A surface hopping method for chemical reaction dynamics in solution described by diabatic representation: an analysis of tunneling and thermal activation

We present a surface hopping method for chemical reaction in solution based on diabatic representation, where quantum mechanical time evolution of the vibrational state of the reacting nuclei as well as the reaction-related electronic state of the system are traced simultaneously together with the classical motion of the solvent. The method is effective in describing the system where decoherence between reactant and product states is rapid. The diabatic representation can also give a clear picture for the reaction mechanism, e.g., thermal activation mechanism and a tunneling one. An idea of molecular orbital theory has been applied to evaluate the solvent contribution to the electronic coupling which determines the rate of reactive transition between the reactant and product potential surfaces. We applied the method to a model system which can describe complex chemical reaction of the real system. Two numerical examples are presented in order to demonstrate the applicability of the present method, where the first example traces a chemical reaction proceeded by thermal activation mechanism and the second examines tunneling mechanism mimicking a proton transfer reaction.     

Generalized electronic diabatic approach to structural similarity in two‐dimensional potential energy surfaces of various topologies

Active site properties in some proteins can be affected by conformational fluctuations of neighbor residues, even when the latter are not involved directly in the binding process. A local environment thus appears to alter the relevant potential energy surface and its reaction paths. Here, some aspects of this phenomenon are simulated within a generalized electronic diabatic (GED) scheme to study the geometry and structural similarity for a class of two‐dimensional (2D) energy surfaces. The electronic quantum state is a linear superposition of diabatic basis functions, each of which is taken to represent a single (pure) electronic state for the isolated material system. Here, we describe a model reaction of isomerization by shifts in amplitudes for three diabatic species (reactant, product, and an open‐shell transition state) coupled in an external field. The “effective” 2D energy surface in the field is characterized in terms of critical points, and the amplitudes along the main reaction paths. A new feature is the introduction of a phase diagram where all possible potential‐energy‐surface topologies (consistent with three‐state systems in two linear coordinates) are matched with actual model parameters. By varying the coupling strengths between diabatic states, we classify regions of this phase diagram in terms of electronic and structural similarities; some regions comprise models whose reaction paths have geometries that belong to the catchment region of the reactant, yet are electronically akin to the diabatic transition state or product. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Quasiclassical trajectory study of the Cl + Hl → HCl + I reaction

Monte Carlo quasiclassical trajectory calculations have been carried out for the reaction Cl + Hl → HCl + I for 300, 1000, and 2000 K. A semi-empirical potential-energy surface (London equation) was obtained by “transfering” parameters from surfaces computed for other reaction systems. The computed results are in general accord with experimental measurements. Thermal rate coefficients, differential scattering cross sections, and product vibrational and rotational distributions were computed for the three temperatures. Angular scattering distributions are in agreement with experiment only at elevated temperatures.     

Restricted open-shell Kohn-Sham theory: simulation of the pyrrole photodissociation

The authors study the photodissociation reactions of pyrrole and N-methylpyrrole using first-principles molecular dynamics. The first excited state is described with restricted open-shell Kohn-Sham theory. They find a small barrier in the excited state potential energy surface. The possibility of energy redistribution near the Franck-Condon region leads to two different reaction channels in on-the-fly simulations on a single diabatic potential energy surface. The results are discussed in comparison with previous ab initio calculations and with experiments.     

The photodissociation of ozone in the Hartley band: a theoretical analysis

Three-dimensional diabatic potential energy surfaces for the lowest four electronic states of ozone with 1A' symmetry-termed X, A, B, and R-are constructed from electronic structure calculations. The diabatization is performed by reassigning corresponding energy points. Although approximate, these diabatic potential energy surfaces allow one to study the uv photodissociation of ozone on a level of theory not possible before. In the present work photoexcitation in the Hartley band and subsequent dissociation into the singlet channel, O3X+hnu-->O(1D)+O2(a 1Deltag), are investigated by means of quantum mechanical and classical trajectory calculations using the diabatic potential energy surface of the B state. The calculated low-resolution absorption spectrum as well as the vibrational and rotational state distributions of O2(a 1Deltag) are in good agreement with available experimental results.     

