2ps orbital

Coulomb potential felt by a 2p orbital s electron at a point r in the ls 2s 2p 2p configuration description of the carbon atom is ... 

The above mean-field potential is used to find the 2p orbital of the carbon atom, which is then used to define the mean-field potential experienced by, for example, an electron in the 2s orbital ... 

Figure B3.1.6. Polarized orbital pairs involving 2s and 2p orbitals.

When elements in Period 2 form covalent bonds, the 2s and 2p orbitals can be mixed or hybridised to form new, hybrid orbitals each of which has. effectively, a single-pear shape, well suited for overlap with the orbital of another atom. Taking carbon as an example the four orbitals 2s.2p.2p.2p can all be mixed to form four new hybrid orbitals (called sp because they are formed from one s and three p) these new orbitals appear as in Figure 2.9. i.e. they... 

In ethene the situation is rather different here, each carbon atom has one 2s and two 2p orbitals hybridised to form three sp single-pear orbitals which are trigonal planar (shown shaded in each half of Figure 2. JO). The remaining 2p orbital is not hybridised,... 

The element before carbon in Period 2, boron, has one electron less than carbon, and forms many covalent compounds of type BX3 where X is a monovalent atom or group. In these, the boron uses three sp hybrid orbitals to form three trigonal planar bonds, like carbon in ethene, but the unhybridised 2p orbital is vacant, i.e. it contains no electrons. In the nitrogen atom (one more electron than carbon) one orbital must contain two electrons—the lone pair hence sp hybridisation will give four tetrahedral orbitals, one containing this lone pair. Oxygen similarly hybridised will have two orbitals occupied by lone pairs, and fluorine, three. Hence the hydrides of the elements from carbon to fluorine have the structures... 

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

I le u. . erlap between the 2pK and 2p orbitals in this new coordinate system is j(2p — 2p ). If tile zei o differential overlap approximation were applied, then different results would be oliLiined for the two coordinate systems unless the overlap in the new, transformed svntem was also ignored. 

Notice that the total number of a orbitals arising from the interaction of the 2s and 2p orbitals is equal to the number of aos that take part in their formation. Notice also that this is true regardless of whether one thinks of the interactions involving bare 2s and 2p... 

An example of the interaetion of 3 s Rydberg orbitals of a moleeule whose 2s and 2p orbitals are the valenee orbitals and of the evolution of these orbitals into united-atom orbitals is given below. 

As another example, the 2s and 2p orbitals on the two N atoms of N2 can be formed into pairs of sp hybrids on each N atom plus a pair of p atomic orbitals on each N atom. The sp hybrids directed... 

What is the eontribution to the total energy of the level of Carbon made by the two 2p orbitals alone Of eourse, the two Is and two 2s spin-orbitals eontribute to the total energy, but we artifieially ignore all sueh eontributions in this example to simplify the problem. 

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. 

---