The Aufbau Principle

Note the distinction between a transition and J-block element. Elements in groups 3-12 inclusive are collectively called J-block elements, but by the lUPAC rulings, a transition metal is an element, an atom of which possesses an incomplete fi -shell or which gives rise to a cation with an incomplete fi -shell. Thus, elements in group 12 are not classed as transition elements. Collective names for some of the groups of elements in the periodic table are given in Table 1.4. 

Similarly, we can write the electron configuration of beryllium as l/2s and represent it with the orbital diagram 

With both the I5 and the 2s orbitals filled to capacity, the next electron, which is needed for the electron configuration of boron, must reside in the 2p subshell. Because all three 2p oibitals are of equal energy, or degenerate, the electron can occupy any one of them. By convention, we nsually show the first electron to occupy the p subshell in the first empty box in the oibital diagram 

Electrons are placed in orbitals to give the lowest total electronic energy to the atom. This means that the lowest values of n and / are filled first. Because the orbitals within each subshell (p, d, etc.) have the same energy, the orders for values of wi and nis are indeterminate. 

The Pauli exclusion principle requires that each electron in an atom have a unique set of quantum numbers. At least one quantum number must be different from those of every other electron. This principle does not come from the Schrddinger equation, but from experimental determination of electronic structures. 

Hund s rule is a consequence of the energy required for pairing electrons in the same orbital. When two negatively charged electrons occupy the same region of space (same orbital) in an atom, they repel each other, with a Coulombic energy of repulsion, II per pair of electrons. As a result, this repulsive force favors electrons in different orbitals (different regions of space) over electrons in the same orbitals. 

In addition, there is an exchange energy, Og, which arises from purely quantum mechanical considerations. This energy depends on the number of possible exchanges between two electrons with the same energy and the same spin. For example, the electron configuration of a carbon atom is Is 2s 2p. The 2p electrons can be placed in thep orbitals in three ways  

Each of these corresponds to a state having a particular energy. State (1) involves Coulombic energy of repulsion, because it is the only one that pairs electrons in the same orbital. The energy of this state is higher than that of the other two by 11 as a result of electron-electron repulsion. 

Limitations on the values of the quantum numbers lead to the familiar aufbau (German, Aujbau, building up) principle, where the buildup of electrons in atoms results from continually increasing the quantum numbers. Any combination of the quantum numbers presented so far correctly describes electron behavior in a hydrogen atom, where there is only one electron. Flowever, interactions between electrons in polyelectronic atoms require that the order of filling of orbitals be specified when more than one electron is in the same atom. In this process, we start with the lowest n, I, and m, values (1, 0, and 0, respectively) and either of the m values (we will arbitrarily use — 5 first). Three mles will then give us the proper order for the remaining electrons as we increase the quantum numbers in the order m , m, I, and n. 

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Much of quantum chemistry attempts to make more quantitative these aspects of chemists view of the periodic table and of atomic valence and structure. By starting from first principles and treating atomic and molecular states as solutions of a so-called Schrodinger equation, quantum chemistry seeks to determine what underlies the empirical quantum numbers, orbitals, the aufbau principle and the concept of valence used by spectroscopists and chemists, in some cases, even prior to the advent of quantum mechanics. 

MOs around them - rather as we construct atomic orbitals (AOs) around a single bare nucleus. Electrons are then fed into the MOs in pairs (with the electron spin quantum number = 5) in order of increasing energy using the aufbau principle, just as for atoms (Section 7.1.1), to give the ground configuration of the molecule. 

F. L. Pilar, 4s Is Always Above 3d Or, How to Tell the Orbitals From the Wavefunctions, Journal of Chemical Education, 55 2—6, 1978 E. R. Scerri, M. Melrose, Why the 4s Orbital Is Occupied Before the 3d, Journal of Chemical Education, 73(6) 498—503, 1996 L. G. Vanquickenborne, K. Pier loot, D. Devoghel, Transition Metals and the Aufbau Principle, Journal of Chemical Education, 71 469-471, 1994. 

LOWDIN S REMARKS ON THE AUFBAU PRINCIPLE AND A PHILOSOPHER S VIEW OF AB INITIO QUANTUM CHEMISTRY. 

Transition Metals and the Aufbau Principle, Journal of Chemical Education, 1994 71 469-471. 

Before estabiishing the connection between atomic orbitals and the periodic table, we must first describe two additionai features of atomic structure the Pauli exclusion principle and the aufbau principle. 

In applying the aufbau principle, remember that a full description of an electron requires four quantum numbers ... 

