We present an overview of the role of quantum coherence in influencing nonadiabatic processes in the condensed phase. Equations of motion for mixed quantum-classical dynamics are derived from the Consistent Histories interpretation of quantum mechanics. Application of the methods toward computing the excited state lifetime of an excess electron in water and heavy water provides a unique demonstration of our method.
The present work focuses on the characterization of the reaction between cyanoacetylene and cyano radical by electronic structure calculations of the stationary points along the minimum energy path. One channel, leading to C4N2 (2-Butynedinitrile) + H, was selected due to the importance of its products. Using different ab initio methods, a number of stationary points of the potential energy surface were characterized. The energy values of these minima were compared in order to weight the computational costs in relation to chemical accuracy. The results of this works suggests that B2PLYP (and B…
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 …
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…
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…
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…
The kinetics, dynamics and conformational specificities for the ionic Diels-Alder reaction (polar cycloaddition) of maleic anhydride with 2,3-dibromobutadiene radical ions have been studied theoretically using multisurface adiabatic reactive molecular dynamics. A competition of concerted and stepwise reaction pathways was found and both the s-cis and s-trans conformers of of the diene are reactive. The analysis of the minimum dynamic path of the reaction indicates that both, rotations and vibrations of the reactant molecules are important for driving the system towards the transition state. Th…
Radical pair recombination reactions are known to be sensitive to the application of both low and high magnetic fields. The application of a weak magnetic field reduces the singlet yield of a singlet-born radical pair, whereas the application of a strong magnetic field increases the singlet yield. The high field effect arises from energy conservation: when the magnetic field is stronger than the sum of the hyperfine fields in the two radicals, ${\rm S}\to {\rm T}_{\pm}$ transitions become energetically forbidden, thereby reducing the number of pathways for singlet to triplet interconversion. T…
Recently, spin-selective radical pair reactions have been studied using concepts from quantum measurement theory. In this Article, we show that the approach taken by Kominis (Physical Review E, 83, 2011, 056118) leads to erroneous results due to a problematic treatment of quantum jumps. Correct consideration of quantum jumps leads to either the traditional master equation or the Jones-Hore master equation.
Chemically induced dynamic nuclear polarization is a ubiquitous phenomenon in photosynthetic reaction centers. The relevant nuclear spin observables are a direct manifestation of the radical-pair mechanism. We here use quantum trajectories to describe the time evolution of radical-pairs, and compare their prediction of nuclear spin observables to the one derived from the radical-pair master equation. While our approach provides a consistent description, we unravel a major inconsistency within the conven- tional theory, thus challenging the theoretical interpretation of numerous CIDNP experimen…
In his Comment on a recent paper by two of us Kominis claims that the recently proposed quantum measurement model for spin-selective reactions of radical pairs leads to ambiguous predictions in a simple case. Here we show that this claim is based on a confusion between the unreacted and unrecombined portions of the radical pairs, and to an incorrect interpretation of the improper density matrices used in both our model and the conventional Haberkorn model of such reactions. We further show that if this error is corrected then the supposed ambiguity is resolved.
Radical-ion-pair reactions were recently shown to represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts. We here propose a concrete experimental test that can clearly discriminate among the fundamental master equations currently attempting to describe the quantum dynamics of these reactions. The proposed measurement based on photon statistics of fluorescing radical pairs is shown to be model-independent and capable of elucidating the singlet-triplet decoherence inherent in the radical-ion-pair recombination process.
Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective radical-ion pair reactions was introduced most recently, bringing to three the competing theories, including the one traditionally used in spin chemistry. We here consider entropy as a fundamental concept enabling a comparison of the predictions of these theories against what is physically acceptable on quite general grounds.
