Reactive domains of energy hypersurfaces and the stability of minimum energy reaction paths

Special properties of the Riemannian metric for energy hypersurfaces, defined within the framework of the Born-Oppenheimer approximation, are utilized in devising a partitioning scheme for domains of nuclear coordinates. The chemically important coordinate domains are distinguished from domains of lesser importance by their curvature properties. Conditions are derived for the stability of minimum energy reaction paths, and the effects of instability regions are investigated. Instability domains along minimum energy paths may allow small vibrational perturbations to alter the outcome of the chemical reaction.     

Gradient extremals

Gradient extremals on N-dimensional energy hypersurfaces V=V(x ₁ x _n ) are curves defined by the condition that the gradient V is an eigenvector of the hessian matrix V. For variations which are restricted to any (N–1) dimensional hypersurface V(x ₁ x _N ) = V ₀= constant, the absolute value of the gradient V is an extremum at those points where a gradient extremal intersects this surface. In many, though not all, cases gradient extremals go along the bottom of a valley or along the crest of a ridge. The properties of gradient extremals are discussed through a detailed differential analysis and illustrated by an explicit example. Multidimensional generalizations of gradient extremals are defined and discussed.Operated for the U.S. Department of Energy by Iowa State University under Contract No. W-7405-ENG-82. This work was supported by the Office of Basic Energy Sciences     

Catchment region partitioning of energy hypersurfaces,I

The space of internal coordinates of a molecular system is partitioned into catchment regions of various critical points of the energy hypersurface. The partitioning is based on an ordering of steepest descent paths into equivalence classes. The properties of these catchment regions and their boundaries are analyzed and the concepts of chemical structure, reaction path and reaction mechanism are discussed within the framework of the Born-Oppenheimer and energy hypersurface approximations. Relations between catchment regions and the chemically important reactive domains of energy hypersurfaces, as well as models for branching of reaction mechanisms, caused by instability domainsD , 1, are investigated.     

A gradient extremal walking algorithm

Gradient extremals define stream beds connecting stationary points on molecular potential energy surfaces. Using this concept we have developed an algorithm to determine transition states. We initiate walks at equilibrium geometries and follow the gradient extremals until a stationary point is reached. As an illustration we have investigated the mechanism for exchange of protons on carbon in methylenimine (H₂C=NH) using a multi-reference self-consistent-field wave function.     

Following gradient extremal paths

Summary For any point on a gradient extremal path, the gradient is an eigenvector of the hessian. Two new methods for following the gradient extremal path are presented. The first greatly reduces the number of second derivative calculations needed by using a modified updating scheme for the hessian. The second method follows the gradient extremal using only the gradient, avoiding the hessian evaluation entirely. The latter algorithm makes it possible to use gradient extremals to explore energy surfaces at higher levels of theory for which analytical hessians are not available.Dedicated to Prof. Klaus Ruedenberg     

Gradient extremals and valley floor bifurcations on potential energy surfaces

Gradient extremals are curves in configuration space denned by the condition that the gradient of the potential energy is an eigenvector of the Hessian matrix. Solutions of a corresponding equation go along a valley floor or along a crest of a ridge, if the norm of the gradient is a minimum, and along a cirque or a cliff or a flank of one of the two if the gradient norm is a maximum. Properties of gradient extremals are discussed for simple 2D model surfaces including the problem of valley bifurcations.     

Topology of energy hypersurfaces

Some of the basic notions of chemistry, associated with an energy function of several variables, are shown to be of topological character. Properties of potential energy hypersurfaces, structural relations, models for interconversion processes and transformations between such models suggest a topological theory (reaction topology) for the analysis of potential energy hypersurfaces. By introducing appropriate topologies into the nuclear configuration spaceR and equivalent topologies on the energy hypersurfaceE, rigorous definitions are given for fundamental chemical concepts such asmolecular structure andreaction mechanism. These definitions are based on the properties of the expectation value of energy, a quantum mechanical observable. Topologies based on curvature, structural and energetic relations of the energy hypersurface are proposed for a theoretical interpretation of molecular processes.     

Quantum chemical reaction networks,reaction graphs and the structure of potential energy hypersurfaces

Global properties of the Born-Oppenheimer energy expectation value functional, defined over the nuclear configuration space R, are analyzed. Quantum chemical reaction graphs and reaction networks are defined in terms of intersection graphs of connected sets of nuclear geometries, representing various chemical structures. The set of all possible reaction mechanisms on the given energy hypersurface and the associated activation energy conditions are analyzed using reachability matrices defined over digraphs D ^s() and D ^s(, E).     

