Strange Kinetics of the C(2)H(6) + CN Reaction Explained

In this paper, we employ state of the art quantum chemical and transition state theory methods in making a priori kinetic predictions for the abstraction reaction of CN with ethane. This reaction, which has been studied experimentally over an exceptionally broad range of temperature (25-1140 K), exhibits an unusually strong minimum in the rate constant near 200 K. The present theoretical predictions, which are based on a careful consideration of the two distinct transition state regimes, quantitatively reproduce the measured rate constant over the full range of temperature, with no adjustable parameters. At low temperatures, the rate-determining step for such radical-molecule reactions involves the formation of a weakly bound van der Waals complex. At higher temperatures, the passage over a subthreshold saddle point on the potential energy surface, related to the formation and dissolution of chemical bonds, becomes the rate-determining step. The calculations illustrate the changing importance of the two transition states with increasing temperature and also clearly demonstrate the need for including accurate treatments of both transition states. The present two transition state model is an extension of that employed in our previous work on the C2H4 + OH reaction [J. Phys. Chem. A 2005, 109, 6031]. It incorporates direct ab initio evaluations of the potential in classical phase space integral based calculations of the fully coupled anharmonic transition state partition functions for both transition states. Comparisons with more standard rigid-rotor harmonic oscillator representations for the "inner" transition state illustrate the importance of variational, anharmonic, and nonrigid effects. The effects of tunneling through the "inner" saddle point and of dynamical correlations between the two transition states are also discussed. A study of the kinetic isotope effect provides a further test for the present two transition state model.     

A reaction surface Hamiltonian study of malonaldehyde

We report calculations using a reaction surface Hamiltonian for which the vibrations of a molecule are represented by 3N-8 normal coordinates, Q, and two large amplitude motions, s(1) and s(2). The exact form of the kinetic energy operator is derived in these coordinates. The potential surface is first represented as a quadratic in Q, the coefficients of which depend upon the values of s(1),s(2) and then extended to include up to Q(6) diagonal anharmonic terms. The vibrational energy levels are evaluated by solving the variational secular equations, using a basis of products of Hermite polynomials and appropriate functions of s(1),s(2). Our selected example is malonaldehyde (N=9) and we choose as surface parameters two OH distances of the migrating H in the internal hydrogen transfer. The reaction surface Hamiltonian is ideally suited to the study of the kind of tunneling dynamics present in malonaldehyde. Our results are in good agreement with previous calculations of the zero point tunneling splitting and in general agreement with observed data. Interpretation of our two-dimensional reaction surface states suggests that the OH stretching fundamental is incorrectly assigned in the infrared spectrum. This mode appears at a much lower frequency in our calculations due to substantial transition state character.     

一种确定反应中间态几何特征和能量的综合性方法

通过综合使用传统的过渡态优化算法、数学统计工具以及人工神经网络算法(ANN)找到一种不依赖于反应物起始构象而得到化学反应中过渡态结构和能量的方法. 在两个反应物互相接近的过程中, 每一步的几何构象都对应着一个系统能量值. 本研究的目的是尽可能地收集处在反应能量面上的这种能量点值. 通过采用几何参数作为自变量对势能面进行模拟研究, 得到了势能面上对应过渡态结构的一阶鞍点. 采用乙醛负离子和甲醛作为反应物, 对经典的醛醇缩合反应中的亲核进攻步骤进行了研究. 对内禀反应坐标(IRC)路径的计算是从反应物的三组不同起始构象出发, 最终获得了反应势能面上的96个点. 本研究中的势能面采用人工神经网络算法进行模拟研究, 并利用交叉验证方法评估得到的结果, 避免了采用人工神经网络算法时过度拟合情况的发生.     

Activation Energy and Transition State Determination of the Olefin Insertion Process of Metallocene Catalysts Using a Semiempirical Molecular Orbital Calculation

