Reaction rates in a theory of mechanochemical pathways

If one applies mechanical stress to a molecule in a defined direction then one generates a new, effective potential energy surface (PES). Changes for minima and saddle points (SP) by the stress are described by Newton trajectories on the original PES (Quapp and Bofill, Theor. Chem. Acc. 2016, 135, 113). The barrier of a reaction fully breaks down for the maximal value of the norm of the gradient of the PES along a pulling Newton trajectory. This point is named barrier breakdown point (BBP). Depending on the pulling direction, different reaction pathways can be enforced. If the exit SP of the chosen pulling direction is not the lowest SP of the reactant valley, on the original PES, then the SPs must change their role anywhere: in this case the curve of the log(rate) over the pulling force of a forward reaction can show a deviation from the normal concave curvature. We discuss simple, two‐dimensional examples for this model to understand more deeply the mechanochemistry of molecular systems under a mechanical stress. © 2016 Wiley Periodicals, Inc.     

Mechanochemistry on the Müller–Brown surface by Newton trajectories

Chemical processes which suffer the application of mechanical force are theoretically described by effective potential energy surface (PES). We worked out (W. Quapp, J. M. Bofill, Theor. Chem. Acc. 2016, 135, 113) that the changes due to the force for the minimums and for the saddle points can be described by Newton trajectories (NT) of the original PES. If the force is so high that the saddle point disappears into a shoulder then the mechanochemical action is fulfilled: the pulling force breaks down the reaction barrier. The point is named barrier breakdown point. Different families of NTs form corridors on the original PES which describe qualitative different actions of the force. The border regions of such corridors are governed by the valley‐ridge inflection points (VRI) of the surface. Here, we discuss all this on the basis of the well‐known Müller–Brown surface, and we describe a new kind of NT‐corridor.     

Ab initio calculation and quasi‐classical dynamics study of the two lowest potential energy surfaces of the O(1D)+HBr system*

The lowest singlet 1¹A′ and 1¹A″ potential energy surfaces (PES) of the O(¹D)+HBr system have been ab initio computed. The complete active space self‐consistent field (CASSCF) method was used in most of the calculations, considering all the valence orbitals as active. The calculations were complemented with both analytical gradient calculations to characterize the stationary points and multireference configuration interaction (MRCI) calculations at selected nuclear geometries to improve the determination of the barrier heights and of the energetics. Electronic energy values for both PESs were then independently fitted by polynomial expansions in bond order coordinates. On the fitted surfaces quasi‐classical trajectories were separately run. Single‐surface calculations behave qualitatively different for the ground and the excited PES at low collision energies. A satisfactory agreement with existing experimental data was obtained by using the ground PES while calculations performed on the excited 1¹A″ PES worsened the agreement. However, when collision energy is increased, detailed experimental distributions are less well reproduced by calculations on the ground PES. This may imply the participation via nonadiabatic transitions of the 2¹A′ PES at higher energies while the adiabatic ground singlet PES well describes reactive scattering at low collision energy. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

长寿命轨线形成的模式识别研究

设计了6个参数来定量表征共线势能面的几何特征,并寻48个具有不同几何特征的LEPS型势能面,在以7个参数表征的不同的动态条件下应用Venus94程序进行准经典轨线(QCT)计算。随后,应用模式识别研究了势能面的特征及动态因素对长寿命轨线形成的影响,初步证实了若干知的并发现了若干新的影响长寿命轨线形成的主要影响因素并据此建了长寿命轨线形成的定性预测模型。     

Interpolating moving least-squares methods for fitting potential energy surfaces: an application to the H2CN unimolecular reaction