Radical-ion-pair reactions were recently shown to represent a rich biophysical laboratory for the application of quantum measurement theory methods and concepts. We here show that radical-ion-pair reactions essentially form a non-linear biochemical double slit interferometer. Quantum coherence effects are visible when "which-path" information is limited, and the incoherent limit is approached when measurement-induced decoherence sets in. Based on this analogy with the optical double slit experiment we derive and elaborate on the fundamental master equation of spin-selective radical-ion-pair re…
Relaxation processes can have a large effect on the spin selective electron transfer reactions of radical pairs. These processes are often treated using phenomenological relaxation superoperators or with some model for the microscopic relaxation mechanism treated within Bloch-Redfield-Wangsness theory. Here, we demonstrate that an alternative perturbative relaxation theory, based on the Nakajima-Zwanzig equation, has certain advantages over Redfield theory. In particular, the Nakajima-Zwanzig equation does not suffer from the severe positivity problem of Redfield theory in the static disorder …
We elaborate on the physical meaning of the non-linear master equation that was recently derived to account for spin-selective radical-ion-pair reactions. Based on quite general arguments, we show that such a non-linear master equation is indeed to be expected.
While many studies have been reported on the reactions of aliphatic hydrocarbons, the chemistry of cyclic hydrocarbons has not been explored extensively. In the present work, a theoretical study of the gas-phase unimolecular decomposition of cyclic alkyl radicals was performed by means of quantum chemical calculations at the CBS-QB3 level of theory. Energy barrier and high-pressure limit rate constants were calculated systematically. Thermochemical data were obtained from isodesmic reactions and the contribution of hindered rotors was taken into account. Classical transition state ...
Chemistry in the ultracold regime enables fully quantum-controlled interactions between atoms and molecules, leading to the discovery of the hidden mechanisms in chemical reactions which are usually curtained by thermal averaging in the high temperature. Recently a couple of diatomic molecules have been cooled to ultracold regime based on laser cooling techniques, but the chemistry associated with these simple molecules is highly limited. In comparison, free radicals play a major role in many important chemical reactions, but yet to be cooled to submillikelvin temperature. Here we propose a no…
Despite the fact that the majority of current models assume that interstellar complex organic molecules (iCOMs) are formed on dust-grain surfaces, there is some evidence that neutral gas-phase reactions play an important role. In this paper, we investigate the reaction occurring in the gas phase between methylamine (CH$_3$NH$_2$) and the cyano (CN) radical, for which only fragmentary and/or inaccurate results have been reported to date. This case study allows us to point out the pivotal importance of employing quantum-chemical calculations at the state of the art. Since the two major products …
We propose a method for controlling a class of low temperature chemical reactions. Specifically, we show the hydrogen abstraction channel in the reaction of formaldehyde (H$_{2}$CO) and the hydroxyl radical (OH) can be controlled through either the molecular state or an external electric field. We also outline experiments for investigating and demonstrating control over this important reaction. To this end, we report the first Stark deceleration of the H$_{2}$CO molecule. We have decelerated a molecular beam of H$_{2}$CO essentially to rest, producing cold molecule packets at a temperature of …
Magnetic field effects (MFE) in certain chemical reactions have been well established in the last five decades and are attributed to the evolution of transient radical-pairs whose spin dynamics are determined by local and external magnetic fields. The majority of existing experimental techniques used to probe these reactions only provide ensemble averaged reaction parameters and spin chemistry, hindering the observation of the potential presence of quantum coherent phenomena at the single molecule scale. Here, considering a single nitrogen vacancy (NV) centre as quantum sensor, we investigate …
Radical-ion pairs, fundamental for understanding photosynthesis and the avian magnetic compass, were recently shown to be biological open quantum systems. We here show that the coupling of the radical-pair's spin degrees of freedom to its decohering vibrational reservoir leads to a shift of the radical-pair's magnetic energy levels. The Lamb shift Hamiltonian is diagonal in the singlet-triplet basis, and results in a singlet-triplet energy splitting physically indistinguishable from an exchange interaction. This could have significant implications for understanding the energy level structure a…
It has been recently shown that radical-ion pairs and their reactions are a paradigm biological system manifesting non-trivial quantum effects, so far invisible due to the phenomenological description of radical-ion-pair reactions used until now. We here use the quantum-mechanically consistent master equation describing magnetic-sensitive radical-ion-pair reactions to explain experimental data [C. R. Timmel and K. B. Henbest, Phil. Trans. R. Soc. Lond. A {\bf 362}, 2573 (2004); C. T. Rodgers, S. A. Norman, K. B. Henbest, C. R. Timmel and P. J. Hore, J. Am. Chem. Soc. {\bf 129} 6746 (2007)] on …
A short comment on "The Jones-Hore theory of radical-ion-pair reactions is not self-consistent" (arXiv:1010.3888v3) is presented. In the comment, it is pointed out that the paper includes a misconception about the Jones-Hore approach in Chem. Phys. Lett. 488 (2010) 90-93. The re-formulation is presented and it is demonstrated that the Jones-Hore theory is consistent at least on the point claimed by I. K. Kominis in the paper.
