Dietmar Heidrich

The Reaction Path in Chemistry: Current Approaches and Perspectives

An introduction to the nomenclature and usage of the reaction path concept D. Heidrich. From reaction path to reaction mechanism: Fundamental groups and symmetry rules P. G. Mezey. Loose definitions of reaction path X. Chapuisat. Role and treatment of zero eigenvalues of rotation in the Cartesian force constant matrix along the reaction path T. Iwai, A. Tachibana. The invariance of the reaction path description in any coordinate system W. Quapp. Second-order methods for the optimization of molecular potential energy surfaces T. Helgaker et al. Gradient extremals and their relation to the minimum energy path W. Quapp et al. Density functional theory - calculations of potential energy surfaces and reaction paths G. Seifert, K. Kruger. Using the reaction path concept to obtain rate constants from ab initio calculations A. D. Isaacson. Direct dynamics methods for the calculation of reaction rates D. G. Truhlar. Ab initio studies of reaction paths in excited- state hydrogen transfer processes A. L. Sobolewski, W. Domcke. Viewing the reaction path with the help of time-resolved femtosecond spectroscopy C. Meier, V. Engel. Index.

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

Analysis of the concept of minimum energy path on the potential energy surface of chemically reacting systems

Some confusion regarding the properties of minimum energy paths is evident in the literature. We show that a way of steepest descent on a potential surface can be defined independently upon the choice of the coordinate systems. The result is applied to mass-weighted coordinates and their use is critically reviewed. Fukuis IRC appears to be a special case of the steepest descent path starting from a saddle point. The impossibility to define a general ascent path is illustrated and the relations of IRC to real trajectories are discussed.

Exploring the potential energy surface of the ethyl cation by new procedures

Abstract The MP2/6-31G ∗∗ potential energy hypersurface (PES) of the chemically interesting molecule ion, C 2 H 5 + , is analyzed by new procedures proposed by us recently. The reaction paths (RPs) start from the minima or saddle points by following the so-called reduced gradient procedure and/or its modification, the tangent search concept (TASC). The minimum energy paths (MEP) obtained by TASC are fine approximations of those gradient extremals, which follow the valley floor (or ridge) along the smallest (absolute) eigenvalue of the Hessian. It is the valley floor gradient extremal which is also termed the streambed of the PES. Tracing the streambed uphill we locate saddle points of the H-scrambling in C 2 H 5 + . The potential energy surface of this cation is used to systematically explore the properties of RP definitions with particular focus to RP bifurcations. The intrinsic reaction coordinate (IRC), which is mostly used as MEP in chemistry, is included for the purpose of comparison.

Saddle points of index 2 on potential energy surfaces and their role in theoretical reactivity investigations

After a general characterization of “second order” saddle points two boundary cases are derived and illustrated by examples. The utilization of the classification is pointed out. One type, the virtual saddle point of index 2 (V-SP 2), may be understood as “geometrical” superposition of two saddles of index 1 (transition structures) which belong to relatively independent processes within the chemical system.

Der elektrophile angriff auf ungesättigte systeme—VII1: Theoretische untersuchungen zum einfluss des lösungsmittels auf die stabilität der kationenstrukturen

Zusammenfassung Mit der Erfassung elektrostatischer Wechselwirkungen auf der Basis des Solvatonen-Modells wird eine theoretische Abschatzung der Unterschiede in den Solvatationsenergien klassischer und nichtklassischer Strukturen des protonierten Ethylens, Benzols, der Xylole und des Pyrrols vorgenommen. Die Methode wurde an der Wiedergabe einiger bekannter Solvatationsenergien und Stabilisierungstrends gepruft und zur Interpretation sowie Vorhersage von Solvatationseffekten auf H-Verschiebungen in den protonierten Spezies sowie auf die Positionsselektivitat beim elektrophilen Angriff herangezogen.