The periodic table provides the answer. Each cut in the ribbon of the elements falls at the end of the p block. This indicates that when the n p orbitals are full, the next orbital to accept electrons is the ( + 1 )s orbital. For example, after filling the 3 orbitals from A1 (Z = 13) to Ar (Z = 18), the next element, potassium, has its final electron in the 4 S orbital rather than in one of the 3 d orbitals. According to the aufbau principle, this shows that the potassium atom is more stable with one electron in its 4 orbital than with one electron in one of its 3 (i orbitals. The 3 d orbitals fill after the 4 S orbital is full, starting with scandium (Z = 21). 

A neutral helium atom has two electrons. To write the ground-state electron configuration of He, we apply the aufbau principle. One unique set of quantum numbers is assigned to each electron, moving from the most stable orbital upward until all electrons have been assigned. The most stable orbital is always ly( = l,/ = 0, JW/ = 0 ). 

To write the configuration of any other element, we first consult the periodic table to find its location relative to the noble gases. Then we specify the noble gas configuration and build the remaining portion of the configuration according to the aufbau principle. Example applies this procedure to indium. 

The aufbau principle allows us to assign quantum numbers to aluminum s 13 electrons without ambiguity. The first 12 electrons fill the 1 2s, 2 p, and 3 s energy levels, and the last electron can occupy any 3 p orbital... 

Three different arrangements of two 2 p electrons obey the Pauli and the aufbau principles. 

The aufbau principle must be obeyed when an electron is added to a neutral atom, so the electron goes into the most stable orbital available. Hence, we expect trends in electron affinity to parallel trends in orbital stability. However, electron-electron repulsion and screening are more important for negative ions than for neutral atoms, so there is no clear trend in electron affinities as ft increases. Thus, there is only one general pattern ... 

C08-0030. Write brief explanations of (a) screening (b) the Pauli exclusion principle (c) the aufbau principle (d) Hund s rule and (e) valence electrons. 

The electrons in molecules obey the aufbau principle, meaning that they occupy the most stable orbitals available to them. 

Quantum mechanics may be used to determine the arrangement of the electrons within an atom if two specific principles are applied the Pauli exclusion principle and the Aufbau principle. The Pauli exclusion principle states that no two electrons in a given atom can have the same set of the four quantum numbers. For example, if an electron has the following set of quantum numbers n = 1, l = 0, m = 0, and ms= +1/2, then no other electron may have the same set. The Pauli exclusion principle limits all orbitals to only two electrons. For example, the ls-orbital is filled when it has two electrons, so that any additional electrons must enter another orbital. 

The second principle, the Aufbau principle, describes the order in which the electrons enter the different orbitals and sublevels. The arrangement of electrons builds up from the lowest energy level. The most stable arrangement of... 

When following the Aufbau principle, the orbitals begin filling at the lowest energy and continue to fill until we account for all the electrons in an atom. Filling begins with the n = 1 level followed by the n = 2 level, and then the n = 3 level. However, there are exceptions in this sequence. In addition, Hund s rule states that the sublevels within a particular orbital will half fill before the electrons pair up in a sublevel. 

Figure 7-1 illustrates the Aufbau principle diagrammatically. The orbitals begin filling from the bottom of the diagram (lowest energy) with two electrons maximum per individual sublevel (line on the diagram). 

Why is the electron configuration of chromium, ls22s22p63s23p64s13d5, an exception to the Aufbau principle ... 

Aufbau principle The Aufbau principle states that the electrons in an atom fill the lowest energy levels first. 

Use the aufbau principle to write complete electron configurations and complete orbital diagrams for atoms of the following elements sodium, magnesium, aluminum, silicon, phosphorus, sulfur, chlorine, and argon (atomic numbers 11 through 18). 

The chart below shows electron configurations and partial orbital diagrams for the 18 elements of period 4. You would expect the filling pattern shown for potassium (Z = 19) through vanadium (Z = 23). However, an unexpected deviation from the pattern occurs with chromium (Z = 24). The same thing happens with copper (Z = 29). All other configurations for period 4 conform to the aufbau principle. 

Use the aufbau principle to write complete electron configurations for the atom of the element that fits the following descriptions. 

For each of the elements below, use the aufbau principle to write the full and condensed electron configurations and draw partial orbital diagrams for the valence electrons of their atoms. You may consult the periodic table in Appendix C, or any other periodic table that omits electron configurations. 

Use the aufbau principle to write the condensed ground state electron configurations for nitrogen, phosphorus, and arsenic. 

Name the two elements in period 4 whose electron configurations are not accurately predicted by the aufbau principle. 

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