In order to improve the understanding of the low temperature combustion of ethanol, high-level ab initio calculations were performed for elementary reactions involving hydroxyethylperoxy radicals. These radicals come from the addition of hydroxethyl radicals (?CH3CHOH and ?CH2CH2OH) on oxygen molecule. Unimolecular reactions involving hydroxyethylperoxy radicals and their radical products were studied at the CBS-QB3 level of theory. The results allowed to highlight the principal ways of decomposition of these radicals. Calculations of potential energy surfaces showed that the principal channel…
Recently there has been much interest in the chirality induced spin selectivity effect, whereby electron spin polarisation, which is dependent on the molecular chirality, is produced in electrode-molecule electron transfer processes. Naturally, one might consider if a similar effect can be observed in simple molecular charge transfer reactions, for example in light-induced electron transfer from an electron donor to an electron acceptor. In this work we explore the effect of electron transfer on spins in chiral single radicals and chiral radical pairs using Nakajima-Zwanzig theory. In these ca…
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…
The reaction between the amidogen, NH, radical and the ethyl, C2H5, radical has been investigated by performing electronic structure calculations of the underlying doublet potential energy surface. Rate coefficients and product branching ratios have also been estimated by combining capture and RRKM calculations. According to our results, the reaction is very fast, close to the gas-kinetics limit. However, the main product channel, with a yield of ca. 86-88% in the range of temperatures investigated, is the one leading to methanimine and the methyl radical. The channels leading to the two E-, Z…
We investigate the ultracold reaction dynamics of magnetically trapped NH($X ^3Σ^-$) radicals using rigorous quantum scattering calculations involving three coupled potential energy surfaces. We find that the reactive NH + NH cross section is driven by a short-ranged collisional mechanism, and its magnitude is only weakly dependent on magnetic field strength. Unlike most ultracold reactions observed so far, the NH + NH scattering dynamics is non-universal. Our results indicate that chemical reactions can cause more trap loss than spin-inelastic NH + NH collisions, making molecular evaporative …
Advanced oxidation processes that utilize highly oxidative radicals are widely used in water reuse treatment. In recent years, the application of sulfate radical (SO$_4\cdot^-$) as a promising oxidant for water treatment has gained increasing attention. To understand the efficiency of SO$_4\cdot^-$ in the degradation of organic contaminants in wastewater effluent, it is important to be able to predict the reaction kinetics of various SO$_4\cdot^-$-driven oxidation reactions. In this study, we utilize density functional theory (DFT) and high-level wavefunction-based methods (including computati…
We devise a novel technique to control the shape of polymer molecular weight distributions (MWDs) in atom transfer radical polymerization (ATRP). This technique makes use of recent advances in both simulation-based, model-free reinforcement learning (RL) and the numerical simulation of ATRP. A simulation of ATRP is built that allows an RL controller to add chemical reagents throughout the course of the reaction. The RL controller incorporates fully-connected and convolutional neural network architectures and bases its decision upon the current status of the ATRP reaction. The initial, untraine…
Radical-ion pairs and their reactions have triggered the study of quantum effects in biological systems. This is because they exhibit a number of effects best understood within quantum information science, and at the same time are central in understanding the avian magnetic compass and the spin transport dynamics in photosynthetic reaction centers. Here we address radical-pair reactions from the perspective of quantum metrology. Since the coherent spin motion of radical-pairs is effected by an external magnetic field, these spin-dependent reactions essentially realize a biochemical magnetomete…
Towards Application of Nanodiamonds for in-situ Monitoring of Radicals in Liquid Phase Chemical Reactions
RPTU University（莱布尼茨技术大学）；State Research Center OPTIMAS, RPTU University（OPTIMAS州立研究中心，莱布尼茨技术大学）；Kiel University（基尔大学）；Kiel Nano, Surface and Interface Science (KiNSIS), Kiel University（基尔纳米、表面与界面科学研究所（KiNSIS），基尔大学）
