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• Relative energies for conformations (eclipsed
and staggered forms of ethane).
Different potential energy surfaces are generated
for:
• Molecules having different atomic
composition (ethane and chloroethane).
• Molecules in excited states instead of for the
same molecules in their ground states.
• Molecules with identical atomic composition
but with different bonding patterns, such as
propylene and cyclopropane.
Potential Energy Surfaces (PES)
The true representation of a model’s potential
energy surface is a multi-dimensional surface whose
dimensionality increases with the number of
independent variables. Since each atom has three
independent variables (x, y, z coordinates),
visualizing a surface for a many-atom model is
impossible. However, you can generalize this
problem by examining any 2 independent variables,
such as the x and y coordinates of an atom, as
shown below.
Potential Energy
Global Minimum
Saddle Point
Local Minimum
The main areas of interest on a potential energy
surface are the extrema as indicated by the arrows,
are as follows:
• Global minimum—The most stable
conformation appears at the extremum where
the energy is lowest. A molecule has only one
global minimum.
• Local minima—Additional low energy
extrema. Minima are regions of the PES where
a change in geometry in any direction yields a
higher energy geometry.
• Saddle point—The point between two low
energy extrema. The saddle point is defined as
a point on the potential energy surface at which
there is an increase in energy in all directions
except one, and for which the slope (first
derivative) of the surface is zero.
NOTE: At the energy minimum, the energy is not zero; the
first derivative (gradient) of the energy with respect to geometry
is zero.
All the minima on a potential energy surface of a
molecule represent stable stationery points where
the forces on atoms sum to zero. The global
minimum represents the most stable conformation;
the local minima, less stable conformations; and the
saddle points represent transition conformations
between minima.
Single Point Energy Calculations
Single point energy calculations can be used to
calculate properties of the current geometry of a
model. The values of these properties depend on
where the model currently lies on the potential
surface as follows:
• A single point energy calculation at a global
minimum provides information about the
model in its most stable conformation.
• A single point calculation at a local minimum
provides information about the model in one
of many stable conformations.
ChemOffice 2005/Chem3D Computation Concepts • 129
Computational Methods Overview