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Electronic Structure Theory describes the motions of electrons in atoms or
molecules. Generally this is done in the context of the BornOppenheimer
Approximation, which says that electrons are so much lighter (and therefore
faster) than nuclei that they will find their optimal distribution for any
given nuclear configuration. The electronic energy at each nuclear
configuration is the potential energy that the nuclei feel, so solving the
electronic problem for a range of nuclear configurations gives the potential
energy surface.
Because the electrons are so small, one needs to use quantum mechanics to
solve for their motion. Quantum mechanics tells us that the electrons will
not be localized at particular points in space, but they are best thought of
as ``matter waves'' which can interfere. The probability of finding a
single electron at a given point in space is given by
for its wavefunction at the point . The wavefunction can
be determined by solving the timeindependent Schrödinger equation
. If the problem is timedependent, then the
timedependent Schrödinger equation
must be used instead; otherwise, the
solutions to the timeindependent problem are also solutions to the
timedependent problem when they are multiplied by the energy
dependent phase factor
. Since we have fixed the nuclei
under the BornOppenheimer approximation, we solve for the nonrelativistic
electronic Schrödinger equation:

(1) 
where refer to electrons and refer to nuclei. In atomic
units, this simplifies to:

(2) 
This Hamiltonian is appropriate as long as relativistic effects are not
important for the system in question. Roughly speaking, relativistic
effects are not generally considered important for atoms with atomic number
below about 25 (Mn). For heavier atoms, the inner electrons are held more
tightly to the nucleus and have velocities which increase as the atomic
number increases; as these velocities approach the speed of light,
relativistic effects become more important. There are various approaches
for accounting for relativistic effects, but the most popular is to use
relativistic effective core potentials (RECPs), often along with the
standard nonrelativistic Hamiltonian above.
Next: Properties Predicted by Electronic
Up: intro_estruc
Previous: Introduction
David Sherrill
20030807