The radical-pair mechanism was introduced in the 1960's to explain anomalously large EPR and NMR signals in chemical reactions of organic molecules. It has evolved to the cornerstone of spin chemistry, the study of the effect electron and nuclear spins have on chemical reactions, with the avian magnetic compass mechanism and the photosynthetic reaction center dynamics being prominent biophysical manifestations of such effects. In recent years the radical-pair mechanism was shown to be an ideal biological system where the conceptual tools of quantum information science can be fruitfully applied…
Radical-ion-pair reactions, central for understanding the avian magnetic compass and spin transport in photosynthetic reaction centers, were recently shown to be a fruitful paradigm of the new synthesis of quantum information science with biological processes. We show here that the master equation so far constituting the theoretical foundation of spin chemistry violates fundamental bounds for the entropy of quantum systems, in particular the Ozawa bound. In contrast, a recently developed theory based on quantum measurements, quantum coherence measures, and quantum retrodiction, thus exemplifyi…
We have produced a cryogenic buffer-gas cooled beam of the diatomic molecular radical CH (methylidyne). This molecule is of interest for studying cold chemical reactions and fundamental physics measurements. Its light mass and ground-state structure make it a promising candidate for electrostatic guiding and Stark deceleration, which allows for control over its kinetic energy. This control can facilitate studies of reactions with tuneable collision energies and trapping for precise spectroscopic studies. Here, we have demonstrated electrostatic guiding of CH with fluxes up to $10^9$ molecules …
Sets of systematic laboratory experiments are presented -- combining Ultra High Vacuum cryogenic and plasma-line deposition techniques -- that allow us to compare H/D isotopic effects in the reaction of H2O (D2O) ice with the hydroxyl radical OD (OH). The latter is known to play a key role as intermediate species in the solid-state formation of water on icy grains in space. The main finding of our work is that the reaction H2O + OD --> OH + HDO occurs and that this may affect the HDO/H2O abundances in space. The opposite reaction D2O + OH --> OD + HDO is much less effective, and also given the…
The recently proposed natural orbital functional second-order Møller-Plesset (NOF-MP2) method is capableof achieving both dynamic and static correlation even for those systems with significant multiconfigurational character. We test its reliability to describe the electron correlation in radical formation reactions, namely, in the homolytic X-H bond cleavage of LiH, BH, CH4, NH3, H2O and HF molecules. Our results are compared with CASSCF and CASPT2 wavefunction calculations and the experimental data. For a dataset of 20 organic molecules, the thermodynamics of C-H homolytic bond cleavage, in w…
Many organic molecules have been observed in the interstellar medium thanks to advances in radioastronomy, and very recently the presence of urea was also suggested. While those molecules were observed, it is not clear what the mechanisms responsible to their formation are. In fact, if gas-phase reactions are responsible, they should occur through barrierless mechanisms (or with very low barriers). In the past, mechanisms for the formation of different organic molecules were studied, providing only in a few cases energetic conditions favorable to a synthesis at very low temperature. A particul…
Radical-ion-pair reactions, central in photosynthesis and the avian magnetic compass mechanism, have recently shown to be a paradigm system for applying quantum information science in a biochemical setting. The fundamental quantum master equation describing radical-ion-pair reactions is still under debate. We here use quantum retrodiction to produce a rigorous refinement of the theory put forward in Phys. Rev. E {\bf 83}, 056118 (2011). We also provide a rigorous analysis of the measure of singlet-triplet coherence required for deriving the radical-pair master equation. A Monte-Carlo simulatio…
We explored how steric effects influence the rate of hydrogen atom transfer (HAT) reactions between oxyradicals and alkanes. Quantum chemical computations of transition states show that activation barriers and reaction enthalpies are both influenced by bulky substituents on the radical, but less so by substituents on the alkane. The activation barriers correlate with reaction enthalpies via the Evans-Polanyi relationship, even when steric effects are important. Dispersion effects can additionally stabilize transition states in some cases.
