molecular mechanical methods assume that the motions of the nuclei of a
molecule are independent of the motions of surrounding electrons. In ab initio
calculations, the Born – Oppenheimer approximation — separation of the move-
ment of atom nuclei and electrons is possible because electrons move much
more rapidly than nuclei — is used to solve the Schr ö dinger equation ( HΨ = EΨ )
with a large but fi nite basis set of atomic orbitals. In practice, most ab initio
methods use the Hartree – Fock approximation, which represents the many -
electron wavefunction as a sum of products of one - electron wavefunctions,
termed molecular orbitals. Many different basis sets of orbitals have been
generated for use with ab initio calculations. A practical minimal basis set
(such as the popular STO - 3G representation, STO = Slater - type orbitals or
Slater - type basis functions) for lithium and beryllium would contain 1 s , 2 s , and
2 p occupied atomic orbitals supplemented by a set of unoccupied (in the atom)
but energetically low - lying p - type functions. Minimal basis sets do not ade-
quately describe nonspherical (anisotropic) electron distributions in molecules.
One fi nds this basis set in computer modeling programs, but it should not be
expected to yield realistic results for any inorganic complexes. To remedy this,
one “ splits ” the valence description into “ inner ” and “ outer ” components. The
result is the split - valence basis set, and the valence manifolds of main - group
elements for instance are represented by two complete sets ofs - and p - type
functions. A simple split - valence basis set is called 3 - 21G. For heavier main -
group elements, unoccupied (in the atom) but energetically low - lying d - type
functions are added to create the 3 - 21G( ) basis set. Polarization basis
sets account for the displacement in molecular orbitals resulting from
hybridization (ansp hybrid would be an example). Two popular polarization
basis sets are the 6 - 31G and 6 - 31G representations. Ab initio methods
provide excellent accounts of equilibrium and transition state geometries and
conformations as well as reaction thermochemistry. They are computationally
very intensive and are usually limited to molecules containing 50 atoms
or less.
4.4.3 Density Function Theory,
Density functional models attempt to describe the total energy of a molecular
system also from the standpoint of Hartree – Fock theory — the many - electron
wavefunction as a sum of products of one - electron wavefunctions, termed
molecular orbitals. These methods accurately describe equilibrium and transi-
tion - state geometries as well as thermochemistry. For density functional
models, one must calculate the kinetic energy (KE) of the individual electrons
(nuclear KE is zero in the Born – Oppenheimer approximation), the attractive
potential energy between nuclei and electrons, and the repulsive potential
energy between electrons (the Coulomb electron repulsive term in Hartree –
Fock theory adjusted by the exchange term which takes into account a
repulsive overestimation). The exchange and correlation terms ( Ecorrelation =
Etrue − EHartree – Fock − Erelativistic ) in so - called “ local ” density functional models
QUANTUM MECHANICS-BASED COMPUTATIONAL METHODS 171