The Aufbau Principle

~ Benison Zerrudo

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Aufbau Principle. This figure includes a chart used to order the filling of electrons into atoms. At the top is a blue circle labeled “1 s.” In a row beneath this circle are 6 additional blue circles labeled “2 s” through “7 s.” A column to the right begins just right of 2 s and contains pink circles labeled 2 p through 7 p. A column to the right begins just right of 3 p and contains yellow circles labeled 3 d through 6 d. No circles are placed to the right of the 7 s and 7 p circles. A final column on the right begins right of 4 d. It includes grey circles labeled, “4 f” and, “5 f.” No circles are placed right of 6 d. Through these circles, arrows are included in the figure pointing down and to the left. The first arrow begins in the upper right and passes through 1 s. The second arrow begins just below and passes through 2 s. The third arrow passes through 2 p and 3 s. The fourth arrow passes through 3 p and 4 s. This pattern of parallel arrows pointing downward to the left continues through all circles completing the pattern 1 s 2 s 2 p 3 s 3 p 4 s 3 d 4 p 5 s 4 d 5 p 6 s 4 f 5 d 6 p 7 s 5 f 6 d 7 p.
Figure 1. This diagram depicts the energy order for atomic orbitals and is useful for deriving ground-state electron configurations. Source: OpenStax Chemistry 2e

The Aufbau Principle (OpenStax Chemistry 2e)

To determine the electron configuration for any particular atom, we can “build” the structures in the order of atomic numbers. Beginning with hydrogen, and continuing across the periods of the periodic table, we add one proton at a time to the nucleus and one electron to the proper subshell until we have described the electron configurations of all the elements. This procedure is called the Aufbau principle, from the German word Aufbau (“to build up”). Each added electron occupies the subshell of lowest energy available (in the order shown in Figure 1), subject to the limitations imposed by the allowed quantum numbers according to the Pauli exclusion principle. Electrons enter higher-energy subshells only after lower-energy subshells have been filled to capacity. Figure 1 illustrates the traditional way to remember the filling order for atomic orbitals. Since the arrangement of the periodic table is based on the electron configurations, Figure 2 provides an alternative method for determining the electron configuration. The filling order simply begins at hydrogen and includes each subshell as you proceed in increasing Z order. For example, after filling the 3p block up to Ar, we see the orbital will be 4s (K, Ca), followed by the 3d orbitals.

Aufbau Principle. In this figure, a periodic table is shown that is entitled, “Electron Configuration Table.” Beneath the table, a square for the element hydrogen is shown enlarged to provide detail. The element symbol, H, is placed in the upper left corner. In the upper right is the number of electrons, 1. The lower central portion of the element square contains the subshell, 1s. Helium and elements in groups 1 and 2 are shaded blue. In this region, the rows are labeled 1s through 7s moving down the table. Groups 3 through 12 are shaded orange, and the rows are labeled 3d through 6d moving down the table. Groups 13 through 18, except helium, are shaded pink and are labeled 2p through 6p moving down the table. The lanthanide and actinide series across the bottom of the table are shaded grey and are labeled 4f and 5f, respectively.
Figure 2. This periodic table shows the electron configuration for each subshell. By “building up” from hydrogen, this table can be used to determine the electron configuration for any atom on the periodic table. Source: OpenStax Chemistry 2e

We will now construct the ground-state electron configuration and orbital diagram for a selection of atoms in the first and second periods of the periodic table. Orbital diagrams are pictorial representations of the electron configuration, showing the individual orbitals and the pairing arrangement of electrons. We start with a single hydrogen atom (atomic number 1), which consists of one proton and one electron. Referring to Figure 1 or Figure 2, we would expect to find the electron in the 1s orbital. By convention, ms = + ½ value is usually filled first. The electron configuration and the orbital diagram are:

Following hydrogen is the noble gas helium, which has an atomic number of 2. The helium atom contains two protons and two electrons. The first electron has the same four quantum numbers as the hydrogen atom electron (n = 1, l = 0, ml = ms = + ½). The second electron also goes into the 1s orbital and fills that orbital. The second electron has the same n, l, and ml quantum numbers, but must have the opposite spin quantum number, ms = + ½. This is in accord with the Pauli exclusion principle: No two electrons in the same atom can have the same set of four quantum numbers. For orbital diagrams, this means two arrows go in each box (representing two electrons in each orbital) and the arrows must point in opposite directions (representing paired spins). The electron configuration and orbital diagram of helium are:

In this figure, the element symbol H e is followed by the electron configuration, “1 s superscript 2.” An orbital diagram is provided that consists of a single square. The square is labeled below as “1 s.” It contains a pair of half arrows: one pointing up and the other down.
The n = 1 shell is completely filled in a helium atom.
The next atom is the alkali metal lithium with an atomic number of 3. The first two electrons in lithium fill the 1s orbital and have the same sets of four quantum numbers as the two electrons in helium. The remaining electron must occupy the orbital of next lowest energy, the 2s orbital (Figure 1 or Figure 2). Thus, the electron configuration and orbital diagram of lithium are:
In this figure, the element symbol L i is followed by the electron configuration, “1 s superscript 2 2 s superscript 1.” An orbital diagram is provided that consists of two individual squares. The first square is labeled below as, “1 s.” The second square is similarly labeled, “2 s.” The first square contains a pair of half arrows: one pointing up and the other down. The second square contains a single upward pointing arrow.
An atom of the alkaline earth metal beryllium, with an atomic number of 4, contains four protons in the nucleus and four electrons surrounding the nucleus. The fourth electron fills the remaining space in the 2s orbital.
In this figure, the element symbol B e is followed by the electron configuration, “1 s superscript 2 2 s superscript 2.” An orbital diagram is provided that consists of two individual squares. The first square is labeled below as, “1 s.” The second square is similarly labeled, “2 s.” Both squares contain a pair of half arrows: one pointing up and the other down.
An atom of boron (atomic number 5) contains five electrons. The n = 1 shell is filled with two electrons and three electrons will occupy the n = 2 shell. Because any s subshell can contain only two electrons, the fifth electron must occupy the next energy level, which will be a 2p orbital. There are three degenerate 2p orbitals (ml = −1, 0, +1) and the electron can occupy any one of these p orbitals. When drawing orbital diagrams, we include empty boxes to depict any empty orbitals in the same subshell that we are filling.
In this figure, the element symbol B is followed by the electron configuration, “1 s superscript 2 2 s superscript 2 2 p superscript 1.” The orbital diagram consists of two individual squares followed by 3 connected squares in a single row. The first square is labeled below as, “1 s.” The second is similarly labeled, “2 s.” The connected squares are labeled below as, “2 p.” All squares not connected contain a pair of half arrows: one pointing up and the other down. The first square in the group of 3 contains a single upward pointing arrow.

Carbon (atomic number 6) has six electrons. Four of them fill the 1s and 2s orbitals. The remaining two electrons occupy the 2p subshell. We now have a choice of filling one of the 2p orbitals and pairing the electrons or of leaving the electrons unpaired in two different, but degenerate, p orbitals. The orbitals are filled as described by Hund’s rule: the lowest-energy configuration for an atom with electrons within a set of degenerate orbitals is that having the maximum number of unpaired electrons. Thus, the two electrons in the carbon 2p orbitals have identical n, l, and ms quantum numbers and differ in their ml quantum number (in accord with the Pauli exclusion principle). The electron configuration and orbital diagram for carbon are:

