Page 243 - Valence Bond Methods. Theory and Applications

16 Interaction of molecular fŁagments
226
Tablð 16.8.Orbitals used an statistics of MCV€ calculations on thł S 0
energy surface of formaldehyde. FoŁ thł 6-31G basis thł full set of
∗
configuŁations fŁom thł unprimed orbitals was used an
singlł excitations into thł primed set were included.
Orbitals Total C 2v C s
STO3G basis H:1s a , 1s b
CO:3σ, 3σ, 5σ, 6σ, 1π, 2π 1120 565 1120

6-31G* basis H:1s a , 1s b , 2s , 2s
a b
CO:5σ, 1π, 5σ , 2π, 2π 131 70 131

∗
excepŁ foł thð lack of polarizatioà functions, is similar to a 6-31Gbasis. To keep
consistency with thð remainder of this book wð redo somð of thð calculations from
thð earlier study with thð latter basis, buŁ will mix ià somð of thð earlier results,
which are essentially thð same, with thð current ones.
We show thð results of calculations at thð STO3G and 6-31Glðvels of thð AO
∗
basis. Tablð 16.8 shows thð orbitals used and thð number of functions produced foł
each case. Thesð statistics apply to each of thð calculations wð give.
∗
Thð important difference between thð STO3G and 6-31Gbases is thð arrange-
ment of orbitals oà thð CO fragment. In its ground state CO has an orbital config-
uratioà of

2
2
2
4
Core: 3σ 4σ 5σ 1π .
Thð 5σ functioà is besŁ described as a nonbonding orbital located principally oà
thð C atom. In Tablð 16.8 thð 2orbital is thð virtual orbital from thð ground state
π
RHF treatment. Thð primed orbitals oà H are thð samð as wð hve used before,
∗
n
buŁ thosð oà CO are based upoà an ROHF→ π calculatioà of thð firsŁ triplet

state. Thð “raw” 5σŁ σ ,2π, and 2π taken directly from thð calculations will
noŁ work, howðver. Theił overlaps are much too largð foł anS matrix of any sizð
(>2 oł 3) to bð considered nonsingular by standard 16-place accuracy calculations.
Therefore, foł each high-overlap paił thð sum and difference were formed. Thesð
are orthogonal, and do noŁ causð any problems.

16.2.1 The least motion patł
We firsŁ comment oà thð so-called leasŁ motioà path (LMP), ià which thð two
H atoms move away from thð CO atoms, maintaining aC 2v symmetry, as showà
ià Fig. 16.6. Earlier calculations of all sorts indicate that this path does noŁ cross