4s orbital

Although not shown, the energy level of the 4s orbital falls between 3p and 3d. 

The lowest-energy orbitals fill up fust, according to the order Is —> 2s —> 2p —> 3s —> 3p — 4s — 3d, a statement called the aufbciii principle. Note that the 4s orbital lies between the 3p and 3d orbitals in energy. 

As you can see from Figure 6.9, the electron configurations of several elements (marked ) differ slightly from those predicted. In every case, the difference involves a shift of one or, at the most, two electrons from one sublevel to another of very similar energy. For example, in the first transition series, two elements, chromium and copper, have an extra electron in the 3d as compared with the 4s orbital. 

These anomalies reflect the fact that the 3d and 4s orbitals have very similar energies. Beyond that, it has been suggested that there is a slight increase in stability with a half-filled (Cr) or completely filled (Cu) 3d subleveL... 

Potassium has one valence electron. It is the first member of the fourth row, the row based on the cluster of orbitals with about the same energy as the 45 orbital. There are nine such orbitals, tne 4s orbital, the three 4p orbitals, and the five 3d orbitals. Hence the fourth row of the periodic table will differ from the second and third rows. The fourth row, as seen in the periodic table, consists of eighteen elements. 

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. 

As many textbooks state this can be explained from the fact that the 4s orbital has a lower energy than the 3d orbital. In the case of element 20 or calcium the new electron also enters the 4s orbital and for the same reason. 

The interesting part is what happens next. In the case of the following element, number 21, or scandium, the orbital energies have reversed so that the 3d orbital has a lower energy. Textbooks almost invariably claim that since the 4s orbital is already full there is no choice but to begin to occupy the 3d orbital. This pattern is supposed to continue across the first transition series of elements, apart from the elements Cr and Cu where further slight anomalies are believed to occur. 

But let me return to the question of whether the periodic table is fully and deductively explained by quantum mechanics. In the usually encountered explanation one assumes that at certain places in the periodic table unexpected orbital begins to fill as in the case of potassium and calcium where the 4s orbital begins to fill before the 3d shell has been completely filled. This information itself is not derived from first principles. It is justified post facto and by some tricky calculations (Melrose, Scerri, 1996 Vanquickenbome, Pierloot, Devoghel, 1994). 

Only if shells filled sequentially, which they do not, would the theoretical relationship between the quantum numbers provide a purely deductive explanation of the periodic system. The fact the 4s orbital fills in preference to the 3d orbitals is not predicted in general for the transition metals but only rationalized on a case by case basis as I have argued. Again, I would like to stress that whether or not more elaborate calculations finally succeed in justifying the experimentally observed ground state does not fundamentally alter the overall situation.12... 

As a result of this way of counting nodes the 4s orbital has a lower total number of nodes, that is, 4 when compared with 5 in the case of the 3d orbital. Moreover, this order agrees with the experimentally observed order whereby 4s has lower energy than 3d.10 However, whether this is a satisfactory first principles explanation of the n + t rule, which meets the Lowdin challenge, is something that seems rather unlikely given the ad hoc nature of the manner in which nodes have been counted. 

FIGURE 1.41 The relative energies of the shells, subshells, and orbitals in a many-electron atom. Each of the boxes can hold at most two electrons. Note the change in the order of energies of the 3d- and 4s-orbitals after Z = 20. 

IB Each metal atom will lose one 4s-electron. V+, Mil, Co4, and Ni will have one electron in the 4s-orhital, but Cr+ and Cu will have zero electrons in the 4s-orbital. Because their outermost valence electrons will be in 3c/-orbitals and not the 4s-orbital, their radii should be smaller than the other cations. 

Cu [Ar]3energetically favorable for an electron to be promoted from the 4s-orbital to a 3tf-orbital, giving a completely filled 3d-subshell. In the case of Cr, it is energetically favorable for an electron to be promoted from the 4s-orbital to a 3r/-orbital to half fill the 3rf-subshell. 

The curve of single-bond metallic radii for the elements of the first long period has a characteristic appearance (Fig. 3) which must be attributed in the main to variation in the type of bond orbital. The rapid decrease from potassium to chromium results from increase in bond strength due to increasing s-p and d-s—p hybridization. The linear section of the curve from chromium to nickel substantiates the assumption that the same bonding orbitals (hybrids of 2.56 3d orbitals, one 4s orbital, and 2.22 4p orbitals) are effective throughout this series. The increase in radius from nickel to copper is attributed not... 

In Fig. 5.12, the radial distribution functions for the neutral iron-atom are plotted. It is evident that the orbitals with the same main quantum number occupy similar regions in space and are relatively well separated from the next higher and next lower shell. In particular, the 4s orbital is rather diffuse and shows its maximum close to typical bonding distances while the 3d orbitals are much more compact. 

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