State-to-state reaction probabilities within the quantum transition state framework

Rigorous quantum dynamics calculations of reaction rates and initial state-selected reaction probabilities of polyatomic reactions can be efficiently performed within the quantum transition state concept employing flux correlation functions and wave packet propagation utilizing the multi-configurational time-dependent Hartree approach. Here, analytical formulas and a numerical scheme extending this approach to the calculation of state-to-state reaction probabilities are presented. The formulas derived facilitate the use of three different dividing surfaces: two dividing surfaces located in the product and reactant asymptotic region facilitate full state resolution while a third dividing surface placed in the transition state region can be used to define an additional flux operator. The eigenstates of the corresponding thermal flux operator then correspond to vibrational states of the activated complex. Transforming these states to reactant and product coordinates and propagating them into the respective asymptotic region, the full scattering matrix can be obtained. To illustrate the new approach, test calculations study the D + H(2)(ν, j) → HD(ν', j') + H reaction for J = 0.     

Ab initio potential energy surfaces of the ion-molecule reaction: C2H2 + O+

High level ab initio calculations using complete active space self-consistent field and multi reference single and double excitation configuration interaction methods with cc-pVDZ (correlation consistent polarized valence double zeta) and cc-pVTZ (triple zeta) basis sets have been performed to elucidate the reaction mechanism of the ion-molecule reaction, C2H2(1Sigmag+) + O+(4S), for which collision experiment has been performed by Chiu et al. [J. Chem. Phys. 109, 5300 (1998)]. The minor low-energy process leading to the weak spin-forbidden product C2H2+ (2Piu) + O(1D) has been studied previously and will not be discussed here. The major pathways to form charge-transfer (CT) products, C2H2+ (2Piu) + O(3P) (CT1) and C2H2+ (4A2) + O(3P) (CT2), and the covalently bound intermediates are investigated. The approach of the oxygen atom cation to acetylene goes over an energy barrier TS1 of 29 kcal/mol (relative to the reactant) and adiabatically leads the CT2 product or a weakly bound intermediate Int1 between CT2 products. This transition state TS1 is caused by the avoided crossing between the reactant and CT2 electronic states. As the C-O distance becomes shorter beyond the above intermediate, the C1 reaction pathway is energetically more favorable than the Cs pathway and goes over the second transition state TS2 of a relative energy of 39 kcal/mol. Although this TS connects diabatically to the covalent intermediate Int2, there are many states that interact adiabatically with this diabatic state and these lead to the other charge-transfer product CT1 via either of several nonadiabatic transitions. These findings are consistent with the experiment, in which charge transfer and chemical reaction products are detected above 35 and 39 kcal/mol collision energies, respectively.     

On the quantum theory of electron transfer: effect of potential surfaces of the reactants and products

In this study the electron transfer theory for the high frequency intramolecular mode and low frequency medium mode has been rederived using different methods. For a single-mode case when the reactant surface is not in a thermal equilibrium but in a thermocoherent state the authors have derived the rate and discussed about the quantum features of the rate. In the limit of very low and very high temperatures the expressions are derived analytically and compared with the case of thermal distribution. Secondly, a Franck-Condon factor for a multimode displaced, distorted, and Duschinsky rotated adiabatic potential surfaces has been derived to obtain the rate. Lastly, a systematic investigation is made to show the temperature dependence on the rate due to displacement, distortion, and Duschinsky rotation of the harmonic potential energy surfaces of the reactant and product manifold.     

State-to-state reactive scattering in six dimensions using reactant-product decoupling: OH + H2 → H2O + H (J = 0)

We extend to full dimensionality a recently developed wave packet method [M. T. Cvitas? and S. C. Althorpe, J. Phys. Chem. A 113, 4557 (2009)] for computing the state-to-state quantum dynamics of AB + CD → ABC + D reactions and also increase the computational efficiency of the method. This is done by introducing a new set of product coordinates, by applying the Crank-Nicholson approximation to the angular kinetic energy part of the split-operator propagator and by using a symmetry-adapted basis-to-grid transformation to evaluate integrals over the potential energy surface. The newly extended method is tested on the benchmark OH + H(2) → H(2)O + H reaction, where it allows us to obtain accurately converged state-to-state reaction probabilities (on the Wu-Schatz-Fang-Lendvay-Harding potential energy surface) with modest computational effort. These methodological advances will make possible efficient calculations of state-to-state differential cross sections on this system in the near future.     