Transition state spectroscopy of open shell systems: Angle-resolved photodetachment spectra for the adiabatic singlet states of OHF

In this work three-dimensional potential energy surfaces of the first five singlet states of OHF are developed based on fits of more than 10,000 highly accurate ab initio points. An approximate treatment is presented for the calculation of the anisotropy parameter describing the electron angular distribution photodetached from a molecular anion. This method is used to calculate the angle-resolved photoelectron spectra in the photodetachment of OHF⁻. The wave packet formed in the neutral OHF system is placed at the transition state region, and yields the formation of OH + F and HF + O products. The results are compared with the recent experimental measurements published by Neumark [D.M. Neumark, Phys. Chem. Chem. Phys. 7 (2005) 433]. The intensity found at low electron kinetic energy including these five states and the three lower triplet states is found to be low. To analyze the effect of higher electronic states more excited ¹Σ⁻, ³Σ⁺ and ³Δ states are calculated at collinear geometry. The agreement with the experimental data improves, thus demonstrating that the correct simulation of the photodetachment spectrum at 213 nm involves at least 12 electronic states. All the structures of the experimental spectra are semiquantitatively reproduced finding an overall good agreement. It is concluded that the main problem of the simulation is in the intensity and anisotropy parameters. An alternative to their calculation would be to fit their values to reproduce the experimental results, but this would require to separate the contribution arising from different final electronic states.     

Geometric and electronic similarities between transition structures for electrocyclizations and sigmatropic hydrogen shifts

This paper reports new theoretical evidence that supports previous proposals concerning the similarity between transition structures for electrocyclizations and sigmatropic hydrogen shifts. This evidence was obtained using two recently proposed methodologies, namely the so-called generalized population analysis and the formalism of molecular quantum similarity indices. Analysis of multicenter bond indices shows that the transition structures for cationic [1,n] hydrogen shifts do indeed have three-center indices that are similar to those of other three-center carbocations. In addition, the close resemblance of the electronic structures of electrocyclic and sigmatropic transition structures that differ by only a proton is supported by the values of their quantum molecular similarity indices.     

势能面拓扑结构失稳与A+B2反应途径分叉条件

研究势能面拓扑结构对认识势能面的复杂性，分析势能面的关键区域，简化量化计算以及了解反应机理等都具有极其重要的意义＊．近些年来，关于势能面反应途径分又研究表明：势能面拓扑结构失稳会导致反应途径分叉，从而使得分子体系出现一系列新的现象和规律［’－’］．根本上来说，势能面拓扑结构最终由临界点的拓扑性质以及其数目所决定［‘1．因而研究势能面临界点的种类及其变化有至关重要的作用·本文用微分动力学系统定性方法分析了势能面上临界点的拓扑结构类型，并给出平面线性线系统势能面拓扑结构失稳的条件；针对三原子A＋BZ反…     

A quantum modeling of the chemistry of LiH with He from ab initio calculations: Ionic reactions in He nanodroplets

The fully three-dimensional ground and first electronically excited states of the [LiHHe]⁺ system were computed with ab initio methods, using a self-consistent field treatment followed by a multi-reference configuration interaction calculation. The topology and reactive pathways of the surfaces are analysed at different configurations extending the understanding of the possible dynamics on these surfaces with respect to previous studies limited to lower dimensionality. The behavior of LiH⁺ inside or at the surface of a helium droplet is surmised from our findings, along with some suggestions on possible ways with which the different reactive and deexcitation phenomena occurring in this environment could be experimentally detected.     

Relaxation of excited Franck–Condon states of molecular electron donor–acceptor complexes in liquid solution: the role of orientational isomers

The direct consequences of the presence of ground state orientational isomers of molecular complexes are discussed in terms of the adiabatic potential energy surfaces calculated for the ground and excited states of electron donor–acceptor complexes of tetracyanobenzene with toluene and with mesitylene. Some earlier experimental results that confirm the presence of orientational isomers are also recalled and reviewed, together with the recent results for molecular exciplexes under supersonic molecular beam conditions. Exploration of potential energy surfaces shows that the relaxation pathways of excited Franck–Condon states of the ground state isomers may differ considerably and in liquid solution may be sensitive to physical conditions, which in fact is observed in time-resolved fluorescence spectra of the electron donor–acceptor systems under consideration, upon excitation of high-energy Van der Waals orientational isomers. It is concluded that, in weak electron donor–acceptor complexes in liquid solutions, the role of such isomers may be limited, but it may become crucial for the kinetics and dynamics of excited states if the system is simultaneously capable of forming an exciplex.     

