chlorine or bromine (see below) and because, strictly speaking, the Schr€odinger
equation, the fundamental equation of quantum chemistry, is an approximation to a
relativistic equation, the Dirac^6 equation.
Relativity was discovered in by Einstein in 1905, when he formulated the special
theory of relativity, which deals with nonaccelerated motion in the absence of
significant gravitational fields (general relativity, published by Einstein in 1915,
is concerned with accelerated motion and gravitation). Special relativity predicted a
relationship between mass and energy, the famousE¼mc^2 equation and, of more
direct relevance to computational chemistry, showed that the mass of a particle
increases with its velocity, dramatically so near the velocity of light. In heavier
elements the inner electrons are moving at a significant fraction of the speed of
light, and the relativistic increase in their masses affects the chemistry of these
elements (actually, some physicists do not like to think in terms of rest mass
and relativistic mass, but that is a controversy that need not concern us here).
In computational chemistry relativistic effects on electrons are usually accounted
for by what are called effective core potentials or pseudopotentials (Chapter 5,
Section 5.3.3.7, and Chapter 8, Section 8.3).
4.2.4 The Nuclear Atom
The “nuclear atom” is the picture of the atom as a positive nucleus surrounded by
negative electrons. Although the idea of atoms in speculative philosophy goes back
to at least the time of Democritus,^7 the atom as the basis of a scientifically credible
theory emerges only in nineteenth century, with the rationalization by Dalton^8 in
1808 of the law of definite proportions. Nevertheless, atoms were regarded by many
scientists of the positivist school of Ernst Mach as being at best a convenient
hypothesis, despite the success of the atomistic Maxwell–Boltzmann^9 kinetic
(^6) Paul Adrien Maurice Dirac, born Bristol, England, 1902. Ph.D. Cambridge, 1926. Professor,
Cambridge, Dublin Institute for Advanced Studies, University of Miami, Florida State University.
Nobel prize in physics 1933 (shared with Schr€odinger). Known for his mathematical elegance, for
connecting relativity with quantum theory, and for predicting the existence of the positron. Died
Tallahassee, Florida, 1984.
(^7) Democritus, Greek philosopher, born Abdera, Thrace (the eastern Balkans) ca. 470BC. Died ca.
370 BC.
(^8) John Dalton, born Eaglesfield, England, 1766. Considered the founder of quantitative chemical
atomic theory: law of definite proportions, pioneered determination of atomic weights. Cofounder
of British Association for the Advancement of Science. Died Manchester, England, 1844.
(^9) Ludwig Boltzmann, born Vienna 1844. Ph.D. Vienna. Professor Graz, Vienna. Developed the
kinetic theory of gases independently of Maxwell (viz., Boltzmann constant’s,k). Firm supporter
of the atomic theory in opposition to Mach and Ostwald, helped develop concept of entropy (S).
Died Duino, Austria (now in Italy), 1906 (suicide incurred by depression). Inscribed on
gravestone: S¼k log W.
92 4 Introduction to Quantum Mechanics in Computational Chemistry