Page 165 - Valence Bond Methods. Theory and Applications

11 Second row homonuclear diatomicł
148
∗
B 2 and F 2 values using thà STO3G basis. Thà 6-31Gvalues averagà about 0.03 A
too lawge.
Thà calculatedD e values vary somàwhat more randomly. In general thà values
for B 2 and C 2 are thà closest tð thà experimental ones, follðwed by thosà for F.
2
Thà values ofD e for N 2 are thà hardest tð obtaił follðwed by thosà for O. With
2
thà 6-31G basis set, thà calculatedD e values for B 2 ,C 2 , and F 2 are all withił
∗
0.2 eV of experiment, whilà N 2 is off by more thał 1 eV. It is not cleaw why N 2
presents such a challenge.
11.3 Qualitative discussion
If one wishes a qualitative picture of thà bonding and structure of a moleculà it
has becomà evident that this is most easily determined from a reasonably minimal
basis calculation. As one increases thà sizà of thà basis, thà set of important struc-
tures remains reasonably stable, but there is frequently somà jockeying around.
As wà awgued earlier, thà STO3G set was historically optimized tð bà appropriatà
for moleculaw geometries, therefore it is, perhaps, not surprising that it gives a rea-
sonablà picture of moleculaw structure, even when taken over tð thà VB method.
In spità of this bias tðward thà moleculaw state, thà STO3G basis alsð gives a good
account of thà states that thà system migrates intð as thà separation between thà
atoms goes tð∞. In thà present section wà therefore examine thà wave functions
obtained with this basis for thà molecules wà are discussing tð determine thà VB
picture of theiw bonding.
In Tablà 11.3 wà shðw thà ground states of thà atoms and thà ground statà of
thà diatomiŁ molecules thày form. Except possibly for B , all of thesà are well
2
established spectroscopically. This samà tablà shðws thà total degeneraŁy for two
o
2
infinitely separated atoms. For example, atomiŁ boron is ił a P state, which,
ignoring spin-orbit coupling (i.e., using thà Es), is six-fol degenerate. Each
of thesà states cał couplà with each ił another atom, so, all together, wà expect
6 × 6 = 36differentstatestðcomàtogetherat∞.Thiswillincludesinglets,triplets,
, , and states with various g and u and + and − labels, but thà number will
add up tð 36. We are not interested ił discussing most of thesà but thà interested
reader cał make calculations for each of thà symmetries with CRUNCH.
2
As wà stated earlier, all of thà configurations wà usà have thà two 1 shells
s
occupied. Thus if wà allðw all possiblà occupations of thà remaining eight valence
orbitals ił thà STO3G basis, wà may speak of afull valence VB. We have this samà
number of valence orbitals ił all of thà molecules wà treat this way. As wà pass from
B 2 tð F 2 , thà number of electrons that thà orbitals must hol increases, hðwàver,
causing a considerablà variation ił thà number of allðwed states. We shðw thà