Eric Scerri
Department of Chemistry & Biochemistry
UCLA
Los Angeles, CA 90095
website: http://ericscerri.com
The Periodic Table
and the Aufbau
One of the biggest topics in the teaching and learning of
chemistry is the use of the aufbau principle to predict the electronic
configurations of atoms and to explain the periodic table of the elements. This method has been taught to many
generations of students and is a favorite among instructors and textbooks when
it comes to setting questions. In this
blog I am going to attempt to blow the lid off the aufbau because it is deeply flawed, or at least the sloppy version of the aufbau. The flaw is rather subtle and seems to have
escaped the attention of nearly all chemistry and physics textbooks and the
vast majority of chemistry professors that I have consulted on the subject.
The error comes from what may be an innocent attempt to simplify
matters or maybe just an understandable slip as I will try to explain. Whatever the cause there is no excuse for
perpetuating this educational myth as I will try to explain.
So what’s the
problem?
The aufbau method was originally proposed by the great
Danish physicist Niels Bohr who was the first to bring quantum mechanics to the
study of atomic structure and one of the first to give a fundamental
explanation of the periodic table in terms of arrangements of electrons
(electronic configurations). Bohr
proposed that we can think of the atoms of the periodic table as being
progressively built up starting from the simplest atom of all, that of hydrogen
which contains just one proton and one electron. The other atoms differ from hydrogen by the
addition of one proton and one electron.
Helium has two protons and two electrons, lithium has three of each,
beryllium has four of each, all the way to uranium which at that time, (1913),
was the heaviest known atom, weighing in at 92 protons and 92 electrons. Neutron numbers vary and are quite irrelevant
to this story incidentally.
The next ingredient is a knowledge of the atomic orbitals
into which the electrons are progressively placed in an attempt to reproduce
the natural sequence of electrons in atoms that occur in the real world. Oddly enough these orbitals, at least in
their simplest form, nowadays come from solving the Schrödinger equation for the hydrogen
atom but let’s not get too sidetracked for the moment.
The orbitals
The different atomic orbitals come in various kinds that are
distinguished by labels such as s, p, d and f.
Each shell of electrons can be broken down into various orbitals and as
we move away from the nucleus each shell contains a progressively larger number
of kinds of orbitals. Here is the well-known
scheme,
First shell contains 1s
orbital only
Second shell contains 2s
and 2p orbitals
Third shell contains 3s, 3p and 3d orbitals
Fourth shell contains 4s, 4p, 4d and 4f orbitals and so
on.
The next part is that one needs to know how many of these
orbitals occur in each shell. The answer
is provided by the simple formula 2(l+
1) where l
takes different values depending on whether we are speaking of s, p, d or f
orbitals.
For s orbitals l
= 0, for p orbitals l = 1, for d orbitals l = 2 and so on.
As a result there are potentially one s orbital, three p
orbitals, five d orbitals, seven f orbitals and so on for each shell.
So far so good. Now
comes the magic ingredient which claims to predict the order of filling of
these orbitals and here is where the fallacy lurks. Rather than filling the shells around the
nucleus in a simple sequential sequence, where each shell must fill completely
before moving onto the next shell, we are told that the correct procedure is
more complicated. But we are also
reassured that there is a nice simple pattern that governs the order of shell
and consequently of orbitals filling.
And this is finally the point at which the aufbau diagram,
which I am going to claim lies at the heart of the trouble, is trotted out.
The order of filling is said to be obtained by starting at
the top of the diagram and following the arrows pointing downwards and towards
the left-hand margin of this diagram.
Following this procedure gives us the order of filling of orbitals with
electrons according to this sequence,
1s < 2s < 2p
< 3s < 3p < 4s < 3d < 4p < 5s < 4d …
This recipe when combined with a knowledge of how many
electrons can be accommodated in each kind of orbital and the number of such
available orbital in each shell is now supposed to give us a prediction of the
complete electronic configuration of all but about 20 atoms in which further
irregularities occur, such as the cases of chromium and copper. Again I don’t want to get side-tracked and so
will concentrate on one of the far more numerous regular configurations.
