Counter-propagating wave packets in the quantum transition state approach to reactive scattering.

In transition state (TS) region almost all systems (reactions) have weak van der waals complex structures. When these systems include heavy atom transfer, the forming quantum tunneling effects are suppressed. At TS region these reactions, especially including insertion minimum energy wells, demonstrate to rapidly the formation of product molecules at low temperature region. This study has focused on H+LiF system, one of systems that have this feature. In this system, since unstable H--F--Li complex quasibound states have the barriers in the TS, it is important to investigate and understand to depending on specific quantum states of the initial and the product molecule for this reaction. The results in collision energy range of 0-0.8 eV were obtained and corrected by using Reel Wave Packet (RWP) methods. Integral reaction cross sections as a function of collision energy were calculated via simple J-shifting (SJS) and reaction rate constants were examined in temperature range of 100-1000 0 K.

Initial state-selected reaction probabilities for the H+CH(4)→H(2)+CH(3) reaction are computed for vanishing total angular momentum by full-dimensional calculations employing the multiconfigurational time-dependent Hartree approach. An ensemble of wave packets completely describing reactivity for total energies up to 0.58 eV is constructed in the transition state region by diagonalization of the thermal flux operator. These wave packets are then propagated into the reactant asymptotic region to obtain the initial state-selected reaction probabilities. Reaction probabilities for reactants in all rotational states of the vibrational 1A(1), 1F(2), and 1E levels of methane are presented. Vibrational excitation is found to decrease reactivity when reaction probabilities at equivalent total energies are compared but to increase reaction probabilities when the comparison is done at the basis of equivalent collision energies. Only a fraction of the initial vibrational energy can be utilized to promote the reaction. The effect of rotational excitation on the reactivity differs depending on the initial vibrational state of methane. For the 1A(1) and 1F(2) vibrational states of methane, rotational excitation decreases the reaction probability even when comparing reaction probabilities at equivalent collision energies. In contrast, rotational energy is even more efficient than translational energy in increasing the reaction probability when the reaction starts from the 1E vibrational state of methane. All findings can be explained employing a transition state based interpretation of the reaction process.

The passage to the classical result from the quantum-mechanical theory of scattering is investigated. Two concrete cited examples clearly indicate that classical physics is not retrieved in the high-energy limit. It is contended that the approach to this limit must envisage a modification of the incident wave function and not the energy. Then explicit analytical results which show the dependence of the scattering cross-sections on the nature of the incoming wave packets are derived. The first-order corrections arising out of the finite width of the two types of incident wave packets considered in the present work contain interesting new physics. The insight gained from these results together with the inclusion of the effect of the spreading of the wave packet suggests a more comprehensive formulation of Bohm’s criteria for the validity of the classical approximation in scattering. The augmented criteria provide significant clarification and revision of our present understanding of the classical limit situation of the scattering phenomena. The implications and possible applications of the new results are discussed.

We investigate the transition-state (TS) region of the potential energy surface (PES) of the reaction tBu3P + H2 + B(C6F5)3 → tBu3P-H(+) + (-)H-B(C6F5)3 and the dynamics of the TS passage at room temperature. Owing to the conformational inertia of the phosphane⋅⋅⋅borane pocket involving heavy tBu3P and B(C6F5)3 species and features of the PES E(P⋅⋅⋅H, B⋅⋅⋅H | B⋅⋅⋅P) as a function of P⋅⋅⋅H, B⋅⋅⋅H, and B⋅⋅⋅P distances, a typical reactive scenario for this reaction is a trajectory that is trapped in the TS region for a period of time (about 350 fs on average across all calculated trajectories) in a quasi-bound state (scattering resonance). The relationship between the timescale of the TS passage and the effective conformational inertia of the phosphane⋅⋅⋅borane pocket leads to a prediction that isotopically heavier Lewis base/Lewis acid pairs and normal counterparts could give measurably different reaction rates. Herein, the predicted quasi-bound state could be verified in molecular collision experiments involving femtosecond spectroscopy.

How the non-reacting moiety of a molecule influences a polyatomic reaction has been a topic of much research interest. Here we present a comprehensive investigation of the D + CH4 → HD + CH3 reaction, a benchmark polyatomic elementary reaction with CH3 as the non-reacting moiety, employing a high-resolution crossed molecular beams apparatus and an accurate seven-dimensional wave packet method. An interesting angular distribution of the CH3(v’ = 1) product umbrella bending vibrational state is observed to scatter more in the sideways direction than the CH3(v’ = 0) one. By monitoring the wave functions on a dividing surface in the transition state region, the CH3 umbrella bending mode is established as a reporter mode that faithfully reveals how the D atom dynamically approaches CH4 at different total angular momenta or impact parameters. This discovery of the reporter mode provides an opportunity for the detailed study of polyatomic reaction dynamics.

