Computational Chemistry

equation was published, Heisenberg^17 published his matrix mechanics approach to
calculating atomic (and in principle molecular) properties. The matrix approach is
at bottom equivalent to Schr€odinger’s use of differential equations, but the latter has
appealed to chemists more because, like physicists of the time, they were unfamiliar
with matrices (Section 4.3.3), and because the wave approach lends itself to a
physical picture of atoms and molecules while manipulating matrices perhaps tends
to resemble numerology. Matrix mechanics and wave mechanics are usually said to
mark the birth of quantummechanics(1925, 1926), as distinct from quantum theory
(1900). We can think of quantum mechanics as the rules and equations used to
calculate the properties of molecules, atoms, and subatomic particles.
Wave mechanics grew from the work of de Broglie,^18 who in 1923 was led to
this “wave-particle duality” by his ability to deduce the Wien blackbody equation
(Section 4.2.1) by treating light as a collection of particles (“light quanta”) analo-
gous to an ideal gas [ 14 ]. This suggested to de Broglie that light (traditionally
considered a wave motion) and the atoms of an ideal gas were actually not
fundamentally different. He derived a relationship between the wavelength of
a particle and its momentum, by using the time-dilation principle of special
relativity, and also from an analogy between optics and mechanics. The reasoning
below, while perhaps less profound than de Broglie’s, may be more accessible.
From the special theory of relativity, the relation between the energy of a photon
and its mass is

Ep¼mc^2 '(4:15)

where c is the velocity of light. From the Planck equation4.3for the emission and
absorption of radiation, the energyEpof a photon may be equated with the energy
changeDEof an oscillator, and we may write

Ep¼hn '(4:16)

From Eqs.4.15and4.16

mc^2 ¼hn (4.17)

Sincen¼c/l, Eq.4.17can be written

mc¼h=l (4.18)

(^17) Werner Heisenberg, born W€urzburg, Germany, 1901. Ph.D. Munich, 1923. Professor, Leipzig
University, Max Planck Institute. Nobel Prize 1932 for his famous uncertainty principle of 1927.
Director of the German atomic bomb/reactor project 1939–1945. Held various scientific adminis-
trative positions in postwar (Western) Germany 1945–1970. Died Munich 1976.
(^18) Louis de Broglie, born Dieppe, 1892. Ph.D. University of Paris. Professor Sorbonne, Institut
Henri Poincare ́(Paris). Nobel Prize in physics 1929. Died Paris, 1987.
98 4 Introduction to Quantum Mechanics in Computational Chemistry