Electron Configuration Tool
- This tool generates the filling order of atomic orbitals and electron configurations of the periodic system of elements according to the Madelung and Rydberg rules.
- To use the tool, submit an atomic number (Z), symbol, or name.
- Z values must be integers between 1 and 120.
- This tool has evolved over time. As of February 27 of 2016, the tool uses an algorithm based on the tutorial A Novel Mnemonic for the Rydberg Rule (Garcia, 2016). That is, the electron configurations of elements in groups 1 and 2 are written according to the Madelung Rule, where the filling order of atomic orbitals is given by the energy levels sequence
εnl = (n - 1)p << ns < (n - 2)f < (n - 1)d < np (1)
By contrast, the electron configurations of elements in groups 3 to 18 are written according to the Rydberg Rule. This rule states that the filling order of atomic orbitals is given by
εnl = (n - 1)p << (n - 2)f < (n - 1)d < ns < np (2)
In sequences (1) and (2), n = 1, 2, 3, ... is the principal quantum number and l = 0, 1, 2, 3 ... the azimuthal quantum number, corresponding to the s, p, d, and f atomic orbitals (Goudsmit & Richards, 1964). In both sequences, < represents an energy gap and << a large energy gap (Schwarz, 2013, 2010a, 2010b; Schwarz and Rich, 2010; Wang, Qiu, Fang, and Schwarz, 2006; Wang and Schwarz, 2009). Figure 1 shows the mnemonics that summarize these rules and sequences.
(a) Madelung Mnemonic
(b) Rydberg Mnemonic
Figure 1. Mnemonics summarizing the Madelung (a) and Rydberg (b) rules. The arrows in (a) correspond to a constant (n + l) value while in (b) this value is maximized. The large energy gaps (<<) are depicted in the arrows as resembling a backbone. These energy gaps have been found responsible for the periodicity of elements (Wang & Schwarz, 2009; Restrepo & Pachón, 2007).
As explained in the tutorial, sequence (2) can be derived from sequence (1) by reordering the ns orbitals, like this
Madelung and Rydberg Rules
Figure 2. Qualitative derivation of the Rydberg Rule from the Madelung Rule. A complete explanation of this diagram is available (Garcia, 2016).
Said reordering can be used to justify the following algorithm, which is the one used by our tool.
- Because our tool processes Z values ranging from 1 to 120, we use the electron configuration of unbinilium, 120Ubn, as a reference configuration. So we assume that for a free neutral atom of Ubn in vacuum, its configuration is given by sequence (1).
- The reference configuration is stored as a $k => $v associative array where $k = nl orbitals and $v = number of electrons in $k. All electron configurations are obtained by parsing and deconstructing the reference configuration.
- Next, a Z value is obtained from the query and compared against a loop that processes configurations derived from the reference configuration. If Z belongs to an element from groups 3 to 18, we simply reorder its configuration according to sequence (2). The entire process is transparent to the end user.
- Finally, computed and experimentally determined electron configurations are compared and both results returned. For this purpose, we use the results excellently documented by Scerri (2012a, 2012b, 2013), Schwarz (2013, 2010a, 2010b), Schwarz and Rich (2010), Wang, Qiu, Fang, and Schwarz (2006), and Wang and Schwarz (2009).
- As the tool uses the most recent results (Gunther, 2015; Kramida et al., 2014; Saito, 2000; Sato et al., 2015; Siegfried, 2015; Vanquickenborne, et al., 1994; Wikipedia, 2016a, 2016b, 2016c), some results might differ from outdated chemistry resources and sites, particularly from those that incorrectly apply the Madelung Rule and its many flaws across the periodic system of elements.
- Computational chemists, researchers, teachers, and students.
- Explain the "anomalous" electron configuration of scandium (Z = 21).
- According to Scerri (2013), palladium (Z = 46) can be said to be doubly anomalous. Why?
- As stated by Schwarz and Rich (2010), it is misleading to consider the electron configurations of the ground states of free neutral atoms as the dominant configurations of bonded atoms in chemical substances. Why?
We would like to thank professors Eric Scerri and Eugen Schwarz for value added comments and feedback during the course of publishing our tool and companion tutorial article.
- Garcia, E. (2016). A Novel Mnemonic for the Rydberg Rule. Minerazzi.
- Goudsmit, S. A., & Richards, P. I. (1964). The Order Of Electron Shells In Ionized Atoms; Proceedings of the National Academy of Sciences. Vol. 51, P. 664-671.
- Gunther, M. (2015). Lawrencium experiment could shake periodic table. Chemistry World, RSC.org.
- Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team (2014). NIST Atomic Spectra Database Ionization Energies Data.
- Restrepo, G., and Pachón, L. A. (2007). Mathematical Aspects of the Periodic Law. Foundations of Chemistry, Vol 9, 2, pp 189-214.
- Saito, S. (2000). Electronic Structure of Superheavy Elements JAERI-CONF--2000-002.
- Sato, T. K., Asai, M., [...] Trautmann, N. (2015). Measurement of the first ionization potential of lawrencium, element 103. Nature, doi: 10.1038/nature14342.
- Scerri, E. (2012a). Trouble in the periodic table. Education in Chemistry. January, 2012.
- Scerri, E. (2012b). The Periodic Table: A Very Short Introduction. Paperback; Oxford University Press.
- Scerri, E. (2013). The trouble with the aufbau principle. Education in Chemistry. November, 2013
- Schwarz, W. H. E. (2013). 100th Anniversary of Bohr's Model of the Atom. Angew. Chem. Int. Ed., 52, 2-13. DOI: 10.1002/anie.201306024.
- Schwarz, W. H. E. (2010a). The Full Story of the Electron Configurations of the Transition Elements. Journal of Chemical Education Vol. 87 No. 4.
- Schwarz, W. H. E. (2010b). Relativistic Methods for Chemists: 10 (Challenges and Advances in Computational Chemistry and Physics). Chapter 1, p 56. Edited by Maria Barysz and Yasuyuki Ishikawa. Springer.
- Schwarz, W. H. E., & Rich, R. L. (2010). Theoretical Basis and Correct Explanation of the Periodic System: Review and Update. Journal of Chemical Education, Vol. 87 No. 4.
- Siegfried, T. (2015). Old periodic table could resolve today's element placement dispute. Science News. April, 2015.
- Vanquickenborne, L. G., K. Pierloot, K., & Devoghel, D. (1994). Transition Metals and the Aufbau Principle. Journal of Chemical Education, Vol. 71, p 469-471.
- Wang, S. G., Qiu, Y. X., Fang, H., & Schwarz, W. H. E. (2006). The Challenge of the So-Called Electron Configurations of the Transition Metals. Chem. Eur. J. DOI: 10.1002/chem.200500945.
- Wang, S., & Schwarz, W. H. E. (2009). Icon of Chemistry: The Periodic System of Chemical Elements in the New Century. Angew. Chem. Int. Ed. 48, 2-14.
- Wikipedia (2016a). Electron configuration.
- Wikipedia (2016b). Nickel.
- Wikipedia (2016c). Lawrencium.
Contact us for any suggestion or question regarding this tool.