Newton trajectories for finding stationary points on molecular potential energy surfaces

We present a new algorithm for computing Newton trajectories based on the Quadratic String Method (QSM) and explain how this can be used to find key stationary points on the molecular potential energy surface (PES). This method starts by using the intersections of Newton trajectories to locate stationary points on the PES. These points could then be used to determine the minimum energy path. The new method, called QSM-NT, is shown to be efficient and reliable for both analytical potential energy surfaces and potential energy surfaces computed from quantum chemistry calculations. The advantages and pitfalls of this method for exploring PES are discussed. In particular, the problem of discontinuous Newton trajectories is elucidated.     

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     

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.     

氟氯甲醇及其异构体的气相离解反应研究

在G3(MP2)水平上,通过对CH2ClFO的势能面(PES)上关键驻点的能量计算,共找到3种中间体,14个过渡态,20种产物通道,并对氟氯甲醇(CHClFOH)及其异构体(CH2FOCl和CH2ClOF)的气相解离机理进行了讨论。结果表明：四中心的1,2-HX(X=Cl,F)消去反应是氟氯甲醇的主要通道,但对于其同分异构体,OCl和OF键断裂又是强竞争过程。     

Analysis of the reactivity on the c7h6 potential energy surface

The reactivity and decomposition kinetics on the C(7)H(6) potential energy surface (PES) were investigated, determining structures of stationary points at the B3LYP/6-31+G(d,p) level and energies at the CCSD(T)/cc-pVTZ level with extension to the complete basis set limit. For the reactions characterized by a significant multireference character, the energies were calculated at the CASPT2/cc-pVTZ level. The portion of the PES investigated consisted of 27 wells connected by 39 saddle points. Of the 27 wells, 16 can be accessed through transition states having activation energies smaller than the dissociation threshold. In agreement with previous theoretical studies, it was found that the main interconversion channel takes place on the singlet PES and connects phenylcarbene, cycloheptatetrane, spiroheptatriene, fulvenallene, and three ethynylcyclopentadiene isomers. Two new mechanisms are proposed for the formation of 5-ethynylcyclopentadiene and for the conversion of spiroheptatriene to fulvenallene. The unimolecular decomposition kinetics was thoroughly investigated. It was found that the fastest high pressure decomposition channel, at the temperatures at which C(7)H(6) undergoes unimolecular decomposition (1500--2000 K), leads to the formation of cyclopentadienylidene and acetylene. The rate of crossing from the singlet to the triplet PES may affect considerably this reaction channel, as it is formally spin forbidden. The alternative pathway, which is the decomposition to fulvenallenyl, is however only a factor of 2--3 slower and significantly less activated (82 vs 96 kcal/mol).     

CASPT2 study of the potential energy surface of the HSO2 system

The importance of the HSO(2) system in atmospheric and combustion chemistry has motivated several works dedicated to the study of associated structures and chemical reactions. Nevertheless controversy still exists in connection with the reaction SH + O(2)→ H + SO(2) and also related to the role of the HSOO isomers in the potential energy surface (PES). Here we report high-level ab initio calculation for the electronic ground state of the HSO(2) system. Energetic, geometric, and frequency properties for the major stationary states of the PES are reported at the same level of calculations: CASPT2/aug-cc-pV(T+d)Z. This study introduces three new stationary points (two saddle points and one minimum). These structures allow the connection of the skewed HSOO(s) and the HSO(2) minima defining new reaction paths for SH + O(2) → H + SO(2) and SH + O(2) → OH + SO. In addition, the location of the HSOO isomers in the reaction pathways have been clarified.     

CH_3SGN与O_2气相反应机理的理论研究

在G3(MP2)水平上,通过对CH_3S与O_2rcyi2rvylce dm (PES)上关键驻点的能 量计算,共找到4种中间体,9个过渡态,6种产物通道,并对这些气相反应机理进 行了讨论,同时应用TST－RRKM理论对主要反应的速率进行计算。结果表明:CH_3S 与O_2反应在低温下以生成CH_3SOO为主,并与实验结果吻合;在中高温下以消去和 抽提反应为主,分别生成CH_3 + SO_2和CH_2S + HO_2,其它产物较少。     

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.     