A unified perspective on the hydrogen atom transfer and proton-coupled electron transfer mechanisms in terms of topographic features of the ground and excited potential energy surfaces as exemplified by the reaction between phenol and radicals

The relation between the hydrogen atom transfer (HAT) and proton-coupled electron transfer (PCET) mechanisms is discussed and is illustrated by multiconfigurational electronic structure calculations on the ArOH + R(*) --> ArO(*) + RH reactions. The key topographic features of the Born-Oppenheimer potential energy surfaces that determine the predominant reaction mechanism are the conical intersection seam of the two lowest states and reaction saddle points located on the shoulders of this seam. The saddle point corresponds to a crossing of two interacting valence bond states corresponding to the reactant and product bonding patterns, and the conical intersection corresponds to the noninteracting intersection of the same two diabatic states. The locations of mechanistically relevant conical intersection structures and relevant saddle point structures are presented for the reactions between phenol and the N- and O-centered radicals, (*)NH2 and (*)OOCH3. Points on the conical intersection of the ground doublet D0 and first excited doublet D1 states are found to be in close geometric and energetic proximity to the reaction saddle points. In such systems, either the HAT mechanism or both the HAT mechanism and the proton-coupled electron transfer (PCET) mechanism can take place, depending on the relative energetic accessibility of the reaction saddle points and the D0/D1 conical intersection seams. The discussion shows how the two mechanisms are related and how they blend into each other along intermediate reaction paths. The recognition that the saddle point governing the HAT mechanism is on the shoulder of the conical intersection governing the PCET mechanism is used to provide a unified view of the competition between the two mechanisms (and the blending of the two mechanisms) in terms of the prominent and connected features of the potential energy surface, namely the saddle point and the conical intersection. The character of the dual mechanism may be understood in terms of the dominant valence bond configurations of the intersecting states, which are zero-order approximations to the diabatic states.     

General rules for predicting where a catalytic reaction should occur on metal surfaces: a density functional theory study of C-H and C-O bond breaking/making on flat,stepped, and kinked metal surfaces

To predict where a catalytic reaction should occur is a fundamental issue scientifically. Technologically, it is also important because it can facilitate the catalyst's design. However, to date, the understanding of this issue is rather limited. In this work, two types of reactions, CH(4) <--> CH(3) + H and CO <--> C + O on two transition metal surfaces, were chosen as model systems aiming to address in general where a catalytic reaction should occur. The dissociations of CH(4) --> CH(3) + H and CO --> C + O and their reverse reactions on flat, stepped, and kinked Rh and Pd surfaces were studied in detail. We find the following: First, for the CH(4) <--> Ch(3) + H reaction, the dissociation barrier is reduced by approximately 0.3 eV on steps and kinks as compared to that on flat surfaces. On the other hand, there is essentially no difference in barrier for the association reaction of CH(3) + H on the flat surfaces and the defects. Second, for the CO <--> C + O reaction, the dissociation barrier decreases dramatically (more than 0.8 eV on Rh and Pd) on steps and kinks as compared to that on flat surfaces. In contrast to the CH(3) + H reaction, the C + O association reaction also preferentially occurs on steps and kinks. We also present a detailed analysis of the reaction barriers in which each barrier is decomposed quantitatively into a local electronic effect and a geometrical effect. Our DFT calculations show that surface defects such as steps and kinks can largely facilitate bond breaking, while whether the surface defects could promote bond formation depends on the individual reaction as well as the particular metal. The physical origin of these trends is identified and discussed. On the basis of our results, we arrive at some simple rules with respect to where a reaction should occur: (i) defects such as steps are always favored for dissociation reactions as compared to flat surfaces; and (ii) the reaction site of the association reactions is largely related to the magnitude of the bonding competition effect, which is determined by the reactant and metal valency. Reactions with high valency reactants are more likely to occur on defects (more structure-sensitive), as compared to reactions with low valency reactants. Moreover, the reactions on late transition metals are more likely to proceed on defects than those on the early transition metals.     

