Approaches for obtaining accurate rate constants for hydrogen abstraction by a chlorine atom

We have assessed computational methodologies for calculating the rate constants for hydrogen abstraction by Cl(?) for a selection of 12 reactions. For the conventional approach of calculating higher-level [B2K-PLYP/aug'-cc-pV[(T+d),(Q+d)]Z] single-point energies at lower-level [BH&H-LYP/6-31+G(d,p)] stationary points, large deviations from experimental rate constants are found in a number of cases in which the activation energy is very low. These discrepancies are due largely to deviations in the calculated activation energies and can be further traced to the inability of the low level to adequately locate the transition structures. We have examined several alternative approaches for calculating rate constants, namely, IRCmax, IRCmax at 0 K (ZK-IRCmax, with zero-point vibration energies (ZPVEs) incorporated), variational transition-state theory (VTST), and VTST with the inclusion of an Eckart tunneling correction (VTST+E). We find that the low level gives reasonable values for the ZPVEs and thermal enthalpy and entropy corrections that are required in such approaches. While the VTST+E approach yields the closest agreement with experimental rate constants for the systems considered, we find that the simpler IRCmax approach gives adequate values and is able to avoid the major shortcomings of the conventional approach in a cost-effective manner.     

Calculating rate constants with updated Hessians using variational transition state theory with multidimensional tunneling

Variational transition state theory with multidimensional tunneling (VTST/MT) has been used for calculating the rate constants of reactions. The updated Hessians have been used to reduce the computational costs for both geometry optimization and trajectory following procedures. In this paper, updated Hessians are used to reduce the computational costs while calculating the rate constants applying VTST/MT. Although we found that directly applying the updated Hessians will not generate good vibrational frequencies along the minimum energy path (MEP), however, we can either re-compute the full Hessian matrices at fixed intervals or calculate the Block Hessians, which is constructed by numerical one-side difference for the Hessian elements in the "critical" region and Bofill updating scheme for the rest of the Hessian elements. Due to the numerical instability of the Bofill update method near the saddle point region, we have suggested a simple strategy in which we follow the MEP until certain percentage of the classical barrier height from the barrier top with full Hessians computed and then performing rate constant calculation with the extended MEP using Block Hessians. This strategy results a mean unsigned percentage deviation (MUPD) around 10% with full Hessians computed till the point with 80% classical barrier height for four studied reactions. This proposed strategy is attractive not only it can be implemented as an automatic procedure but also speeds up the VTST/MT calculation via embarrassingly parallelization to a personal computer cluster.     

The importance of tunneling in the first hydrogenation step in ammonia synthesis over a Ru(0001) surface

The hydrogenation of nitrogen (N(ads)+H(ads)-->NH(ads)) on metal surfaces is an important step in ammonia catalysis. We investigate the reaction dynamics of this hydrogenation step by time independent scattering theory and variational transition state theory (VTST) including tunneling corrections. The potential energy surface is derived by hybrid density functional theory on a model cluster composed of 12 ruthenium atoms resembling a Ru(0001) surface. The scattering calculations are performed on a reduced dimensionality potential energy hypersurface, where two dimensions are treated explicitly and all others are included implicitly by the zero-point correction. The VTST calculations include quantum effects along the reaction coordinate by applying the small curvature tunneling scheme. Even at room temperature (where ruthenium already shows catalytic activity) we find rate enhancement by tunneling by a factor of approximately 70. Inspection of the reaction probabilities shows that the major contribution to reactivity comes from the vibrational ground state of the reactants into vibrationally excited product states. The reaction rates are higher than determined in previous studies, and are compatible with experimental overall rates for ammonia synthesis.     

