of-magnitude errors and in general do not obey detailed balance. As opposed to MLJ theory, which is based on wavefunctions, instanton theory is based on path integrals and thus does not require solutions of the Schr\"odinger equation, nor even global knowledge of the ground- and excited-state potentials within the subsystem. It can thus be efficiently applied to complex, anharmonic multidimensional subsystems without making further approximations. In addition to predicting accurate rates, instanton theory gives a high level of insight into the reaction mechanism by locating the dominant tunnelling pathway as well as providing information on the reactant and product vibrational states involved in the reaction and the activation energy in the bath similarly to what would be found with MLJ theory.Comment: 21 pages, 4 figure

3.8-Micron Photometry During the Secondary Eclipse of the Extrasolar Planet HD 209458b

We report infrared photometry of the extrasolar planet HD 209458b during the time of secondary eclipse (planet passing behind the star). Observations were acquired during two secondary eclipses at the NASA Infrared Telescope Facility (IRTF) in September 2003. We used a circular variable filter (1.5-percent bandpass) centered at 3.8 microns to isolate the predicted flux peak of the planet at this wavelength. Residual telluric absorption and instrument variations were removed by offsetting the telescope to nearby bright comparison stars at a high temporal cadence. Our results give a secondary eclipse depth of 0.0013 +/- 0.0011, not yet sufficient precision to detect the eclipse, whose expected depth is approximately 0.002 - 0.003. We here elucidate the current observational limitations to this technique, and discuss the approach needed to achieve detections of hot Jupiter secondary eclipses at 3.8 microns from the ground.Comment: 5 pages, 5 figures, in press for MNRA

A coercive policy-making state? How the EU is alienating its citizens

The remit of EU institutions has expanded inexorably, writes Jeremy Richardson (Oxford/University of Canterbury), all while their policy-making style has shifted from a consensus-based process towards a more coercive, top-down one. At the same time, the EU's focus on interest groups might have also exacerbated the problem of the democratic deficit by distancing the EU from broader public opinion. These realities have contributed to both Brexit and the broader ‘populist revolt’ across Member States

The changing British policy style: from governance to government

Jeremy Richardson explains how the British policy-making style has been steadily shifting away from governance and towards government. Here he examines some of the main features that characterise this long process, and concludes that Brexit should usher in a return to governance

Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems

We propose a new quantum transition-state theory for calculating Fermi's golden-rule rates in complex multidimensional systems. This method is able to account for the nuclear quantum effects of delocalization, zero-point energy and tunnelling in an electron-transfer reaction. It is related to instanton theory but can be computed by path-integral sampling and is thus applicable to treat molecular reactions in solution. A constraint functional based on energy conservation is introduced which ensures that the dominant paths contributing to the reaction rate are sampled. We prove that the theory gives exact results for a system of crossed linear potentials and also the correct classical limit for any system. In numerical tests, the new method is also seen to be accurate for anharmonic systems, and even gives good predictions for rates in the Marcus inverted regime.Comment: 18 pages and 6 figure

Elucidating the NuclearQuantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene

We address the double hydrogen transfer (DHT) dynamics of the porphycene molecule: A complex paradigmatic system where the making and breaking of H-bonds in a highly anharmonic potential energy surface requires a quantum mechanical treatment not only of the electrons, but also of the nuclei. We combine density-functional theory calculations, employing hybrid functionals and van der Waals corrections, with recently proposed and optimized path-integral ring-polymer methods for the approximation of quantum vibrational spectra and reaction rates. Our full-dimensional ring-polymer instanton simulations show that below 100 K the concerted DHT tunneling pathway dominates, but between 100 K and 300 K there is a competition between concerted and stepwise pathways when nuclear quantum effects are included. We obtain ground-state reaction rates of $2.19 \times 10^{11} \mathrm{s}^{-1}$ at 150 K and $0.63 \times 10^{11} \mathrm{s}^{-1}$ at 100 K, in good agreement with experiment. We also reproduce the puzzling N-H stretching band of porphycene with very good accuracy from thermostatted ring-polymer molecular dynamics simulations. The position and lineshape of this peak, centered at around 2600 cm$^{-1}$ and spanning 750 cm$^{-1}$, stems from a combination of very strong H-bonds, the coupling to low-frequency modes, and the access to $cis$-like isomeric conformations, which cannot be appropriately captured with classical-nuclei dynamics. These results verify the appropriateness of our general theoretical approach and provide a framework for a deeper physical understanding of hydrogen transfer dynamics in complex systems

Microcanonical and thermal instanton rate theory for chemical reactions at all temperatures

Semiclassical instanton theory is used to study the quantum effects of tunnelling and delocalization in molecular systems. An analysis of the approximations involved in the method is presented based on a recent first-principles derivation of instanton rate theory [J. Chem. Phys., 2016, 144, 114106]. It is known that the standard instanton method is unable to accurately compute thermal rates near the crossover temperature. The causes of this problem are identified and an improved method is proposed, whereby an instanton approximation to the microcanonical rate is defined which is integrated numerically to obtain a thermal rate at any temperature. No new computational algorithms are required, but only data analysis of a number of standard instanton calculations

A Ground-Based Search for Thermal Emission from the Exoplanet TrES-1

Eclipsing planetary systems give us an important window on extrasolar planet atmospheres. By measuring the depth of the secondary eclipse, when the planet moves behind the star, we can estimate the strength of the thermal emission from the day side of the planet. Attaining a ground-based detection of one of these eclipses has proven to be a significant challenge, as time-dependent variations in instrument throughput and atmospheric seeing and absorption overwhelm the small signal of the eclipse at infrared wavelengths. We gathered a series of simultaneous L grism spectra of the transiting planet system TrES-1 and a nearby comparison star of comparable brightness, allowing us to correct for these effects in principle. Combining the data from two eclipses, we demonstrate a detection sensitivity of 0.15% in the eclipse depth relative to the stellar flux. This approaches the sensitivity required to detect the planetary emission, which theoretical models predict should lie between 0.05-0.1% of the stellar flux in our 2.9-4.3 micron bandpass. We explore the factors that ultimately limit the precision of this technique, and discuss potential avenues for future improvements.Comment: 10 pages, 1 table, four figures, accepted for publication in PAS