What is the Moeller diagram and how does it work?

The Moeller diagram is a useful resource for both chemical engineers and students of this discipline. What it does is provide you with a visual representation of the molecular structures to know how the atoms themselves join together. This conjunction is what ends up forming a three-dimensional space.

It is true that, at first glance, it seems like a somewhat complex matter. However, it is still a fascinating topic. Thanks to this tool—which is now more than a century old— The electronic configuration of atoms is calculated in a simple and, above all, visual way. That is its biggest advantage. Below, we offer you all the data.

Moeller diagram: what it is and what it is for

The Moeller diagram is a graph that serves to calculate the electronic configuration of an atom using its atomic number (Z). If you study chemistry, this tool will help you better understand the elemental properties of substances, as well as their reactions. Also to memorize its structure in a simple way.

This resource, also known as the “rain method” or “diagonal rule”, It was created by the German physicist Erwin Madelung in 1881. To understand it, it is necessary to delve into the principle that this same scientist formulated and that we know as “Madelung’s rule.” Take note of the utilities that this pattern presents.

Determine the electronic configuration of a chemical element

A canonical book for many students and that goes in depth, both in this resource and in the different areas of this discipline, is organic chemistry (2013), by Robert Neilson Boyd and Robert T Morrison. The main advantage you will get with this rule is to establish the order in which the atomic orbitals are filled. of a chemical element.

All of this allows you, little by little, to glimpse its electronic configuration and detect the three-dimensional geometry of a molecule, as well as the arrangement of its atoms. In that way, you will better understand the chemical and physical properties of substances such as oxygen, calcium, zirconium, etc.

Thanks to this tool, the development of chemistry advanced and great technological developments were created. Likewise, among its utilities are also the following:

Predict the chemical properties of an element. Clarify the group and period of an element in the periodic table. Delve into the chemical reactions of elements based on their atomic nature.

Understand chemical bonds

If you are wondering what the Moeller diagram is useful for, one of its purposes is to understand the chemical bonds of each electronic configuration. By detecting this feature, Even the charge distribution and polarity of the molecule can be determined.

Madelung’s rule

When carrying out a Moeller pattern it is essential to understand Madelung’s rule. The Inference International Review of Science magazine delves into its significance in the field of natural sciences. What this chemical principle allows you to do is determine the order in which electrons fill the atomic orbitals in an atom or ion. Let’s see more data:

Aufbau’s rule: Madelung’s first rule states that electrons first fill the lowest energy orbitals before occupying the highest orbitals. In other words, lower energy level orbitals fill sooner.Hund’s rule: The second rule tells you that, when orbitals of the same sublevel are filled, electrons occupy each orbital with parallel spins before pairing them. This minimizes electronic repulsion and therefore the energy of the system.The sequence from which it starts: The main purpose of Madelung’s rule is that it makes it easier for you to determine the filling sequence of atomic orbitals. It does so following a very specific sequence based on the energy of the sublevels. It is as follows: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

How to carry out Moeller graphical representation?

The most decisive moment arrives. To carry out your Moeller pattern you must create a table in which the key elements that make it up appear. Although it may seem like it, it is not difficult. It has its logic. Once you understand the elements that make it up, you will be able to discover, little by little, the electronic configuration of an atom. These are the steps:

Chart Elements

Main levels: They start from the quantum number (n) in the left column of the diagram and are organized from lowest to highest in descending order.Atomic orbitals: They are always arranged according to their shape and are identified by the letters “s”, “p”, “d” and “f”.Sublevels: They refer to the numbers located on the right side of the table. Keep in mind that a level usually has, on average, several sublevels.The diagonal strokes: They are the arrows that intercept the sublevels. They start with the smallest (1s), from top to bottom and from right to left.

Basic steps for its implementation

Find the atomic number: You have to start by clarifying the element in the periodic table. The atomic number refers to the number of protons in the nucleus of an atom.Draw the Moeller pattern: Draw the graph with as many circles as there are electrons in the element. Remember that the number of electrons in an atom is equal to the atomic number.Apply Madelung’s rule: Start by putting the electrons in the lowest orbitals, according to Madelung’s rule that we have described before. Remember that this principle establishes the order in which the atomic orbitals are filled.Orbital placement: The next step is to continue placing the electrons in the following orbitals, until each and every one has been assigned.

Examples and exceptions

The Moeller diagram is applied to the vast majority of elements in the periodic table. But be careful, because there are exceptions and, an example of this, are transition metals, as well as certain elements with high atomic numbers that violate the Aufbau principle. Below, we give you an example of each of them.

Example 1: Oxygen (Z = 8)

The Moeller diagram for oxygen is as follows: 1s² 2p⁶. In this case, you can see that oxygen has 8 electrons, so the diagram would have 8 circles. The first 2 electrons are placed in the 1s orbital and the next 6 electrons are placed in the 2p orbital.

Example 2: Hydrogen (Z = 1)

The Moeller pattern for hydrogen looks like this: 1s¹. Hydrogen has 1 electron, therefore the diagram has 1 circle. The electron is placed in the 1s orbital.

Example 3: Calcium (Z = 20)

In this case, the Moeller diagram for calcium has a slightly more complex pattern: 1s² 2s² 2p⁶ 3s² 3p⁶. As you can see, calcium has 20 electrons, so the pattern would be represented with 20 circles. The first 10 electrons are placed in the 1s, 2s, and 2p orbitals. The next 10 electrons go into the 3s and 3p orbitals.

Exceptions

Chromium (Z = 24): It has an electron configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵. According to Madelung’s rule, chrome should have the following pattern: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁴. However, the actual configuration of chromium has an electron in the 4s orbital, rather than the 3d orbital.Nickel (Z = 28): Its representation would be the following: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁸. As the Madelung norm explains, its electronic organization should be 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁷. But in reality, it has 8 electrons in the 3d subshell, instead of 7 electrons.Copper (Z = 29): It is organized as follows: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d¹⁰. In this case, the same thing happens as in the previous ones. Does not fit. Its actual electronic symbolization has 10 electrons and not 9 electrons.

Moeller’s tool, an instrument of value

The Moeller graph is a useful tool for visualizing and understanding the organization of electrons in an atom. We could define it as a valuable resource for science in general and, above all, as a very pedagogical strategy in the study of chemistry.

If you are just beginning to understand it, be patient. We recommend practicing whenever you can. Engineers have been using it for decades to theoretically predict the performance of systems and facilities. It is fascinating to know that many of the instruments that are part of our daily lives were designed with this formulation.

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