Quantum real wave-packet dynamics of the N(4S)+NO(X2Pi)-->N2(X1Sigma(g)+)+O(3P) reaction on the ground and first excited triplet potential energy surfaces: rate constants, cross sections, and product distributions

The reaction N+NO-->N(2)+O was studied by means of the time-dependent real wave-packet (WP) method and the J-shifting approximation. We consider the ground 1 (3)A(") and first excited 1 (3)A(') triplet states, which correlate with both reactants and products, using analytical potential energy surfaces (PESs) recently developed in our group. This work extends our previous quantum dynamics study, and probabilities, cross sections, and rate constants were calculated and interpreted on the basis of the different shapes of the PESs (barrierless 1 (3)A(") and with barrier 1 (3)A(') surfaces, respectively). The WP rate constant (k(1)) shows a weak dependence on T(200-2500 K), as the dominant contribution to reactivity is provided by the barrierless ground PES. There is a good agreement of WP k(1) with the measurements and variational transition state theory (VTST) data, and also between the WP and VTST k(1)(1 (3)A(")) results. Nevertheless, there is a large discrepancy between the WP and VTST k(1)(1 (3)A(')) results. Product state distributions were also calculated for the much more reactive 1 (3)A(") PES. There is an excellent agreement with the experimental average fraction of vibrational energy in N(2)(25+/-3%), the only measured dynamics property of this reaction.     

A simple analytical estimate of the bound-free Franck–Condon factors for a transition to a repulsive exponential potential in a diatomic molecule

An analytical study of the bound-free (b-f) Franck–Condon (FC) factors is proposed for an electronic transition in a diatomic molecule. The case where the continuous state is characterized by an exponential repulsive potential curve is investigated. The paper focuses on the qualitative characterization of the b-f FC factors in terms of physical parameters. A simple analytical estimate is proposed which matches exactly the b-f FC factors for small kinetic energy. This analysis allows us to define the short- and long-range domains of the exponential repulsive potential curve. Depending on the equilibrium position of the bonding curve (which may fall into the short- or long-range domain), the behaviour of the b-f FC factors is qualitatively different. The relation with the Wigner threshold laws is established.     

Self‐Consistent Variational Transition State Theory with Multidimensional Tunneling Calculations in an Embarrassingly Parallel Scheme

Variational Transition State Theory with Multidimensional Tunneling (VTST/MT) has been successfully used for calculating rate constants of reactions in gas and condensed phases. The current software implementation of VTST/MT is, however, based on the assumption of a fast, serial evaluation of the energetic information of a given molecular structure. We propose a simple and effective parallel method for performing VTST/MT calculations utilizing a cost effective Linux based PC cluster. Five different parallel computing schemes for choosing structures and computing their Hessians along a pre‐defined Minimum Energy Path were developed. We found that the Energy Block and Asymmetric Cyclic Execution (EBACE) scheme, which is also most physically intuitive, results in converged rate constants with the least number of Hessians computed. We believe that carrying out the VTST/MT calculation in parallel makes it more attractive for calculating the rate constants of complex chemical systems.     

CF3CH2CH3+OH的反应机理及动力学性质的理论研究

采用密度泛函理论BB1K/6-31+G(d,p)计算了反应CF₃CH₂CH₃+OH各反应通道上驻点的稳定结构和振动频率, 并分别在BMC-CCSD, MC-QCISD和G3(MP2)水平上进行了单点能校正. 运用变分过渡态理论, 在BMC-CCSD//BB1K, MC-QCISD//BB1K, G3(MP2)//BB1K以及BB1K水平上计算了各反应通道的速率常数, 讨论了-CH₂和-CH₃基团上H提取通道对总反应的贡献, 并与已有实验和理论结果进行了对比. 计算结果表明, BMC-CCSD水平上的速率常数与实验测量值符合得很好, 进而给出了该水平上反应在200~1000 K温度范围内速率常数k(cm³?molecule^-1?s^-1)的三参数表达式: k=1.90×10^-21T^3.21exp(-292.62/T).     

