Atomic orbital filling

The periodic table in block form, showing the filling sequence of the atomic orbitals. Filling proceeds from left to right across each row and from the right end of each row to the left end of the succeeding row. 

Table 1.1 An arrangement showing the relationship between the atomic orbitals filled and the number of elements in the various groups and periods of the Periodic Table. Both the major blocks mimic the arrangement of the elements in the 18-group Periodic Table ...

FIGURE 2-9 Atomic Orbital Filling in the Periodic Table. 

We write electron configurations for molecular orbitals as we do for atomic orbitals, filling in electrons in the order of increasing energy levels. The number of molecular orbitals always equals the number of atomic orbitals that were combined. The Pauh exclusion principle and Hund s rule govern the filling of molecular orbitals. 

In many crystals there is sufficient overlap of atomic orbitals of adjacent atoms so that each group of a given quantum state can be treated as a crystal orbital or band. Such crystals will be electrically conducting if they have a partly filled band but if the bands are all either full or empty, the conductivity will be small. Metal oxides constitute an example of this type of crystal if exactly stoichiometric, all bands are either full or empty, and there is little electrical conductivity. If, however, some excess metal is present in an oxide, it will furnish electrons to an empty band formed of the 3s or 3p orbitals of the oxygen ions, thus giving electrical conductivity. An example is ZnO, which ordinarily has excess zinc in it. 

There are several issues to consider when using ECP basis sets. The core potential may represent all but the outermost electrons. In other ECP sets, the outermost electrons and the last filled shell will be in the valence orbital space. Having more electrons in the core will speed the calculation, but results are more accurate if the —1 shell is outside of the core potential. Some ECP sets are designated as shape-consistent sets, which means that the shape of the atomic orbitals in the valence region matches that for all electron basis sets. ECP sets are usually named with an acronym that stands for the authors names or the location where it was developed. Some common core potential basis sets are listed below. The number of primitives given are those describing the valence region. 

When assigning electrons to MOs the same rules apply as for writing electron con figurations of atoms Electrons fill the MOs m order of increasing orbital energy and the... 

Hund s rule (Section 1 1) When two orbitals are of equal en ergy they are populated by electrons so that each is half filled before either one is doubly occupied Hybrid orbital (Section 2 6) An atomic orbital represented as a mixture of vanous contributions of that atom ss p d etc orbitals... 

Valence bond theory (Section 2 3) Theory of chemical bond mg based on overlap of half filled atomic orbitals between two atoms Orbital hybridization is an important element of valence bond theory... 

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2, but in somewhat different ways. Both assume that electron waves behave like more familiar waves, such as sound and light waves. One important property of waves is called interference in physics. Constructive interference occurs when two waves combine so as to reinforce each other (in phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2.2). Recall from Section 1.1 that electron waves in atoms are characterized by then- wave function, which is the same as an orbital. For an electron in the most stable state of a hydrogen atom, for example, this state is defined by the I5 wave function and is often called the I5 orbital. The valence bond model bases the connection between two atoms on the overlap between half-filled orbitals of the two atoms. The molecular orbital model assembles a set of molecular- orbitals by combining the atomic orbitals of all of the atoms in the molecule. 

We will limit ourselves here to transition metals. It is well known that in these metals, the cohesive properties are largely dominated by the valence d electrons, and consequently, sp electrons can be neglected save for the elements with an almost empty or filled d valence shelP. Since the valence d atomic orbitals are rather localized, the d electronic states in the solid are well described in the tight-binding approximation. In this approximation, the cohesive energy of a bulk crystal is usually written as ... 

Figure 1.17 Molecular orbitals of H2- Combination of two hydrogen 1 s atomic orbitals leads to two H2 molecular orbitals. The lower-energy, bonding MO is filled, and the higher-energy, antibonding MO is unfilled.

Relative energies, so far as filling order is concerned, for the molecular orbitals formed by combining 2s and 2p atomic orbitals. 

For purposes of illustration, consider a lithium crystal weighing one gram, which contains roughly 1023 atoms. Each Li atom has a half-filled 2s atomic orbital (elect conf. Li = ls22s1). When these atomic orbitals combine, they form an equal number, 1023, of molecular orbitals. These orbitals are spread over an energy band covering about 100 kJ/moL It follows that the spacing between adjacent MOs is of the order of... 

Apparent anomalies in the filling of electron orbitals in atoms occur in chromium and copper. In these elements an electron expected to fill an s-orbital fills the d-orbitals instead, (a) Explain why these anomalies occurs, (b) Similar anomalies are known to occur in seven other elements. Using Appendix 2C, identify those elements and indicate for which ones the explanation used to rationalize the chromium and copper electron configurations is valid, (c) Explain why there are no elements in which electrons fill ( / + I )s-orbitals instead of np-orbitals. 

There are three cases The original p orbital may have contained two, one, or no electrons. Since the original double bond contributes two electrons, the total number of electrons accommodated by the new orbitals is four, three, or two. A typical example of the first situation is vinyl chloride, CH2—CH—CI. Although the p orbital of the chlorine atom is filled, it still overlaps with the double bond. The four electrons occupy the two molecular orbitals of lowest energies. This is our first example of resonance involving overlap between unfilled orbitals and a filled orbital. Canonical forms for vinyl chloride are... 

Which a — 2 orbital does the third electron in a lithium atom occupy Screening causes the orbitals with the same principal quantum number to decrease in stability as / increases. Consequently, the 2 S orbital, being more stable than the 2 orbital, fills first. Similarly, 3 S fills before 3 p, which fills before 3 d, and so on. 

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). 

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