ABSTRACT
We want to provide a compact reminder of the framework of molecular electronic structure theory to those turning to computational chemistry. This chapter contains an account of the fundamental assumptions of quantum mechanics, including some of the rather few exact solutions to model problems, the algebra of operators, and an illustration of the uncertainty principle. Quantum mechanics is well outside our human intuition, and we salute
those adventurous scientists who were able to see so deeply into its strange world. The adventure begins with Planck’s amazing account of the blackbody radiation spectrum based on the idea that energy is exchanged in parcels (1901) [1] and Einstein’s adoption of that principle to explain the photoelectric effect in 1905 [2]. Bohr’s daring model of the hydrogen spectrum, incorporating quantization of angular momentum (1913) [3], recaptured the numerical representation of H atom absorption and emission frequencies observed by Balmer (1885) [4]. All these advancesmade reference to the constant h that Planck hadused to fit the blackbody radiation spectrum. This constant played a role in resolving the curious duality of wave and
particle at the very small scale. Prince Louis De Broglie [5] proposed that every object with momentum had also an associated wavelength.*
l ¼ h mv
¼ h p
The De Broglie wavelength l is immeasurably small for macroscopic objects such as baseballs, ball bearings, or rifle bullets, and classical mechanics is excellent for describing these macroscopic objects. However, for subatomic particles, and in particular the electron, the De Broglie wavelength is comparable in size to chemical bonds.
