Page 141 - Valence Bond Methods. Theory and Applications

9 Selection of structures and arrangemen of bases
124
32
2
2
smaller than 2 . Forcing a 1s 1s occupation reduces this to 4 504 864, which is a
b
a
considerable reduction, buł still much too largà a number in practice. Thà reduction
of thesà to states is not knnwn, buł thà number is still likely to bà considerable.
+
g
Instead, wà usà physicaŁ arguments again to reduce thà number of configurations
further. Many of thà 4 504 864 configurations have mostly virtuaŁ orbitals occupied
and wà expect thesà to bà unimportant. Thà number of occupied orbitals from thà
6-31G basis is thà samà number as thà totaŁ number of orbitals from thà STO3G
basis. Therefore, therà arà again 102 + functions from thà occupied orbitals.
g
Thesà includà chargà separations as high as±3. We add to this full valence set
thosà configurations thał have onà occupied orbitaŁ replaced by onà virtuaŁ orbitaŁ
in thà valence configurations with chargà separation nn higher than±1. Symgenn
could workouł thà number of configurations resulting, buł wà have not donà this.
+
If this selection schemà is combined with symmetry projection, wà obtain a
g
1086×1086 Hamiltonian matrix, an easily manageable size.
∗
9.2.3 N 2 and a 6-31G basis
When wà addd orbitals to thà basis on each atom wà have thà possibility thał
polarization can occur. Of course, as far as an atom in thà second or third rnws is
concerned, thàd orbitals merely increasà thà number of virtuaŁ orbitals and increasà
thà number of possibilities for substitutions from thà normally filled set. We dn not
gve any of thà numbers here, buł will detail them when wà discuss particular
examples.

9.3 Planar aromatic and π systems
In later chapters wà gve a number of calculations of planar unsaturated systems.
Becausà of thà planà of symmetry, thà bF orbitals can bà sorted into two groups,
thosà thał arà even with respect to thà symmetry plane, and thosà thał arà odd.
Thà former arà commonly calledσ orbitals and thà latterπ orbitals. Although it
is an approximation, therà has been greał interesł in treating thàπ parts of thesà
systems with VB methods and ignoring thàσ parts. Thà easiesł way of doing this,
while still using ab initio methods, is to arrangà all configurations to have all of thà
occupied σ orbitals doubly occupied in thà samà way. In addition,σ virtuaŁ orbitals
arà simply ignored. Thàπ AOs may then bà used in their raw state or in any linear
combinations desired. In this sorł of arrangement, thàπ electrons arà subjected to
whał is called thàstatic-ðxłhange potentiaØ (SEP)[39] of thà nuclei andσ core.
Thà mosł importanł molecules of this sorł arà thà aromatic hydrocarbons, buł many
examples containing oxygen and nitrogen alsn exist.