The transition state of the olefin insertion process of metallocene catalysts can be determined by adopting the semiempirical PM3 model. In computational chemistry, the computational methods most employed are the ab initio method and density functional theory, which are very time consuming. The semiempirical molecular orbital method requires much less computational resources than the above methods. However, the accuracy and reliability of the semiempirical molecular orbital method remains to be determined. The PM3 model is the most recently developed the semiempirical molecular orbital method and can also be applied to transition metal calculations. This study is intended to investigate the reliability of computational results determined using semiempirical PM3 model on metallocene catalysts through comparison with published results on the density functional theory (DFT). The saddle point finding procedure is adopted to find the transition state of the ethylene insertion process of metallocene catalysts. Results on the geometry and energy trends of the ethylene insertion process of metallocene catalysts determined using the PM3 model are in good agreement with the DFT results. In addition, the saddle point of the potential energy surface of ethylene insertion is verified in accordance with the eigenvalue of the vibrational frequency spectrum. Correct eigenvalues indicate that the correct saddle point of the potential energy surface of ethylene insertion has been successfully located. Hence, the eigenvalue of the vibrational frequency spectrum is a valuable reference in terms of saddle point justification. Computational results and vibrational frequency spectrum analysis demonstrate that the PM3 model can be used to locate the correct saddle point of the potential energy surface. The results obtained using the PM3 model confirm that the eigenvalue of the transition state lies nearly on the vibrational frequency spectrum. The eigenvalues are also analyzed, providing a valuable reference for further studies of the transition state of olefin insertion of metallocene catalysts. The activation energies for the olefin insertion reaction are also studied for evaluation of the catalyst.     

Bending dynamics of acetylene: new modes born in bifurcations of normal modes

Semiclassical techniques are used to analyze highly excited pure bending vibrational dynamics from spectra of C2H2. An analytic bifurcation approach is developed, based on critical points of a classical version of the quantum fitting Hamiltonian. At high energy four new types of anharmonic modes are born in bifurcations of the normal modes: local, orthogonal, precessional, and counter-rotator. Visual insight into their nature is obtained with the help of computer-generated three-dimensional animations. The connection between the local mode and the acetylene-vinylidene isomerization "reaction mode" is considered.     

THEORETICAL APPROACHES TO PROTEIN STRUCTURE-FUNCTION ANALYSIS (Ⅰ)——DIRECTED PERTURBATION CONFORMATIONAL ANALYSIS

A new computational technique called directed perturbation conformational analysis has been developed for use in protein model building and structure-function studies. Designed to perform an efficient local search of a macromolecular potential energy surface, the algorithm can be used to locate multiple energy minimum conformers via low energy transition state structures from a single starting or trial structure. The algorithm contains developments to stabilize transition state optimizations for systems described by many degrees of freedom displaying anharmonic potential energy surfaces. It has been found to be efficient in the generation of alternative equilibrium structures from a given trial structure when compared with those generated from a standard molecular dynamics simulation of N-acetyl, N'-methyl-deca-L-alaninamide.     

A quantum reaction dynamics study of the translational, vibrational, and rotational motion effects on the HD + H3+ reaction

Time-dependent, quantum reaction dynamics wavepacket approach is employed to investigate the impacts of the translational, vibrational, and rotational motion on the HD+H(3)(+) → H(2)D(+) + H(2) reaction using the Xie-Braams-Bowman potential energy surface [Z. Xie, B. J. Braams, and J. M. Bowman, J. Chem. Phys. 122, 224307 (2005)]. We treat this five atom reaction with a seven-degree-of-freedom model by fixing one Jacobi and one torsion angle related to H(3) (+) at the lowest saddle point geometry of the potential energy surface. The initial state selected reaction probabilities show that the rotational excitations of H(+)-H(2) greatly enhance the reactivity with the reaction probabilities increased double at high rotational states compared to the ground state. However, the vibrational excitations of H(3) (+) hinder the reactivity. The ground state reaction probability shows no reaction threshold for this exoergic reaction, and as the translational energy increases, the reaction probability decreases. Furthermore, reactive resonances and zero point energy play very important roles on the reaction dynamics. The obtained integral cross section has the character of an exoergic reaction without a threshold: it decreases with the translational energy increasing. The calculated thermal rate constants using this seven-degree-of-freedom model are in agreement with a later experiment measurement.     

Multidimensional quantum dynamical study of beta-hydrogen transfer in a cationic rhodium complex

The dynamics of migratory insertion and beta-hydrogen elimination in the cationic complex [CpRh(PH3)H(C2H4)]+ is studied from a quantal point of view. On the basis of DFT results for the relevant stationary points of the potential energy surface, three coordinates are identified that vary strongly during the reaction. A suitable three-dimensional grid, along with an appropriate kinetic energy operator, are constructed that are employed in the subsequent wave packet propagations. The latter are performed in the spirit of transition state spectroscopy and start from the various saddle points of the potential energy surface. Vibrational periods and lifetimes for these elementary processes, relevant to homogeneous catalysis, are obtained in this way for the first time. This work is considered to provide the basis for a subsequent treatment of equilibrium rate constants and to shed new light on the electronic factors governing these prototypical reaction steps.     