Flux correlation functions and the quantum transition state concept are important tools for the accurate description of polyatomic reaction processes. Combined with the multi-configurational time-dependent Hartree approach, they facilitate rigorous full-dimensional calculations of cumulative and initial-state selected reaction probabilities for six atom reactions. In recent work [R. Welsch, F. Huarte-Larrañaga, and U. Manthe, J. Chem. Phys. 136, 064117 (2012)], an approach which allows one to calculate also state-to-state reaction probabilities within the quantum transition state concept has been introduced. This article presents further developments. Alternative generalized flux correlation functions are introduced and discussed. Equations for the calculation of fully state-resolved differential cross section using arbitrary definitions of the body fixed frame are derived. An approach for the efficient calculation of partially state-resolved observables as a function of the collision energy is introduced. Finally, numerical test studying the D + H2 reaction illustrate important aspects of the formalism.

The elementary vapor-phase reaction between Cl atoms and HCHO has been studied by ab initio methods. Calculations at the MP2, MP3, MP4(SDTQ), CCSD, CCSD(T), and MRD-CI levels of theory show that the reaction is characterized by a low electronic barrier; excluding the effects of spin-orbit splitting in Cl, our best estimate at the MRD-CI/aug-cc-pVTZ//RHF-RCCSD(T)/aug-cc-pVTZ level of theory predicts a Born-Oppenheimer barrier height of 0.7 kJ mol-1. The energies of the lowest six electronic states as resulting from MRD-CI calculations are presented at discrete points along the reaction path, and two avoided crossings are found in the transition state region. The spin-orbit splitting in Cl is also calculated along the reaction path; it is not negligible in the transition state region and is found to increase the barrier by only 1.4 kJ mol-1 at the RCCSD(T)/aug-cc-pVTZ transition state geometry. The minimum energy path of the reaction connects an energetically weakly stabilized adduct on the flat potential surface on the reactant side and an energetically strongly stabilized postreaction adduct. The reaction rate coefficient and the kinetic isotope effects were calculated using improved canonical variational theory with small curvature tunneling (ICVT/SCT), and the results were compared to experimental data. The experimental reaction rate coefficient is reproduced within its uncertainty limits by variational transition state theory with interpolated single-point energy corrections (ISPE) at the MP4(SDTQ) level of theory and by conventional transition state theory with interpolated optimized energies (IOE) at the MRD-CI//RCCSD(T) level of theory and interpolated optimized geometries at the RCCSD(T) level of theory on an MP2/aug-cc-pVTZ potential energy surface when employing scaled vibrational frequencies.

Laser atom/ion–molecule reaction interaction through dipole moments leads to potential energy surface crossings in ion molecule (Li+ + CH4) and barrier reshaping in atom–molecule reaction (Li + CH4). We will show here by using gauge representation (electric field gauge) that we can create laser-induced surface crossing in the region (4 au) where the dipole moment changes sign for the LiH + CH3+ Li+ + CH4 reaction and reshape the barrier height (increase/decrease the height) by changing the laser phase for Li + CH4 → LiH + CH3 where dipole moment changes sign in the transition state region.

Probing the Energy Landscape of Protein Folding/Unfolding Transition States

We report real wave packet (WP) calculations of reaction probabilities, cross sections, rate constants, and product distributions of the reaction N(4S)+O2(X 3∑g−)→NO(X 2∏)+O(3P). We propagate initial WPs corresponding to several O2 levels, and employ reactant coordinates and a flux method for calculating initial-state-resolved observables, or product coordinates and an asymptotic analysis for calculating state-to-state quantities. Exact or J-shifting calculations are carried out at total angular momentum J=0 or J>0, respectively. We employ the recent X 2A′ S3 potential energy surface (PES) by Sayós et al. and the earlier a 4A′ PES by Duff et al. In comparing S3 results with the WP ones of a previous X 2A′ S2 PES, we find lower S3 energy thresholds and larger S3 probabilities, despite the higher S3 barrier. This finding is due to the different features of the doublet PESs in the reactant and product channels, at the transition state, and in the NO2 equilibrium region. We analyze the effects of the O2 initial level and show that tunneling through the S3 barrier enhance the room-temperature rate constant by ∼3.7 times with respect to the previous S2 WP rate. The agreement with the room-temperature experimental result is thus notably improved. The NO vibrational distribution is inverted and the rotational ones are strongly oscillating. We explain these nonstatistical results showing that the reaction partners approach each other with a large impact parameter. The WP vibrational distribution is however different from that observed, which is oscillating. WP calculations show that the new S3 PES describes accurately several features of the X 2A′ state, although a lowering of its barrier height by ∼0.56 kcal/mol should bring calculated and observed rate constants in full agreement.

