Chemical reactions in multidimensional driven systems are typically described by a time-dependent rank-1 saddle associated with one reaction and several orthogonal coordinates (including the solvent bath). To investigate reactions in such systems, we develop a fast and robust method ---viz., local manifold analysis (LMA)--- for computing the instantaneous decay rate of reactants. Specifically, it computes the instantaneous decay rates along saddle-bound trajectories near the activated complex by exploiting local properties of the stable and unstable manifold associated with the normally hyperbolic invariant manifold (NHIM). The LMA method offers substantial reduction of numerical effort and increased reliability in comparison to direct ensemble integration. It provides an instantaneous flux that can be assigned to every point on the NHIM and which is associated with a trajectory ---regardless of whether it is periodic, quasi-periodic, or chaotic--- that is bound on the NHIM. The time average of these fluxes in the driven system corresponds to the average rate through a given local section containing the corresponding point on the NHIM. We find good agreement between the results of the LMA and direct ensemble integration obtained using numerically constructed, recrossing-free dividing surfaces.
The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that channel the system towards and away from the transition state. The existence of these structures can only be guaranteed if the invariant hyper-sphere is normally hyperbolic, i.e., the dynamics within the transition state is not too strongly chaotic. We study the dynamics within the transition state for the hydrogen exchange reaction in three degrees of freedom.…
Quantifying anisotropy in the chemical reactions of mesoscopic crystals has mostly resorted on the combination of electron microscopy and diffraction. In this work, we established crystal-facet-resolved kinetic measurements of oxidation reactions in 2D transition metal dichalcogenides (TMDs) using optical second-harmonic generation spectroscopy and scanning probe microscopy. We show the in-plane anisotropy of their bond-breaking reactions is governed by their structure and strongly material-dependent among four TMDs. The facet-resolved analysis directly revealed that the reactions proceed fast…
The nuclear tunneling crossover temperature ($T_c$) of hydrogen transfer reactions in supported molecular-switch architectures can lie close to room temperature. This calls for the inclusion of nuclear quantum effects (NQE) in the calculation of reaction rates even at high temperatures. However, standard computations of NQE relying on parametrized dimensionality-reduced models, quickly become inadequate in these environments. In this letter, we study the paradigmatic molecular switch based on porphycene molecules adsorbed on metallic surfaces with full-dimensional calculations that combine den…
The usual identification of reactive trajectories for the calculation of reaction rates requires very time-consuming simulations, particularly if the environment presents memory effects. In this paper, we develop a new method that permits the identification of reactive trajectories in a system under the action of a stochastic colored driving. This method is based on the perturbative computation of the invariant structures that act as separatrices for reactivity. Furthermore, using this perturbative scheme, we have obtained a formally exact expression for the reaction rate in multidimensional s…
Canonical instanton theory is a widespread approach to describe the dynamics of chemical reactions in low temperature environments when tunneling effects become dominant. It is a semiclassical theory which requires locating classical periodic orbits on the upside-down potential energy surface, so-called instantons, and the computation of second order quantum corrections. The calculation of these corrections usually involves a matrix diagonalization. In this paper we present an alternative approach, which requires to solve only linear systems of equations involving sparse matrices. Furthermore,…
Nuclear magnetic resonance (NMR) spectroscopy provides detailed information pertaining to dynamic processes through line-shape changes, which have been traditionally limited to equilibrium conditions. However, there is a wealth of information to be gained by studying chemical reactions under off-equilibrium conditions -- e.g., in states that arise upon mixing reactants that subsequently undergo chemical changes -- and in monitoring the formation of reaction products in real time. Herein, we propose and demonstrate a time-resolved kinetic NMR experiment that combines rapid mixing techniques, co…
The photosystem II reaction center (PSII-RC) performs the primary energy conversion steps of oxygenic photosynthesis. While the PSII-RC has been studied extensively, the similar timescales of energy transfer and charge separation, and the severely overlapping pigment transitions in the Qy region have led to multiple models of its charge separation mechanism and excitonic structure. Here we combine two-dimensional electronic spectroscopy (2DES) with a continuum probe and two-dimensional electronic vibrational spectroscopy (2DEV) to study the cyt b559-D1D2 PSII-RC at 77K. This multispectral comb…
The results of accurate quantum reactive scattering calculations for the D + HD($v=4$, $j=0$) $\to$ D + HD($v'$, $j'$), D + HD($v=4$, $j=0$) $\to$ H + D$_2$($v'$, $j'$) and H + D$_2$($v=4$, $j=0$) $\to$ D + HD($v'$,$j'$) reactions are presented for collision energies between $1\,μ{\rm K}$ and $100\,{\rm K}$. The ${\it ab\ initio}$ BKMP2 PES for the ground electronic state of H$_3$ is used and all values of total angular momentum between $J=0-4$ are included. The general vector potential approach is used to include the geometric phase. The rotationally resolved, vibrationally resolved, and tota…
