S orbitals configurations

An example of an atom s orbital configuration is illustrated in Figure 6.3 for the element magnesium. 

To provide further insight why the SCF mean-field model in electronic structure theory is of limited accuracy, it can be noted that the average value of the kinetic energy plus the attraction to the Be nucleus plus the SCF interaction potential for one of the 2s orbitals of Be with the three remaining electrons in the s 2s configuration is ... 

An example will help illustrate these ideas. Consider the formaldehyde molecule H2CO in C2v symmetry. The configuration which dominates the ground-state waveflinction has doubly occupied O and C 1 s orbitals, two CH bonds, a CO a bond, a CO n bond, and two 0-centered lone pairs this configuration is described in terms of symmetry adapted orbitals as follows (Iai22ai23ai2lb2 ... 

FIGURE 2 8 sp Hybridization (a) Electron configuration of carbon in its most stable state (b) Mixing the s orbital with the three p orbitals generates four sp hybrid orbitals The four sp hybrid orbitals are of equal energy therefore the four valence electrons are distributed evenly among them The axes of the four sp orbitals are directed toward the corners of a tetrahedron... 

The effect of configurational mixing of higher-lying s orbitals into the ligand field d-orbital basis set is also likely to favour elongation rather than contraction. ... 

Let s now look at an ab initio CIS calculation on pyridine. As a routine first step, I optimized the molecular geometry (yet to be discussed) at the HF/6-31G level of theory. It is interesting to examine the ab initio orbital configuration (Figure 11.3). 

An atom consists of a positively charged nucleus surrounded by one or more negatively charged electrons. The electronic structure of an atom can be described by a quantum mechanical wave equation, in which electrons are considered to occupy orbitals around the nucleus. Different orbitals have different energy levels and different shapes. For example, s orbitals are spherical and p orbitals are dumbbell-shaped. The ground-state electron configuration of an... 

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. 

An S term, like an s orbital, is non-degenerate. Therefore, while the effect of a crystal field (of any symmetry) will be to shift its energy, there can be no question of its splitting. The ground term for the configuration is S. In an octahedral crystal field, this is relabelled Aig, in tetrahedral symmetry, lacking a centre of inversion, it is labelled M]. 

A lithium atom has three electrons. The first two electrons fill lithium s lowest possible energy level, the 1. S orbital, and the third electron occupies the 2 5 orbital. The three representations for the ground-state electron configuration... 

Often, an s orbital contains only one electron rather than two. Five of the exceptional ground-state configurations have a common pattern and are easy to remember Cr and Mo are d, and Cu, Ag, and Au are S". The... 

For any cation, the empty 4 S orbital is slightly higher in energy than the partially filled 3 d orbital. Thus, the isoelectronic V and Cr cations both have the [Ar] 3 d configuration. On the other hand, the isoelectronic neutral atom scandium has the configuration [Ar]4 3 d ... 

The configurations of these elements show that a 3 5 electron is removed to ionize magnesium, whereas a 3 electron is removed to ionize aluminum or silicon. Screening makes the 3 S orbital significantly more stable than a 3 p orbital, and this difference in stability more than offsets the increase in nuclear charge in going from magnesium to aluminum. 

High spin Fe2+ has the configuration 3 de (tig eg). Although we could examine the relationship between Rv and dS as for Mn2+, Co2+, and Ni2+, we prefer in this case to look at Ry as a function of the occupation of the combination of 3d and 4s orbital by ligand electrons which is measured by the Mossbauer isomer shift. In general, the coefficient f0, fn, and fs are not known for Fe2+. In addition, possible spin-orbit coupling makes it difficult to determine the spin reduction by magnetic structures. However, the isomer shift allows us to determine approximately the occupancy of the 4 s orbitals and there are many experimental results available. 

After writing the molecular orbital configuration, the vector sums are obtained. For example, in H2 the two bonding electrons reside in a a orbital, and they are paired so S = + Vi + — Vi) = 0. As shown earlier, for a cr orbital the m is 0 so the two electrons combined have ML = 0. Therefore, the ground state for the H2 molecule is 2E. As in the case of atoms, all filled shells have E S = 0, which results in a JE state. 

This energy is not likely to be repaid during compound formation. The reason for such a high second ionization energy for lithium is because the electron configuration of Li+ is Is2 which has a filled s orbital. It is the special stability of the filled s orbital which prevents the formation of Li2+ ions. Also, the formation of Li2+ requires 14 times more energy than the formation of Li+ and so is much less likely. 

Let us first consider the charge and spin distributions for atoms and ions of the first transition series (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn). The neutral ground-state TM electron configurations are of generic form s2d , except at n = 4 (Cr sM5) and n = 9 (Cu s d1") where the well-known anomalies associated with the special stability of half-filled and filled d shells are manifested. The simplest picture of ionic bonding therefore involves metal ionization from an s orbital to give the... 

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