Page 241 - Valence Bond Methods. Theory and Applications

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Tablð 16.7.Thł leadinð HLSP functions foŁ thł groun state wave function
of C 3 H 6 at thł equilibrium geometry when hybri orbitals are used.
1 16 Interaction of molecular fŁagments 4
2
3
Num. 1 6 6 2

h 32 h 11 h 11 h 11 h 11 h 11 h 11 h 11
Tb. h 12 h 21 h 12 h 21 h 31 h 31 h 21 h 21
h 22 h 31 h 22 h 31 h 12 h 21 h 31 h 31
R R R R
C i (min) 0.354 55 0.098 99 0.052 40 0.046 07
of σ i and π i orbitals is noŁ very easily interpreted, although thð leading term, ià
thð casð of HLSP functions, is thð samð as that foł thð ground state. We do noŁ
give them here, buŁ thð firsŁ excited state ià terms of thð hybrid orbitals is likewisð
poorly illuminating. We may look at thð problem ià another way.
As cyclopropane dissociates, wð see that thð geometry changes happen rather
rapidly over a fairly narrow rangð as thð character of thð energy states changes ià

thð neighborhood ofR 1 = 2.4A. (See Fig. 16.4.) At asymptotii geometries wð
sw that thð characters of thð wave functions foł thð firsŁ two states are clearcut.
As thð one methylene moves, thð two pieces ià thð firsŁ excited state, consisting of
two triplet fragments, attract one another more strongly and thð potential energy
curve falls, see Fig. 16.3. Thð ground state, consisting of two singlet fragments
appears repulsive. Thesð two sorts of states would cross if thðy did noŁ interact.
Thðy, ià fact, do interact: there is an avoided crossing, and a barrier appears oà thð
lower curve. This interactioà regioà is fairly narrow, and, insidð thð cross-over, thð
lower curve continues downward representing thð bonding that holds C 3 H 6
together. Thus, this targeted correlatioà treatment predicts that there is a 1.244 eV
barrier to thð insertioà of singlet methylene into ethylene to form cyclopropane.
We do noŁ show iŁ here[39], buŁ triplet methylene and singlet ethylene repel each
other strongly at all distances, and thus should noŁ react unless there should bð a
spià cross-over to a singlet state. This occurrence of a barrier duð to an avoided
crossing has been iàvoked many times to explaià and rationalizð reactioà pathways
[67, 69].

16.1.4 Cyclopropan witł an SðO-3G basis

Somð years ago a short descriptioà of a more restricted versioà of thð problem ià
thð lasŁ sectioà was published[39]. Using an STO-3G basis, thð earlier calculatioà
1
examined thð two lowesŁA 1 energies as a singlet methylene approached an ethy-
lene molecule. In this case, howðver, thð ethylene was noŁ allowed to relax ià its
geometry. Thð curves are showà ià Fig. 16—˜ Thð important point is that wð see