Question

(Bonus: 10 points) 19. Based on the shapes of p and d orbitals and the necessary match of symmetry, please predict and sketch all of the possible orbital interactions between the p orbitals of atom A and the d orbitals of atom B for the formation of bonding and antibonding orbitals.

Answer 1

In the heavier elements, particularly the transition metals, d orbitals can be involved in bonding. The possible combinations are shown. When the z axes are collinear, two dz2 orbitals can
combine end-on for s bonding. The dxz and dyz orbitals form p orbitals. When atomic orbitals meet from two parallel planes and combine side to side, as do the dx2-y2 and dxy orbitals
with collinear z axes, they form 1d2 delta orbitals. (The d notation indicates sign
changes on C4 rotation about the bond axis.) Sigma orbitals have no nodes that include the line connecting the nuclei, pi orbitals have one node that includesthe line connecting the nuclei, and delta orbitals have two nodes that include the line connecting the nuclei. Again, some orbital interactions are forbidden on the basis of symmetry; e.g pz and dxz have zero net overlap if the z axis is chosen as the bond axis since the pz would approach the dxz orbital along a
dxz node as shown. It is noteworthy in this case that px and dxz would be eligible to interact
in a p fashion on the basis of the assigned coordinate system. This example emphasizes the importance of maintaining a consistent coordinate system when assessing orbital interactions.

Interactions of d Orbitals.
(a) Formation of molecular orbitals.
(b) Atomic orbital combinations that do not form molecular orbitals.
P, and dxz s and d-2 s and dyz 00 88 box no interaction o interaction no interaction

d2 orbitals end-to-end 202.98 100 000 8810289 d ord orbitals in the same plane d2 - y2 or d orbitals in parallel planes

These are the possible interactions between p and d orbitals of two atoms to form bonding and nonbonding molecular orbitals.