Chemically induced dynamic nuclear polarization is a signature of spin order appearing in many photosynthetic reaction centers. Such polarization, significantly enhanced above thermal equilibrium, is known to result from the nuclear spin sorting inherent in the radical pair mechanism underlying long-lived charge-separated states in photosynthetic reaction centers. We will here show that the recently understood fundamental quantum dynamics of radical-ion-pair reactions open up a new and completely unexpected venue towards obtaining CIDNP signals. The fundamental decoherence mechanism inherent i…
We present a combined experimental and theoretical study focussing on the quantum tunneling of atoms in the reaction between CH4 and OH. The importance of this reaction pathway is derived by investigating isotope substituted analogs. Quantitative reaction rates needed for astrochemical models at low temperature are currently unavailable both in the solid state and in the gas phase. Here, we study tunneling effects upon hydrogen abstraction in CH4 + OH by focusing on two reactions: CH4 + OD -> CH3 + HDO and CD4 + OH -> CD3 + HDO. The experimental study shows that the solid-state reaction rate R…
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 lif…
Stereo-Electronic Factors Influencing the Stability of Hydroperoxyalkyl Radicals: Transferability of Chemical Trends across Hydrocarbons and ab initio Methods
A popular hypothesis ascribes magnetoreception to a magnetosensitive recombination reaction of a pair of radicals in the protein cryptochrome. Many theoretical studies of this model have ignored inter-radical interactions, particularly the electron-electron dipolar coupling (EED), which have a detrimental effect on the magnetosensitivity. Here, we set out to elucidate if a radical pair allowed to undergo internal motion can yield enhanced magneto-sensitivity. Our model considers the effects of diffusive motion of one radical partner along a one-dimensional reaction coordinate. Such dynamics co…
Hydrogen addition and abstraction reactions play an important role as surface reactions in the buildup of complex organic molecules in the dense interstellar medium. Addition reactions allow unsaturated bonds to be fully hydrogenated, while abstraction reactions recreate radicals that may undergo radical-radical recombination reactions. Previous experimental work has indicated that double and triple C--C bonds are easily hydrogenated, but aldehyde -C=O bonds are not. Here, we investigate a total of 29 reactions of the hydrogen atom with propynal, propargyl alcohol, propenal, allyl alcohol, and…
We present a conspectus of recent joint spectroscopic and computational studies which provided novel insight into the photochemistry of hydrogen-bonded complexes of the heptazine (Hz) chromophore with hydroxylic substrate molecules (water and phenol). It was found that a functionalized derivative of Hz, tri-anisole-heptazine (TAHz), can photooxidize water and phenol in a homogeneous photochemical reaction. This allows the exploration of the basic mechanisms of the proton-coupled electron-transfer (PCET) process involved in the water photooxidation reaction in well-defined complexes of chemical…
The Radical Pair Mechanism is a canonical model for the magnetosensitivity of chemical reaction processes. The key ingredient of this model is the hyperfine interaction that induces a coherent mixing of singlet and triplet electron spin states in pairs of radicals, thereby facilitating magnetic field effects (MFEs) on reaction yields through spin-selective reaction channels. We show that the hyperfine interaction is not a categorical requirement to realize the sensitivity of radical reactions to weak magnetic fields. We propose that, in systems comprising three instead of two radicals, dipolar…
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 …
