2,443 research outputs found
Analytic continuation of Wolynes theory into the Marcus inverted regime
The Wolynes theory of electronically nonadiabatic reaction rates [P. G.
Wolynes, J. Chem. Phys. 87, 6559 (1987)] is based on a saddle point
approximation to the time integral of a reactive flux autocorrelation function
in the nonadiabatic (golden rule) limit. The dominant saddle point is on the
imaginary time axis at , and provided
lies in the range ,
it is straightforward to evaluate the rate constant using information obtained
from an imaginary time path integral calculation. However, if lies outside this range, as it does in the Marcus inverted regime, the
path integral diverges. This has led to claims in the literature that Wolynes
theory cannot describe the correct behaviour in the inverted regime. Here we
show how the imaginary time correlation function obtained from a path integral
calculation can be analytically continued to , and
the continuation used to evaluate the rate in the inverted regime. Comparisons
with exact golden rule results for a spin-boson model and a more demanding
(asymmetric and anharmonic) model of electronic predissociation show that the
theory it is just as accurate in the inverted regime as it is in the normal
regime.Comment: 9 pages, 8 figure
Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei
Light nuclei at room temperature and below exhibit a kinetic energy which
significantly deviates from the predictions of classical statistical mechanics.
This quantum kinetic energy is responsible for a wide variety of isotope
effects of interest in fields ranging from chemistry to climatology. It also
furnishes the second moment of the nuclear momentum distribution, which
contains subtle information about the chemical environment and has recently
become accessible to deep inelastic neutron scattering experiments. Here we
show how, by combining imaginary time path integral dynamics with a carefully
designed generalized Langevin equation, it is possible to dramatically reduce
the expense of computing the quantum kinetic energy. We also introduce a
transient anisotropic Gaussian approximation to the nuclear momentum
distribution which can be calculated with negligible additional effort. As an
example, we evaluate the structural properties, the quantum kinetic energy, and
the nuclear momentum distribution for a first-principles simulation of liquid
water
Radical pair intersystem crossing: Quantum dynamics or incoherent kinetics?
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 molecular
wires
Nuclear quantum effects in water exchange around lithium and fluoride ions
We employ classical and ring polymer molecular dynamics simulations to study
the effect of nuclear quantum fluctuations on the structure and the water
exchange dynamics of aqueous solutions of lithium and fluoride ions. While we
obtain reasonably good agreement with experimental data for solutions of
lithium by augmenting the Coulombic interactions between the ion and the water
molecules with a standard Lennard-Jones ion-oxygen potential, the same is not
true for solutions of fluoride, for which we find that a potential with a
softer repulsive wall gives much better agreement. A small degree of
destabilization of the first hydration shell is found in quantum simulations of
both ions when compared with classical simulations, with the shell becoming
less sharply defined and the mean residence time of the water molecules in the
shell decreasing. In line with these modest differences, we find that the
mechanisms of the exchange processes are unaffected by quantization, so a
classical description of these reactions gives qualitatively correct and
quantitatively reasonable results. We also find that the quantum effects in
solutions of lithium are larger than in solutions of fluoride. This is partly
due to the stronger interaction of lithium with water molecules, partly due to
the lighter mass of lithium, and partly due to competing quantum effects in the
hydration of fluoride, which are absent in the hydration of lithium.Comment: 12 pages, 8 figure
How to remove the spurious resonances from ring polymer molecular dynamics
Two of the most successful methods that are presently available for
simulating the quantum dynamics of condensed phase systems are centroid
molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite
their conceptual differences, practical implementations of these methods differ
in just two respects: the choice of the Parrinello-Rahman mass matrix and
whether or not a thermostat is applied to the internal modes of the ring
polymer during the dynamics. Here we explore a method which is halfway between
the two approximations: we keep the path integral bead masses equal to the
physical particle masses but attach a Langevin thermostat to the internal modes
of the ring polymer during the dynamics. We justify this by showing
analytically that the inclusion of an internal mode thermostat does not affect
any of the desirable features of RPMD: thermostatted RPMD (TRPMD) is equally
valid with respect to everything that has actually been proven about the method
as RPMD itself. In particular, because of the choice of bead masses, the
resulting method is still optimum in the short-time limit, and the transition
state approximation to its reaction rate theory remains closely related to the
semiclassical instanton approximation in the deep quantum tunneling regime. In
effect, there is a continuous family of methods with these properties,
parameterised by the strength of the Langevin friction. Here we explore
numerically how the approximation to quantum dynamics depends on this friction,
with a particular emphasis on vibrational spectroscopy. We find that a broad
range of frictions approaching optimal damping give similar results, and that
these results are immune to both the resonance problem of RPMD and the
curvature problem of CMD
Mean-Field Theory of Water-Water Correlations in Electrolyte Solutions
Long-range ion induced water-water correlations were recently observed in
femtosecond elastic second harmonic scattering experiments of electrolyte
solutions. To further the qualitative understanding of these correlations, we
derive an analytical expression that quantifies ion induced dipole-dipole
correlations in a non-interacting gas of dipoles. This model is a logical
extension of Debye-H\"uckel theory that can be used to qualitatively understand
how the combined electric field of the ions induces correlations in the
orientational distributions of the water molecules in an aqueous solution. The
model agrees with results from molecular dynamics simulations and provides an
important starting point for further theoretical work
Spin-dependent charge recombination along para-phenylene molecular wires
We have used an efficient new quantum mechanical method for radical pair
recombination reactions to study the spin-dependent charge recombination along
PTZ--Ph--PDI molecular wires. By comparing our
results to the experimental data of E. Weiss {\em et al.} [J. Am. Chem. Soc.