Some examples
To see how this simplified and ultimately flawed method
works let me consider a few examples.
The atom of magnesium has a total of 12 electrons. Using the method above this means that we
obtain an electronic configuration of,
1s2, 2s2,
2p6, 3s2
in beautiful agreement with experiments which can examine
the configuration directly through the spectra of atoms. Let’s look at another example, an atom of calcium
which has 20 electrons. Following the
well-known method gives a configuration of,
1s2, 2s2,
2p6, 3s2, 3p6, 4s2
and once again there is perfect agreement with experiments
on the spectrum of calcium atoms.
But now let’s see what happens for the very next atom, namely
scandium with its 21 electrons.
According to the time honored aufbau method the configuration should be,
1s2, 2s2,
2p6, 3s2, 3p6, 4s2, 3d1
and indeed it is. But
many books proceed to spoil the whole thing by claiming, not unreasonably
perhaps, that the final electron to enter the atom of scandium is a 3d electron
when in fact experiments point quite clearly to the fact that the 3d orbital is
filled before the 4s orbital.
The correct version can be found in very few textbooks but seems to have
been unwittingly forgotten or distorted in many cases by generations of
instructors and textbook authors as I mentioned at the outset. How can such an odd situation arise?
Why the mistake
occurs
But how can such an apparently blatant mistake have occurred
and taken such root in chemical education circles? The answer is as interesting as it is
subtle. First of all there is the fact
that the overall configuration is in fact correctly given by following the
sloppy approach. But if one asks
questions about the order of filling the sloppy approach gives the wrong answer
as I have been pointing out. But even
worse, it has led many teachers and textbooks to invent all kinds of contorted
schemes in order to explain why even though the 4s orbital fills preferentially
(as it does in the sloppy version) it is also the 4s electron that is
preferentially ionized to form an ion of Sc+. Since these contortions are pure inventions I
will not waste the reader’s time by looking into them. They are quite simply incorrect since as a
matter of fact, the 4s orbital fills last and consequently, as simple logic
dictates, is the first orbital to lose an electron on forming a positive
ion.
What’s the
evidence?
But how can I be so confident in claiming that the vast
majority of chemistry teachers, professors and textbook authors have erred in
presenting the sloppy version. The
answer is that one can just consider the experimental evidence on the ions of
any particular transition metal atom such as scandium,
Sc3+ (tri-positive
ion) 1s2,
2s2, 2p6, 3s2, 3p6, 3d0, 4s0
Sc2+ (di-positive
ion) 1s2, 2s2, 2p6, 3s2,
3p6, 3d1, 4s0
Sc1+ (mono-positive ion) 1s2, 2s2,
2p6, 3s2, 3p6, 3d1, 4s1
Sc (neutral atom) 1s2, 2s2, 2p6,
3s2, 3p6, 3d1, 4s2
On moving from the Sc3+ ion to that of Sc2+ it is plain to see that the additional electron
enters a 3d orbital and not a 4s orbital as the sloppy scheme dictates. Similarly on moving from this ion to the Sc1+ ion the additional
electron enters a 4s orbital as it does in finally arriving at neutral scandium
atom or Sc. Similar patterns and
sequences are observed for the subsequent atoms in the periodic table including
titatium, vanadium, chromium(with further complications), manganese and so on.
Psychological factors
I have been thinking about what psychological factors
contribute to the retention of the sloppy aufbau. As I already mentioned it does give the
correct overall configuration for all but about 20 atoms that show anomalous
configurations, such as chromium, copper, molybdenum and many others.
Another factor is that it gives chemistry professors the
impression that they really can predict the way in which the atom is built-up
starting from a bare nucleus to which electrons are successively added. Presumably it also gives students the
impression that they can make similar predictions and perhaps convinces them of
the worthiness of the aufbau and scientific knowledge in general.
