Chemistry Reference
In-Depth Information
10.2 CHOOSING A FUNCTIONAL
The diagram in Fig. 10.1 emphasizes that density functional theory only
describes a precisely defined mathematical problem once the exchange-
correlation functional has been specified. Before choosing a functional to
use, it is crucial that you understand the similarities and differences between
the various functionals that are in common use. One useful classification of
functionals has been described by John Perdew and co-workers
1
with refer-
ence to the Biblical account of Jacob in Genesis 28, where Jacob “
...
had a
dream
...
and the angels of God were ascending and descending on it.” Jacob's
ladder, as it illustrates this categorization of functionals for DFT, is illustrated
in Fig. 10.2. Higher rungs represent functionals that include more and more
physical information as steps toward the “perfect method” in which the
Schr¨dinger equation is solved without approximation. To complete the
...
a ladder was set on the earth with its top stretching to heaven
Figure 10.2
Illustration of Perdew's classification of DFT functionals using “Jacob's ladder,”
reaching rung by rung between Earth and “Heaven.” The physical ingredients included in the
functionals from each rung are summarized on the right.