Coarse-graining in interaction space: a systematic approach for replacing long-range electrostatics with short-range potentials

A short-range effective potential for long-range electrostatic interactions in homogeneously disordered condensed phase systems has been determined with a novel approach to coarse-graining in interaction space. As opposed to coarse-graining the system resolution, this approach "coarsens" the system's interactions by mapping multiple configurations of an accurate long-range atomistic potential onto a more efficient, short-range effective potential with a force-matching (FM) method. Developing an empirical potential in this manner is fundamentally different from existing strategies because it utilizes condensed-phase (as opposed to gas-phase) atomistic interactions to determine general pair potentials defined on distance meshes (as opposed to fitting predetermined functional forms). The resulting short-range ( approximately 10 A) effective potential reproduces structural, dynamical, and many thermodynamic properties of liquid water, ions in water, and hydrophobes in water, with unprecedented accuracy. The effective potential is also shown to be transferable to a nonaqueous molten salt system. With continued development, such effective potentials may provide an accurate and highly efficient alternative to Ewald-based long-range electrostatics methods.     

Dispersion-corrected energy decomposition analysis for intermolecular interactions based on the BLW and dDXDM methods

As the simplest variant of the valence bond (VB) theory, the block-localized wave function (BLW) method defines the intermediate electron-localized state self-consistently at the DFT level and can be used to explore the nature of intermolecular interactions in terms of several physically intuitive energy components. Yet, it is unclear how the dispersion interaction affects such a kind of energy decomposition analysis (EDA) as standard density functional approximations neglect the long-range dispersion attractive interactions. Three electron densities corresponding to the initial electron-localized state, optimal electron-localized state, and final electron-delocalized state are involved in the BLW-ED approach; a density-dependent dispersion correction, such as the recently proposed dDXDM approach, can thus uniquely probe the impact of the long-range dispersion effect on EDA results computed at the DFT level. In this paper, we incorporate the dDXDM dispersion corrections into the BLW-ED approach and investigate a range of representative systems such as hydrogen-bonding systems, acid-base pairs, and van der Waals complexes. Results show that both the polarization and charge-transfer energies are little affected by the inclusion of the long-range dispersion effect, which thus can be regarded as an independent energy component in EDA.     

Gas phase chemistry in gallium nitride CVD: Theoretical determination of the Arrhenius parameters for the first Ga-C bond homolysis of trimethylgallium

Experimental evidence suggests that the energy of activation for the first homolytic Ga-C bond fission of GaMe3 of Ea = 249 kJ/mol, measured by Jacko and Price in a hot-wall tube reactor, is affected by surface catalytic effects. In this contribution, the rate constant for this crucial step in the gas-phase pyrolysis of GaMe3 has been calculated by variational transition state theory. By a basis set extrapolation on the MP2/cc-pVXZ level and a correlation correction from CCSD(T)/cc-pVDZ level, a theoretical "best estimate" for the bond energy of Delta H(289K) = 327.2 kJ/mol was derived. For the VTST calculation on the B3LYP/cc-pVDZ level, the energies were corrected to reproduce this bond energy. Partition functions of the transitional modes were approximated by a hindered rotor approximation to be valid along the whole reaction coordinate defined by the Ga-C bond length. On the basis of the canonical transition state theory, reaction rates were determined using the maxima of the free energy Delta G++. An Arrhenius-type rate law was fitted to these rate constants, yielding an apparent energy of activation of Ea = 316.7 kJ/mol. The preexponential factor A = 3.13 x 10(16) 1/s is an order of magnitude larger than the experimental results because of a larger release of entropy at the transition state as compared to that of the unknown surface catalyzed mechanism.     

Temperature dependence of carbon-13 kinetic isotope effects of importance to global climate change

We report here a theoretical study of the 13C kinetic isotope effect (KIE) and its temperature dependence for the reaction OH + CH4 --> H2O + CH3, the major sink of atmospheric methane in the troposphere. The KIE values at various atmospherically significant temperatures were determined by direct dynamics using variational transition state theory with multidimensional tunneling contributions (VTST/MT). The potential energy surfaces (PESs) were generated by hybrid density functional theory as well as by recently developed doubly hybrid density functional theory methods. Comparisons of our calculated KIEs with experimental data and theoretical values in the literature reveal the critical contributions due to multidimensional tunneling and torsion anharmonicity as well as the critical issue of the choice of internal rotational axis.     

