2,034 research outputs found
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 at 150 K
and 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 and spanning 750 cm, stems from a combination of very strong
H-bonds, the coupling to low-frequency modes, and the access to -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
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