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.     

Ab initio, VTST and QCT study of the 3A potential energy surface implied in the N(D)+O2(XΣg)→O(P)+NO(XΠ) reaction

A detailed ab initio study based on the CASSCF and CASPT2 methods has been carried out on the 3²A^′ potential energy surface (PES) involved in the reaction between N(²D) and O₂ to produce O(³P) and NO. All the stationary points have been characterised and a grid of more than 800 points has been fitted to an analytical function. This PES has been used to obtain the rate constant of this reaction at different levels of theory (statistical and quasiclassical trajectory methods, taking into account recent data of our own on other PESs involved in the reaction) and has been compared with the experimental results obtaining a good agreement.     

He-ThO(1Σ+) interactions at low temperatures: elastic and inelastic collisions, transport properties, and complex formation in cold 4He gas

We present an ab initio study of cold (4)He + ThO((1)Σ(+)) collisions based on an accurate potential energy surface (PES) evaluated by the coupled cluster method with single, double, and noniterative triple excitations using an extended basis set augmented by bond functions. Variational calculations of rovibrational energy levels show that the (4)He-ThO van der Waals complex has a binding energy of 10.9 cm(-1) in its ground J = 0 rotational state. The calculated energy levels are used to obtain the temperature dependence of the chemical equilibrium constant for the formation of the He-ThO complex. We find that complex formation is thermodynamically favored at temperatures below 1 K and predict the maximum abundance of free ground-state ThO(v = 0, j = 0) molecules between 2 and 3 K. The calculated cross sections for momentum transfer in elastic He + ThO collisions display a rich resonance structure below 5 cm(-1) and decline monotonically above this collision energy. The cross sections for rotational relaxation accompanied by momentum transfer decline abruptly to zero at low collision energies (<0.1 cm(-1)). We find that Stark relaxation in He + ThO collisions can be enhanced by applying an external dc electric field of less than 100 kV∕cm. Finally, we present calculations of thermally averaged diffusion cross sections for ThO in He gas, and find these to be insensitive to small variations of the PES at temperatures above 1 K.     

Static field ionization of the spherically confined hydrogen atom

The ionization of the hydrogen atom confined in a spherical potential well and subjected to a static electric field is studied, using the diffusion Monte Carlo (DMC) method. Atomic ionization within a potential well is found to be a stationary, gradual, and reversible process. The value of the electric field at the onset of ionization is of the order of 0.1 atomic units, and depends on the symmetry of the atomic wave function and on the confinement dimension. By decreasing the confinement sphere, the difference between the bound and ionized states disappears, showing that strict confinement leads to pressure ionization of the atom. The off-center case is studied characterizing the potential energy surface (PES), and the transition between field-induced and pressure-induced ionization is confirmed. Except for very weak fields, the minimum of the PES is reached when the proton is in contact with the boundary of the well.     

Combustion chemistry: important features of the C3H5 potential energy surface, including allyl radical, propargyl + H2, allene + H, and eight transition states

The C(3)H(5) potential energy surface (PES) encompasses molecules of great significance to hydrocarbon combustion, including the resonantly stabilized free radicals propargyl (plus H(2)) and allyl. In this work, we investigate the interconversions that take place on this PES using high level coupled cluster methodology. Accurate geometries are obtained using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)] combined with Dunning's correlation consistent quadruple-ζ basis set cc-pVQZ. The energies for these stationary points are then refined by a systematic series of computations, within the focal point scheme, using the cc-pVXZ (X = D, T, Q, 5, 6) basis sets and correlation treatments as extensive as coupled cluster with full single, double, and triple excitation and perturbative quadruple excitations [CCSDT(Q)]. Our benchmarks provide a zero-point vibrational energy (ZPVE) corrected barrier of 10.0 kcal mol(-1) for conversion of allene + H to propargyl + H(2). We also find that the barrier for H addition to a terminal carbon atom in allene leading to propenyl is 1.8 kcal mol(-1) lower than that for the addition to a central atom to form the allyl radical.     

