S-orbitals hydrogen

Because the Schrodinger equation cannot be solved exactly for polyelectron atoms, it has become the practice to approximate the electron configuration by assigning electrons to hydrogen-like orbitals. These orbitals are designated by the same labels as for hydrogen s orbitals and have the same spatial characteristics described in the previous section, Orbitals. ... 

Each carbon atom is bonded to two other atoms, and there are no nonbonding valence electrons. Each carbon atom needs two hybrid orbitals to form the sigma bond framework. Hybridization of the s orbital with one p orbital gives two hybrid orbitals, directed 180° apart, for each carbon atom. Overlap of these sp hybrid orbitals with each other and with the hydrogen s orbitals gives the sigma bond framework. Experimental results have confirmed this linear (180°) structure. 

There are now eight different spatial orbitals, hybrid orbitals, the other four being close to atomic hydrogen s-orbitals. The expansion of each of the VB orbitals in terras of M the basis functions located on the nuclei allows the orbitals to distort from the pure atomic shape. The SCVB wave... 

The remaining three m.o.s require a little more attention. The reason is that 2p is no longer a non-bonding orbital it has a non-zero overlap with the hydrogen s orbitals. Thus, the m.o. of lowest energy is altered by constructive interference from 2p (represented by z) and becomes... 

FIGURE 5.4 Four representations of hydrogen s orbitals, (a) A contour plot of the wave function amplitude for a hydrogen atom in its Is, 2s, and 3s states. The contours identify points at which i//takes on 0.05, 0.1, 0.3, 0.5, 0.7, and 0.9 of its maximum value. Contours with positive phase are shown in red those with negative phase are shown in blue. Nodal contours, where the amplitude of the wave function is zero, are shown in black. They are connected to the nodes in the lower plots by the vertical green lines, (b) The radial wave functions plotted against distance from the nucleus, r. (c) The radial probability density, equal to the square of the radial wave function multiplied by 1. (d) The "size" of the orbitals, as represented by spheres whose radius is the distance at which the probability falls to 0.05 of its maximum value. 

The second situation referred to above, viz systems containing conjugated double bonds, is perhaps more important to the present discussion. The classical example of such a system is benzene. The molecular orbital treatment regards the six G—G bonds and the six G—H bonds as completely localized molecular orbitals compounded out of carbon sp2 hybrid atomic orbitals and the hydrogen s orbital. So far the treatment is identical with the electron pair theory, discussed in Chapter 4. The G—G bonds will be or bonds formed by the overlap of two sp2 hybrid atomic orbitals, one from each carbon atom and the C—H bonds will also be a bonds formed by the overlap of one sp2 hybrid atomic orbital of carbon with the s atomic orbital of hydrogen. The six carbon 2p atomic orbitals that remain will form completely non-localized molecular orbitals. Thus each 2pt electron will be regarded as existing in the field of six nuclei and will possess a wave function of the form ... 

The overlap of a hydrogen s orbital with a carbon p orbital to result in crc H and [Pg.128]

Fig. 2. Relativistic corrections for hydrogenic s orbitals (as percentage of the non relativistic value).

The symmetry-adapted combinations of hydrogen s-orbitals that we use to build the methylene MOs must be either symmetric or antisymmetric with respect to reflection in this plane. The individual AOs do not fulfill this condition, but can be combined to give the two symmetry-adapted combinations shown in Fig. 2.9. These combinations can then be used to build the MOs. 

Fig. 2.12 The interaction of the carbon py-AO with the antisymmetric combination of hydrogen s-orbitals to give the CH-bonding jtcjj2 MO and the antibonding These MOs are designated Jt because of their nodal plane. They are...

Let us construct the MOs of linear and bent AH2 shown in 7.1 and 7.2, respectively, where the central atom A contributes four valence atomic orbitals 5, and z. We will construct the MOs based upon the perturbation method of Chapter 3, and so it is convenient to construct AIL from A and 11 H units. The orbitals of H H are the in-phase and out-of-phase combinations of hydrogen s orbitals shown in 7.3, where the energy gap between and is small since the 11 H distance in 7.1 and 7.2 is large in most cases of interest. 

The interaction diagram for the orbitals of A and H is shown in Figure 9.1. The p and py orbitals of A do not overlap with the hydrogen s orbital, and so become the //v itnd Hy nonbonding orbitals (9.1) of AH, respectively. According to the perturbation treatment of Chapter 3. fJAit- ah derived as shown in 9.2. In this... 

The bond orbitals of AH which result from combining the sp hybrid orbitals of A with a hydrogen s orbital arc shown in Figure 9.2. One sp hybrid orbital interacts with hydrogen s to form the Oah and levels, and the remaining three... 

---