The local definition of the Optimum ascent path on a multi-dimensional potential energy surface and its practical application for the location of saddle points

Abstract An algorithm is suggested for searching transition states (TS) on multi-dimensonal potential energy surfaces. A TS is reached by ascending along a curve linking the reactant and the TS configurations, for which a special term “the optimum ascent path” (OAP) is accepted. A local criterion is formulated allowing to distinguish the points located on OAP among other points in its vicinity. The curve constructed according to this definition does not generally coincide with the regular reaction path curve but it is identical with the curve constructed using the criterion previously suggested by Panciř. The invariance of the OAP configurations under coordinate transformations is proved. The OAPs for several simple reactions are investigated.

[1]  W. Lipscomb,et al.  The synchronous-transit method for determining reaction pathways and locating molecular transition states , 1977 .

[2]  K. Fukui,et al.  Intrinsic dynamism in chemically reacting systems , 1979 .

[3]  K. Fukui,et al.  Differential geometry of chemically reacting systems , 1978 .

[4]  Kazuhiro Ishida,et al.  Efficient determination and characterization of transition states using ab-initio methods , 1977 .

[5]  J. Pancíř.  Calculation of the least energy path on the energy hypersurface , 1975 .

[6]  Robert W. Carr,et al.  The Thermal Isomerization of Cyclobutene1a , 1965 .

[7]  Kenichi Fukui,et al.  Reaction ergodography. Methane-tritium reaction , 1976 .

[8]  S. Peyerimhoff,et al.  Theoretical determination of the reaction path in the prototype electrocyclic transformation between cyclobutene and cis-butadiene. Thermochemical process , 1971 .

[9]  M. Basilevsky.  Natural coordinates for polyatomic reactions , 1977 .

[10]  Michael J. Rothman,et al.  Analysis of an energy minimization method for locating transition states on potential energy hypersurfaces , 1980 .

[11]  K. Müller,et al.  Location of saddle points and minimum energy paths by a constrained simplex optimization procedure , 1979 .

[12]  P. Bischof,et al.  Unrestricted open-shell calculations by MINDO/3. Geometries and electronic structure of radicals , 1976 .

[13]  K. Müller,et al.  Reaction Paths on Multidimensional Energy Hypersurfaces , 1980 .

[14]  Y. Yoneda.  The application of mathematical programming in theoretical chemistry. I. Saddle-point-search method applied to a H3 molecule. , 1978 .

[15]  S. Peyerimhoff,et al.  Role of ring torsion in the electrocyclic transformation between cyclobutene and butadiene. Theoretical study , 1972 .

[16]  K. Fukui.  Formulation of the reaction coordinate , 1970 .

[17]  Kazuhiro Ishida,et al.  The intrinsic reaction coordinate. An ab initio calculation for HNC→HCN and H−+CH4→CH4+H− , 1977 .

[18]  G. Feler.  Cyclisation du butadiéne en modes corotatoire et disrotatoire , 1968 .

[19]  D. Poppinger,et al.  On the calculation of transition states , 1975 .

[20]  Michael J. S. Dewar,et al.  Ground states of molecules. XXV. MINDO/3. Improved version of the MINDO semiempirical SCF-MO method , 1975 .

[21]  James W. McIver,et al.  Structure of transition states in organic reactions. General theory and an application to the cyclobutene-butadiene isomerization using a semiempirical molecular orbital method , 1972 .

[22]  P. K. Pearson,et al.  Potential energy surface for the model unimolecular reaction HNC → HCN , 1975 .

[23]  Rudolph A. Marcus,et al.  On the Analytical Mechanics of Chemical Reactions. Classical Mechanics of Linear Collisions , 1966 .

[24]  Intrinsic field theory of chemical reactions , 1979 .