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.     

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.     

Six-dimensional potential energy surface of the dissociative chemisorption of HCl on Au(111) using neural networks

We constructed a six-dimensional potential energy surface(PES)for the dissociative chemisorption of HCl on Au(111)using the neural networks method based on roughly 70000 energies obtained from extensive density functional theory(DFT)calculations.The resulting PES is accurate and smooth,based on the small fitting errors and good agreement between the fitted PES and the direct DFT calculations.Time-dependent wave packet calculations show that the potential energy surface is very well converged with respect to the number of DFT data points,as well as to the fitting process.The dissociation probabilities of HCl initially in the ground rovibrational state from six-dimensional quantum dynamical calculations are quite diferent from the four-dimensional fixed-site calculations,indicating it is essential to perform full-dimensional quantum dynamical studies for the title molecule-surface interaction system.     

Resonances in three-dimensional H + HLi scattering: a time-dependent wave packet dynamical study

This paper examines the resonances in H + HLi scattering. The signature of these resonances is obtained from the oscillations in its reaction probability versus energy curves. They are identified here from a set of pseudospectra calculated for different initial locations of a stationary Gaussian wave packet on the ab initio potential energy surface (PES) reported by Dunne, Murrel, and Jemmer. The nuclear motion on this PES is monitored with the aid of a time-dependent wave packet method and the pseudospectrum are calculated by Fourier transforming the time autocorrelation function of the initial wave packet. The resonances are further examined and assigned by computing their eigenfunctions through spectral quantization algorithm. Both the linewidth as well as decay lifetimes of the resonances are reported.     

Search of manifolds of nonsymmetric Valley-Ridge inflection points on the potential energy surface of HCN

The potential energy surface (PES) of a chemical reaction contains Valley-Ridge inflection points (VRI) if??an often occurring phenomenon??the reaction path branches. In this paper, we introduce a new direct search method to detect these VRI points. It is based on an inductive execution of Gauss?CNewton steps. For the first time, we were able to find not only singular nonsymmetric VRI points, but also whole VRI manifolds on the PES of HCN.     

Density functional theory study of H and H2 interacting with NiAl(110)

We present results of extensive density functional theory (DFT) calculations for H and H2 interacting with NiAl(110). Continuous representations of the full dimensional potential energy surface (PES) for the H/NiAl(110) and H2/NiAl(110) systems are obtained by interpolation of the DFT results using the corrugation reducing procedure. We find a minimum activation energy barrier of approximately 300 meV for dissociative adsorption of H2, which is consistent with the energy threshold obtained in molecular beam experiments for H2 (nu=0). We explain vibrational enhancement observed in experiments as the consequence of vibrational softening in the entrance channel over the most reactive surface site. The H2/NiAl(110) PES shows a high surface site selectivity: for energies up to 0.1 eV above threshold, H2 adsorption can only take place around top-Ni sites (within a circle of radius approximately 0.3 A). A strong energetic corrugation is observed: energy barriers for dissociation vary by more than 1 eV between the most and the least reactive sites. In contrast, geometric corrugation is much less pronounced and comparable to that of low index single metal surfaces like Cu or Pt.     

Ab initio studies on the thermolysis of azetidine

The reaction mechanism of the thermolysis of azetidine to form ethylene and methylen-imine has been studied by ab initio SCF MO method at STO--3G and 3-21G levels. Two possible step-wise pathways are explored. One is the breaking of C--C bond as the first step, while the other is thebreaking of C--N bond. All the stationary points on the potential energy surface (PES) are fully optimiz-ed. MP2 / 3-21G single point calculations on all stationary points and MCSCF / STO-3G computationsfor some stationary points are also carried out. The calculations indicate that azetidine decomposesvia biradicaloid intermediates and the cleavage of C--N bond is preferable to that of C--C bond.