Cl+HD反应产物的极化与态分布

利用准经典轨线理论,在BW2和G3两个势能面上,研究了Cl+HD反应的动力学.计算结果表明,产物的转动取向对势能面及反应体系的质量因子非常敏感.在BW2势能面上,计算的两个产物的转动取向强于在G3势能面上计算的结果,而无论是在BW2势能面上还是在G3势能面上,DCl产物的取向都强于HCl产物的取向.计算结果还表明,在不同的势能面上反应物的转动激发对反应的影响有着显著的不同.在BW2势能面上,反应物的初始转动激发有利于Cl+HD反应的进行;而在G3势能面上,反应物的初始转动激发消弱了反应的反应性.     

Multireference configuration interaction calculations for the F(2P)+HCl-->HF+Cl(2P) reaction: a correlation scaled ground state (1 2A') potential energy surface

This paper presents a new ground state (1 (2)A(')) electronic potential energy surface for the F((2)P)+HCl-->HF+Cl((2)P) reaction. The ab initio calculations are done at the multireference configuration interaction+Davidson correction (MRCI+Q) level of theory by complete basis set extrapolation of the aug-cc-pVnZ (n=2,3,4) energies. Due to low-lying charge transfer states in the transition state region, the molecular orbitals are obtained by six-state dynamically weighted multichannel self-consistent field methods. Additional perturbative refinement of the energies is achieved by implementing simple one-parameter correlation energy scaling to reproduce the experimental exothermicity (DeltaE=-33.06 kcalmol) for the reaction. Ab initio points are fitted to an analytical function based on sum of two- and three-body contributions, yielding a rms deviation of <0.3 kcalmol for all geometries below 10 kcalmol above the barrier. Of particular relevance to nonadiabatic dynamics, the calculations show significant multireference character in the transition state region, which is located 3.8 kcalmol with respect to F+HCl reactants and features a strongly bent F-H-Cl transition state geometry (theta approximately 123.5 degrees ). Finally, the surface also exhibits two conical intersection seams that are energetically accessible at low collision energies. These seams arise naturally from allowed crossings in the C(infinityv) linear configuration that become avoided in C(s) bent configurations of both the reactant and product, and should be a hallmark of all X-H-Y atom transfer reaction dynamics between ((2)P) halogen atoms.     

Quasiclassical trajectory calculations of the reaction C+C2H2-->l-C3H, c-C3H+H, C3+H2 using full-dimensional triplet and singlet potential energy surfaces

Full-dimensional, density functional theory (B3LYP/6-311g(d,p))-based potential energy surfaces (PESs) are reported and used in quasi-classical calculations of the reaction of C with C(2)H(2). For the triplet case, the PES spans the region of the reactants, the complex region (with numerous minima and saddle points) and the products, linear(l)-C(3)H+H, cyclic(c)-C(3)H+H and c-(3)C(3)+H(2). For the singlet case, the PES describes the complex region and products l-C(3)H+H, c-C(3)H+H and l-(1)C(3)+H(2). The PESs are invariant under permutation of like nuclei and are fit to tens of thousands of electronic energies. Energies and harmonic frequencies of the PESs agree well the DFT ones for all stationary points and for the reactant and the products. Dynamics calculations on the triplet PES find both l-C(3)H and c-C(3)H products, with l-C(3)H being dominant at the energies considered. Limited unimolecular reaction dynamics on the singlet PES find both products in comparable amounts as well as the C(3)+H(2) product.     

New ab initio coupled potential energy surfaces for the Br(2P(3∕2), 2P(1∕2)) + H2 reaction

The three lowest (1A('), 2A('), and 1A(')) adiabatic potential energy surfaces (PESs) for the Br((2)P) + H(2) reactive system have been computed based on the multi-reference configuration interaction (MRCI) method including the Davidson's correction with a large basis set. These three adiabatic PESs have been transformed to a diabatic representation, leading to four coupling potentials. In addition, the spin-orbit matrix elements were also obtained using the Breit-Pauli Hamiltonian and the unperturbed MRCI wavefunctions in the Br + H(2) channel and the transition state region. Consequently, six coupling potentials were obtained and their characteristics were extensively discussed. Nonadiabatic quantum dynamics calculations for this system have been realized with these realistic diabatic potentials instead of previous semi-empirical diabatic potentials. Based on two-state model nonadiabatic calculations for the Br((2)P(3∕2), (2)P(1∕2)) + H(2) reaction, the Br((2)P(1∕2)) + H(2) reaction was found to show less reactivity than the Br((2)P(3∕2)) + H(2) reaction at collision energies beyond the threshold of the Br((2)P(3∕2)) + H(2) reaction. Our results are consistent with the previous studies on the XH(2) (X = F, Cl) system, which indicate that the adiabatically forbidden channel is dominant at low energies in the open-shell halogen atom plus H(2) reactions.     

