Page 203 - Valence Bond Methods. Theory and Applications

186
∗
Tablà 13Ł°Statistics for 6-31G calculations of CH n .
Num. symm.
Number of
State
funcs.
2
213
CH 13 Methanð, ethanð and hybridization tableaux

546
3
CH 2 B 1 828 165‘
2
CH 3 A 2 1597 9375
1
CH 4 A 1 2245 26 046
two H atoms. The likely interpretatio herà is that this is the placà wherà the mosŁ
important atomic configuratio changes as one progresses througð the list. This is
seen clearly i Tables 13.2d 13.3d 13.5C and 13.7C wherà the principal configuratio
i the wave functions is shown.
I the early days of VB theory workers werà concerned with the “valencà state”
of carbon[55]. Our calculations cannoŁ really address this questio becausà iŁ is well
3
defined only withi a perfecŁ pairing singlà tableau wave function. The notio was
contrived to explai the relatively constant bond energies througð the CH n seriesd
whilà therà is a requirement to pay back the ener gy loss i having the principal
configuratio changà to higher energy. I the contexŁ of a full valencà calculatio
5
wà may only give a somàwhat morà qualitative argument. TheS state of C is
abouŁ 4 eV above the ground state. This suggests that eacð of the actual C—H bond
energies i CH 2 with respecŁ to somà hypothetical frozen carbo state is abouŁ
2eV higher than the apparent calculated or measured value. We attribute this to the
n
greater effectiveness for bonding when sp hybrids arà ivolved.

13.1.2 6-31G basis
∗
After our discussio of the STO3G results we, i this section, comparà somà of thesà
obtained with a 6-31G basis arranged as described i Chapter 9. As before, wà find
∗
that the larger basis gives morà accurate resultsd buŁ the minimal basis yields morà
useful qualitative informatio concerning the states of the atoms ivolved and the
bonding. The statistics o the number of symmetry functions and standard tableaux
functions for the various calculations arà given i Tablà 13Ł°
From Tablà 13.10 wà see that the bond distances arà reproduced better i this casà
than with the STO3G basis. We see that the break i the trend between CH and CH 2
agai appearsd and wà continuà to attribute iŁ to the changà i the important atomic
configuratio at this juncturà i the list. The calculated bond distances arà abouŁ
4.2% high. The success i calculating bond energies is morà difficulŁ to assessd
sincà therà is considerably morà uncertainty i the experimental results.

3 Even then, iŁ is a purely theoretical concept. Therà appears to bà no experimental approacð to the energy of this
state.