Chapter 4
Introduction to Quantum Mechanics
in Computational Chemistry
It is by logic that we prove, but by intuition that we discover.
J.H. Poincare ́, ca. 1900AbstractA historical view demystifies the subject. The focus is strongly on
chemistry. The application of quantum mechanics (QM) to computational chemis-
try is shown by explaining the Schr€odinger equation and showing how this equation
led to the simple H€uckel method, from which the extended H€uckel method
followed. This sets the stage well for ab initio theory, inChapter 5.
QM grew out of studies of blackbody radiation and of the photoelectric effect.
Besides QM, radioactivity and relativity contributed to the transition from classical
to modern physics. The classical Rutherford nuclear atom, the Bohr atom, and the
Schr€odinger wave-mechanical atom are discussed. Hybridization, wavefunctions,
Slater determinants and other basic concepts are explained. For obtaining eigen-
vectors and eigenvalues from the secular equations the elegant and simple matrix
diagonalization method is explained and used. All the necessary mathematics is
explained.
4.1 Perspective
Chapter 1outlined the tools that computational chemists have at their disposal,
Chapter 2set the stage for the application of these tools to the exploration of
potential energy surfaces, andChapter 3introduced one of these tools, molecular
mechanics. In this chapter you will be introduced toquantum mechanics, and to
quantum chemistry, the application of quantum mechanics to chemistry. Molecular
mechanics is based on classical physics, physics beforemodernphysics; one of the
cornerstones of modern physics is quantum mechanics, and ab initio (Chapter 5),
semiempirical (Chapter 6), and density functional (Chapter 7) methods belong to
quantum chemistry. This chapter is designed to ease the way to an understanding of
E.G. Lewars,Computational Chemistry,
DOI 10.1007/978-90-481-3862-3_4,#Springer ScienceþBusiness Media B.V. 2011
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