Computational Chemistry

energy

geometry

geometry

optimized structure

.

input structure

Fig. 2.16 An efficient optimization algorithm knows approximately in which direction to move
and how far to step, in an attempt to reach the optimized structure in relatively few (commonly
about five to ten) steps

bond length, q

0

qe

E

E–E 0 = k(q–q 0 )^2

Input structure

Pi(Ei, qi)

Equilibrium (optimized) structure

Po(E 0 , q 0 )

Fig. 2.17 The potential energy of a diatomic molecule near the equilibrium geometry is approxi-
mately a quadratic function of the bond length. Given an input structure (i.e. given the bond length
qi), a simple algorithm would enable the bond length of the optimized structure to be found in one
step, if the function were strictly quadratic

2.4 Geometry Optimization 27