Regarding the validity of the time-dependent Kohn-Sham approach for electron-nuclear dynamics via trajectory surface hopping

The implementation of fewest-switches surface-hopping (FSSH) within time-dependent Kohn-Sham (TDKS) theory [Phys. Rev. Lett. 95, 163001 (2005)] has allowed us to study successfully excited state dynamics involving many electronic states in a variety of molecular and nanoscale systems, including chromophore-semiconductor interfaces, semiconductor and metallic quantum dots, carbon nanotubes and graphene nanoribbons, etc. At the same time, a concern has been raised that the KS orbital basis used in the calculation provides only approximate potential energy surfaces [J. Chem. Phys. 125, 014110 (2006)]. While this approximation does exist in our method, we show here that FSSH-TDKS is a viable option for computationally efficient calculations in large systems with straightforward excited state dynamics. We demonstrate that the potential energy surfaces and nonadiabatic transition probabilities obtained within the TDKS and linear response (LR) time-dependent density functional theories (TDDFT) agree semiquantitatively for three different systems, including an organic chromophore ligating a transition metal, a quantum dot, and a small molecule. Further, in the latter case the FSSH-TDKS procedure generates results that are in line with FSSH implemented within LR-TDDFT. The FSSH-TDKS approach is successful for several reasons. First, single-particle KS excitations often give a good representation of LR excitations. In this regard, DFT compares favorably with the Hartree-Fock theory, for which LR excitations are typically combinations of multiple single-particle excitations. Second, the majority of the FSSH-TDKS applications have been performed with large systems involving simple excitations types. Excitation of a single electron in such systems creates a relatively small perturbation to the total electron density summed over all electrons, and it has a small effect on the nuclear dynamics compared, for instance, with thermal nuclear fluctuations. In such cases an additional, classical-path approximation can be made. Third, typical observables measured in time-resolved experiments involve averaging over many initial conditions. Such averaging tends to cancel out random errors that may be encountered in individual simulated trajectories. Finally, if the flow of energy between electronic and nuclear subsystems is insignificant, the ad hoc FSSH procedure is not required, and a straightforward mean-field, Ehrenfest approach is sufficient. Then, the KS representation provides rigorously a convenient and efficient basis for numerically solving the TDDFT equations of motion.     

Statistical theory for the kinetics and dynamics of roaming reactions

We present a statistical theory for the effect of roaming pathways on product branching fractions in both unimolecular and bimolecular reactions. The analysis employs a separation into three distinct steps: (i) the formation of weakly interacting fragments in the long-range/van der Waals region of the potential via either partial decomposition (for unimolecular reactants) or partial association (for bimolecular reactants), (ii) the roaming step, which involves the reorientation of the fragments from one region of the long-range potential to another, and (iii) the abstraction, addition, and/or decomposition from the long-range region to yield final products. The branching between the roaming induced channel(s) and other channels is obtained from a steady-state kinetic analysis for the two (or more) intermediates in the long-range region of the potential. This statistical theory for the roaming-induced product branching is illustrated through explicit comparisons with reduced dimension trajectory simulations for the decompositions of H(2)CO, CH(3)CHO, CH(3)OOH, and CH(3)CCH. These calculations employ high-accuracy analytic potentials obtained from fits to wide-ranging CASPT2 ab initio electronic structure calculations. The transition-state fluxes for the statistical theory calculations are obtained from generalizations of the variable reaction coordinate transition state theory approach. In each instance, at low energy the statistical analysis accurately reproduces the branching obtained from the trajectory simulations. At higher energies, e.g., above 1 kcal/mol, increasingly large discrepancies arise, apparently due to a dynamical biasing toward continued decomposition of the incipient molecular fragments (for unimolecular reactions). Overall, the statistical theory based kinetic analysis is found to provide a useful framework for interpreting the factors that determine the significance of roaming pathways in varying chemical environments.     

