The rate constants for recombination and exchange processes are studied in terms of two different flux correlation approaches: one is the Yamamoto approach, which is based on the linear response theory, and the other is the Miller one. Using those approaches we consider two exactly solvable cases, i.e., the free particle and the parabolic potential models. Since the rate constants for recombination and exchange processes are calculated by Laplace transforms of the flux correlation functions, the two approaches give different results. In the present calculation, we find that the rate constant in the Yamamoto approach is larger than that in the Miller approach by about 40% at low temperature ($\sim 100$ K) and high pressure ($\sim 1$ GPa). The difference is considerable in the region where quantum effects dominate.
The rate constants for recombination and exchange reactions are calculated using the flux correlation approach with a general form of the Boltzmannized flux operator, which can simultaneously describe the Kubo and traditional half-split forms. First, we consider an exactly solvable model, i.e., the free particle case, in terms of a new scaling function. Next, as a non-trivial case, we study the recombination and exchange reactions at very high pressure. Since the rate constant is calculated by Laplace transform of the flux correlation function, the result depends on how the Boltzmannized flux …
In theories of spin-dependent radical pair reactions, the time evolution of the radical pair, including the effect of the chemical kinetics, is described by a master equation in the Liouville formalism. For the description of the chemical kinetics, a number of possible reaction operators have been formulated in the literature. In this work, we present a framework that allows for a unified description of the various proposed mechanisms and the forms of reaction operators for the spin-selective recombination processes. Based on the concept that master equations can be derived from a microscopic …
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 elect…
We present a study on ion-atom-atom reaction A+A+B$^+$ in a wide range of systems and collision energies ranging from 100$~μ$K to 10$^5~$K, analyzing the two possible products: molecules and molecular ions. The dynamics is performed via a direct three-body formalism based on a classical trajectory method in hyperspherical coordinates developed in [J. Chem. Phys. $\textbf{140}$, 044307 (2014)]. Our chief finding is that the dissociation energy of the molecular ion product acts as a threshold energy separating the low and high energy regimes. In the low energy regime, the long-range tail of the …
Direct dissociative recombination and resonant ion-pair formation reactions of $\mathrm{HeH^+}$ are theoretically studied using time-dependant wave-packets methods. The wave packets are propagated on potential energy curves that are in either the adiabatic representation or the diabatic representation. The reaction cross sections are computed for collisions of different isotopes of $\mathrm{He}$ and $\mathrm{H}$. The reactions are modeled in the collision energy range 0 eV to 50 eV. Final states distributions are also investigated for the $\mathrm{^4HeH^+}$ dissociative recombination reaction,…
We present a practical semiclassical method for computing the electron spin dynamics of a radical in which the electron spin is hyperfine coupled to a large number of nuclear spins. This can be used to calculate the singlet and triplet survival probabilities and quantum yields of radical recombination reactions in the presence of magnetic fields. Our method differs from the early semiclassical theory of Schulten and Wolynes [J. Chem. Phys. 68, 3292 (1978)] in allowing each individual nuclear spin to precess around the electron spin, rather than assuming that the hyperfine coupling-weighted sum…
In open-shell atoms and ions, processes such as photoionization, combination (Raman) scattering, electron scattering and recombination, are often mediated by many-electron compound resonances. We show that their interference (neglected in the independent-resonance approximation) leads to a coherent contribution, which determines the energy-averaged total cross sections of electron- and photon-induced reactions obtained using the optical theorem. In contrast, the partial cross sections (e.g., electron recombination, or photon Raman scattering) are dominated by the stochastic contributions. Thus…
The standard quantum mechanical expressions for the singlet and triplet survival probabilities and product yields of a radical pair recombination reaction involve a trace over the states in a combined electronic and nuclear spin Hilbert space. If this trace is evaluated deterministically, by performing a separate time-dependent wavepacket calculation for each initial state in the Hilbert space, the computational effort scales as $O(Z^2\log Z)$, where $Z$ is the total number of nuclear spin states. Here we show that the trace can also be evaluated stochastically, by exploiting the properties of…
In this paper we outline a physically motivated framework for describing spin-selective recombination processes in chiral systems, from which we derive spin-selective reaction operators for recombination reactions of donor-bridge-acceptor molecules, where the electron transfer is mediated by chirality and spin-orbit coupling. In general the recombination process is selective only for spin-coherence between singlet and triplet states, and it is not in general selective for spin polarisation. We find that spin polarisation selectivity only arises in hopping mediated electron transfer. We describ…
We have used an efficient new quantum mechanical method for radical pair recombination reactions to study the spin-dependent charge recombination along PTZ$^{\bullet+}$--Ph$_n$--PDI$^{\bullet-}$ 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 $n=2-5$. These spin-dependent rate constants have not been extracted previously from the experimental data because they require fitting its magnetic field…
A recombination reaction model for high-temperature chemical kinetics is derived from ab initio simulations data. A kinetic recombination rate model is derived using a recently developed ab initio state-specific dissociation model and the principle of microscopic reversibility. When atoms recombine, the kinetic rate model shows that product molecules have high favoring for high vibrational energy states. A continuum recombination rate model is then derived analytically from the kinetic recombination rate model. Similarly, the expression for the average vibrational energy of recombining molecul…
H$_2$ premixed flames are well known for a long, trailing region where the unburnt H$_2$ and the super-equilibrium concentrations of radicals left past the fuel consumption layer gradually decay to thermodynamic equilibrium. This recombination region, it's argued here, is a second order effect induced by the premature quenching of the shuffle reactions, which inhibits the decay to equilibrium in the first approximation. Its structure and kinetics are studied in detail to capture the small but finite reaction rates accounting for its characteristic length scale, which is large enough to render …
A dataset of fully quantum flux-flux correlation functions and reaction rate constants was constructed for organic heterogeneous catalytic surface reactions. Gaussian process regressors were successfully fitted to training data to predict previously unseen test set reaction rate constant products and Cauchy fits of the flux-flux correlation function. The optimal regressor prediction mean absolute percent errors were on the order of 0.5% for test set reaction rate constant products and 1.0% for test set flux-flux correlation functions. The Gaussian process regressors were accurate both when loo…
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the $λ$--$\newrho$ model for irreversible bimolecular reactions which was introduced in [arXiv:0903.1298]. The formulae relating the experimentally measurable quantities (reaction rate constants and diffusion constants) with the algorithm parameters are derived. The probability of geminate recombination is also investigated.
