Box and Arrow Orbital Configurations using

Pauli Exclusion Principle and Hund's Rule

There is yet another way to writing electron configurations. It is called the "Box and Arrow" (or circle and X) orbital configuration.

Sublevels can be broken down into regions called "orbitals". An orbital is defined as the most probable location for finding an electron. Each orbital holds 2 electrons.

This sublevel configuration can be broken down into orbitals (boxes).

1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 .

Video below on how the sublevels build.

There are a few rules for the box and arrow configurations.

Aufbau Principle - electrons fill orbitals starting at the lowest available energy state before filling higher states (1s before 2s).

Pauli Exclusion Principle

An orbital can hold 0, 1, or 2 electrons only, and if there are two electrons in the orbital, they must have opposite (paired) spins.

When we draw electrons, we use up and down arrows. So, if an electron is paired up in a box, one arrow is up and the second must be down.

(Therefore, no two electrons in the same atom can have the same set of four Quantum Numbers . )

incorrect; electrons must spin in opposite directions

correct; the electrons have opposite spins

When filling sublevels other than s, electrons are placed in individual orbitals before they are paired up.

Electrons fill like people do on a bus. You would never sit right next to someone you did not know if there are free seats available, unless of course all the seats are taken then you must pair up.

So when working with the p sublevel, electrons fill like this. up, up, up. down, down, down. take a look

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Hund's Rules

The Aufbau section discussed how that electrons fill the lowest energy orbitals first, and then move up to higher energy orbitals only after the lower energy orbitals are full. However, there a problem with this rule. Certainly, 1s orbitals should be filled before 2s orbitals, because the 1s orbitals have a lower value of n, and thus a lower energy. What about the three different 2p orbitals? In what order should they be filled? The answer to this question involves Hund's rule.

Hund's rule states that:

Every orbital in a sublevel is singly occupied before any orbital is doubly occupied.
All of the electrons in singly occupied orbitals have the same spin (to maximize total spin).

When assigning electrons to orbitals, an electron first seeks to fill all the orbitals with similar energy (also referred to as degenerate orbitals) before pairing with another electron in a half-filled orbital. Atoms at ground states tend to have as many unpaired electrons as possible. In visualizing this process, consider how electrons exhibit the same behavior as the same poles on a magnet would if they came into contact; as the negatively charged electrons fill orbitals, they first try to get as far as possible from each other before having to pair up.

Example \(\PageIndex<1>\): Nitrogen Atoms

Consider the correct electron configuration of the nitrogen (Z = 7) atom: 1s 2 2s 2 2p 3

The p orbitals are half-filled; there are three electrons and three p orbitals. This is because the three electrons in the 2p subshell will fill all the empty orbitals first before pairing with electrons in them.

Keep in mind that elemental nitrogen is found in nature typically as dinitrogen, N₂, which requires molecular orbitals instead of atomic orbitals as demonstrated above.

Example \(\PageIndex<2>\): Oxygen Atoms

Next, consider oxygen (Z = 8) atom, the element after nitrogen in the same period; its electron configuration is: 1s 2 2s 2 2p 4

Oxygen has one more electron than nitrogen; as the orbitals are all half-filled, the new electron must pair up. Keep in mind that elemental oxygen is found in nature typically as dioxygen, \(O_2\), which has molecular orbitals instead of atomic orbitals as demonstrated above.

Hund's Rule Explained

According to the first rule, electrons always enter an empty orbital before they pair up. Electrons are negatively charged and, as a result, they repel each other. Electrons tend to minimize repulsion by occupying their own orbitals, rather than sharing an orbital with another electron. Furthermore, quantum-mechanical calculations have shown that the electrons in singly occupied orbitals are less effectively screened or shielded from the nucleus. Electron shielding is further discussed in the next section.

For the second rule, unpaired electrons in singly occupied orbitals have the same spins. Technically speaking, the first electron in a sublevel could be either "spin-up" or "spin-down." Once the spin of the first electron in a sublevel is chosen, however, the spins of all of the other electrons in that sublevel depend on that first spin. To avoid confusion, scientists typically draw the first electron, and any other unpaired electron, in an orbital as "spin-up."