Classical trajectories have been used to compute rates for the unimolecular reaction H2CN-->H+HCN on a fitted ab initio potential energy surface (PES). The ab initio energies were obtained from CCSD(T)/aug-cc-pvtz electronic structure calculations. The ab initio energies were fitted by the interpolating moving least-squares (IMLS) method. This work continues the development of the IMLS method for producing ab initio PESs for use in molecular dynamics simulations of many-atom systems. A dual-level scheme was used in which the preliminary selection of data points was done using a low-level theory and the points used for fitting the final PES were obtained at the desired higher level of theory. Classical trajectories were used on various low-level IMLS fits to tune the fit to the unimolecular reaction under study. Procedures for efficiently picking data points, selecting basis functions, and defining cutoff limits to exclude distant points were investigated. The accuracy of the fitted PES was assessed by comparing interpolated values of quantities to the corresponding ab initio values. With as little as 330 ab initio points classical trajectory rate constants were converged to 5%-10% and the rms error over the six-dimensional region sampled by the trajectories was a few tenths of a kcal/mol.     

用神经网络方法拟合的反应体系H＋CH4←→H2＋CH3的一个全域势能面

利用神经网络力法,基于47783个高精度从头算能量点构建了反应体系H＋CH4←→H2＋CH3的一个全域势能面．通过大最的准经典轨线以及量子散射计算测试了势能面的收敛性质．这个势能面对于拟合过程以及从头算点的数目都已经完全收敛,拟合误差很小县比Shepard插值的势能面计算速度更快,代表了此标志性多原子反应体系最好的势能面．     

Using swarm intelligence for finding transition states and reaction paths

We describe an algorithm that explores potential energy surfaces (PES) and finds approximate reaction paths and transition states. A few (≈6) evolving atomic configurations ("climbers") start near a local minimum M1 of the PES. The climbers seek a shallow ascent, low energy, path toward a saddle point S12, cross over to another valley of the PES, and climb down to a new minimum M2 that was not known beforehand. Climbers use both energy and energy derivatives to make individual decisions, and they use relative fitness to make team-based decisions. In sufficiently long runs, they keep exploring and may go through a sequence M1-S12-M2-S23-M3 ... of minima and saddle points without revisiting any of the critical points. We report results on eight small test systems that highlight advantages and disadvantages of the method. We also investigated the PES of Li(8), Al(7)(+), Ag(7), and Ag(2)NH(3) to illustrate potential applications of this new method.     

Efficiency considerations in the construction of interpolated potential energy surfaces for the calculation of quantum observables by diffusion Monte Carlo

A modified Shepard interpolation scheme is used to construct global potential energy surfaces (PES) in order to calculate quantum observables--vibrationally averaged internal coordinates, fully anharmonic zero-point energies and nuclear radial distribution functions--for a prototypical loosely bound molecular system, the water dimer. The efficiency of PES construction is examined with respect to (a) the method used to sample configurational space, (b) the method used to choose which points to add to the PES data set, and (c) the use of either a one- or two-part weight function. The most efficient method for constructing the PES is found to require a quantum sampling regime, a combination of both h-weight and rms methods for choosing data points and use of the two-part weight function in the interpolation. Using this regime, the quantum diffusion Monte Carlo zero-point energy converges to the exact result within addition of 50 data points. The vibrationally averaged O-O distance and O-O radial distribution function, however, converge more slowly and require addition of over 500 data points. The methods presented here are expected to be applicable to both other loosely bound complexes as well as tightly bound molecular species. When combined with high quality ab initio calculations, these methods should be able to accurately characterize the PES of such species.     

Quasiclassical trajectories on a finite element density functional potential energy surface: The C++H2O reaction revisited

A new method for the representation of potential energy surfaces (PESs) based on the p version of the finite element method is presented and applied to the PES of the [COH2]+ system in order to study the C++H2O-->[COH]++H reaction through the quasiclassical trajectory method. Benchmark ab initio computations have been performed on the most relevant stationary points of the PES through a procedure that incorporates basis set extrapolations, the contribution of the core correlation energy, and scalar relativistic corrections. The electronic structure method employed to compute the many points needed to construct the PES is a hybrid density functional approach of the B3LYP type with geometry-dependent parameters, which improves dramatically the performance with respect of the B3LYP method. The trajectory computations shed light on the behavior of the COH2+ complex formed in the collision. At a fixed relative translational energy of 0.62 eV, which corresponds to the crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], the complex dissociates significantly into the reactants (37%). However, the behavior for a thermal sampling at T=300 K is significantly different because only 9% of the trajectories where capture occurs lead to dissociation into the reactants. The latter kind of behavior is coherent with the view that simple ion-molecule reactions proceed quite often at the capture rate provided it is corrected by the fraction of the electronic states which, being nearly degenerate for the reactants, become attractive at short distances. For both T=300 K and crossed beam conditions, the trajectory computations indicate that COH2+ is the critical intermediate, in agreement with a recent work [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003)] and in contrast with the interpretation of the crossed beam experiments. Besides, virtually all trajectories generate COH++H (>99%), but a significant proportion of the isoformyl cation is formed with enough vibrational energy as to surmount the COH+-HCO+ isomerization barrier, about 37% at T=300 K.     

