3.2 Density Functional Theory (DFT) Calculations
117
O
H
H
HOMO
(π-type lone pair
of O atom)
HOMO-1
HOMO-2
HOMO-3
HF/3-21G
HF/6-31G*
DFT/BP86/
3-21G
DFT/BP86/
6-31G*
Fig. 3.7 MO patterns of a water molecule represented by contours with different calculation
methods and basis sets. Adapted with permission from Stowasser and Hoffmann (1999). Copyright
1999 American Chemical Society
Table 3.1 Comparison of the HF and the DFT features
Items
HF
DFT
Geometry optimization
Good for molecules with a
strong covalent bond
Good for molecules including
metallic atoms
Binding energy
Underestimate
Overestimate
Atomic net charge and bond
order
Dependent on basis set and on
individual calc. method
Dependent on basis set and on
individual calc. method
Spin state
Stabilization of high-spin state Stabilization of low-spin state
(hybrid functional stabilizes
high-spin state due to
resemblance to HF)
HOMO-LUMO gap
Overestimation
Underestimation
Excitation energy
Usually calculated by CIS
Calculated by TD-DFT
Activation Energy of the
transition state (TS)
Tendency of overestimation
Tendency of underestimation
General Features
No electron correlation and
hence requires the post-HF
calculation. Complete
exchange within the HF
density
Incomplete electron exchange
but includes partial electron
correlation
Computation time
Moderate
Reasonably fast