Essentials of Computational Chemistry

470 13 HYBRID QUANTAL/CLASSICAL MODELS
180
180
6
8
20
150
150
10
15
6
8
10
15
20
120
10
15
120
10
20
90
90
8
60
8
6
60
6
15
20
20
8
30
8
30
10
15
20
10
10
10
20
15
0
0
y
y
8
6
4
8
8
20
4
−30
4
−30
8
20
15
2
2
−60
6
6
10
1
6
−60
6
8
−90
1
20
20
1
−90
10
8
2
4
10
−120
8
4
10
15
−120
−150
8
4
4
2
6
−150
30 60 90 120 150 180
−180
−180 −150 −120 −90 −60 −30 0
f
(b)
30 60 90 120 150 180
−180
−180 −150 −120 −90 −60 −30 0
f
(a)
Figure 13.4 Torsional potential energy surfaces about the two C–O bonds linking the anomeric centers of sucrose at the MM3 level (a),
2-tetrahydrofuranyl-2-tetrahydropyranyl ether at the MM3 level (b), the same ether at the HF/6-31G(d) level (c), and the sum of the difference
between the last two with the first (d). Thus, the last surface may be viewed either as the effect of the sucrose hydroxyl groups on the energy
surface, evaluated at the MM3 level, added to the framework surface calculated at the ab initio level, or as an MM3 surface that has been
partially ‘corrected’ quantum mechanically. Solid triangles represent anomeric torsions in sucrose units found in various X-ray crystal structures.
Note that the hybrid surface is the only one that clusters the large majority of these triangles within low-energy contours