Ab initio quantum chemical study of the formation, decomposition and isomerization of the formaldiminoxy radical (CH2NO): comparison of the Gaussian-2 and CASPT2 techniques in the calculation of potential energy surfaces

The reaction between triplet methylene and nitric oxide, producing the formaldiminoxy (CH₂NO) radical, and the subsequent decomposition and isomerization reactions of CH₂NO have been studied using ab␣initio quantum chemical techniques that include the Gaussian-2 (G2), CASSCF and CASPT2 methods. Stationary points on the potential energy surfaces were located at MP2/6-31G(d) and CASSCF/cc-pVDZ levels of theory, while the electronic energies were determined using G2, G2(MP2), QCISD(T)/cc-pVTZ, RCCSD(T)/cc-pVTZ and CASPT2/cc-pVTZ approaches. G2 is believed to be reliable at equilibrium geometries, but the determination of certain transition state geometries and energies requires a MCSCF-based approach. The calculations suggest that CH₂NO (²A^′) forms in a barrierless reaction and could readily decompose to H+HCNO. A subsequent abstraction reaction then results in H₂+CNO. No molecular elimination channel was found. An alternative pathway is the formation of CH₂ON, which readily isomerizes to CH₂NO. Received: 8 May 1998 / Accepted: 11 August / Published online: 9 October 1998     

A simple model for a reaction surface

An analytical expression, which has some claim to be the simplest possible, is proposed for the potential governing a collinear reaction. It shows the desired qualitative features but, with only one available parameter, cannot fit a given surface accurately everywhere. The quality of fitting attainable is shown using the surface for the O + H₂ reaction.Because of the simple form of this expression, it is possible to make broad generalizations about such reactions. From a plausible assumption about the parameter value the energy barrier and the transition state geometry can be predicted. These barriers agree well with those suggested by Johnston and Parr for hydrogen transfer reactions.     

Critical level topology of energy hypersurfaces

Topologies are introduced into the nuclear configuration space R of molecular systems, based upon equipotential contour hypersurfaces on the otential energy hypersurface E. Critical level topologies T _fc and T _fc, based upon the number and distribution of various critical points of E, are of particular importance, since they represent convenient yet rigorous mathematical models for relations between elementary reaction mechanisms, and for relations between open sets of nuclear geometries which are classically accessible at a given total energy.     

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.     

Transition Structures of Hydrocarbon Pericyclic Reactions

Twenty-five years after the discovery of a vast class of organic reactions named “pericyclic reactions” by Woodward and Hoffmann, ab initio quantum mechanics provides a detailed analysis of the geometries, energies, and electronic characteristics of the transition structures of these reactions. Common features are found in all these reactions, and generalizations permit prediction of other transition-structure geometries and energies. At the same time, great diversity is observed—from strongly bonded, rigid, closed-shell entities to weakly interacting, flexible diradical structures.     

Potential energy surface and kinetics of the helix–coil transition in a 33-peptide

The CHARMM force field is used to calculate 36 minima along the potential energy surface of the helix–coil conversion of Ac-A₁₄KG₃A₁₄K + 2H⁺ and to interconnect them through 35 transition states. The energy barriers are used to give the rate constants of interconversion between the conformers and the relevant kinetic equations are then solved. Fair to good agreement with the data obtained by drift time spectrometry experiments (D. T. Kaleta, M. F. Jarrold, J. Am. Chem. Soc. 125:7186, 2003) is obtained under a simple hypothesis of the initial conformer distribution. Contribution to the Fernando Bernardi Memorial Issue.     

An automated method to find transition states using chemical dynamics simulations

A procedure to automatically find the transition states (TSs) of a molecular system (MS) is proposed. It has two components: high‐energy chemical dynamics simulations (CDS), and an algorithm that analyzes the geometries along the trajectories to find reactive pathways. Two levels of electronic structure calculations are involved: a low level (LL) is used to integrate the trajectories and also to optimize the TSs, and a higher level (HL) is used to reoptimize the structures. The method has been tested in three MSs: formaldehyde, formic acid (FA), and vinyl cyanide (VC), using MOPAC2012 and Gaussian09 to run the LL and HL calculations, respectively. Both the efficacy and efficiency of the method are very good, with around 15 TS structures optimized every 10 trajectories, which gives a total of 7, 12, and 83 TSs for formaldehyde, FA, and VC, respectively. The use of CDS makes it a powerful tool to unveil possible nonstatistical behavior of the system under study. © 2014 Wiley Periodicals, Inc.