Interpolating moving least-squares methods for fitting potential energy surfaces: computing high-density potential energy surface data from low-density ab initio data points

A highly accurate and efficient method for molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating-moving-least-squares (IMLS)-based method is developed using low-density ab initio Hessian values to compute high-density PES parameters suitable for accurate and efficient PES representation. The method is automated and flexible so that a PES can be optimally generated for classical trajectories, spectroscopy, or other applications. Two important bottlenecks for fitting PESs are addressed. First, high accuracy is obtained using a minimal density of ab initio points, thus overcoming the bottleneck of ab initio point generation faced in applications of modified-Shepard-based methods. Second, high efficiency is also possible (suitable when a huge number of potential energy and gradient evaluations are required during a trajectory calculation). This overcomes the bottleneck in high-order IMLS-based methods, i.e., the high cost/accuracy ratio for potential energy evaluations. The result is a set of hybrid IMLS methods in which high-order IMLS is used with low-density ab initio Hessian data to compute a dense grid of points at which the energy, Hessian, or even high-order IMLS fitting parameters are stored. A series of hybrid methods is then possible as these data can be used for neural network fitting, modified-Shepard interpolation, or approximate IMLS. Results that are indicative of the accuracy, efficiency, and scalability are presented for one-dimensional model potentials as well as for three-dimensional (HCN) and six-dimensional (HOOH) molecular PESs.     

Geometrical properties of the potential energy of the soft-sphere binary mixture

We report a detailed study of the stationary points (zero-force points) of the potential energy surface (PES) of a model structural glassformer. We compare stationary points found with two different algorithms (eigenvector following and square gradient minimization), and show that the mapping between instantaneous configuration and stationary points defined by those algorithms is as different as to strongly influence the instability index K versus temperature plot, which relevance in analyzing the liquid dynamics is thus questioned. On the other hand, the plot of K versus energy is much less sensitive to the algorithm employed, showing that the energy is the good variable to discuss geometric properties of the PES. We find new evidence of a geometric transition between a minima-dominated phase and a saddle-point-dominated one. We analyze the distances between instantaneous configurations and stationary points, and find that above the glass transition, the system is closer to saddle points than to minima.     

Searching for saddle points of potential energy surfaces by following a reduced gradient

The old coordinate driving procedure to find transition structures in chemical systems is revisited. The well-known gradient criterion, ∇E( x )= 0 , which defines the stationary points of the potential energy surface (PES), is reduced by one equation corresponding to one search direction. In this manner, abstract curves can be defined connecting stationary points of the PES. Starting at a given minimum, one follows a well-selected coordinate to reach the saddle of interest. Usually, but not necessarily, this coordinate will be related to the reaction progress. The method, called reduced gradient following (RGF), locally has an explicit analytical definition. We present a predictor–corrector method for tracing such curves. RGF uses the gradient and the Hessian matrix or updates of the latter at every curve point. For the purpose of testing a whole surface, the six-dimensional PES of formaldehyde, H₂CO, was explored by RGF using the restricted Hartree–Fock (RHF) method and the STO-3G basis set. Forty-nine minima and saddle points of different indices were found. At least seven stationary points representing bonded structures were detected in addition to those located using another search algorithm on the same level of theory. Further examples are the localization of the saddle for the HCN⇌CNH isomerization (used for steplength tests) and for the ring closure of azidoazomethine to 1H-tetrazole. The results show that following the reduced gradient may represent a serious alternative to other methods used to locate saddle points in quantum chemistry. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1087–1100, 1998     