It is commonly believed that it is unfavourable for adsorbed H atoms on carbonaceous surfaces to form H$_2$ without the help of incident H atoms. Using ring-polymer instanton theory to describe multidimensional tunnelling effects, combined with ab initio electronic structure calculations, we find that these quantum-mechanical simulations reveal a qualitatively different picture. Recombination of adsorbed H atoms, which was believed to be irrelevant at low temperature due to high barriers, is enabled by deep tunnelling, with reaction rates enhanced by tens of orders of magnitude. Furthermore, w…
Quantum reactive scattering calculations for the hydrogen exchange reaction H + H$_2$($v=4$, $j=0$) $\to$ H + H$_2$($v'$, $j'$) and its isotopic analogues are reported for ultracold collision energies. Due to the unique properties associated with ultracold collisions, it is shown that the geometric phase effectively controls the reactivity. The rotationally resolved rate coefficients computed with and without the geometric phase are shown to differ by up to four orders of magnitude. The effect is also significant in the vibrationally resolved and total rate coefficients. The dynamical origin o…
Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state trajectory. Here, we extend our recent methods by constructing points on the NHIM accurately even for multidimensional cases. We also advance the implementation of machine learning approaches to construct smooth versions of the NHIM from a known high-accuracy set of its points. That is, we expand on our earlier use of neural nets, and introduce the use of Gauss…
We calculated reaction rate constants including atom tunneling of the reaction of dihydrogen with the hydroxy radical down to a temperature of 50 K. Instanton theory and canonical variational theory with microcanonical optimized multidimensional tunneling (CVT/$μ$OMT) were applied using a fitted potential energy surface [J. Chem. Phys. 138, 154301 (2013)]. All possible protium/deuterium isotopologues were considered. Atom tunneling increases at about 250 K (200 K for deuterium transfer). Even at 50 K the rate constants of all isotopologues remain in the interval $ 4 \cdot 10^{-20}$ to $4 \cdot…
Time-resolved imaging of chemically active valence electron densities is a long sought goal, as these electrons dictate the course of chemical reactions. However, x-ray scattering is always dominated by the core and inert valence electrons, making time-resolved x-ray imaging of chemically active valence electron densities extremely challenging. To image such electron densities, we demonstrate an effective and robust method, which emphasizes the information encoded in weakly scattered photons. The degenerate Cope rearrangement of semibullvalene, a pericyclic reaction, is used as an example to v…
A quantum mechanical coupled-channel scattering calculation on the Stark-Werner potential energy surface is used to study the F + H2(v=0; j=0,1,2) ---> H + HF(v', j') reaction at collision energies of 1.84, 2.74, and 3.42 kcal/mol. The dependence of the vibrationally and rotationally resolved differential cross sections on the product vibrational levels v'=0, 1, 2, and 3 as well as on the reactant and product rotational levels is analyzed. The HF(v'=3) center-of-mass forward scattering peak is shown to be caused by the superposition of two effects, namely, the absence of the HF(v'=3; j') produ…
We extend state-to-state chemistry to a realm where besides vibrational, rotational and hyperfine quantum states magnetic quantum numbers are also resolved. For this, we make use of the Zeeman effect which energetically splits levels of different magnetic quantum numbers. The chemical reaction which we choose to study is three-body recombination in an ultracold quantum gas of $^{87}$Rb atoms forming weakly-bound Rb$_2$ molecules. Here, we find the propensity rule that the total $m_F$ quantum number of the two atoms forming the molecule is conserved. Our method can be employed for many other re…
We analyze the classical phase space dynamics of a three degree of freedom Hamiltonian that models multiple bond breaking and forming reactions. The model Hamiltonian, inspired from studies on double proton transfer reactions, allows for exploring the dynamical consequences of higher index saddles on multidimensional potential energy surfaces. Studies have shown that coupling of low frequency transverse modes to the reaction coordinate can significantly influence the reaction mechanism, concerted or sequential, as inferred from a reduced dimensional analysis. Using the notion of dynamically co…
We report the first study of time-resolved high-harmonic spectroscopy (TR-HHS) of a bond-making chemical reaction. We investigate the transient change of the high harmonic signal from 1,3-cyclohexadiene (CHD), which undergoes ring-opening and isomerizes to 1,3,5-hexatriene (HT) upon photoexcitation. By associating the change of the harmonic yield with the changes of the ionization energy and vibrational frequency of the molecule due to the isomerization, we find that the electronic excited state of CHD created via two-photon absorption of 3.1 eV photons relaxes almost completely within 80 fs t…
