The Building-Up Principle

The exclusion principle and the consequences of shielding are our keys to understanding the structures of complex atoms and ions, chemical periodicity, and molecular structure. 

The extension of the procedure used for H, He, and Li to other atoms is called the building-up principle. The building-up principle specifies an order of occupation of atomic orbitals that in most cases reproduces the experimentally determined ground state configurations of atoms and ions. 

At this point let s summarize what our examination of the first ten elements has revealed about ground-state electron configurations and the properties of electrons in atoms  

No two electrons in the same atom can have the same four quantum numbers. This is the Pauli exclusion principle. 

Each orbital can be occupied by a maximum of two electrons. They must have opposite spins, or different electron spin quantum numbers. 

The most stable arrangement of electrons in a subshell is the one that has the greatest number of parallel spins. This is Hund s rule. 

Atoms in which one or more electrons are unpaired are paramagnetic. Atoms in which all the electron spins are paired are diamagnetic. 

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The procedure that we have been using is called the building-up principle. It can be summarized by two rules. To predict the ground-state configuration of a neutral atom of an element with atomic number Z with its Z electrons ... 

The building-up principle is also commonly called the Aufbmt principle, from the German word for building up. ... 

We account for the ground-state electron configuration of an atom by using the building-up principle in conjunction with Fig. 1.41, the Pauli exclusion principle, and Hund s rule. 

The ground-state electron configurations tor Cr and Cu are not those predicted by the building-up principle. Give their actual electron configurations and explain what causes them to deviate from the expected configuration. 

In the heavier transition-metal elements, especially the lanthanoids and actinoids, there are numerous exceptions to the regular order of orbital occupation predicted by the building-up principle. Suggest why more exceptions would be noted for these elements. 

In the molecular orbital description of homonuclear diatomic molecules, we first build all possible molecular orbitals from the available valence-shell atomic orbitals. Then we accommodate the valence electrons in molecular orbitals by using the same procedure we used in the building-up principle for atoms (Section 1.13). That is,... 

When N valence atomic orbitals overlap, they form N molecular orbitals. The ground-state electron configuration of a molecule is deduced by using the building-up principle to accommodate all the valence electrons in the available molecular orbitals. The bond order is the net number of bonds that hold the molecule together. 

Step 3 Note the total number of electrons present in the valence shells of the two atoms. If the species is an ion, adjust the number of electrons to account for the charge. Step.4 Accommodate the electrons in the molecular orbitals according to the building-up principle. 

The ground-state electron configurations of diatomic molecules are deduced by forming molecular orbitals from all the valence-sbell atomic orbitals of the two atoms and adding the valence electrons to the molecular orbitals in order of increasing energy, in accord ivith the building-up principle. 

Suggest the form that the orbital energy-level diagram would take for a square planar complex with the ligands in the xy plane, and discuss how the building-up principle applies. Hint The d -orbital has more electron density in the xy plane than the dzx- or d -orbitals but less than the dXJ,-orbital. 

The electronic configurations of isolated atoms, up to Z = 36, can be predicted using the building-up principle. There are three important rules to follow ... 

FIGURE 1.33 The order in which atomic orbitals are occupied according to the building-up principle. Each time an electron is added, we move one place to the right until all the electrons (Z electrons for an element of atomic number Z) have been accommodated. 

STRATEGY (a) To proceed systematically, use the two rules of the building-up principle. Because titanium is in Period 4, we predict its valence ) shell will have n = 4. Because it is the second transition metal, we predict it will have two d-electrons. (b) There is a shortcut particularly... 

FIGURE 1.34 The names of the blocks of the periodic table are based on the last subshell being occupied in an atom of an element according to the building-up principle. The numbers of electrons that each type of orbital can accommodate are shown by the numbers across the bottom of the table. The colors of the blocks match the colors we are using for the corresponding orbitals. 

The organization of the periodic table (Section B) can be explained now that we know about electron configurations (Box 1.2). The table is divided into s, p, d, and f blocks, named for the last subshell that is occupied according to the building-up principle (Fig. 1.34). Two elements are exceptions. Strictly, helium belongs in the s block, but it is shown in the p... 

The blocks of the periodic table are named for the last orbital to be occupied according to the building-up principle. The periods are numbered according to the principal quantum number of the valence shell. 

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