Influence of Molecular Structure on the Dimerization Reactivity of Germaaromatic Compounds： a Theoretical Study

Density functional theory (DFT) calculations, at the B3LYP/6-311G** level of theory, were performed to study the reaction mechanism and potential energy surface of the [2 + 2], [4 + 2] and [4 + 4] dimerization reactions of some germaaromatic compounds. The influence of reactant's molecular structure and benzene solvent on the potential energy surface of the studied reactions was investigated. Our calculation results show that [2 + 2] and [4 + 4] reactions are concerted and synchronous processes; while [4 + 2] reactions proceed via a concerted but asynchronous way in general. [2 + 2] and [4 + 2] reactions of germabenzenes and 1-germana- phthalene proceed much more easily than the corresponding [4 + 4] reaction, both thermo- dynamically and kinetically; while most [4 + 2] paths have lower activation barrier than the corres- ponding [2 + 2] ones. As the number of six-membered aromatic rings in reactant molecules becomes larger, [2 + 2], [4 + 2] and [4 + 4] reactions become easier to proceed. The influence of substituents at the Ge atom of germabenzenes on the potential energy surface of [2 + 2] and [4 + 2] reactions correlates with their electronic properties and volume. Solvent effect is not crucial for the potential energy surfaces of the studied reactions.     

Reaction dynamics of OH+(3Sigma-)+C2H2 studied with crossed beams and density functional theory calculations

The reactions between OH+(3Sigma-) and C2H2 have been studied using crossed ion and molecular beams and density functional theory calculations. Both charge transfer and proton transfer channels are observed. Products formed by carbon-carbon bond cleavage analogous to those formed in the isoelectronic O(3P)+C2H2 reaction, e.g., 3CH2 + HCO+, are not observed. The center of mass flux distributions of both product ions at three different energies are highly asymmetric, with maxima close to the velocity and direction of the precursor acetylene beam, characteristic of direct reactions. The internal energy distributions of the charge transfer products are independent of collision energy and are peaked at the reaction exothermicity, inconsistent with either the existence of favorable Franck-Condon factors or energy resonance. In proton transfer, almost the entire reaction exothermicity is transformed into product internal excitation, consistent with mixed energy release in which the proton is transferred with both the breaking and forming bonds extended. Most of the incremental translational energy in the two higher-energy experiments appears in product translational energy, providing an example of induced repulsive energy release.     

Total reactive cross section for K + Br2 in the energy range of 0–4 eV

3-D classical trajectory calculations were performed using diabatic as well as adiabatic potential energy surfaces. Non-adiabatic transitions were allowed and localized at the avoided crossing of the two adiabatic surfaces. The transition probability was calculated according to the Landau—Zener formalism. The total cross sections for the reaction K + Br₂ → KBr + Br were calculated and compared with experimental data. The total cross sections, calculated with the aid of adiabatic potential energy surfaces, were, contrary to those with diabatic surfaces, in very good agreement with the measured total reactive cross sections over the whole energy range of 0–4 eV.     

Direct calculation of coupled diabatic potential-energy surfaces for ammonia and mapping of a four-dimensional conical intersection seam

We used multiconfiguration quasidegenerate perturbation theory and the fourfold-way direct diabatization scheme to calculate ab initio potential-energy surfaces at 3600 nuclear geometries of NH3. The calculations yield the adiabatic and diabatic potential-energy surfaces for the ground and first electronically excited singlet states and also the diabatic coupling surfaces. The diabatic surfaces and coupling were fitted analytically to functional forms to obtain a permutationally invariant 2 x 2 diabatic potential-energy matrix. An analytic representation of the adiabatic potential-energy surfaces is then obtained by diagonalizing the diabatic potential-energy matrix. The analytic representation of the surfaces gives an analytic representation of the four-dimensional conical intersection seam which is discussed in detail.