Interpolating moving least-squares methods for fitting potential energy surfaces: a strategy for efficient automatic data point placement in high dimensions

An accurate and efficient method for automated molecular global potential energy surface (PES) construction and fitting is demonstrated. An interpolating moving least-squares (IMLS) method is developed with the flexibility to fit various ab initio data: (1) energies, (2) energies and gradients, or (3) energies, gradients, and Hessian data. The method is automated and flexible so that a PES can be optimally generated for trajectories, spectroscopy, or other applications. High efficiency is achieved by employing local IMLS in which fitting coefficients are stored at a limited number of expansion points, thus eliminating the need to perform weighted least-squares fits each time the potential is evaluated. An automatic point selection scheme based on the difference in two successive orders of IMLS fits is used to determine where new ab initio data need to be calculated for the most efficient fitting of the PES. A simple scan of the coordinate is shown to work well to identify these maxima in one dimension, but this search strategy scales poorly with dimension. We demonstrate the efficacy of using conjugate gradient minimizations on the difference surface to locate optimal data point placement in high dimensions. Results that are indicative of the accuracy, efficiency, and scalability are presented for a one-dimensional model potential (Morse) as well as for three-dimensional (HCN), six-dimensional (HOOH), and nine-dimensional (CH4) molecular PESs.     

Conformational preferences and internal rotation in alkyl- and phenyl-substituted thiourea derivatives

Potential energy surfaces (PES) for rotation about the N-C(sp(3)) or N-C(aryl) bond and energies of stationary points on PES for rotation about the C(sp(2))-N bond are reported for methylthiourea, ethylthiourea, isopropylthiourea, tert-butylthiourea, and phenylurea, using the MP2/aug-cc-pVDZ method. Analysis of alkylthioureas shows that conformations, with alkyl groups cis to the sulfur atom, are more stable (by 0.4-1.5 kcal/mol) than the trans forms. All minima adopt anti configurations with respect to nitrogen pyramidalization, whereas syn configurations are not stationary points on the MP2 potential surface. In contrast, analysis of phenylthiourea reveals that a trans isomer in a syn geometry is the global minimum, whereas a cis isomer in an anti geometry is a local minimum with a relative energy of 2.7 kcal/mol. Rotation about the C(sp(2))-N bond in alkyl and phenyl thioureas is slightly more hindered (9.1-10.2 kcal/mol) than the analogous motion in the unsubstituted molecule (8.6 kcal/mol). The maximum barriers to rotation for the methyl, ethyl, isopropyl, tert-butyl, and phenyl substituents are predicted to be 1.2, 8.9, 8.6, 5.3, and 0.9 kcal/mol, respectively. Corresponding PESs are consistent with the experimental dihedral angle distribution observed in crystal structures. The results of the electronic structure calculations are used to benchmark the performance of the MMFF94 force field. Systematic discrepancies between MMFF94 and MP2 results were improved by modification of selected torsion parameters and one of the van der Waals parameters for sulfur.     

Kinetics of model energy landscapes: an approach to complex systems

An idealized potential energy surface (PES), simply a PES-like network of stationary points, is demonstrated to be a useful tool to study kinetic relaxation of complex energy landscapes. Combined with a master equation, we show that if constructed with proper regularity, the kinetics of the PES is easy to predict and understand by carefully examining the eigenmodes of the master equation. By modifying the idealized PES model to make it more and more complicated, we demonstrate a systematic method to study the complex kinetics on large PES. The idealized PES model is used to explore the feasibility and the robustness of statistical sampling of large PES. We develop several sampling strategies, such as the "rough topography sampling" and the "low barrier saddle sampling" in the idealized PES model and find they are also applicable to a realistic PES of the 13-atom Morse cluster with range parameter rho= 6. To measure the robustness of the sampling methods, we compare the eigenvalue spectra, the eigenvector similarity and the relaxation times of the total energy of the full and sample PESs.     