Locating saddle points of any index on potential energy surfaces by the generalized gentlest ascent dynamics

The system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) is tested to determine the saddle points of the potential energy surface of some molecules. The method has been proposed earlier [E and Zhou in Nonlinearity 24:1831 (2011)]. We additionally use the metric of curvilinear internal coordinates. By a number of examples, we explain the possibilities of a GAD curve; it can find the transition state of interest by a gentlest ascent, directly or indirectly, or not. A GAD curve can be a model of a reaction path, if it does not contain a turning point for the energy. We further discuss generalized GAD formulas for the search of saddle points of a higher index. We calculate diverse examples.     

Time-dependent wave packet study on trans-cis isomerization of HONO

Using a full six-dimensional ab initio potential energy surface and nuclear motion Hamiltonian, time-dependent computations were performed for the cis-trans isomerization of HONO. The multiconfiguration time-dependent Hartree method was used to propagate the six-dimensional wave packets. The initial excitations were chosen to be excitations of the local stretch modes and the HON local bend mode. The energy redistribution within 2 to 5 ps in the energy region of the OH stretching modes in both isomers was analyzed. The Fourier transformed frequency domain spectra were attributed to the eigenstates calculated previously by the time-independent variational approach. The results are also compared with classical trajectory computations of Thomson et al. on empirical surfaces. In agreement with matrix experiments, the cis-->trans isomerization was found to be much faster than the opposite interconversion. The intramolecular dynamics were found to be very complex involving numerous weakly excited delocalized eigenstates and anharmonic resonances. Particularly in the cis-isomer, the excitation of the HON bending local mode leads to fast energy redistribution in cis-trans delocalized modes. Neither the excitation of the OH stretching local mode in the cis nor in the trans form produces a fast isomerization, in agreement with the strongly localized characters of the corresponding eigenstates calculated variationally by Richter et al. and the gas phase spectra of HONO.     

Finite-Temperature Dimer Method for Finding Saddle Points on Free Energy Surfaces

The dimer method and its variants have been shown to be efficient in finding saddle points on potential surfaces. In the dimer method, the most unstable direction is approximately obtained by minimizing the total potential energy of the dimer. Then, the force in this direction is reversed to move the dimer toward saddle points. When the finite-temperature effect is important for a high-dimensional system, one usually needs to describe the dynamics in a low-dimensional space of reaction coordinates. In this case, transition states are collected as saddle points on the free energy surface. The traditional dimer method cannot be directly employed to find saddle points on a free energy surface since the surface is not known a priori. Here, we develop a finite-temperature dimer method for searching saddle points on the free energy surface. In this method, a constrained rotation dynamics of the dimer system is used to sample dimer directions and an efficient average method is used to obtain a good approximation of the most unstable direction. This approximated direction is then used in reversing the force component and evolving the dimer toward saddle points. Our numerical results suggest that the new method is efficient in finding saddle points on free energy surfaces. © 2019 Wiley Periodicals, Inc.     

Hydride transfer in liver alcohol dehydrogenase: quantum dynamics, kinetic isotope effects, and role of enzyme motion.

The quantum dynamics of the hydride transfer reaction catalyzed by liver alcohol dehydrogenase (LADH) are studied with real-time dynamical simulations including the motion of the entire solvated enzyme. The electronic quantum effects are incorporated with an empirical valence bond potential, and the nuclear quantum effects of the transferring hydrogen are incorporated with a mixed quantum/classical molecular dynamics method in which the transferring hydrogen nucleus is represented by a three-dimensional vibrational wave function. The equilibrium transition state theory rate constants are determined from the adiabatic quantum free energy profiles, which include the free energy of the zero point motion for the transferring nucleus. The nonequilibrium dynamical effects are determined by calculating the transmission coefficients with a reactive flux scheme based on real-time molecular dynamics with quantum transitions (MDQT) surface hopping trajectories. The values of nearly unity for these transmission coefficients imply that nonequilibrium dynamical effects such as barrier recrossings are not dominant for this reaction. The calculated deuterium and tritium kinetic isotope effects for the overall rate agree with experimental results. These simulations elucidate the fundamental nature of the nuclear quantum effects and provide evidence of hydrogen tunneling in the direction along the donor-acceptor axis. An analysis of the geometrical parameters during the equilibrium and nonequilibrium simulations provides insight into the relation between specific enzyme motions and enzyme activity. The donor-acceptor distance, the catalytic zinc-substrate oxygen distance, and the coenzyme (NAD(+)/NADH) ring angles are found to strongly impact the activation free energy barrier, while the donor-acceptor distance and one of the coenzyme ring angles are found to be correlated to the degree of barrier recrossing. The distance between VAL-203 and the reactive center is found to significantly impact the activation free energy but not the degree of barrier recrossing. This result indicates that the experimentally observed effect of mutating VAL-203 on the enzyme activity is due to the alteration of the equilibrium free energy difference between the transition state and the reactant rather than nonequilibrium dynamical factors. The promoting motion of VAL-203 is characterized in terms of steric interactions involving THR-178 and the coenzyme.     