Example \(\PageIndex<3>\): Carbon and Oxygen

Consider the electron configuration for carbon atoms: 1s 2 2s 2 2p 2 : The two 2s electrons will occupy the same orbital, whereas the two 2p electrons will be in different orbital (and aligned the same direction) in accordance with Hund's rule.

Consider also the electron configuration of oxygen. Oxygen has 8 electrons. The electron configuration can be written as 1s 2 2s 2 2p 4 . To draw the orbital diagram, begin with the following observations: the first two electrons will pair up in the 1s orbital; the next two electrons will pair up in the 2s orbital. That leaves 4 electrons, which must be placed in the 2p orbitals. According to Hund’s rule, all orbitals will be singly occupied before any is doubly occupied. Therefore, two p orbital get one electron and one will have two electrons. Hund's rule also stipulates that all of the unpaired electrons must have the same spin. In keeping with convention, the unpaired electrons are drawn as "spin-up", which gives (Figure 1).

Purpose of Electron Configurations

When atoms come into contact with one another, it is the outermost electrons of these atoms, or valence shell, that will interact first. An atom is least stable (and therefore most reactive) when its valence shell is not full. The valence electrons are largely responsible for an element's chemical behavior. Elements that have the same number of valence electrons often have similar chemical properties.

Electron configurations can also predict stability. An atom is most stable (and therefore unreactive) when all its orbitals are full. The most stable configurations are the ones that have full energy levels. These configurations occur in the noble gases. The noble gases are very stable elements that do not react easily with any other elements. Electron configurations can assist in making predictions about the ways in which certain elements will react, and the chemical compounds or molecules that different elements will form.

Hund's Rules

1. The term with maximum multiplicity lies lowest in energy

Note: Some references, such as Haken & Wolf, use Hund's Rule #1 to apply to the nature of full shells and subshells. Full shells and subshells contribute nothing to the total angular momenta L and S. If you call this Hund'e Rule #1, then the above rules will be bumped up one in number. I don't know which is the more common practice.

Hund's Rule #1

The term with the maximum multiplicity lies lowest in energy.

These sketches are conceptual only. No attempt has been made to do any realistic scaling.

Note that the energies we are discussing here are electric potential energies, so that a negative electron in the vicinity of a positive nucleus will have a negative energy leading to a bound state. Any force between the electrons will tend to counter that, contributing a positive potential energy which makes the electrons less tightly bound, or higher in potential energy.

Hund's Rule #2

For a given multiplicity, the term with the largest value of L lies lowest in energy.

The basis for this rule is essentially that if the electrons are orbiting in the same direction (and so have a large total angular momentum) they meet less often than when they orbit in opposite directions. Hence their repulsion is less on average when L is large.

These influences on the atomic electron energy levels is sometimes called the orbit-orbit interaction. The origin of the energy difference lies with differences in the coulomb repulsive energies between the electrons.

For large L value, some or all of the electrons are orbiting in the same direction. That implies that they can stay a larger distance apart on the average since they could conceivably always be on the opposite side of the nucleus. For low L value, some electrons must orbit in the opposite direction and therefore pass close to each other once per orbit, leading to a smaller average separation of electrons and therefore a higher energy.

Hund's Rule #3

For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy.

When the shell is more than half full, the opposite rule holds (highest J lies lowest). The basis for the rule is the spin-orbit coupling. The scalar product S·L is negative if the spin and orbital angular momentum are in opposite directions. Since the coefficient of S·L is positive, lower J is lower in energy.

Exceptions to Hund's Rules

Hund's rules presume L-S coupling and presume that the electrons can be considered to be in a unique configuration. Neither is always true. For heavier elements, the "j-j coupling" scheme often gives better agreement with experiment.

Hund's Rule

Definition - What does Hund's Rule mean?

Hund's rule states that a larger total spin state of an atom sometimes makes the atom more stable.

According to Hund's rule:

Each orbital in a sublevel is separately occupied before any orbital is doubly occupied.
All of the electrons in separately occupied orbitals have an equivalent spin (to maximize total spin).