Application of the modified Shepard interpolation method to the determination of the potential energy surface for a molecule-surface reaction: H2 + Pt(111)

We have used a modified Shepard (MS) interpolation method, initially developed for gas phase reactions, to build a potential energy surface (PES) for studying the dissociative chemisorption of H2 on Pt(111). The aim was to study the efficiency and the accuracy of this interpolation method for an activated multidimensional molecule-surface reactive problem. The strategy used is based on previous applications of the MS method to gas phase reactions, but modified to take into account special features of molecule-surface reactions, like the presence of many similar reaction pathways which vary only slightly with surface site. The efficiency of the interpolation method was tested by using an already existing PES to provide the input data required for the construction of the new PES. The construction of the new PES required half as many ab initio data points as the construction of the old PES, and the comparison of the two PESs shows that the method is able to reproduce with good accuracy the most important features of the H2 + Pt(111) interaction potential. Finally, accuracy tests were done by comparing the results of dynamics simulations using the two different PESs. The good agreement obtained for reaction probabilities and probabilities for rotationally and diffractionally inelastic scattering shows clearly that the MS interpolation method can be used efficiently to yield accurate PESs for activated molecule-surface reactions.     

The structural stability principle and branching points on multidimensional potential energy surfaces

The chemically interesting potential energy surfaces (PES) are considered on which the conditions underlying application of structural stability principle and Morse inequalities are violated. The possibility of treatment of singular branching points on a PES slope in terms of intrinsic reaction curves (IRC) is discussed.     

Embedding of the saddle point of index two on the PES of the ring opening of cyclobutene

The ring opening of cyclobutene is characterized by a competition of the two different pathways: a usual pathway over a saddle of index one (SP₁) along the conrotatory behavior of the end groups, as well as a “forbidden” pathway over a saddle point of index two (SP₂) along the disrotatory behavior of the end CH₂ groups. We use the system of ordinary differential equations for the method of the gentlest ascent dynamics (GAD) to determine saddle points of the potential energy surface (PES) of the ring opening of cyclobutene to cis‐butadiene. We apply generalized GAD formulas for the search of a saddle point of index two. To understand the relation of the different regions of the PES (around minimums, around SPs of index one or two) we also calculate valley‐ridge inflection (VRI) points on the PES using Newton trajectories (NT). VRIs and the corresponding singular NTs subdivide the regions of “attraction” of the different SPs. We calculate the connections of the SP₂ (in its different symmetry versions) with different SPs of index one of the PES by different “reaction pathways.” We compare the possibilities of the tool of the GAD curves for the exploration of PESs with these of NT. The barrier of the disrotatory SP₂ is somewhat higher than the barrier of the conrotatory SP₁, however, pathways across the slope to the SP₂ open additional reaction valleys. © 2015 Wiley Periodicals, Inc.     

Quasiclassical trajectory calculations of the OH+NO2 association reaction on a global potential energy surface

We report a full-dimensional potential energy surface (PES) for the OH+NO(2) reaction based on fitting more than 55,000 energies obtained with density functional theory-B3LYP6-311G(d,p) calculations. The PES is invariant with respect to permutation of like nuclei and describes all isomers of HOONO, HONO(2), and the fragments OH+NO(2) and HO(2)+NO. Detailed comparison of the structures, energies, and harmonic frequencies of various stationary points on the PES are made with previous and present high-level ab initio calculations. Two hydrogen-bond complexes are found on the PES and confirmed by new ab initio CASPT2 calculations. Quasiclassical trajectory calculations of the cross sections for ground rovibrational OH+NO(2) association reactions to form HOONO and HONO(2) are done using this PES. The cross section to form HOONO is larger than the one to form HONO(2) at low collision energies but the reverse is found at higher energies. The enhancement of the HOONO complex at low collision energies is shown to be due, in large part, to the transient formation of a H-bond complex, which decays preferentially to HOONO. The association cross sections are used to obtain rate constants for formation of HOONO and HONO(2) for the ground rovibrational states in the high-pressure limit.