{\bf 126}, 5577 (2004)], we are able to extract the spin-dependent (singlet and
triplet) charge recombination rate constants for wires with . These
spin-dependent rate constants have not been extracted previously from the
experimental data because they require fitting its magnetic field-dependence to
the results of quantum spin dynamics simulations. We find that the triplet
recombination rate constant decreases exponentially with the length of the
wire, consistent with the superexchange mechanism of charge recombination.
However, the singlet recombination rate constant is nearly independent of the
length of the wire, suggesting that the singlet pathway is dominated by an
incoherent hopping mechanism. A simple qualitative explanation for the
different behaviours of the two spin-selective charge recombination pathways is
provided in terms of Marcus theory. We also find evidence for a magnetic
field-independent background contribution to the triplet yield of the charge
recombination reaction, and suggest several possible explanations for it. Since
none of these explanations is especially compelling given the available
experimental evidence, and since the result appears to apply more generally to
other molecular wires, we hope that this aspect of our study will stimulate
further experimental work.Comment: 12 pages, 10 figure
Asymmetric recombination and electron spin relaxation in the semiclassical theory of radical pair reactions
We describe how the semiclassical theory of radical pair recombination
reactions recently introduced by two of us [D. E. Manolopoulos and P. J. Hore,
J. Chem. Phys. 139, 124106 (2013)] can be generalised to allow for different
singlet and triplet recombination rates. This is a non-trivial generalisation
because when the recombination rates are different the recombination process is
dynamically coupled to the coherent electron spin dynamics of the radical pair.
Furthermore, because the recombination operator is a two-electron operator, it
is no longer sufficient simply to consider the two electrons as classical
vectors: one has to consider the complete set of 16 two-electron spin operators
as independent classical variables. The resulting semiclassical theory is first
validated by comparison with exact quantum mechanical results for a model
radical pair containing 12 nuclear spins. It is then used to shed light on the
spin dynamics of a carotenoid-porphyrin-fullerene (CPF) triad containing
considerably more nuclear spins which has recently been used to establish a
'proof of principle' for the operation of a chemical compass [K. Maeda et al.,
Nature 453, 387 (2008)]. We find in particular that the intriguing biphasic
behaviour that has been observed in the effect of an Earth-strength magnetic
field on the time-dependent survival probability of the photo-excited C+PF-
radical pair arises from a delicate balance between its asymmetric
recombination and the relaxation of the electron spin in the carotenoid
radical
Spin-selective electron transfer reactions of radical pairs: beyond the Haberkorn master equation
Radical pair recombination reactions are normally described using a quantum
mechanical master equation for the electronic and nuclear spin density
operator. The electron spin state selective (singlet and triplet) recombination
processes are described with a Haberkorn reaction term in this master equation.
Here we consider a general spin state selective electron transfer reaction of a
radical pair and use Nakajima-Zwanzig theory to derive the master equation for
the spin density operator, thereby elucidating the relationship between
non-adiabatic reaction rate theory and the Haberkorn reaction term. A second
order perturbation theory treatment of the diabatic coupling naturally results
in the Haberkorn master equation with an additional reactive scalar electron
spin coupling term. This term has been neglected in previous spin chemistry
calculations, but we show that it will often be quite significant. We also show
that beyond second order in perturbation theory, i.e., beyond the Fermi golden
rule limit, an additional reactive singlet-triplet dephasing term appears in
the master equation. A closed form expression for the reactive scalar electron
spin coupling in terms of the Marcus theory parameters that determine the
singlet and triplet recombination rates is presented. By performing simulations
of radical pair reactions with the exact Hierarchical Equations of Motion
(HEOM) method, we demonstrate that our master equations provide a very accurate
description of radical pairs undergoing spin-selective non-adiabatic electron
transfer reactions. The existence of a reactive electron spin coupling may well
have implications for biologically relevant radical pair reactions such as
those which have been suggested to play a role in avian magnetoreception
The inefficiency of re-weighted sampling and the curse of system size in high order path integration
Computing averages over a target probability density by statistical
re-weighting of a set of samples with a different distribution is a strategy
which is commonly adopted in fields as diverse as atomistic simulation and
finance. Here we present a very general analysis of the accuracy and efficiency
of this approach, highlighting some of its weaknesses. We then give an example
of how our results can be used, specifically to assess the feasibility of
high-order path integral methods. We demonstrate that the most promising of
these techniques -- which is based on re-weighted sampling -- is bound to fail
as the size of the system is increased, because of the exponential growth of
the statistical uncertainty in the re-weighted average
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