A two transition state model for radical-molecule reactions: a case study of the addition of OH to C2H4

A two transition state model is applied to the study of the addition of hydroxyl radical to ethylene. This reaction serves as a prototypical example of a radical-molecule reaction with a negative activation energy in the high-pressure limit. The model incorporates variational treatments of both inner and outer transition states. The outer transition state is treated with a recently derived long-range transition state theory approach focusing on the longest-ranged term in the potential. High-level quantum chemical estimates are incorporated in a variational transition state theory treatment of the inner transition state. Anharmonic effects in the inner transition state region are explored with direct phase space integration. A two-dimensional master equation is employed in treating the pressure dependence of the addition process. An accurate treatment of the two separate transition state regions at the energy and angular momentum resolved level is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is predicted to occur at about 130 K, with significant effects from both transition states over the 10 to 400 K temperature range. Modest adjustment in the ab initio predicted inner saddle point energy yields theoretical predictions which are in quantitative agreement with the available experimental observations. The theoretically predicted capture rate is reproduced to within 10% by the expression [4.93 x 10(-12) (T/298)(-2.488) exp(-107.9/RT) + 3.33 x 10(-12) (T/298)(0.451) exp(117.6/RT); with R = 1.987 and T in K] cm3 molecules(-1) s(-1) over the 10-600 K range.     

Molecular interactions and crystal packing in nematogen: Computational thermodynamic approach

A computational thermodynamic approach of molecular interactions in a nematogen p-n-alkyl benzoic acid (nBAC) molecule with an alkyl group butyl (4BAC) has been carried out with respect to translational and orientational motion. The atomic net charge and dipole moment at each atomic center were evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh-Schrödinger perturbation theory along with multicentered-multipole expansion method were employed to evaluate long-range intermolecular interactions, while a 6-exp potential function was assumed for short-range interactions. Various possible geometrical arrangements of molecular pairs with regard to different energy components were considered, and the energetically favorable configuration was found to understand the crystal packing picture. Furthermore, these interaction energy values are taken as input to calculate the configurational entropy at room temperature (300 K), nematic-isotropic transition temperature (386 K) and above transition temperature (450 K) during different modes of interactions. An attempt has been made to describe interactions in a nematogen at molecular level, through which one can simplify the system to make the model computationally feasible in understanding the delicate interplay between energy and entropy, that accounts for mesomorphism and there by to analyze the molecular structure of a nematogen.     

Variational transition state theory rate constants and H/D kinetic isotope effects for CH3 + CH3OCOH reactions

The rate constants and H/D kinetic isotope effect for hydrogen abstraction reactions involving isotopomers of methyl formate by methyl radical are computed employing methods of the variational transition state theory (VTST) with multidimensional tunneling corrections. The energy paths were built with a dual-level method using the moller plesset second-order perturbation theory (MP2) method as the low-level and complete basis set (CBS) extrapolation as the high-level energy method. Benchmark calculations with the CBS_D-T approach give an enthalpy of reaction at 0 K for R1 (−4.5 kcal/mol) and R2 (−4.2 kcal/mol) which are in good agreement with the experiment, that is, −4.0 and − 4.8 kcal/mol. For the reactional paths involving the isotopomers CH₃ + CH₃OCOH → CH₄ + CH₃OCO and CH₃ + CH₃OCOD → CH₃D + CH₃OCO, the value of k^H/k^D (T = 455 K) using the canonical VTST/small-curvature tunneling approximation method is 6.7 in close agreement with experimental value (6.2). © 2019 Wiley Periodicals, Inc.     

Structural properties and thermodynamics of water clusters: a Wang-Landau study

The temperature dependence of structural properties and thermodynamic behavior of water clusters has been studied using Wang-Landau sampling. Four potential models, simple point charge/extended (SPC/E), transferable intermolecular potential 3 point (TIP3P), transferable intermolecular potential 4 point (TIP4P), and Gaussian charge polarizable (GCP), are compared for ground states and properties at finite temperatures. Although the hydrogen bond energy and the distance of the nearest-neighbor oxygen pair are significantly different for TIP4P and GCP models, they approach to similar ground state structures and melting transition temperatures in cluster sizes we considered. Comparing with TIP3P, SPC/E model provides properties closer to that of TIP4P and GCP.     

