Energy hypersurface, characterization

Stable adsorption complexes are characterized by local minima on the potential energy hypersurface. The reaction pathway between two stable minima is determined by computation of a transition state structure, a saddle point on the potential energy hypersurface, characterized by a single imaginary vibrational mode. The Cartesian displacements of atoms that participate in this vibration characterize movements of these atoms along the reaction coordinate between sorption complexes. 

Potential energy hypersurfaces form the basis for the complete description of a reacting chemical system, if they are throughly researched (see also part 2.2). Due to the fact that when the potential energy surface is known and therefore the geometrical and electronical structure of the educts, activated complexes, reactive intermediates, if available, as well as the products, are also known, the characterizations described in parts 3.1 and 3.2 can be carried out in theory. 

By ab initio MO and density functional theoretical (DPT) calculations it has been shown that the branched isomers of the sulfanes are local minima on the particular potential energy hypersurface. In the case of disulfane the thiosulfoxide isomer H2S=S of Cg symmetry is by 138 kj mol less stable than the chain-like molecule of C2 symmetry at the QCISD(T)/6-31+G // MP2/6-31G level of theory at 0 K [49]. At the MP2/6-311G //MP2/6-3110 level the energy difference is 143 kJ mol" and the activation energy for the isomerization is 210 kJ mol at 0 K [50]. Somewhat smaller values (117/195 kJ mor ) have been calculated with the more elaborate CCSD(T)/ ANO-L method [50]. The high barrier of ca. 80 kJ mol" for the isomerization of the pyramidal H2S=S back to the screw-like disulfane structure means that the thiosulfoxide, once it has been formed, will not decompose in an unimolecular reaction at low temperature, e.g., in a matrix-isolation experiment. The transition state structure is characterized by a hydrogen atom bridging the two sulfur atoms. 

A point K of M where the gradient of E(K) vanishes [where the tangent hyperplane to E(K) is "horizontal"], is a point where the force of deformation is zero, i.e., point K represents an equilibrium configuration. Such a point is called a critical point, and is denoted by K(A,i). Here, the first derivatives being zero, the second partial derivatives of the energy hypersurface are used to characterize the critical points. The first quantity in the parentheses, X, is the critical point index (and not the "order of critical point" as it is sometimes incorrectly called). The index A, of a critical point is defined as the number of negative eigenvalues of the Hessian matrix H(K(A,i)), defined by the elements... 

Ramquet, M.-N., Dive, G., Dehareng, D. Critical points and reaction paths characterization on a potential energy hypersurface. J. Chem. Phys. 2000,112, 4923-34. 

The exploration, characterization, and representation of potential energy hypersurfaces (PES) of chemical systems consisting of N interacting atoms is a task of increasing importance especially as a basis for modern reactivity theory. 

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