Computational Chemistry

results in Fig. 6.9, where there were some large differences between the semiem-
pirical and HF/3-21G values, and even between AM1 and PM3. For example, for
the protonated species using the Mulliken method, AM1 and PM3 gave the oxygen
a small negative charge, ca."0.1, but the HF/3-21G method gave it a large negative
charge,"0.63; even stranger, the terminal carbon had charges of 0.09, 0.23, and
"0.25 by the AM1, PM3, and HF methods. In Fig.7.8the biggest differences
among corresponding parameters is for the electrostatic potential charges in the
protonated species, where the charges on the oxygen ("0.35 and"0.63) and on the
carbonyl carbon (0.41 and 0.76) differ by a factor of about two. With both B3LYP
and HF the terminal carbon of the enolate is counterintuitively assigned a bigger
negative electrostatic potential charge than the oxygen, as was the case for AM1
and DFT. The calculated negative charge on the formally positive oxygen of the
protonated molecule was commented on in Section 6.3.4. As with the semiempiri-
cal values, bond orders are less variable here than are the charges, but even for this

..

O–

• 0.67 B3LYP / 6-31G*


• 0.80 HF / 3-21G


• 0.48


• 0.67

1.60

1.42

1.59

1.49

Mulliken charges and bond orders

O+

H

• 0.41


• 0.63

1.38

1.18

0.26

0.45

1.24

1.15

• 0.23


• 0.25

1.64

1.59

Electrostatic potential charges and Löwdin bond orders

O+

H

• 0.35


• 0.63

1.70

1.55

0.41

0.76

1.35

1.29

• 0.004


• 0.03

1.78

1.76

O–

• 0.71 B3LYP / 6-31G*


• 0.82 HF / 3-21G

1.84

1.69

1.71

1.61

• 0.92
  –1.13

Fig. 7.8 Atom charges and bond orders calculated using B3LYP/6-31G* and HF/3-21G methods.
Note that charges and bond orders involving hydrogens have been omitted

490 7 Density Functional Calculations