Quantenchemische modellierung der potentialhyperfläche des äthylkations im bereich der klassischen und nichtklassischen strukturen

Zusammenfassung Es werden Eigenschaften der Potentialhyperflache des protonierten Athylens mit semiempirischen Methoden (CNDO/2-FK, MINDO/2, MINDO/3) berechnet. Diese nach Ubereinstimmung mit neuen strengen theoretischen Energiedaten fur den Stabilitatsunterschied von klassischem und nichtklassischem Athylkation ausgewahlten Methoden errechnen keinen stationaren Punkt in dem Bereich der Hyperflachen, wo bisher das stabilere der beiden klassischen Kationen angenommen wurde. Das H-ecliptische klassische Kation ist auf der CNDO/2-FK- und MINDO/2-Hyperflache ein Sattelpunkt, uber den der H-Austausch im Athylkation ablaufen sollte; auf der MINDO/3-Flache ist ihm ein flaches Minimum aufgepragt. Die angefuhren und weitere quantenchemische Verfahren (NDDO, ab inito) werden auf Ubereinstimmung in den berechneten Geometrien und Ladungsverteilungen untersucht.

The place of sioh groups in the absolute acidity scale from ab initio calculations

Abstract The deprotonation energy of a (H 3 Si)O-H group as a simplified structural element of silica gel and aluminosilicates is estimated from ab initio calculations on H 2 O, CH 3 0H and SiH 3 0H to be near 1475 kJ/mol. Results of the effect of Lewis acids on the Bronsted acidity of SiOH are given.

Quantenchemische untersuchungen zum mechanismus der elektrophilen substitution—III : Zur stabilität und struktur von [H,CH3]-σ-komplexen (ipso-Addukten) protonierter methylbenzole☆

Zusammenfassung [H,CH 3 ]-σ-Komplexe des Toluols und der drei isomeren Xylole, die durch elektrophilen H + -Angriff auf substituierte Aromatenpositionen (ipso-Angriff) oder durch H-Verschiebungen aus den isomeren σ-Komplexen entstehen, werden mit der CNDO/2-FK-MO-Methode untersucht. Diese Komplexe (ipso-Addukte) erweisen sich dabei wie die [H,H]-σ-Komplexe als Minima auf den Potentialhyperflachen der Aromaten/H + -Systeme. Ihre geometrische Struktur und relativen Stabilitaten werden angegeben und vergleiche mit experimentellen Daten in Losung angestellt. Es finden sich Hinweise, dass die isomeren σ-Komplexe eines substituierten Benzols durch das Losungsmittel unterschiedlich stabilisiert werden.

Gradient Extremals and Their Relation to the Minimum Energy Path

The concept of the reaction path (RP) of potential energy surfaces (PES) has gained increasing importance in theoretical chemistry [1,2]. Qualitatively, the RP is a curve in the configuration space of the atoms forming the chemical system which connects two minimizers of the PES along points of minimal energy in comparison to neighbouring points. The energy profile over the reaction path should be a “valley floor” leading via a point of highest energy, the saddle po i nt of index 1 of the PES. This point corresponds to the transition structure of the “transition state theory” . The fundamental problem in handling PES is the problem of dimensionality. Molecules with a number of atoms more than N=4 force an overwhelming number of net points in the dimension n=3N-6. The RP concept is a promising way out. It requires finding an algorithm for chemically reasonable one-dimensional curves of the PES determinable by differential properties of the PES — gradient and Hessian matrix — without knowledge of the whole, or of large parts of the PES. Slope and curvature of E(x)=E(x 1, ..., x n ) can be calculated from the gradient vector, g(x)=∇(x), and from the Hessian matrix (second derivatives, H(x)=∇∇TE(x), of the PES), respectively. [ We shall denote geometrical vectors in the configuration space and column matrices of their Cartesian coordinates by boldface lower-case letters, second order tensors and square matrices of their components by caligraphic upper-case letters. Scalars are often denoted by greek letters.]