3d orbitals

Fig. 2.7 The addition of a 3d orbital to 2p gives a distorted orbital. (Figure adapted from Hehre WJ, L Radom, p i)R Sdileycr and ] A Hehre 1986. Ab initio Molecular Orbital Theory. New York, Wiley.)...

The hydrogenie atom energy expression has no 1-dependenee the 2s and 2p orbitals have exaetly the same energy, as do the 3s, 3p, and 3d orbitals. This degree of degeneraey is only present in one-eleetron atoms and is the result of an additional symmetry (i.e., an additional operator that eommutes with the Hamiltonian) that is not present onee the atom eontains two or more eleetrons. This additional symmetry is diseussed on p. 77 of Atkins. 

The presenee of radial nodes also indieates that the eleetron has radial kinetie energy. The 3s orbital with 2 radial nodes has more radial kinetie energy than does the 3p whieh, in turn, has more than the 3d. On the other hand, the 3d orbital has the most angular energy... 

In Figure 1.8 the real wave functions for the f, 2p and 3d orbitals are plotted in the form of polar diagrams, the construction of which may be illustrated by the simple case of the 2p orbital. The wave function in Equation (f.43) is independent of 4> and is simply proportional to cos 6. The polar diagram consists of points on a surface obtained by marking off, on lines drawn outwards from the nucleus in all directions, distances proportional to I cos 6 at a constant value of R2i(r). The resulting surface consists of two touching spheres. 

For all orbitals except s there are regions in space where 0, ) = 0 because either Yimt = 0 or = 0. In these regions the electron density is zero and we call them nodal surfaces or, simply, nodes. For example, the 2p orbital has a nodal plane, while each of the 3d orbitals has two nodal planes. In general, there are I such angular nodes where = 0. The 2s orbital has one spherical nodal plane, or radial node, as Figure 1.7 shows. In general, there are (n — 1) radial nodes for an ns orbital (or n if we count the one at infinity). 

Transition metal atoms are distinguished from other atoms by their having partially filled 3d, Ad or 5d orbitals. Here we consider only metals of the first transition series. Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn, in which the 3d orbital is involved. 

A number of MO calculations has been carried out, and these have had mixed success in predicting chemical reactivity or spectroscopic parameters such as NMR chemical shifts and coupling constants. Most early calculations did not take into account the contribution of the sulfur 3d-orbitals to the ground state, and this accounts for some of the discrepancies between calculations and experimental observations. Of the MO methods used, CNDO/2 and CNDO/S have been most successful the INDO approximation cannot be used because of the presence of the sulfur atom. 

The pA of 1,3-dithiane is 36.5 (Cs" ion pair in THF). The value for 2-phenyl-1,3-dithiane is 30.5. There are several factors which can contribute to the anion-stabilizing effect of sulfur substituents. Bond dipole effects contribute but carmot be the dominant factor because oxygen substituents do not have a comparable stabilizing effect. Polarizability of sulfur can also stabilize the carbanion. Delocalization can be described as involving 3d orbitals on sulfur or hyperconjugation with the a orbital of the C—S bond. MO calculations favor the latter interpretation. An experimental study of the rates of deprotonation of phenylthionitromethane indicates that sulfur polarizability is a major factor. Whatever the structural basis is, there is no question that thio substituents enhance... 

In many of their complexes PF3 and PPI13 (for example) resemble CO (p. 926) and this at one time encouraged the belief that their bonding capabilities were influenced not only by the factors (p. 198) which affect the stability of the a P M interaction which uses the lone-pair of elecU"ons on p and a vacant orbital on M, but also by the possibility of synergic n back-donation from a nonbonding d , pair of electrons on the metal into a vacant 3d , orbital on P. It is, however, not clear to what extent, if any, the a and n bonds reinforce each other, and more recent descriptions are based on an MO approach which uses all (cr and n) orbitals of appropriate symmeU"y on both the phosphine and the metal-containing moiety. To the extent that a and n bonding effects on the stability of metal-phosphorus bonds can be isolated from each otlier and from steric factors (see below) the accepted sequence of effects is as follows ... 

The extent to which each hybrid is incorporated into the full bonding description of the molecule will depend on the extent to which 3d orbitals... 

For H and He, the atomic basis set consists of a single Is orbital. For Li through Ne, the inner-shell electrons are treated as part of the nucleus and the basis functions used are atomic 2s, 2p c, 2py and 2p .. For Na through Al, the inner shell is treated as part of the nucleus and we consider only 3s, 3p, 3pj, and 3pj. orbitals. For Si through Cl we have to decide on whether or not to include the atomic 3d-orbitals in addition, and practice varies. Most authors include them. 

Three LMTO envelopes were used with the tail energies -0.01 Ry, -1 Ry and -2.3 Ry. In the first two of them, s,p,d orbitals were included and in the last one only. s and p were used. It was necessary to treat the Ti 3p and 3-s states in the semi-core state, i.e. to do a so called 2-panel calculation. The basis set for the second panel consisted of 3-s, 3p, 3d orbitals on the Ti sites and 3-s, 3p orbitals on the Si sites. The same quality k-mesh was used in all calculations to ensure maximum cancellation of numerical errors and to obtain accurate energy differences. 

The orbitals in an atom are organized into different layers, or electron shells, of successively larger size and energy. Different shells contain different numbers and kinds of orbitals, and each orbital within a shell can be occupied by two electrons. The first shell contains only a single s orbital, denoted Is, and thus holds only 2 electrons. The second shell contains one 2s orbital and three 2p orbitals and thus holds a total of 8 electrons. The third shell contains a 3s orbital, three 3p orbitals, and five 3d orbitals, for a total capacity of 18 electrons. These orbital groupings and their energy levels are shown in Figure 1.4. 

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. 

You will recall (page 139) that an orbital occupied by an electron in an atom can be represented physically by showing the region of space in which there is a 90% probability of finding the electron. Orbitals are commonly designated by citing the corresponding sublevels. Thus we refer to Is, 2s, 2p, 3s, 3p, 3d,... orbitals. 

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. 

When we add the next electron to form the element scandium, the orbital of lowest energy that is available is one of the 3d orbitals (since the 3d orbitals are slightly lower in energy than the 4p orbitals). As succeeding electrons are added to form other elements, they enter the 3d orbitals until the ten available spaces in these orbitals are filled. 

There are five 3d orbitals available, all more or less of the same energy. Putting a pair of electrons in each of these five orbitals means that a total of ten electrons can be accommodated before we need to go to a higher energy level. Not only scandium but the nine following elements can be built up by adding electrons into 3d orbitals. Not until we get to gallium (element number 31) do we go up to another set of orbitals. 

Again using Figure 22-1, decide which orbital would next be used after the five 3d orbitals have been filled. What orbital would next be used after the 4d set has been filled What element does this correspond to in the periodic table ... 

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