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esults in better estimates of the energy in systems
where energy levels are closely spaced, and where
bond breaking is occurring.
UHF can be run on both open and closed shell
systems. The major caveat to this method is the
time involved. Since alpha and beta electrons are
treated separately, twice as many integrals need to
be solved. As your models get large, the time for the
computation may make it a less satisfactory
method.
Configuration Interaction
The effects of electron-electron repulsion are
underestimated by SCF-RHF methods, which
results in the overestimation of energies.
SCF-RHF calculations use a single determinant that
includes only the electron configuration that
describes the occupied orbitals for most molecules
in their ground state. Further, each electron is
assumed to exist in the average field created by all
other electrons in the system, which tends to
overestimate the repulsion between electrons.
Repulsive interactions can be minimized by
allowing the electrons to exist in more places (i.e.
more orbitals, specifically termed virtual orbitals).
The multi-electron configuration interaction
(MECI) method in MOPAC addresses this
problem by allowing multiple sets of electron
assignments (i.e., configurations) to be used in
constructing the molecular wave functions.
Molecular wave functions representing different
configurations are combined in a manner analogous
to the LCAO approach.
For a particular molecule, configuration interaction
uses these occupied orbitals as a reference electron
configuration and then promotes the electrons to
unoccupied (virtual) orbitals. These new states,
Slater determinants or microstates in MOPAC, are
then linearly combined with the ground state
configuration. The linear combination of
microstates yields an improved electronic
configuration and hence a better representation of
the molecule.
Approximate Hamiltonians
in MOPAC
There are five approximation methods available in
MOPAC:
• AM1
• MNDO
• MNDO-d
• MINDO/3
• PM3
The potential energy functions modify the HF
equations by approximating and parameterizing
aspects of the Fock matrix. The approximations in
semi-empirical MOPAC methods play a role in the
following areas of the Fock operator:
• The basis set used in constructing the 1-
electron atom orbitals is a minimum basis set
of only the s and p Slater Type Orbitals (STOs)
for valence electrons.
• The core electrons are not explicitly treated.
Instead they are added to the nucleus. The
nuclear charge is termed N effective .
For example, Carbon as a nuclear charge of
+6-2 core electrons for a effective nuclear
charge of +4.
• Many of the 2-electron Coulomb and
Exchange integrals are parameterized based on
element.
Choosing a Hamiltonian
Overall, these potential energy functions may be
viewed as a chronological progression of
improvements from the oldest method, MINDO/3
to the newest method, PM5. However, although the
ChemOffice 2005/Chem3D MOPAC Computations • 163
MOPAC Semi-empirical Methods