Potential energy surface

Potential energy surface
A basic potential energy surface, where V, the potential energy, is an explicit function of just two internal coordinates for the linear hydrogen atom exchange reaction, shown above, namely the internuclear distances RAB and RBC, in Angstroms. A trajectory that runs close to the valley bottom is marked in red. [5]
In physical chemistry, a potential energy surface is a two- or three-dimensional plot of the potential energy, or rather thermodynamic potential, i.e. typically Gibbs free energy or Helmholtz free energy, of a chemical reaction, as a function of either time, extent of reaction, change of nuclei arrangement, or concentration of products (or reactants).

History
The first potential energy surface diagram was calculated in 1931 by Mexican-born American theoretical chemist Henry Eyring and Hungarian-born English physical chemist Michael Polanyi, as presented in their famous paper "On Simple Gas Reactions", in which, using the London equation (1927), they described the journey of the nuclei from reactant state of the system to the product state of the system, passing through the crucial intermediate state of activated complex. [1] The pioneering work is said to be the birth of ‘reaction dynamics’. [2] The reaction they dealt with was:

 H + H_2 \rightarrow H_2 + H \,

in which the used semi-empirical procedures, based on quantum-mechanical principles and energies of dissociation, to construct a three-dimensional diagram showing potential energy as a function of the shorter H–H distances in a linear H H ∙ ∙ H complex. Later, Erying and his students carried out dynamical calculations of this kind. [3] The development of these types of diagrams led to the conception of transition state theory in 1935.

Energy landscapes
See main: Energy landscape
In the mid 1980s, energy landscape models were being employed in the study of protein folding. The theory of RNA free energy landscapes was being utilized as early as 1993.

Human chemistry
In human chemistry, the first to apply the logic of potential energy surfaces to the explanation of human chemical reaction dynamics as American chemist David Hwang who, in his 2001 article “The Thermodynamics of Love”, applied the logic Gibbs free energy potential energy surfaces to reaction in which two unattached male M and a female M individuals form a human chemical bonded relationship M-F. [4]

 M + F \rightarrow MF \,

(add discussion)

References
1. (a) Eyring, H. and Polanyi, M. (1931). “Uber Einfache Gasreaktionen” (On Simple Gas Reactions), Zeitschrift fur Physikalische Chemie B, 12:279-311.
(b) Eyring, H. (1931). “The Energy of Activation for Bimolecular Reactions Involving Hydrogen and the Halogens, According to Quantum Mechanics”, J. Amer. Chem. Soc. 53:2537-49.
(c) Polanyi, M. (1932). Atomic Reactions. London: Williams, Norgate.
2. Zewail, Ahmed H., Schryver, Frans C., De Feyter, Steven, and Schweitzer, Gerd. (2001). Femtochemistry (pg. 11). Wiley-VCH.
3. Laidler, Keith. (1993). The World of Physical Chemistry (pg. 246-48). Oxford University Press.
4. Hwang, David. (2001). "The Thermodynamics of Love" (PDF), Journal of Hybrid Vigor, Issue 1, Emory University.
5. Wales, David. (2003). Energy Landscapes: Applications to Clusters, Biomolecules, and Glasses. Cambridge University Press.

Further reading
● Hirst, David M. (1985). Potential Energy Surfaces: Molecular Structure and Reaction Dynamics. Taylor & Francis.
● Atkins, Peter, Paula, Julio de, and Friedman, Ron. (2008). Quanta, Matter, and Change: a Molecular Approach to Physical Chage (section: 20.10: Potential energy surfaces, pgs. 680-82). MacMillan.

External links
Potential energy surface – Wikipedia.

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