The fact remains that it is not possible to predict the
configuration in any of the transition metals, and indeed the lanthanides, or
if it comes down to it even the p-block elements. Let’s go back to scandium. Contrary to the sloppy aufbau that is almost
invariably taught, the 3d orbitals have a lower energy than 4s starting with
this element. If we were to try to
predict the way that the electrons fill in scandium we might suppose that the
final three electrons after the core argon configuration of
1s2, 2s2,
2p6, 3s2, 3p6
would all enter into some 3d orbitals to give,
1s2, 2s2,
2p6, 3s2, 3p6, 3d3
The observed configuration however is,
1s2, 2s2,
2p6, 3s2, 3p6, 3d1, 4s2
What’s really
happening?
This amounts to saying that all three of the final electrons
enter 3d but two of them are repelled into an energetically less favorable
orbital, the 4s, because the overall result is more advantageous for the atom
as a whole. But this is not something
that can be predicted. Why is it 2
electrons, rather than one or even none?
In cases like chromium and copper just one electron is pushed into the
4s orbital. In an analogous case from
the second transition series, the palladium atom, the competition occurs between the 5s and 4d
orbitals. In this case none of the electrons are pushed up into the 5s orbital and the resulting configuration has an outer shell of [Kr]4d10.
None of this can be predicted in simple terms from a rule of
thumb and so it seems almost worth masking this fact by claiming that the
overall configuration can be predicted, at least as far as the cases in which
two electrons are pushed up into the relevant s orbital. To those who like to present a rather
triumphal image of science it is too much to admit that we cannot make these
predictions. The use of the sloppy
aufbau seems to avoid this problem since it gives the correct overall
configuration and hardly anybody smells a rat.
But why do electrons
get pushed up into the relevant s orbital?
Finally, it is natural to now ask why it is that one or two
electrons are usually pushed into a higher energy orbital, other than the
answer I already gave which is to say that doing so produces a more stable atom
overall. The answer lies in the fact
that 3d orbitals are more compact than 4s to consider the first transition, and
as a result any electrons entering 3d orbitals will experience greater mutual
repulsion.
The slightly unsettling feature is that although the
relevant s orbital can relieve such additional electron-electron repulsion
different atoms do not always choose to make full use of this form of
sheltering because the situation is more complicated than the way in which I
have described it. After all there is
the fact that nuclear charge increases as we move through the atoms. At the end of the day there is a complicated
set of interactions between the electrons and the nucleus as well as between
the electrons themselves. This is what
ultimately produces an electronic configuration and contrary to what some
educators would wish for, there is no simple qualitative rule of thumb that can
cope with this complicated situation.
Bottom line
There is absolutely no reason for chemistry professors and
textbook authors to continue to teach the sloppy version of the aufbau. Not only does it give false predictions
regarding the order of electron filling in atoms but it also causes authors and
instructors to tell further educational lies.
They are forced to invent some elaborate explanations in order to undo
the error in an attempt to explain why 4s is occupied preferentially (which it
is not) but also preferentially ionized which it is.
The sloppy version also implies that the 4s orbital has a
lower energy than 3d for all atoms which is not the case, or that the 5s
orbital has a lower energy than 4d which is not the case for all atoms and so
on. Similar issues arise in the f-block
elements.
It is high time that the teaching of aufbau and electronic
configurations were carried out properly in order to reflect the truth of the
matter rather than taking a short-cut and compounding it with a further
imaginary story.
References
The following references are among the few that give the
correct explanation;
S-G.
Wang, W. H. E. Schwarz, Angew. Chem. Int.
Ed. 2009, 48, 19, 3404–3415.
S. Glasstone, Textbook of Physical Chemistry, D. Van Nostrand, New York, 1946.
D.W. Oxtoby, H.P. Gillis, A. Campion,
Principles of Modern Chemistry, Sixth Edition,
Thomson/Brooks Cole, 2007.
General Reference on the Periodic Table
Eric Scerri, A Very Short Introduction to the Periodic Table, Oxford University Press, 2011
