I was reading the Aufbau principle article on Wikipedia Aufbau principle after seeing so many student questions on Chem SE asking about writing electron configurations. Every general chemistry student is made to write electron configurations of elements (and most learn it somewhat mechanically or by rote memory) by various electron filling diagrams.

The Wiki article also talks about the exceptions of the rather famous Cu and Cr electron configurations. However, what is a rather striking part is the row labeled as "Experiment" in their Table shown below. I searched for ages to find a single experimental example of how one would determine the electron configuration of elements beyond hydrogen. Of course, Wikipedia does not write what that elusive experiment is. The author claims opper or chromium's electron configurations is not the one predicted by Madelung's rule, but the experiment says something otherwise. And such elusive experiment is nowhere to be found in any physical chemistry textbooks.

Electron configurations

To look a little deeper, I wanted to see what Madelung wrote his original rule in a book, "Die mathematischen Hilfsmittel des Physikers" 1936, pg 359. The machine translation is

15 Atomic structure (electron catalog) (to p. 301).

The eigenfunction of an atom, consisting of $Z$ electrons and $Z$ -times positively charged nucleus, can be constructed in the case of removed degeneracy in first approximation as a product of $Z$ hydrogen eigenfunctions (cf. p. 356), each of which is defined by four quantum numbers $n, l, > m, s$ defined by $n>0, n-1 \geqq l \geqq 0, s=\pm \frac{1}{2}, m ! > \leqq l$. According to the PAULI principle, no two of these functions may coincide in all four quantum numbers. According to the Bohr principle of structure, an atom with $Z$ electrons is formed from an atom with $(Z-1)$ electrons by adding another one (and increasing the nuclear charge by 1) without changing the quantum numbers of the already existing electrons. Therefore a catalog can be set up, from whose in each case $Z$ first positions the atom is built up in the basic state (cf. the table p. 360 ).

The ordering principle of this catalog is a lexicographic order according to the numbers $(n+l), n, s, m .$ A theoretical justification of just this arrangement is not yet available. One reads from it: 1 The periodic system of the elements. Two atoms are homologous, if in each case their "last electron" in the $l, m, s$ coincides. 2 The spectroscopic character of the basic term, entered in column 10 . There is namely $|\Sigma m|=0,1,2,3 \ldots$ the character $S P, D, F, G, H, I \ldots$ and $(2|\Sigma s|+1)$ the multiplicity. 3 The possibilities for excited states (possible terms), where not all $Z$ electrons are in the first $Z$ positions of the catalog.

The catalog is the representation form of an empirical rule. It idealizes the experience, because in some cases deviations are observed.

It seems Madelung just called this for electron book-keeping and he had no justification for his proposition. He calls it a lexicographic order (lexikographische Ordnung)...but still what specific experiments are we talking about that led to copper's or chromium's electron experimental configurations?


1 Answer 1


The electron configurations can be experimentally determined using spectroscopic measurements. Various spectroscopy techniques have been applied over decades. For example, an arc-lamp containing the element in question can be used to create a high-intensity beam of light containing a large number of transitions. This light can then be analyzed using, for example, a grating spectrograph. Since the advent of lasers, even more precise spectroscopy can be performed using absorption of laser light in gas cells or atomic beams.

These spectroscopic measurements yield long lists of transitions, each of which with a certain frequency and strength. Of course, these patterns do not directly tell us what electron configuration can produce them. Over decades, these data were painstakingly matched with theoretical predictions, slowly converging to an established understanding of the atomic structure.

For the case of chromium, some parts of this history can be found in the paper "Description and Analysis of the First Spectrum of Chromium, Cr I", see https://nvlpubs.nist.gov/nistpubs/jres/51/jresv51n5p247_A1b.pdf. A good starting point to find relevant data on any given atom is the NIST atomic spectra database (https://www.nist.gov/pml/atomic-spectra-database), which contains extensive lists of atomic levels as well as references to relevant experimental publications.

  • $\begingroup$ Roman, thanks but I am interested in the specific experiment(s) that allows the correct knowledge of ground state congifurations of chromium and copper opposed to what is predicted by Madelung rules etc. Mentioning "various spectoscopy techniques" and "theoretical predictions" is a little vague at this moment. Not sure if a theory exists yet that can generate chromium's atomic spectrum. I have seen NIST databases before. $\endgroup$
    – AChem
    Aug 2, 2021 at 17:08
  • $\begingroup$ I do not believe that there is such a thing. Today, from the position of already knowing the result, it might be possible to devise a set of experiments that would exclude all other possibilities and show that the ground state of a certain atom indeed has a given electron configuration. Historically, that is not what happened. The data is complex and the understanding had to be built up step by step in cooperation between experiment and theory. $\endgroup$
    – Roman
    Aug 2, 2021 at 18:30
  • $\begingroup$ Concerning "Not sure if a theory exists yet that can generate chromium's atomic spectrum." The kind of method that can spit out such results completely ab initio has only been developed in the last few years, see for example arxiv.org/pdf/2103.04473.pdf. However, theoretical descriptions that incorporate known experimental parameters to improve their (otherwise limited) precision have existed for many decades, and do indeed describe atoms like Cr very well. $\endgroup$
    – Roman
    Aug 2, 2021 at 18:51

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