A theoretical framework is proposed for an energy decomposition scheme along the reaction coordinate, in which the ensemble average of the potential energy weighted with reactive flux intensity is decomposed into energy components at the per-coordinate level. The decomposed energy quantity is demonstrated to be closely related to the free energy along the reaction coordinate and its connection to the emergent potential energy is provided. We also explore the property of the reactive flux weighted by the potential energy in the subspace of collective variables. A free energy analogue is then pr…
We use transient absorption spectroscopy to monitor the ionization and dissociation products following two-photon excitation of pure liquid water. The two decay mechanisms occur with similar yield for an excitation energy of 9.3 eV, whereas the major channel at 8.3 eV is dissociation. The geminate recombination kinetics of the H and OH fragments, which can be followed in the transient absorption probed at 267 nm, provide a window on the dissociation dynamics at the lower excitation energy. Modeling the OH geminate recombination indicates that the dissociating H atoms have enough kinetic energy…
We introduce a simple method for characterizing reactive pathways in quantum systems. Flux auto- correlation and cross-correlation functions are employed to develop a quantitative measure of dynamical coupling in quantum transition events, such as reactive tunneling and resonant energy transfer. We utilize the method to study condensed-phase proton-coupled electron transfer (PCET) reactions and to determine the relative importance of competing concerted and sequential reaction pathways. Results presented here include numerically exact quantum dynamics simulations for model condensed-phase PCET…
We present a new method for calculating the product yield of a radical pair recombination reaction in the presence of a weak time-dependent magnetic field. This method successfully circumvents the computational difficulties presented by a direct solution of the Liouville-von Neumann equation for a long-lived radical pair containing many hyperfine-coupled nuclear spins. Using a modified formulation of Floquet theory, treating the time-dependent magnetic field as a perturbation, and exploiting the slow radical pair recombination, we show that one can obtain a good approximation to the product yi…
We investigate the thermodynamic implications of two control mechanisms of open chemical reaction networks. The first controls the concentrations of the species that are exchanged with the surroundings, while the other controls the exchange fluxes. We show that the two mechanisms can be mapped one into the other and that the thermodynamic theories usually developed in the framework of concentration control can be applied to flux control as well. This implies that the thermodynamic potential and the fundamental forces driving chemical reaction networks out of equilibrium can be identified in th…
A spectroscopic application of the atom laser is suggested. The spectroscopy termed 2PACC employs the coherent properties of matter-waves from a two pulse atom laser. These waves are employed to control a gas-surface chemical recombination reaction. The method is demonstrated for an Eley-Rideal reaction of a hydrogen or alkali atom-laser pulse where the surface target is an adsorbed hydrogen atom. The reaction yields either a hydrogen or alkali hydride molecule. The desorbed gas phase molecular yield and its internal state is shown to be controlled by the time and phase delay between two atom-…
Temkin's 1963 article on one-way fluxes and flux ratios in steady-state reaction systems bears directly on current research in physical and biological chemistry, such as in the interpretation of metabolic exchange fluxes determined from isotopomer labeling experiments. Yet, originally published in Russian [Dolk. Akad. Nauk SSSR 152, 156-159 (1963)], this article has remained inaccessible to much of the scientific community. Here we provide an English translation of the original article with several additional clarifications and corrections.
Chemical reactions can accelerate, slow down or even be at the very origin of the development of dissolution-driven convection in partially miscible stratifications, when they impact the density profile in the host fluid phase. We numerically analyze the dynamics of this reactive convective dissolution in the fully developed non-linear regime for a phase A dissolving into a host layer containing a dissolved reactant B. We show that for a general A+B$\rightarrow$C reaction in solution, the dynamics vary with the Rayleigh numbers of the chemical species, i.e. with the nature of the chemicals in …