This rule is fairly reliable (with occasional failures) for the determination of the state of a given excited electronic configuration.

Hund's rule is also known as the rule of maximum multiplicity.

Corrosionpedia explains Hund's Rule

According to Hund's rule, electrons are placed into separate orbitals before going into an orbital this is already occupied. This can help predict the properties of atoms, as paired and unmated electrons have distinct properties (specifically with interactions with magnetic fields).

Since electrons are negatively charged, they repel each other. Electrons tend to attenuate repulsion by occupying their own orbitals, instead of sharing an orbital with another electron. For the second rule, unmated electrons in separately occupied orbitals have an equivalent spins. The primary electron in a sublevel could be either "spin-up" or "spin-down."

When atoms come into contact with each other, the outer electrons of those atoms, or valence shell, initially interact. An associate atom is least stable (and therefore most reactive) when its valence shell is not full. The valence electrons are most responsible for an associate element's chemical behavior. Parts that have an equivalent range of valence electrons typically have similar chemical properties.

An associate atom is most stable (and therefore unreactive) once all its orbitals are full of electrons. These configurations are found in the noble gases, which are extremely stable and do not normally react with each other.

Hunds rule?

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When electrons are put into orbitals having the same energy, degenerate orbitals, one electron is put into each orbital before putting a second electron into an orbital.

The term with maximum multiplicity (maximum ) has the highest energy level.

For a given multiplicity, the term with the largest value of has the lowest energy in an orbital.

For atoms with less than half-filled shells, the level with the lowest value of lies lowest in energy. Otherwise, if the outermost shell is more than half-filled, the term with highest value of is the one with the lowest energy.

The rules deal in a simple way how the usual energy interactions dictate the ground state term. The rules assume that the repulsion between the outer electrons is very much greater than the spin-orbit interaction which is in turn stronger than any other remaining interactions. This is referred to as the LS coupling regime.

It can be shown that for full orbitals and suborbitals both the residual electrostatic term (repulsion between protons) and the spin-orbit interaction cannot shift all the energy levels together. Thus when determining the ordering of energy levels in general only the inner valence electrons need to be considered.

Due to the Pauli exclusion principle, six electrons cannot share the same set of quantum numbers within the same system. Therefore, there is room for only two electrons in each spatial orbital. One of these electrons must have (for some chosen direction z), , and the other must have . Hund's second rule states that the lowest energy atomic state is the one which maximizes the sum of the values for all of the electrons in the system, maximizing the number of unpaired electrons.

This rule deals again with reducing the repulsion between electrons. It can be understood from the classical picture that if all electrons are orbiting in the same direction (higher orbital angular momentum) they meet less often than if some of them orbit in opposite directions. In that last case the repulsive force increases, which separates electrons. This adds potential energy to them, so their energy level is higher.

This rule considers the energy shifts due to split-orbit coupling. In the case where the spin-orbit coupling is weak compared to the residual electrostatic, where and are still good quantum numbers the splitting is given by:

Hund's rules applied to Si. The up arrows signify electrons with up-spin. The boxes represent different magnetic quantum numbersAs an example, consider the ground state of silicon. The electronic configuration of Si is . Applying the first rule, only the outer electrons need be considered. The possible multiplets are ; of those, and are not allowed because of the exclusion principle. The second rule now states that the triplet state with has the lowest energy. There is no choice of triplets states, so the first rule is not required. [If the state were allowed, then the third rule would come into force and state that it was more favourable than the state.] The triplet consists of three states, . With only two of six possible electrons in the shell, it is less than half-full and thus is the excited state

For atoms with less than half-filled shells, the level with the lowest value of J lies lowest in energy.

When the shell is more than half full, the opposite rule holds (highest J lies lowest). The basis for the rule is the spin-orbit coupling. The scalar product S·L is negative if the spin and orbital angular momentum are in opposite directions. Since the coefficient of S·L is positive, lower J is lower in energy.

