In class, we did not deal with diatomic molecules involving d-orbitals (transition metals). Here we will do so. A homonuclear transition metal dimer can form bonds from d_(z)^(2)(l)=(0)d_(xz) and d_(yz)(l)=(+-1) and d_(xy) and d_(x)^(2)*y^(2)(l)=(+-2) with filling order σ π δ. (Only one of the pairs of wave functions is given for π and δ. You need to use both.)
σ, Λ = 0, m_(λ) = 0, ψ ^(+-) = (1)/(sqrt(2))(d_(1z^(2))(1)+-d_(2z^(2))(2))
π, Λ = 1, m_(λ) = +-1, ψ _(xz)^(+-) = (1)/(sqrt(2))(d_(1xz)(1)+-d_(2xz)(2))
δ, Λ = 2, m_(λ) = +-2, ψ _(xy)^(+-) = (1)/(sqrt(2))(d_(1xy)(1)+-d_(2xy)(2))
a. Draw the MO level diagram for d-orbital bonding similar to the p-orbital diagram we did in class.
b. Using the inversion operator hat(i), determine the g, u character of each orbital. Include it in your diagram in a).
hat(ı)ψ = +-1ψ, g = +1, u = -1
Hint: it is easier to determine these symmetries from orbital images rather than the wave functions.
c. Now use the reflection operator through the center of the bond but perpendicular to the internuclear axis to determine the bonding or antibonding character of each orbital.
d. Now let's consider an actual molecule (Ti)_(2) with ground state configuration (3s)^(2)(3d)^(2), where the (3s)^(2) orbital is a filled shell you needn't show.
i. Fill in an MO diagram for the ground state of (Ti_(2))_(2).
ii. Determine the term symbols for the GS and order according to Hund's rules.
iii. An excited state of (Ti)_(2) has the d-electron configuration σ(d_(2)^(2))^(2)(π)^(1)(δ)^(1). Determine the allowed terms and order according to Hund's rules.
iv. Write the wave functions for the terms in part ii) above. Show that one of them obeys the Pauli Principle.
