Computational Chemistry

the role of quantum mechanics in computational chemistry. The wordquantum
comes from Latin (quantus, “how much?”, pluralquanta) and was first used in our
sense by Max Planck in 1900, as an adjective and noun, to denote the constrained
quantitiesor amounts in which in which energy can be emitted or absorbed.
Although the termquantum mechanicswas apparently first used by Born (of the
Born–Oppenheimer approximation, Section 2.3) in 1924, in contrast to classical
mechanics, the matrix algebra and differential equation techniques that we now
associate with the term were presented in 1925 and 1926 (Section4.2.6).
“Mechanics” as used in physics is traditionally the study of the behavior of
bodies under the action of forces like, e.g., gravity (celestial mechanics). Molecules
are made of nuclei and electrons, and quantum chemistry deals, fundamentally,
with the motion of electrons under the influence of the electromagnetic force
exerted by nuclear charges. An understanding of the behavior of electrons in
molecules, and thus of the structures and reactions of molecules, rests on quantum
mechanics and in particular on that adornment of quantum chemistry, the Schr€odinger
equation. For that reason we will consider in outline the development of quantum
mechanics leading up to the Schr€odinger equation, and then the birth of quantum
chemistry with (at least as far as molecules of reasonable size goes) the application
of the Schr€odinger equation to chemistry by H€uckel. Thissimple Huckel method€ is
currently disdained by some theoreticians, but its discussion here is justified by the
fact that (1) it continues to be useful in research and (2) it “is immensely useful as a
model, today...Because it is the model which preserves the ultimate physics, that
of nodes in wave functions. It is the model which throws away absolutely every-
thing except the last bit, the only thing that if thrown away would leave nothing. So
it provides fundamental understanding.”^1 A discussion of a generalization of the
simple H€uckel method, the extended H€uckel method, sets the stage forChapter 5.
The historical approach used here, although perforce somewhat superficial, may
help to ameliorate the apparent arbitrariness of certain features of quantum chemis-
try [ 1 , 2 ]. An excellent introduction to quantum chemistry is the text by Levine [ 3 ].
Our survey of the factors that led to modern physics and quantum chemistry will
follow the sequence:

1. The origins of quantum theory: blackbody radiation and the photoelectric effect


2. Radioactivity (brief)


3. Relativity (very brief)


4. The nuclear atom


5. The Bohr atom


6. The wave mechanical atom and the Schr€odinger equation

(^1) Personal communication from Professor Roald Hoffmann, 2002 February 13. See too
Section 4.4.1, footnote.
86 4 Introduction to Quantum Mechanics in Computational Chemistry