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Atomic Structures: Pauli Exclusion Principle, Aufbau Principle & Hund's Rule

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0:00 Review of Quantum Numbers
3:15 Pauli Exclusion Principle
4:22 Hund's Rule
4:46 Aufbau Principle
6:30 Lesson Summary

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Amy has taught university-level earth science courses and has a PhD in Geology.

Review of Quantum Numbers

At this point in studying chemistry, when you visualize an atom, you likely think of a nice orderly structure with a nucleus of positively charged protons and neutral neutrons that are orbited by rings of electrons, much like the structure of the solar system with planets orbiting the sun. This model of an atom follows the Bohr model, which has a positively charged nucleus of protons and neutrons surrounded by fixed rings of electrons called shells.

We can think of atomic structure like a hotel. Just like there are a fixed number of rooms where guests may stay, there are fixed locations where we are likely to find electrons. These fixed locations are called orbitals and their location is defined by their quantum number. Quantum numbers allow us to define the location of an electron within the atomic structure. Much like a hotel room, the orbitals are located at different floors, or levels, of the structure, and can even be described by the shape of the wing in which they are located.

In this model, the shells correspond to energy levels in the atomic structure, with the shells closer to the nucleus having the lowest energy level. This energy level is also defined as the first quantum number, n. So, an electron in the first shell would have a first quantum number (or n) of one. If it was in the second shell, it would have a quantum number of two, and so on. If you think of our hotel analogy, the levels towards the bottom take the least amount of energy to get to, and thus these levels have the lowest energy.

Within each shell, we find subshells that have different shapes depending on their energy level and thus can fit a different number of electrons. They are named after the letters s, p, d, f and so on. These subshells are the second quantum number and are numerically defined as follow:

letter = level (l)

The first shell has just the s subshell. The second has s and p. The third has s, p, and d. The higher the first quantum number or the shell, the more subshells and thus electrons can fit into that structure.

The third quantum number, m sub l, specifies the orientation of a specific orbital at a given n and s. This quantum number allows us to break up each subshell into individual orbitals of two electrons each. We can calculate the number of orbitals by the equation 2l + 1. Thus, according to this equation, the s shell would have 1 orbital with 2 electrons. The p shell would have 3 orbitals with 6 electrons. The d shell would have 5 orbitals with 10 electrons. The f would have 7 orbitals with 14 electrons.

Pauli Exclusion Principle

So, according to these rules, if we look at the first shell, it only contains two electrons in the first subshell. The quantum number can be described as 1s^2. However, another rule is that two electrons cannot have identical quantum numbers. So, if two electrons have to fit inside one s subshell, how will this work?

This matter directly relates to the Pauli Exclusion Principle, which states that two electrons cannot exist in the same location and thus electrons in the same orbital must have opposing spins. Hydrogen only has one electron in the 1s orbital and has a quantum number of 1s^1. Helium has two electrons in this field, so they must have opposing spins, and it has a quantum number of 1s^2.

This spin factor is the fourth quantum number, m, and is described as either +1/2 for a spin 'up' or -1/2 for a spin 'down.'

Hund's Rule

So now that we've reviewed the orbital structure, let's dive in to how the electrons fill these orbitals. Because electrons are both negatively charged, there is a certain amount of repulsion that prevents them from wanting to fill the same space. So, according to Hund's Rule, electrons will fall into empty orbitals of the same energy before electrons begin to pair up into the same orbital.

Aufbau Principle

Closely related to Hund's Rule is the Aufbau Principle, which states that electrons will fill the lower energy levels before moving to higher energy orbitals. Remember that each orbital has two electrons and the number of orbitals at an energy level depends on the first two quantum numbers.

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Let's combine Hund's Rule and the Aufbau Principle by looking at the electron configuration for two very common elements. Nitrogen has an atomic number of 7 and thus has 7 protons and electrons. Next to it on the periodic table is oxygen with an atomic number of 8 and thus 8 protons and electrons. The s subshells are lower energy in the first and second shells and thus fill first. The p subshell is filled with one electron each in nitrogen; however, since oxygen has four electrons that go into this subshell, only when the three orbitals already have one electron does it completely fill an orbital.

