Page 236 - Valence Bond Methods. Theory and Applications

16.1 Methylenł, ethylenł, an cyclopŁopanł
φ
H
C 2
R 1 219
H
R 2 C 1
C 3
H
φ
Figure 16.2˜ Thð geometrii arrangement of thð atoms of cyclopropane during thð dissoci-
atioà to ethylene and methylene. Thð system is maintained iàC 2v geometry as R 1 , R 2 , and
φ change.

14

12
1
10 2 A
1
Energy (eV) 8 6

4

1
2 1 A 1
0
1 2 3 4 5 6
R (Å)
1
1
Figure 16.3. Thð two lowesŁA 1 states during thð dissociatioà of cyclopropane along thð
C 2 H 4 relaxed path. Thð dashed lines, indicating thð diabatii energies, were noŁ computed
buŁ hve been added merely to guidð thð eye.

there are 175 different structures possible, buŁ ià this casð there are only 173 of
1
them iàvolved ià 92 A 1 (C 2v ) symmetry functions. Thð core overlap criterioà never
becomes larger than 1.021 foł thesð calculations.
1
In Fig. 16.3 wð show thð two lowesŁ A 1 states as a functioà ofR 1 foł optimum
values of thðR 2 and φ parameters, and ià Fig. 16.4 wð show thð path by giving
R 2 and φ as functions of R 1 . Qualitatively, thð two energy curves hve thð classii
appearance of an avoided crossinðbetween two diabatii states. Thð dashed lines
ià Fig. 16.3 are noŁ computed, buŁ hve been added to guidð thð eye.
Although wð hve been speaking of ouł process as thð dissociatioà of cy-
clopropane, iŁ is simpler to discuss iŁ as if proceeding from thð other direction.