This review discusses the dynamics of negative ion reactions with neutral molecules in the gas phase. Most anion-molecule reactions proceed via a qualitatively different interaction potential than cationic or neutral reactions. It has been and still is the goal of many experiments to understand these reaction dynamics and the different reaction mechanisms they lead to. We will show how rate coefficients and cross sections for anion-molecule reactions are measured and interpreted to yield information on the underlying dynamics. We will also present more detailed approaches that study either the…
The ab initio calculation of exact quantum reaction rate constants comes at a high cost due to the required dynamics of reactants on multidimensional potential energy surfaces. In turn, this impedes the rapid design of the kinetics for large sets of coupled reactions. In an effort to overcome this hurdle, a deep neural network (DNN) was trained to predict the logarithm of quantum reaction rate constants multiplied by their reactant partition function - rate products. The training dataset was generated inhouse and contains ~1.5 million quantum reaction rate constants for single, double, symmetr…
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 g…
Recent work has shown that in a non-thermal, multidimensional system, the trajectories in the activated complex possess different instantaneous and time-averaged reactant decay rates. Under dissipative dynamics, it is known that these trajectories, which are bound on the normally hyperbolic invariant manifold (NHIM), converge to a single trajectory over time. By subjecting these dissipative systems to thermal noise, we find fluctuations in the saddle-bound trajectories and their instantaneous decay rates. Averaging over these instantaneous rates results in the decay rate of the activated compl…
The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerization reaction HCN $\rightleftharpoons$ CNH. Both algebraic (power law) and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Examination of the decay properties of subsensembles of t…
Phase-modulated wave-packet interferometry is combined with mass-resolved photoion detection to investigate rubidium atoms attached to helium nanodroplets in a molecular beam experiment. The spectra of atomic Rb electronic states show a vastly enhanced sensitivity and spectral resolution when compared to conventional pump-probe wave-packet interferometry. Furthermore, the formation of Rb*He exciplex molecules is probed and for the first time a fully resolved vibrational spectrum for transitions between the lowest excited $5Π_{3/2}$ and the high-lying electronic states $2^2Π$, $4^2Δ$, $6^2Σ$ is…
The kinetics of CH$_2$OO reaction with ozone has been studied by monitoring CH$_2$OO with time-resolved infrared (IR) absorption spectroscopy, which utilized fast chirped IR pulse train from a quantum cascade laser [J. Chem. Phys. 146, 244302 (2017)]. CH$_2$OO was prepared by photolyzing a gas mixture of CH$_2$I$_2$/O$_2$/O$_3$ at 352 nm; the photolysis wavelength was chosen to minimize the photodissociation of O$_3$. The measured rate coefficient at 298 K and 30 Torr is (6.7$\pm$0.5)x10$^{-14}$ cm$^3$sec$^{-1}$, independent of pressure from 30 to 100 Torr. The result indicates that previous a…
Time-Resolved Coulomb Explosion Imaging Unveils Ultrafast Ring Opening of Furan
J. R. Macdonald Laboratory, Department of Physics, Kansas State University（堪萨斯州立大学）；Hefei National Research Center for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China（中国科学技术大学）；European XFEL（欧洲X射线自由电子激光设施）；Max-Planck-Institut für Kernphysik（马克斯·普朗克核物理研究所）
Institute of Theoretical Physics, University of Amsterdam（阿姆斯特丹大学理论物理研究所）；QuSoft, CWI（QuSoft，荷兰数学与计算机科学研究中心）；IRIF & CNRS（IRIF与法国国家科学研究中心）；Toyota Motor Europe, Materials Engineering Division（丰田汽车欧洲公司材料工程部门）；Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit（自由大学化学与药学系）；KdVI, University of Amsterdam（阿姆斯特丹大学KdVI）
Time-resolved direct frequency comb spectroscopy (TRFCS) was used to study the kinetics of the deuterated analogue of the OH+CO->H+CO2 reaction, which is important for atmospheric and combustion chemistry. Complementing our recent work on quantifying the formation rate of the transient trans-DOCO radical, we report measurements of the kinetics of the activated product channel, D+CO2, at room temperature. Simultaneous measurements of the time-dependence of OD and CO2 concentrations allowed us to directly determine the formation rate, branching yield, and dependence on pressure and bath gas of t…
In the synthesis of metallic nanoparticles in microemulsions, we hypothesized that particle size is mainly controlled by the reaction rate. Thus, the changes observed on the particle sizes as reaction conditions, such as concentrations, temperature, type of surfactant used, etc., are varied should not be correlated directly to the modification of those conditions but indirectly to the changes they produce on the reaction rates. By means of time resolved UV-vis spectroscopy, we measured the reaction rates in the production of Pd nanoparticles inside microemulsions at different reactant concentr…
Ultracold molecules offer remarkable opportunities to study chemical reactions at nearly zero temperature. Although significant progresses have been achieved in exploring ultracold bimolecular reactions, the investigations are usually limited to measurements of the overall loss rates of the reactants. Detection of the reaction products will shed new light on understanding the reaction mechanism and provide a unique opportunity to study the state-to-state reaction dynamics. Here we report on the direct observation of an exoergic atom-exchange reaction in an ultracold atom-dimer mixture. Both th…
