Chemistry Reference
In-Depth Information
DFT CALCULATIONS OF
VIBRATIONAL FREQUENCIES
In the previous chapters, you have learned how to use DFT calculations to
optimize the structures of molecules, bulk solids, and surfaces. In many
ways these calculations are very satisfying since they can predict the properties
of a wide variety of interesting materials. But everything you have seen so far
also substantiates a common criticism that is directed toward DFT calcu-
lations: namely that it is a
zero temperature
approach. What is meant by this
is that the calculations tell us about the properties of a material in which the
atoms are localized at “equilibrium” or “minimum energy” positions. In clas-
sical mechanics, this corresponds to a description of a material at 0 K.
The
implication of this criticism is that it may be interesting to know about how
materials would appear at 0 K, but real life happens at finite temperatures.
Much of the following chapters aim to show you how DFT calculations can
give useful information about materials at nonzero temperatures. As a starting
point, imagine a material that is cooled to 0 K. In the context of classical mech-
anics, the atoms in the material will relax to minimize the energy of the
material. We will refer to the coordinates of the atoms in this state as the
equilibrium positions. One of the simplest things that happens (again from
This is true in classical mechanics, but in quantum mechanics it is more accurate to say that
atoms are localized around their energy minima. We return to this idea in Section 5.4 when
we discuss zero point energies.
