From Quantum Mechanics to Quantum Chemistry

Abstract

The birth of quantum mechanics is rooted in the body of research that, at the end of the nineteenth century, dealt with the problem of electromagnetic radiation absorption and emission by an ideal absorbing-emitting system, the black body. The term “black body,” coined in 1860 by Gustav Kirchhoff (1824–1887), designates an ideal body able to emit and absorb all possible frequencies of the electromagnetic spectrum, without reflections. Kirchhoff’s experiments (Kirchhoff 1860) show that the radiation intensity emitted by a black body as a function of frequency depends on its temperature. In 1893, Wilhelm Wien (1864–1928) proved (Wien 1893) that the wavelength of the emission peak is a function of the inverse of the absolute temperature T (dotted curve in the figure below). In 1879, the Slovene physicist and poet Jožef Stefan (1835–1893) resumed research on black body emission. His experiments showed that the energy emitted by a black body per unit time and surface is proportional to the fourth power of the absolute temperature (Stefan 1879, 1881). His pupil, Ludwig Boltzmann, reached in 1884 the same conclusion on a purely theoretical basis, derived from thermodynamics principles. For this reason, the law that he proposed is known as the Stefan–Boltzmann law (Boltzmann 1884). In 1896, Wilhelm Wien computed the spectral density ρ(ν,T) (energy per unit of volume) emitted by a black body in the form $$ \rho (\upsilon, T) = a{\upsilon^3}{e^{{ - b\upsilon /T}}} $$ where ν is the frequency and a and b are empirical constants (Wien 1896). Wien’s law provides a relatively accurate model of the black-body emission in the visible region. However, it strongly deviates from the experimental curve in the far-infrared region. A different theoretical model, providing better agreement in the far infrared but a worse one at higher frequencies, was derived by Lord Rayleigh, based on the energy equipartition theorem (Rayleigh 1900). According to this model, the spectral energy distribution should increase with the square of the frequency, resulting in a very poor fit with experimental data in the ultraviolet region of the spectrum. This phenomenon, called “ultraviolet catastrophe,” contrasted a very rapid increase in the theoretical curve with a decrease in the experimental one, which goes to zero asymptotically (sketched curve in figure). The “ultraviolet catastrophe,” an expression coined by Paul Ehrenfest in 1911, is the direct consequence of the classical energy equipartition principle, which assigns the same average energy, KT/2, to all degrees of freedom of a physical system. The difficulties of the classical approach were also highlighted by Lord Rayleigh (1905) and by James Jeans (1905), who independently arrived in 1905 at the expression $$ \rho (\nu, T) = \frac{{2{\nu^2}KT}}{{{c^2}}} $$ confirming the absurd result obtained by Wien.