Electronic structure of tubular aromatic molecules derived from the metallic (5,5) armchair single wall carbon nanotube

All-electron static and time-dependent DFT electronic calculations, with complete geometrical optimization, are performed on tubular molecules up to C(210)H(20) that are finite sections of the (5,5) metallic single wall carbon nanotube with hydrogen termination at the open ends. We find pronounced C-C bond reconstruction at the tube ends; this initiates bond alternation that propagates into the tube centers. For the especially low band gap molecules C(120)H(20), C(150)H(20), and C(180)H(20), alternation increases, and a second nearly isoenergic structural isomer of different alternation is found. A small residual C-C bond alternation and band gap may be present in the infinite tube. The van Hove band gap forms quickly with length, while the metallic Fermi point (at the crossing of linear bands) forms very slowly with length. There are no end-localized states at energies near the Fermi energy. The HOMO-LUMO gap and the lowest singlet excited state, whose energies show a periodicity with length as previously calculated, are optically forbidden. However, each molecule shows an intense visible "charge transfer" transition, not present in the infinite tube, whose energy varies smoothly with length; this transition should be an identifying signature for these molecules. The static axial polarizability per unit length increases rapidly with N as the "charge transfer" transition moves into the infrared; this indicates increasing metallic character. However, the ionization potential, electron affinity, chemical hardness, and relative energetic stability all show the length periodicity seen in the HOMO-LUMO gap, in contrast to the optical "charge transfer" transition and the static axial polarizability. These periodicities, due to a one-dimensional quantum size effect as originally modeled by Coulson in 1938, nevertheless cancel in the calculated Fermi energy, which varies smoothly toward a predicted bulk work function near 3.9 eV. A detailed study of C(190)H(20) with up to eight extra electrons or holes shows the total energy is closely fit by a simple classical charging model, as is commonly applied to metallic clusters.     

Ab initio dynamic study of the reaction of Cl2LaR (R=H, CH3) with H2

In this paper, a comparison between "static" and "dynamic" determination of the thermodynamic (DeltarF degrees) and kinetic data (DeltarF#) for the reaction of Cl2LaR (R=H, CH3) and H2 is given. A difference is obtained in the case of the reaction between Cl2LaH and H2 and can be attributed to a failure of the "static" approach based on the harmonic approximation. The influence of the zero point energy correction is also analyzed but does not explain the 30% difference between the two calculated activation energies. The influence of the flatness of the potential energy surface around the transition state is proved as no such an effect is observed for the reaction of Cl2LaCH3 and H2.     

Ab initio chemical kinetic study on Cl + ClO and related reverse processes

The reaction of ClO with Cl and its related reverse processes have been studied theoretically by ab initio quantum chemical and statistical mechanical calculations. The geometric parameters of the reactants, products, and transition states are optimized by both UMPW1PW91 and unrestricted coupled-cluster single and double excitation (UCCSD) methods with the 6-311+G(3df) basis set. The potential energy surface has been further refined (with triple excitations, T) at the UCCSD(T)/6-311+G(3df) level of theory. The results show that Cl(2) and O ((3)P) can be produced by chlorine atom abstraction via a tight transition state, while ClOCl ((1)A(1)) and ClClO ((1)A') can be formed by barrierless association processes with exothermicities of 31.8 and 16.0 kcal/mol, respectively. In principle the O ((1)D) atom can be generated with a large endothermicity of 56.9 kcal/mol; on the other hand, its barrierless reaction with Cl(2) can readily form ClClO ((1)A'), which fragments rapidly to give ClO + Cl. The rate constants of both forward and reverse processes have been predicted at 150-2000 K by the microcanonical variational transition state theory (VTST)/Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The predicted rate constants are in good agreement with available experimental data within reported errors.