Geoscience Reference
In-Depth Information
of the system at the same time and therefore the unknown properties must be described in
terms of probability. Erwin Schrödinger used de Broglie's concepts on wave mechanics
to describe the time dependence of a physical quantum state. Schrödinger's attempt to
describe how a quantum state changes over time assumed that because all matter has wave-
like properties, then all physical quantum states could be explained using wave functions.
Initially there was much debate concerning what the wave function (
ψ
) of the equation was.
It is now generally accepted that a wave function is a probability distribution (Born inter-
pretation). The Schrödinger equation is used extensively in modern quantum mechanics to
discover the allowed energy levels of quantum mechanical systems (e.g., atoms, molecules,
and transistors). Schrödinger (
1926a
,b) is seen by many as the most significant contributor
to the wave theory of matter.
These attempts by Bohr, Heisenberg, Born, and Schrödinger to interpret experimen-
tal observations through mathematical formulations became known as the Copenhagen
interpretation.
The principles of the Copenhagen interpretation state that
•
All quantum systems can be completely described by wave functions.
•
The description of nature is probabilistic.
•
Matter has wave-particle duality and experiments can determine only if matter is behav-
ing either as a particle or as a wave.
It is not possible to know the values of all of the properties of any system at the same
•
time. Therefore, the unknown properties can be described only in terms of probability
(Heisenberg's uncertainty principle).
1.2.2 Chemical Bonding and Molecular Orbitals
The interactions between electrons and orbitals within atoms ultimately lead to chemical
bonding and the formation of molecules, and it is these interactions that are mostly respon-
sible for the absorption and light-emitting properties of molecules. Because this topic is
principally concerned with the properties of dissolved organic fluorophores, it is necessary
to focus our attention on the nature of chemical bonding and molecular orbitals. The the-
ory of covalent bonding, as proposed by Gilbert Lewis in
1916
, states that a covalent bond
involves the sharing of two electrons between two atoms. However, this theory predated
the theory of quantum mechanics, and currently there are two basic models that have been
developed to explain how electrons are shared by atoms, the valence bond (VB) theory and
molecular orbital (MO) theory (Hückel,
1930
,
1931
,
1932
; Pauling,
1931
,
1940
). Both of
these theories introduce wave functions from quantum mechanical theory. The following
sections discuss the nature of bonding albeit in a limited way. Useful underpinning reading
can be found from most modern chemistry textbooks (Atkins,
2007
; Atkins et al.,
2009
;
Brady,
2011
).
According to the Bohr theory (
1922
), all electrons in the same orbit (shell) have the
same energy. However, we now know that with the exception of electrons in the first orbit
