A Brief Introduction to Quantum Chemistry- Part 1

Quantum Mechanics arose from deficiencies in classical physical mechanics when applied to small particles, such as electrons and protons.

The first major breakthrough in Quantum Chemistry was the notion that energy was quantized or discrete. Classical mechanics had regarded energy, like all physical observables, as being continuous, and not discrete. In the late 1800’s and 1900’s, major challenges to limitations of classical mechanics were presented.

Imagine that a block of metal being heated to very, very high temperatures. While metals in the real world eventually melt, let us assume that there is object called a blackbody that can absorb and emit back energy of any frequency in a similar fashion to a metal. As most metals are heated, they slowly turn from red, to white, and then finally blue. The same effect is observed when an stove element or a roaring campfire becomes increasingly hot. As the energy used to heat it increases, the box begins to release energy of increasing frequency. The colours that we see can be approximated by the “sum” of the energy being released.

The classical mechanical interpretation yielded a result known as the Rayleigh-Jeans Law. The equation was directly proportional to the temperature, and the square of the frequency. As such, if energy of increasing frequency was used, the energy released should become more intense. The Rayleigh-Jeans approximated the intensity at lower frequencies, such as in range of visible radiation. After a certain frequency, the intensity would then decrease towards zero.

In 1900, Max Planck offered an interesting interpretation. As in classical mechanics, Planck assumed that the energy absorbed and then emitted back from the blackbody was due to the vibrations of electrons. However, Planck made the contradictory assumption that energy of the vibrations/oscillations had to be integral multiples of the frequency, and therefore quantized. Classical mechanics assumed that energy was continuous and could have any value. Planck derived an equation (Planck’s Distribution Law) that was directly proportional to a constant h (now known as Planck’s constant). The Distribution Law was found to be in strong agreement with intensity distributions, and began the notion that energy was quantized.

Photoelectric Effect

The photoelectric effect is observed when high energy light is directly towards a metal surface. If the light is sufficiently high in energy, an electron is ejected from the surface of the metal. Two results were found that were incongruent to classical mechanics.

The first was that the kinetic energy of electron was not determined by the intensity of the light hitting it. Classical mechanics viewed electromagnetic radiation as an electric field that propagated perpendicular to its direction of motion. As its intensity increases, so does the amplitude of the electric field. When the light hits the electron on the metallic surface, the electron begins to vibrate more and more, until it has enough energy to break free, and becomes ejected.

An example in the real world would be pushing people on a swing. Let’s say that a young child sitting in a swing wants to be pushed to a certain height (like the electron being ejected). The child can be pushed in two ways: either in one strong push, or a series of smaller ones. Pushing the child in one strong push is analogous to one very high energy burst of low intensity. Alternatively, one can slowly push child over a duration of time, and the child swings higher and higher each time. This is like light of very low frequency (low energy) but very high intensity.

As such, Classical Mechanics predicted that energy of any frequency should be able to eject an electron, so long as it was intense enough. However, it was experimentally discovered that there was a threshold frequency. When light of lower frequency was used, no electrons were ejected, regardless of the intensity of light used. If the frequency of light used was greater than the threshold frequency, electrons would be ejected. As well, the kinetic energy of those electrons was indirectly proportional to the frequency of light used. Not only did this result contradict Classical Mechanics, it also lead to Albert Einstein’s formulation that radiation existed in “small packets of energy” now known as photons.

Einstein found a relation that expressed the kinetic energy of the ejected electrons to be proportional to the frequency of light and h, Planck’s constant, minus a constant (for a given metal), Φ, known as the work function. The re-appearance of Planck’s constant was truly remarkable. The exact same number had appeared in two totally different experiments. Both dealt with the quantification of energy, and were in agreement with experiment results.

These two results, along with a third that Einstein found concerning molar heat capacities at constant volume, helped strengthen the concept that energy could be quantized in certain systems. This concept of quantization is fundamental for the concepts used in the Schrodinger Wave Equation.

Introduction
Introduction to Quantum Chemistry