Further aspects of the roaming mechanism in formaldehyde dissociation

Recently we reported a novel “roaming” dissociation pathway of formaldehyde in which one of the H atoms strays far from the minimum energy reaction path, explores a broad region of the potential energy surface, then abstracts the remaining H atom to form molecular products, without going near the configuration of the conventional transition state saddle point. The detailed dynamics of the abstraction mechanism and its energy dependence have already been reported. Here, with a combination of experimental and theoretical results, we examine the roaming behavior at the energetic extremes. We show evidence of roaming below the threshold of the radical dissociation channel and consider the implications of this and the possible existence of a transition state for the roaming mechanism. We also show the occurrence of roaming up to 3200 cm⁻¹ above the threshold of the triplet dissociation channel. In addition, we present results affording deeper insight into the dynamics of the roaming mechanism: we show evidence of roaming leading to CO in v = 1, and examine the issue of nuclear spin conservation during dissociation via the roaming mechanism.     

A theoretical study of the dynamic behavior of alkane hydroxylation by a compound I model of cytochrome P450

Dynamic aspects of alkane hydroxylation mediated by Compound I of cytochrome P450 are discussed from classical trajectory calculations at the B3LYP level of density functional theory. The nuclei of the reacting system are propagated from a transition state to a reactant or product direction according to classical dynamics on a Born-Oppenheimer potential energy surface. Geometric and energetic changes in both low-spin doublet and high-spin quartet states are followed along the ethane to ethanol reaction pathway, which is partitioned into two chemical steps: the first is the H-atom abstraction from ethane by the iron-oxo species of Compound I and the second is the rebound step in which the resultant iron-hydroxo complex and the ethyl radical intermediate react to form the ethanol complex. Molecular vibrations of the C-H bond being dissociated and the O-H bond being formed are significantly activated before and after the transition state, respectively, in the H-atom abstraction. The principal reaction coordinate that can represent the first chemical step is the C-H distance or the O-H distance while other geometric parameters remain almost unchanged. The rebound process begins with the iron-hydroxo complex and the ethyl radical intermediate and ends with the formation of the ethanol complex, the essential process in this reaction being the formation of the C-O bond. The H-O-Fe-C dihedral angle corresponds to the principal reaction coordinate for the rebound step. When sufficient kinetic energy is supplied to this rotational mode, the rebound process should efficiently take place. Trajectory calculations suggest that about 200 fs is required for the rebound process under specific initial conditions, in which a small amount of kinetic energy (0.1 kcal/mol) is supplied to the transition state exactly along the reaction coordinate. An important issue about which normal mode of vibration is activated during the hydroxylation reaction is investigated in detail from trajectory calculations. A large part of the kinetic energy is distributed to the C-H and O-H stretching modes before and after the transition state for the H-atom abstraction, respectively, and a small part of the kinetic energy is distributed to the Fe-O and Fe-S stretching modes and some characteristic modes of the porphyrin ring. The porphyrin marker modes of nu(3) and nu(4) that explicitly involve Fe-N stretching motion are effectively enhanced in the hydroxylation reaction. These vibrational modes of the porphyrin ring can play an important role in the energy transfer during the enzymatic process.     

A quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution based on the framework of mixed quantum-classical molecular dynamics

We present a quantum equation of motion for chemical reaction systems on an adiabatic double-well potential surface in solution in the framework of mixed quantum-classical molecular dynamics, where the reactant and product states are explicitly defined by dividing the double-well potential into the reactant and product wells. The equation can describe quantum reaction processes such as tunneling and thermal excitation and relaxation assisted by the solvent. Fluctuations of the zero-point energy level, the height of the barrier, and the curvature of the well are all included in the equation. Here, the equation was combined with the surface hopping technique in order to describe the motion of the classical solvent. Applying the present method to model systems, we show two numerical examples in order to demonstrate the potential power of the present method. The first example is a proton transfer by tunneling where the high-energy product state was stabilized very rapidly by solvation. The second example shows a thermal activation mechanism, i.e., the initial vibrational excitation in the reactant well followed by the reacting transition above the barrier and the final vibrational relaxation in the product well.     

