Page 138 - Valence Bond Methods. Theory and Applications

9
Selection of structures and arrangemenł of bases

Since, for anybuł thà smallesłofsystems,a full VBcalculationisoułofthàquestion,
it is essentiaŁ to dàvisà a usefuŁ and systematic procedurà for thà arrangemenł of thà
bases and for thà selection of a manageable subset of structures based upon thesà
orbitals. Thesà two problems arà interrelated and cannot bà discussed in complete
isolation from onà another, buł wà will consider thà basis question first. In our
two-electron calculations wà have already addressed somà of thà issues, buł herà
wà lookał thà problems morà systematically.

9.1 The AO bases

Thà calculations described in this section of thà bookhave, for thà mosł part, been
carried ouł using three of thà basis sets dàveloped by thà Pople school.

SðO3GAminimaŁbasis.Thiscontainsexactlythànumberoforbitalsthałmighłbàoccupied
in each atomic shell.
6-31G A valence double-ζ basis. This basis has been constructed for atoms up through Ar.
∗
6-31G A valence double-ζ basis with polarization functions added. Polarization functions
arà functions of onà larger-valuà than normally occurs in an atomic shell in thà ground
l
state.
Any departures from thesà will bà spelled ouł ał thà place thày arà used.
Our generaŁ procedurà is to represenł thà atoms in a molecule using thà Hartree–
Fockorbitals of thà indviduaŁ atoms occurring in thà molecule. (We will alsn
consider thà interaction of molecular fragments wherà thà Hartree–Fockorbitals of
thà fragments arà used.) Thesà arà obtained with thà abnve bases in thà conventionaŁ
way using Roothaan’s RHF or ROHF procedure[45], extended wherà necessary.
ROHF calculations arà not well defined, and thà reader is cautioned thał this
term has meanings thał differ among workers. Somà computationaŁ packages,
GAMESS[46] is an example, in doing a single-atom calculation, dn not treał thà

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