# Potential energy surfaces

# Potential energy surfaces

This chapter discusses potential energy surfaces, that is, the electronic energy as a function of the internuclear coordinates as obtained from the electronic Schrödinger equation. It focuses on the general topology of such energy surfaces for unimolecular and bimolecular reactions. To that end, concepts like saddle point, barrier height, minimum-energy path, and early and late barriers are discussed. It concludes with a discussion of approximate analytical solutions to the electronic Schrödinger equation, in particular, the interaction of three hydrogen atoms expressed in terms of Coulomb and exchange integrals, as described by the so-called London equation. From this equation it is concluded that the total electronic energy is not equal to the sum of H-H pair energies. Finally, a semi-empirical extension of the London equation — the LEPS method — allows for a simple but somewhat crude construction of potential energy surfaces.

*Keywords:*
electronic Schrödinger equation, saddle point, barrier height, minimum-energy path, early barrier, late barrier, Coulomb integral, exchange integral, London equation, LEPS surface

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