Decomposition of protonated formic acid: One transition state—Two product channels

The unimolecular chemistry of protonated formic acid, [HCOOH]H(+), has been investigated by analyzing the fragmentation of metastable ions (MI) during flight in a sector mass spectrometer, and by proton transfer to formic acid in a Fourier-transform ion cyclotron resonance (FT-ICR) mass spectrometer. High level ab initio calculations have been used to model the relevant parts of the potential energy surface (PES). In addition, ab initio direct dynamics calculations have been conducted, tracing out 60 different reaction trajectories. The only stable isomer in the mass spectrometric experiments is HC(OH)(2)(+), which is the precursor to both observed ionic products, HCO(+) and H(3)O(+), via the same saddle point of the potential energy surface. The detailed motion of the dissociating molecule during passage of the post-transition state region of the PES therefore determines which product ion is formed. After passing the TS a transient HC(O)OH(2)(+) molecule is first formed. High total energy increases the probability that the nascent water molecule will have sufficient speed to escape the HCO(+) moiety. Otherwise, typically at low energies, the two units recombine, upon which intra-complex proton transfer is very likely. Eventually, this will give the more stable H(3)O(+).     

Chaotic dynamics and vibrational mode coupling in small argon clusters

We have computed the local Kolmogorov entropy of molecular dynamics trajectory segments near the potential energy saddles of model Ar₃ and Ar₅ clusters. In the case of Ar₃ clusters bound with a Lennard-Jones potential, the local Kolmogorov entropy of the cluster is significantly smaller in the saddle region than in other areas of the potential surface. This behavior indicates an increase in the degree of nearly quasiperiodic motion near the Ar₃ saddle due to the partial decoupling of the cluster's vibrational modes there. Lennard-Jones Ar₅ clusters do not exhibit similar behavior, but Ar₅ clusters bound with a short-range Morse potential do. This suggests that the “regularizing” effect of saddle regions is strongly dependent on the shape of the energy surface near the saddle. From these observations, we can determine which features of the saddle are most important in this respect; the flatness of the saddle region seems to be one such feature.     

Effect of a complex formation on the calculated low-pressure rate constant of a bimolecular gas-phase reaction governed by tunneling

Many important bimolecular hydrogen-transfer processes that take place in the atmosphere proceed via a potential energy minimum (hydrogen-bonded complex) that precedes along the minimum energy path the unique saddle point of the reaction, the one corresponding to the hydrogen transfer. It is clear that the one-step low-pressure rate constant of such a reaction does not depend on the existence of any complex along the minimum energy path below the reactant if the reaction takes place by thermal activation over a transition state that lies quite above the reactants (for instance 10 kcal/mol). However, we have quantitatively shown in this article that the scenario notoriously changes if the reaction involves significant tunneling. In this work, we have theoretically calculated the rate constants and their temperature dependence for the reaction HO+HOH→HOH+OH by means of a canonical variational transition state theory and a canonical unified statistical theory (when necessary). Multidimensional tunneling effects have been included with a semiclassical transmission coefficient. Two kinds of modified potential energy surfaces (PESs), obtained from an original ab initio potential energy surface, previously calculated by us, have been used. The Eckart-modified PESs serve to model the hydrogen-abstraction profiles with no complexes along the path, while the Gaussian-modified PESs model the energy profiles with two complexes along the path symmetrically distributed at each side of the abstraction saddle point. Our results show that the existence of those complexes reduces the thickness of the classically forbidden region for energies below the adiabatic barrier, and then tunneling is promoted and the reaction is accelerated. The effect of the complex formation in several kinetic magnitudes, as the Arrhenius parameters and the kinetic isotope effect has also been analyzed. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1685–1692, 1999     

A hierarchical transition state search algorithm

A hierarchical transition state search algorithm is developed and its implementation in the density functional theory program deMon2k is described. This search algorithm combines the double ended saddle interpolation method with local uphill trust region optimization. A new formalism for the incorporation of the distance constrain in the saddle interpolation method is derived. The similarities between the constrained optimizations in the local trust region method and the saddle interpolation are highlighted. The saddle interpolation and local uphill trust region optimizations are validated on a test set of 28 representative reactions. The hierarchical transition state search algorithm is applied to an intramolecular Diels-Alder reaction with several internal rotors, which makes automatic transition state search rather challenging. The obtained reaction mechanism is discussed in the context of the experimentally observed product distribution.     

Intrinsic reaction coordinate calculations for reaction paths possessing branching points

A 3-21+G energy surface corresponding to the proton transfer reaction in the hydroperoxyl anion solvated by one water molecule presents interesting topological features. In particular the intrinsic reaction coordinate that begins at the transition state does not lead to a minimum but to a saddle point of second order passing through two branching points. A new strategy to obtain the true reaction path in these cases is proposed.