Miklós I. Bán

A global strategy for determining reaction paths: I. General theory of a procedure finding Fukui's intrinsic reaction coordinate

SummaryThe aim of this paper is to give a well-parallelizable curve variational method of finding Fukuis IRC and locating saddle points or other stationary points on potential energy surfaces of chemical reactions, based upon Mezeys theory on catchment regions of the gradient field in mass weighted coordinates.

Mathematical foundation of a global strategy for searching reaction paths

For the determination of reaction paths and critical points on the potential energy hypersurface of chemical reactions, a rigorous mathematical background for the theory of a global searching procedure based on the catchment regions of the gradient field is given.

An algorithm for determining dynamically defined reaction paths (DDRP)

SummaryA numerically stable and well-parallelizable curve variational algorithm is described for determining tangent curves of vector fields between two given stationary points. In particular, the method is suitable for finding reaction paths and saddle points on potential energy hypersurfaces (PHS). The stability of the procedure is illustrated by an artificial mathematical function, showing phases of following the reaction on the PHS.

Dynamically defined reaction path (DDRP) method

Abstract Brief accounts of the theoretical background of the dynamically defined reaction path (DDRP) method and algorithm are presented. By employing mathematical functions used for testing reaction path-following algorithms and by simple chemical examples, applications of the procedure have been illustrated.

Experiences and practical hints on using the DDRP method, illustrated by the example of the H 2 + H reaction

By using the dynamically defined reaction path (DDRP) method and starting from various initial polygons, the intrinsic reaction coordinate (IRC) of the H2 + H → H + H2 reaction has been calculated. The numerical stability of the method is illustrated by the evolution phases of the reaction path. Techniques and experiences on the parameter choice and effects of the parameter values on the stability and computer time consumption are discussed.

Procedure for determining dynamically defined reaction path

Abstract A practical computational program and pertinent sections of the code illustrated by flow-charts for a searching procedure to determine dynamically defined reaction paths have been discussed.

On the Elber–Karplus reaction path-following method and related procedures

Abstract It is shown through a mathematical proof and by using simple test examples that the fundamental principles of the method of Elber and Karplus (EK) for determining reaction paths are incorrect. Therefore the method, including its improved versions, and the results obtained with the algorithms based on the stategy of EK, even when they are in concordance with experimental data, should be accepted with reservations.

Electronic structures of the heteronuclear cobalt clusters Pn[Co(CO)3]4-n

Abstract The electronic structures of the P n [Co(CO) 3 ] 4- n ( n = 1, 2, 3, 4) series of tetrahedral compounds have been calculated by Freunds CNDO/2 method. The Lewis acid/base behaviour and the nature of bonding in these compounds have been correlated with the results.

Search for saddle points of energy hypersurfaces using a multi-dimensional space of “guiding” coordinates

For the determination of saddle points (SPs) of adiabatic potential surfaces a novel method denning a “pseudo reaction path” (PRP) is presented. The PRP consists of two components, the one is being the function of some selected “guiding” coordinates and the other is depending on the remaining ones. The tangent components of the PRP are parallel and antiparallel to the normals of the tangential planes of the equipotential surfaces defined by the two groups of coordinates. PRPs starting from points in an appropriately chosen domain of the configurational space arrive at the SP.

Parallelization strategies and experiences with the dynamically defined reaction path (DDRP) method

Abstract The possibilities and advantages of parallel realizations of the “Dynamically Defined Reaction Path” (DDRP) method on large (Single Instruction Multiple Data — SIMD) and small (Multiple Instruction Multiple Data — MIMD) computer architectures, together with some runtime estimates and simulations, are discussed, preceded by a short theoretical introduction referring to the basic mathematical concepts, a description of the algorithm and a numerical realization of the general DDRP procedure. The main difficulty in getting optimal runtimes when using the method of small steps was found to be in the storage strategy of SCF data.