10. Appendix

Two Pseudopotential Methods: Empirical and Ab Initio 559
The EPM stimulated interactions between theorists and experimentalists
and the result was one of the most active collaborations in physics. Not only
were optical and photoemission spectra of solids deciphered, the activities resulted
in new experimental techniques and a much deeper understanding of
the behavior of electrons in solids. The meeting ground between experiment
and theory is usually response functions such as dielectric functions or reflectivity.
In the early phases of this work the actual energy band structures, which
are plots of energy versus wavevector, were the domain of theorists. However,
the introduction of angular resolved photoemission spectroscopy (ARPES)
gave energy bands directly and provided further tests of the EPM.
The EPM band structures obtained in the 1960s and 1970s are still used today.
In addition, the EPM produced the first plots of electronic charge density
for crystals. These plots displayed covalent and ionic bonds and hence gave
considerable structural information. Optical constants, densities of states, and
many other crystal properties were obtained with great precision using EPMderived
energy levels and wavefunctions.
Despite the success of the EPM, there was still considerable motivation to
move to a first-principles or ab initio model. The approach chosen was similar
to Fermi’s. Instead of an EPM potential, the interaction of the valence
electron with the core was described using an ab initio pseudopotential constructed
from a knowledge of atomic wavefunctions. The valence electron–
electron interactions were modeled using a density functional theory which,
with approximations, allows the development of an electron–electron potential
using the electronic charge density. However, the latter approach is appropriate
only for calculating ground-state properties. Excited states such as those
needed to interpret atomic spectra require adjustments to this theory. These
adjustments are complex and require significant computer time compared to
the EPM, but they are successful in reproducing the experimental data and
the approach is completely ab initio.
One of the most important applications of the ab initio pseudopotential
model was the determination of structural properties. It became possible to
explain pressure-induced solid–solid structural transitions and even to predict
new structural phases of solids at high pressure using only atomic numbers
and atomic masses. Bulk moduli, electron–phonon coupling constants, phonon
spectra, and a host of solid-state properties were calculated. The results allowed
microscopic explanations of properties and predictions. An example was
the successful prediction that semiconducting silicon would become a superconducting
hexagonal metal at high pressure.
The two types of pseudopotential approaches, empirical and ab initio, have
played a central role in our conceptual picture of many materials. Often the
resulting model is referred to as the “standard model” of solids. Unlike the
standard model of particle physics, which is sometimes called a theory of everything,
the standard model of solids is most appropriate for those solids with
reasonably itinerant electrons. Despite this restriction, the model is extremely
useful and a triumph of quantum theory.