Transition state spectroscopy of open shell systems: Angle-resolved photodetachment spectra for the adiabatic singlet states of OHF

Methyl transferases (MTases) are a well-studied class of enzymes for which competing enzymatic enhancement mechanisms have been suggested, ranging from structural methyl group CH···X hydrogen bonds (HBs) to electrostatic- and charge-transfer-driven stabilization of the transition state (TS). We identified all Class I MTases for which reasonable resolution (<2.0 Å) crystal structures could be used to form catalytically competent ternary complexes for multiscale (i.e., quantum-mechanical/molecular-mechanical or QM/MM) simulation of the SN2 methyl transfer reaction coordinate. The four Class I MTases studied have both distinct functions (e.g., protein repair or biosynthesis) and substrate nucleophiles (i.e., C, N, or O). While CH···X HBs stabilize all reactant complexes, no universal TS stabilization role is found for these interactions in MTases. A consistent picture is instead obtained through analysis of charge transfer and electrostatics, wherein much of cofactor-substrate charge separation is maintained in the TS region, and electrostatic potential is correlated with substrate nucleophilicity (i.e., intrinsic reactivity).

Variational transition state theory is reformulated in terms of compound state resonances associated with the transition state region. The use of the formalism is illustrated for two-dimensional model problems, which are treated by the adiabatic theory of reactions and by perturbation theory. The limitations of the latter are delineated for the case of a biquadratic (quartic) coupling of the reaction coordinate to a transverse vibration. 51 refs.

We present measured and calculated photodetachment spectra of OHCl−, and we interpret the results in terms of the vibrational structure of the transition state of the O+HCl→OH+Cl reaction. The measured spectra exhibit two distinct features—an intense broad peak at high electron kinetic energies and a less intense shoulder at lower energies. Superimposed on these broad features are several sharper structures, but they are barely discernible from noise in the spectrum. To interpret these spectra, we have used a recently developed global 3A″ potential surface for the O+HCl reaction to calculate Franck–Condon factors, using an L2 method (i.e., expansion in terms of square integrable basis functions) to approximate the scattering wave functions on the reactive surface. Assignment of the spectrum has been assisted using the results of quantum coupled channel calculations for the same surface. The resulting calculated spectrum shows the same broad features as the measured spectrum. There is also fine structure with spacings and energies that are similar to the experiment, but specific features do not match. To interpret both the broad and fine features in the theoretical spectrum, a hierarchical analysis is applied wherein this spectrum is decomposed by a tree construction into components of increasingly higher resolution. The physical meaning of each of these components is then determined by plotting ‘‘smoothed states’’ that are obtained from the tree coefficients. This leads to the conclusion that the two broad features in the spectrum are made up of progressions in hindered rotor states of the Cl–OH complex, with the most intense feature corresponding to OH(v=0) and the weaker shoulder corresponding to OH(v=1). There is evidence for Feshbach resonance features in the v=1 feature, but it appears that most of the fine structure is due to hindered rotor states.

Despite their widespread use for performing advanced computational tasks, digital signal processors suffer from several restrictions, including low speed, high power consumption and complexity, caused by costly analogue-to-digital converters. For this reason, there has recently been a surge of interest in performing wave-based analogue computations that avoid analogue-to-digital conversion and allow massively parallel operation. In particular, novel schemes for wave-based analogue computing have been proposed based on artificially engineered photonic structures, that is, metamaterials. Such kinds of computing systems, referred to as computational metamaterials, can be as fast as the speed of light and as small as its wavelength, yet, impart complex mathematical operations on an incoming wave packet or even provide solutions to integro-differential equations. These much-sought features promise to enable a new generation of ultra-fast, compact and efficient processing and computing hardware based on light-wave propagation. In this Review, we discuss recent advances in the field of computational metamaterials, surveying the state-of-the-art metastructures proposed to perform analogue computation. We further describe some of the most exciting applications suggested for these computing systems, including image processing, edge detection, equation solving and machine learning. Finally, we provide an outlook for the possible directions and the key problems for future research. Metamaterials provide a platform to leverage optical signals for performing specific-purpose computational tasks with ultra-fast speeds. This Review surveys the basic principles, recent advances and promising future directions for wave-based-metamaterial analogue computing systems.