In this figure, the element symbol C is followed by the electron configuration, “1 s superscript 2 2 s superscript 2 2 p superscript 2.” The orbital diagram consists of two individual squares followed by 3 connected squares in a single row. The first blue square is labeled below as, “1 s.” The second is similarly labeled, “2 s.” The connected squares are labeled below as, “2 p.” All squares not connected to each other contain a pair of half arrows: one pointing up and the other down. The first two squares in the group of 3 each contain a single upward pointing arrow.
Nitrogen (atomic number 7) fills the 1s and 2s subshells and has one electron in each of the three 2p orbitals, in accordance with Hund’s rule. These three electrons have unpaired spins. Oxygen (atomic number 8) has a pair of electrons in any one of the 2p orbitals (the electrons have opposite spins) and a single electron in each of the other two. Fluorine (atomic number 9) has only one 2p orbital containing an unpaired electron. All of the electrons in the noble gas neon (atomic number 10) are paired, and all of the orbitals in the n = 1 and the n = 2 shells are filled. The electron configurations and orbital diagrams of these four elements are:
Aufbau Principle. This figure includes electron configurations and orbital diagrams for four elements, N, O, F, and N e. Each diagram consists of two individual squares followed by 3 connected squares in a single row. The first square is labeled below as, “1 s.” The second is similarly labeled, “2 s.” The connected squares are labeled below as, “2 p.” All squares not connected to each other contain a pair of half arrows: one pointing up and the other down. For the element N, the electron configuration is 1 s superscript 2 2 s superscript 2 2 p superscript 3. Each of the squares in the group of 3 contains a single upward pointing arrow for this element. For the element O, the electron configuration is 1 s superscript 2 2 s superscript 2 2 p superscript 4. The first square in the group of 3 contains a pair of arrows and the last two squares contain single upward pointing arrows. For the element F, the electron configuration is 1 s superscript 2 2 s superscript 2 2 p superscript 5. The first two squares in the group of 3 each contain a pair of arrows and the last square contains a single upward pointing arrow. For the element N e, the electron configuration is 1 s superscript 2 2 s superscript 2 2 p superscript 6. The squares in the group of 3 each contains a pair of arrows.

The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the 3s orbital, giving a 1s22s22p63s1 configuration. The electrons occupying the outermost shell orbital(s) (highest value of n) are called valence electrons, and those occupying the inner shell orbitals are called core electrons (Figure 3). Since the core electron shells correspond to noble gas electron configurations, we can abbreviate electron configurations by writing the noble gas that matches the core electron configuration, along with the valence electrons in a condensed format. For our sodium example, the symbol [Ne] represents core electrons, (1s22s22p6) and our abbreviated or condensed configuration is [Ne]3s1.

Aufbau Principle. This figure includes the element symbol N a, followed by the electron configuration for the element. The first part of the electron configuration, 1 s superscript 2 2 s superscript 2 2 p superscript 6, is shaded in purple and is labeled, “core electrons.” The last portion, 3 s superscript 1, is shaded orange and is labeled, “valence electron.” To the right of this configuration is the word “Abbreviation” followed by [ N e ] 3 s superscript 1.

Figure 3 A core-abbreviated electron configuration (right) replaces the core electrons with the noble gas symbol whose configuration matches the core electron configuration of the other element.

Similarly, the abbreviated configuration of lithium can be represented as [He]2s1, where [He] represents the configuration of the helium atom, which is identical to that of the filled inner shell of lithium. Writing the configurations in this way emphasizes the similarity of the configurations of lithium and sodium. Both atoms, which are in the alkali metal family, have only one electron in a valence s subshell outside a filled set of inner shells.

The alkaline earth metal magnesium (atomic number 12), with its 12 electrons in a [Ne]3s2 configuration, is analogous to its family member beryllium, [He]2s2. Both atoms have a filled s subshell outside their filled inner shells. Aluminum (atomic number 13), with 13 electrons and the electron configuration [Ne]3s23p1, is analogous to its family member boron, [He]2s22p1.

The electron configurations of silicon (14 electrons), phosphorus (15 electrons), sulfur (16 electrons), chlorine (17 electrons), and argon (18 electrons) are analogous in the electron configurations of their outer shells to their corresponding family members carbon, nitrogen, oxygen, fluorine, and neon, respectively, except that the principal quantum number of the outer shell of the heavier elements has increased by one to n = 3. Figure 4 shows the lowest energy, or ground-state, electron configuration for these elements as well as that for atoms of each of the known elements.

