Symmetrized atomic orbitals

For the Ain SALQ which must match the totally symmetric atomics orbital, it is obvious (as it was in the tetrahedral case) that all basis orbitals must enter with positive signs and equal weight. Thus, the normalized A,a. SALC has to be... 

The other mechanism is called the Fermi contact interaction and it produces the isotropic splittings observed in solution-phase EPR spectra. Electrons in spherically symmetric atomic orbitals (s orbitals) have finite probability in the nucleus. (Mossbauer spectroscopy is another technique that depends on this fact.) Of course, the strength of interaction will depend on the particular s orbital involved. Orbitals of lower-than-spherical symmetry, such as p or d orbitals, have zero probability at the nucleus. But an unpaired electron in such an orbital can acquire a fractional quantity of s character through hybridization or by polarization of adjacent orbitals (configuration interaction). Some simple cases are described later. 

A spherically symmetrical atomic orbital one per energy level. 

Thus, the simple and robust orbital model serves chemistry as a work horse. Let us take some examples. All die atoms are build on a similar principle. A nodeless, spherically symmetric atomic orbital of the lowest orbital energy is called 1, the second lowest (and also die spherically symmetric, one-radial node) is called 2s, etc. Therefore, when filling orbital energy states by electrons, some electronic shells are formed K(ls ), L(2s 2p ),..., where the maximum for shell orbital occupation by electrons is shown. 

This simple inteipietation gets more complex when further effects are considered, such as contributions to the energy due to the polarization of the spherically symmetric atomic orbitals or the exponent dependence of the Is orbitals (i.e. the dimensions of these orbitals) on the intemuclear distance. When there arc several factors at play (some positive, some negative) and when the final result is of the order of a single component, then we dedde which component carries responsibility for the outcome. The situation is similar to that in Farliament, when two MPs from a small party are blamed for the result of a vote (the party may be called the balancing party) while perhaps 200 others who also voted in a similar manner ate left in peace. 

Section 1 1 A review of some fundamental knowledge about atoms and electrons leads to a discussion of wave functions, orbitals, and the electron con figurations of atoms Neutral atoms have as many electrons as the num ber of protons m the nucleus These electrons occupy orbitals m order of increasing energy with no more than two electrons m any one orbital The most frequently encountered atomic orbitals m this text are s orbitals (spherically symmetrical) and p orbitals ( dumbbell shaped)... 

Using the simplest picture (and neglecting the effect of overlap on the normalization), this doubly occupied og spatial molecular orbital can be thought of as being the symmetric linear combination of the two Is atomic orbitals on the left and right hydrogens, HL and Hr... 

An approach to solving the inverse Fourier problem is to reconstruct a parametrized spin density based on axially symmetrical p orbitals (pz orbitals) centered on all the atoms of the molecule (wave function modeling). In the model which was actually used, the spin populations of corresponding atoms of A and B were constrained to be equal. The averaged populations thus refined are displayed in Table 2. Most of the spin density lies on the 01, N1 and N2 atoms. However, the agreement obtained between observed and calculated data (x2 = 2.1) indicates that this model is not completely satisfactory. 

A carbon atom combining with four other atoms clearly does not use the one 2s and the three 2p atomic orbitals that would now be available, for this would lead to the formation of three directed bonds, mutually at right angles (with the three 2p orbitals), and one different, non-directed bond (with the spherical 2s orbital). Whereas in fact, the four C—H bonds in, for example, methane are known to be identical and symmetrically (tetrahedrally) disposed at an angle of 109° 28 to each other. This may be accounted for on the basis of redeploying the 2s and the three 2p atomic orbitals so as to yield four new (identical) orbitals, which are capable of forming stronger bonds (cf. p. 5). These new orbitals are known as sp3 hybrid atomic orbitals, and the process by which they are obtained as hybridisation ... 

In the previous section the g value was considered as a scalar quantity, which was indeed a good approximation since the unpaired electron on the hydrogen atom occupies a spherically symmetric s orbital. If the unpaired electron exhibits p or d character the electron possesses both spin and orbital angular momentum. As a result the spin is not quantized exactly along the direction of the external field and the g value becomes a tensor... 

The molecular orbitals are labelled a and ir depending on whether they are symmetrical about the internuclear axis or have a nodal plane passing through the nuclei. The m.o. s are numbered in sequence of increasing energy, independent of the numbering of the atomic orbitals. This numbering serves to avoid any confusion in cases where atomic orbitals from different levels are combined, as in... 

Figure 10.4 Shapes of the s, p, and d atomic orbitals. The s orbital (a) is spherically symmetrical about the nucleus. The three p orbitals (b) are figure-of-eight lobes orientated along the three orthogonal axes (only z axis shown). The five d orbitals (c, d, and e) are four quatrefoil lobes, one orientated along the x-y axes, three between the axes, and the fifth (e) a figure-of-eight along the z axis with an additional donut around the nucleus. The orbitals are not drawn to the same scale.

The trigonal bond orbitals in the ten valence electron system as well as the two sets of trigonal lone pair orbitals in the 14 valence electron system are superpositions of it orbitals and o orbitals. The formation of such trigonally symmetric molecular orbitals from a-type and w-type molecular orbitals is entirely analogous in character to the formation of the three (sp2) hybrid atomic orbitals from one (s) and two ip) atomic orbitals which was discussed in the preceding section. This can be visualized by looking at the diatomic molecule... 

---