By Errol G. Lewars
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Extra resources for Computational Chemistry: Introduction to the Theory and Applications of Molecular and Quantum Mechanics
9 kJ mol–1 minimum O H C 1 H 0 kJ mol–1 minimum Fig. 13 The plausible stationary points on the propenol potential energy surface according to AM1 geometry optimization-frequency calculations (the frequencies show if a stationary point is a minimum, a transition state, or a hilltop). A PES scan (Fig. 14) indicated that 1 is the global minimum and 3 is a relative minimum, while 2, 4 and 5 are transition states and 6 is a hilltop; this is confirmed (at the AM1 level at least) by these calculations.
It is not possible, in general, to go from the input structure to the proximate minimum in just one step, but modern geometry optimization algorithms commonly reach the minimum in about ten steps, given a reasonable input geometry. The most widely-used algorithms for geometry optimization  use the first and second derivatives of the energy with respect to the geometric parameters. To get a feel for how this works, consider the simple case of a 1-dimensional PES, as for a diatomic molecule (Fig.
2 Michael Polanyi, Hungarian-British chemist, economist, and philosopher. Born Budapest 1891. D. University of Budapest, 1917. Researcher Kaiser-Wilhelm Institute, Berlin, 1920–1933. Professor of chemistry, Manchester, 1933–1948; of social studies, Manchester, 1948–1958. Professor Oxford, 1958–176. Best known for book “Personal Knowledge”, 1958. Died Northampton, England, 1976. 22 2 The Concept of the Potential Energy Surface Our treatment of a PES can be subjected to a more sophisticated examination, by examining changes in the direction and curvature of the reaction path, the reaction path Hamiltonian (RPH) and the united reaction valley approach (URVA) ; these can reveal deeper detail about a reaction than one obtains only from the energies of the various species (as in the simple treatment of Sect.