F-orbitals

The d and f orbitals have more complex shapes there are five equivalent d orbitals and seven equivalent f orbitals for each principal quantum number, each orbital containing a maximum of 2 electrons with opposed spins. 

The above definitions must be qualified by stating that for principal quantum number I there are only s orbitals for principal quantum number 2 there are only s and p orbitals for principal quantum number 3 there are only s, p and d orbitals for higher principal quantum numbers there are s, p, d and f orbitals. 

The third quantum number m is called the magnetic quantum number for it is only in an applied magnetic field that it is possible to define a direction within the atom with respect to which the orbital can be directed. In general, the magnetic quantum number can take up 2/ + 1 values (i.e. 0, 1,. .., /) thus an s electron (which is spherically symmetrical and has zero orbital angular momentum) can have only one orientation, but a p electron can have three (frequently chosen to be the jc, y, and z directions in Cartesian coordinates). Likewise there are five possibilities for d orbitals and seven for f orbitals. 

Figure A1.2 Models schematically illustrating the angular dependence functions A ,(6, 0). There is no unique way of representing the angular dependence functions of all seven f orbitals. An alternative to the set shown is one f 3, three f i, fy i, and three fx(i2 3j,2), fj.(j,2 3x2), and fj(x2 3x2).

Although it is not shown in Figure 6.7, p orbitals, like s orbitals, increase in size as the principal quantum number n increases. Also not shown are the shapes and sizes of d and f orbitals. We will say more about the nature of d orbitals in Chapter 15. 

The problem is this the third row of the periodic table contains 8, not 18, electrons. It turns out that while quantum numbers provide a satisfying deductive explanation of tbe total number of electrons that any shell can hold, the correspondence of tliese values with the number of elements that occur in any particular period is something of a coincidence. The familiar sequence In which the s, p, d, and f orbitals are filled (see diagram, left) has essentially been determined by empirical means. Indeed. Bohr s failure to derive the order for the filling of the orbitals has been described by some as one of the outstanding problems of quantum mechanics. 

At what distance from the nucleus is the electron IcTmost likely to be found if it occupies (a) a 3[Pg.176]

A mistake often made by those new to the subject is to say that The Laporte rule is irrelevant for tetrahedral complexes (say) because they lack a centre of symmetry and so the concept of parity is without meaning . This is incorrect because the light operates not upon the nuclear coordninates but upon the electron coordinates which, for pure d ox p wavefunctions, for example, have well-defined parity. The lack of a molecular inversion centre allows the mixing together of pure d and p ox f) orbitals the result is the mixed parity of the orbitals and consequent non-zero transition moments. Furthermore, had the original statement been correct, we would have expected intensities of tetrahedral d-d transitions to be fully allowed, which they are not. 

Among atomic orbitals, s orbitals are spherical and have no directionality. Other orbitals are nonspherical, so, in addition to having shape, every orbital points in some direction. Like energy and orbital shape, orbital direction is quantized. Unlike footballs, p, d, and f orbitals have restricted numbers of possible orientations. The magnetic quantum number (fflj) indexes these restrictions. 

The chemistry of all the common elements can be described completely using s, p, and d orbitals, so we need not extend our catalog of orbital shapes to the f orbitals and beyond. 

Valence electrons are all those of highest principal quantum number plus those in partially filled d and f orbitals. 

Elements for which = 1 orbitals are filling (b) elements for which the 5 f orbitals are filling ... 

C08-0088. Use the periodic table to find and list (a) all elements whose ground-state configurations indicate that the 4 5" and 3 d orbitals are nearly equal in energy (b) the elements in the column that has two elements with one valence configuration and two with another valence configuration and (c) a set of elements whose valence configurations indicate that the 6 of and 5 f orbitals are nearly equal in energy. 

Here we try to gain insight into the trends in reactivity of the metals without getting lost in too much detail. We therefore invoke rather crude approximations. The electronic structure of many metals shows numerous similarities with respect to the sp band, with the metals behaving essentially as free-electron metals. Variations in properties are due to the extent of filling of the d band. We completely neglect the lanthanides and actinides where a localized f orbital is filled, as these metals hardly play a role in catalysis. 

Warren, K. D. Ligand Field Theory of f-Orbital Sandwich Complexes. Vol. 33, pp. 97-137. 

Quadrupole splittings are often interpreted from ligand field models with simple rules for the contributions from each occupied f-orbital (see discussion above). However, these models fail even qualitatively in the case of more covalent metal-ligand bonds. An example concerns the quadrupole spUttings of Fe(IV)-oxo sites in their 5 = 1 or 5 = 2 spin states. Here, ligand field considerations do not even provide the correct sign of the quadrupole splitting [60]. 

---