Equations for Calculating Dq and B Yu-sheng Dou Northwest University, Xian, China The electronic lieand field s ~ e c t r aof hiah-sdn s - . s.~ e c i e of cubicsymmetry with d', d', d-,'and dqons consist in general of three bands that arise from threespin-allowed transitions. The assignments and energies of these bands are as follows.' A2 ground state ions (octahedral, d3 and d8, and tetrahedral, d2and d7, species) A2 Al
--
AS
T2 T1(F) T,(P)
"1
= 10Dq
T I ground state ions (octahedral, d2 and d7, and tetrahedral, d3 and d8, species) Ti TI TI
(1)
+ 1504 - 1/2(225f12+ 100Dq2- 180DqB)'" us = (1512)B + 15Dq uz = (1512)fl
(2)
+ 1/2(225fl2+ 100DqZ - 180Dqfl)"2
(3)
' Lever, A. 0. P. J. Chem. Educ. 1968,45,711-712.
Keltle. S. F. A. Coordination Compounds: Nelson. 1969.
-
ul = 5Dq - (1512)B 1/2(225f12 100Dq2 180Dqfl)"2 (4) uz = 15Dq - (15/2)0 1/2(225f12 100Dq2+ 180DqB)l/Z (5) us = (225f12 100Dq2 180DqB)112 (6)
Tz
+ +
A2 TI(P)
+
+ +
+
+
(A g should be added for the octahedral species) If the transitions u l , 02, and ua can be spectroscopically observed, the ligand field parameter Dq and Racah parameter B can be calculated by means of eqs 1-6. If only two transitions are observed, the graphical methods can be used generally in deriving Dq and B.'.2 The graphical methods however are somewhat lacking in precision compared to algebraic solutions based on the above equations. In this article we have given the equations for calculating Dq and B (see table).
Equations lor Calculating Dqand B
v,/10 ",/lo vl/10
V I . Vz. V3
v,.
V?
V % Vs V% V3
134
[9("2+
Y)- (SS(v2-
(v3
+ v2-
(",-2"1)("~(v3-2v&V#
- q v 2 + y3)2)1'2]1340
Journal of Chemical Education
(v2
3v1)/15 ",)/3(5v2-9",) q)13(5v3- 9v,)
+ v3 - 30Dq)H5
-
(v2 -h)/10 ("s - ",)I10
(vs+ v2-3h)/15 -v,(* - 2v,)/3(4v2- 9h) 2 ~ ~ ) ~ ) " ~ (v3 - Zv, IODq)/l5
- -
[ ( S V~ ~(h Z("S 2",)1/40 [(85vs2 4(v3 2 ~ ~ ) ~ ) ' ' ~ - 91rs - 2v2)]/340
-
(VS
+ - 2v2+ 30Dq)/15