In general, the energy levels of the orbitals increase with the first and second quantum numbers, which are the shell and the subshell. However, as you start getting to higher energies, this relationship gets more complicated because the s subshells of higher levels may have lower energy than the d and f subshells of lower levels. The lines on this diagram show the direction of increasing energy:

You will notice that the 4s subshell has lower energy than the 3d subshell. You do not have to memorize these relationships, but just remember that when you start getting to the higher energy levels, consult this chart to help you determine the quantum number.

Lesson Summary

In summary, Hund's Rule, the Aufbau Principle, and the Pauli Exclusion Principle help us define how electrons fill the orbitals within an atomic structure. This helps us predict the location of electrons in an atom as we increase the number of electrons. The Pauli Exclusion Principle states that no two electrons can have the same quantum number, and thus, electrons in the same orbital must have opposite spins. Remember the quantum number is the numerical description of the likely location of the electron, so you can think of it as the electron's address.

The Aufbau Principle states that electrons fill orbitals of lower energy first before moving to higher energy orbitals. So you must fill all of the orbital spaces in the 2s orbital before moving on to the 2p orbitals.

Finally, Hund's Rule says that because of the repulsion between the two negatively charged electrons, a newly added electron will go into an empty orbital of the same energy before going into an orbital that already has an electron present. These rules help us predict how the orbital spaces will be filled by elements on the periodic table as we move to larger elements with more electrons.

Learning Outcomes

Following this lesson, you'll have the ability to:

Define electron shells, orbitals and quantum numbers
Recall what the Bohr model is
Describe the Pauli Exclusion Principle, Hund's Rule and the Aufbau Principle
Explain how the three concepts above can be used to predict how orbital spaces will be filled with electrons

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Hund s

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der Große/Kleine Hund (Astron) Great(er)/Little or Lesser Dog

junger Hund puppy, pup

die Familie der Hunde the dog or canine family

Hunde, die (viel) bellen, beißen nicht (Prov) empty vessels make most noise (Prov)

getroffene Hunde bellen inf if the cap fits, wear it

viele Hunde sind des Hasen Tod (Prov) there is not much one person can do against many

wie Hund und Katze leben to live like cat and dog, to lead a cat-and-dog life

ich würde bei diesem Wetter keinen Hund auf die Straße jagen I wouldn't send a dog out in this weather

damit kann man keinen Hund hinterm Ofen hervorlocken inf that's not going to tempt anybody

müde wie ein Hund sein inf to be dog-tired

er ist bekannt wie ein bunter Hund inf everybody knows him

kein Hund nimmt ein Stück Brot von ihm everyone avoids him like the plague

das ist (ja) zum Junge-Hunde-Kriegen inf it's enough to give you kittens

da wird der Hund in der Pfanne verrückt inf it's enough to drive you crazy inf or round the twist (Brit) inf

da liegt der Hund begraben inf (so) that's what is/was behind it all , (Haken, Problem etc) that's the problem

er ist mit allen Hunden gehetzt inf he knows all the tricks, there are no flies on him (Brit) inf

er ist ein armer Hund he's a poor soul or devil inf

er ist völlig auf dem Hund inf he's really gone to the dogs inf

auf den Hund kommen inf to go to the dogs inf

jdn auf den Hund bringen inf to ruin sb , (gesundheitlich) to ruin sb's health

die Weiber haben/der Suff hat ihn auf den Hund gebracht inf women have/drink has been his ruin or downfall

vor die Hunde gehen inf to go to the dogs inf (=sterben) to die, to perish (=getötet werden) to cop it (Brit) inf , to be killed

du blöder Hund inf you silly or stupid bastard sl

du gemeiner Hund inf you rotten bastard sl

du schlauer or gerissener Hund inf you sly or crafty devil or old fox

schlafende Hunde soll man nicht wecken (prov) let sleeping dogs lie (Prov)

Results found in: English-German

you rat! exp. du Hund!
sly dog exp. gerissener Hund
dirty dog exp. gemeiner Hund
to give a dog a scratch exp. einen Hund kratzen
a poor blighter exp. ein armer Hund

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