CHEM 153 - Advanced Inorganic Chemistry PROBLEM SET 3 (due ...

Use the following orbital splitting diagram to determine the values of ) B in the Cr and
Mn complexes. Expressions for the electron-electron repulsion integrals are given
below. Assume that B = 500 cm !1 and that C/B = 4.
B
d 2 :
3 A 2 [(xz,yz) 2 ] E = 2 ) B + A ! 5B
1 A 1 [(xz,yz) 2 ] E = 2 ) B + A + 7B + 4C
1 B 1 [(xz,yz) 2 ] E = 2 ) B + A + B + 2C
1 B 2 [(xz,yz) 2 ] E = 2 ) B + A +B + 2C
1 E[(xy) 1 (xz,yz) 1 ] E = ) B + A + B + 2C
3 E[(xy) 1 (xz,yz) 1 ] E = ) B + A ! 5B
1 A 1 [(xy) 2 ] E = A + 4B + 3C
d 3 :
2 E[(xz,yz) 3 ] E = 3 ) B + 3A ! 3B + 4C
4 B 1 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A !15B
2 B 1 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A ! 6B + 3C
2 A 1 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A ! 6B + 3C
2 B 2 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A + 5C
2 A 2 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A ! 6B + 3C
2 E[(xy) 2 (xz,yz) 1 ] E = ) B + 3A ! 3B + 4C
3. Use the foregoing orbital splitting pattern and energy expressions in considering
high-spin/low-spin equilibria in tetragonal oxo- and nitrido-metal complexes with d 2
and d 3 configurations.
Assume that the excited-state distortion parameter 8 (as defined in the diagrams on
the following page) is about 3,400 cm !1 for both high- and low-spin states.
a) Find the ) B values at the high-spin/low-spin crossover points for d 2 and d 3
tetragonal oxo- and nitrido-metal complexes. Assume that B = 500 cm !1 and
C/B = 4.
b) Assume that you have a high-spin/low-spin equilibrium in a d 2 tetragonal oxo- or