Aufbau Principle. A periodic table, entitled, “Electron Configuration Table” is shown. The table includes the outer electron configuration information, atomic numbers, and element symbols for all elements. A square for the element hydrogen is pulled out beneath the table to provide detail. The blue shaded square includes the atomic number in the upper left corner, which is 1; the element symbol, H, in the upper right corner; and the outer electron configuration in the lower, central portion of the square. For H, this is 1s superscript 1.

Figure 4. This version of the periodic table shows the outer-shell electron configuration of each element. Note that down each group, the configuration is often similar. Source: OpenStax Chemistry 2e

When we come to the next element in the periodic table, the alkali metal potassium (atomic number 19), we might expect that we would begin to add electrons to the 3d subshell. However, all available chemical and physical evidence indicates that potassium is like lithium and sodium, and that the next electron is not added to the 3d level but is, instead, added to the 4s level (Figure 4). As discussed previously, the 3d orbital with no radial nodes is higher in energy because it is less penetrating and more shielded from the nucleus than the 4s, which has three radial nodes. Thus, potassium has an electron configuration of [Ar]4s1. Hence, potassium corresponds to Li and Na in its valence shell configuration. The next electron is added to complete the 4s subshell and calcium has an electron configuration of [Ar]4s2. This gives calcium an outer-shell electron configuration corresponding to that of beryllium and magnesium.

Beginning with the transition metal scandium (atomic number 21), additional electrons are added successively to the 3d subshell. This subshell is filled to its capacity with 10 electrons (remember that for l = 2 [d orbitals], there are 2l + 1 = 5 values of ml, meaning that there are five d orbitals that have a combined capacity of 10 electrons). The 4p subshell fills next. Note that for three series of elements, scandium (Sc) through copper (Cu), yttrium (Y) through silver (Ag), and lutetium (Lu) through gold (Au), a total of 10 d electrons are successively added to the (n – 1) shell next to the n shell to bring that (n – 1) shell from 8 to 18 electrons. For two series, lanthanum (La) through lutetium (Lu) and actinium (Ac) through lawrencium (Lr), 14 f electrons (l = 3, 2l + 1 = 7 ml values; thus, seven orbitals with a combined capacity of 14 electrons) are successively added to the (n – 2) shell to bring that shell from 18 electrons to a total of 32 electrons.

The periodic table can be a powerful tool in predicting the electron configuration of an element. However, we do find exceptions to the order of filling of orbitals that are shown in Figure 1 or Figure 2. For instance, the electron configurations (shown in Figure 4) of the transition metals chromium (Cr; atomic number 24) and copper (Cu; atomic number 29), among others, are not those we would expect. In general, such exceptions involve subshells with very similar energy, and small effects can lead to changes in the order of filling.

In the case of Cr and Cu, we find that half-filled and completely filled subshells apparently represent conditions of preferred stability. This stability is such that an electron shifts from the 4s into the 3d orbital to gain the extra stability of a half-filled 3d subshell (in Cr) or a filled 3d subshell (in Cu). Other exceptions also occur. For example, niobium (Nb, atomic number 41) is predicted to have the electron configuration [Kr]5s24d3. Experimentally, we observe that its ground-state electron configuration is actually [Kr]5s14d4. We can rationalize this observation by saying that the electron–electron repulsions experienced by pairing the electrons in the 5s orbital are larger than the gap in energy between the 5s and 4d orbitals. There is no simple method to predict the exceptions for atoms where the magnitude of the repulsions between electrons is greater than the small differences in energy between subshells.

Related Topic: The Scientific Method of Chemistry

Source:

Flowers, P., Theopold, K., Langley, R., & Robinson, W. R. (2019, February 14). Chemistry 2e. Houston, Texas: OpenStax. Access for free at: https://openstax.org/books/chemistry-2e

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Related External Link:

The Coulomb-interaction-induced breaking of the Aufbau principle for the hole charging of InGaAs/GaAs quantum dots

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