Aufbau Periodic Table

Science has aptly been described as a search for order in the Universe. It follows that chemistry is a search for order in matter. While the search will always be a work in progress, great strides towards the finding of order in matter resulted in 1869 when Dimitri Mendeleev stood on the shoulders of many others and published his periodic table [1]. The table has since been modified and improved but still has a remarkable resemblance to the original Mendeleev table [2]. Excellent compilations of many alternate periodic tables have been published that use novel and intriguing approaches (e.g., circles, spirals and 3d) [3], but the contemporary versions of the Mendeleev table are the charts found on the walls of thousands of lecture rooms around the world. The periodic table deserves recognition as one of the milestones of science along with contributions from other sciences including but not limited to: physics by Newton and Einstein, biology by Darwin, Rosalind Franklin, Watson and Crick, astronomy by Copernicus and Galileo and geology by Wegener.

The periodic table arranges the 118 known elements according to increasing atomic number and lines up elements in groups with similar chemical reactivity. Today, we know that these groups have analogous outer electron configurations (valence electrons when s and p orbitals are being filled) but remarkably, electrons, protons and neutrons were not discovered until decades after Mendeleev developed his table. In addition, because the importance of protons as the determiner of the element was not discovered until 1913 by Moseley, Mendeleev ordered the elements according to the best available measured parameter which at that time was atomic mass. To his credit, he recognized that this resulted in incorrect alignment of a few of the elements such as I and Te but he prioritized reactivity over atomic mass and put them in their appropriate positions. The typical periodic table now arranged according to increasing atomic number contains the elemental symbol, the atomic number and atomic mass. From the position of the element in the chart, the atomic number and mass, it is possible to ascertain substantial information about each of the elements and to predict meaningful trends going across periods and down groups [4].

Electrons are added to the lowest available energy level of an atom according to the Aufbau Principle and generally are added using the Madelung energy ordering rule. Diagrams have been developed to illustrate the Aufbau Principle [5]. It is possible to deduce the ordering of the sublevels from the periodic table and vice versa to develop the periodic table using the Aufbau Principle. In 1930, a table that combined the concepts of the periodic table with the Aufbau Principle was published by Gardner and Mazzucchelli [6]. The concept was also used by Miguel Catalan [7] and developed further and promoted extensively by Edward Mazurs [8]. Pauling [9] and Halliday and Resnick [10] have also used this approach. Mazurs has described the aufbau-periodic table as "the best representation of the periodic system."

For the Mazurs' tables [8] and others that combined the periodic table with the Aufbau Principle, most of the designers except for Pauling [9] followed the traditional periodic table approach of starting with hydrogen at the top. To conform more to the Aufbau style, this project like Pauling's started with hydrogen at the bottom and built up from there with the energy of the sublevels increasing. (This note was added on 2/9/21 with the finding that Jodogne also used an aufbau model with both build up and build down examples between the years of 1985 and 2020 [16].) One of the original goals was to have the vertical axis represent the relative energy levels of the sublevels. This challenge could not be met as the energy levels are extremely dependent on many variables including atomic number and especially the number of electrons in a sublevel. As can be observed in the graph below [11], the first ionization energy of the elements has multifold variability. For an example, in an Aufbau diagram, the energy levels of all of the 3 p electrons are placed at the same level but the ionization energies of these elements have almost a 3-fold range. This illustrates that electron – electron interaction plays a major role in determining the energy level. It should be noted that the placement of a line on a piece of paper does not fix the energy level and the level moves up or down significantly as electrons are added to the other p orbitals. For the d and f orbitals, the range of values is less than for s and p electrons. (image from ref.[9])