Brief Introduction to Quantum Chemistry- Part 1
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.
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 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.
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, 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 to Quantum Chemistry