252 Table I. Computed Values of the Equilibrium Constant, K,, for the Dissociation of the HF2- Ion at Different Concentrations of KHF2in Water Concn of KHF2, C‘
Kca
Concn of KHF2, Ca
Koa
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
0.246 0.240 0.220 0.137 0.135 0.120 0.105 0.106
2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00
0.105 0.104 0.100 0,100 0.097 0.090 0.085 0.083
In moles/kg of water.
The chemical shift changes of 19F in solutions of NH4HF2 d o not depend entirely on the equilibrium represented by eq 1. I t is evident from the dilution shift in NH,F solutions that solutions containing the NH4+ ion which can hydrolyze and form hydrogen bonds with F- are much more complex. The hydrolytic equilibria and hydrogen-bonding effects which lead to a
low-field shift in NH,F solutions also effect in a more complex manner the chemical shift changes in the NHaHF2 solutions. It is interesting to note, however, that the chemical shift of 19F at infinite dilution is probably about the same for N H 4 H F 2and KHF, solutions. From this study we are able to compare cheniical shifts of‘ 19Fin different hydrogen-bonded environments. If we take the shift of F- ion at infinite dilution in water as zero (some hydrogen- bonded solvation is occurring in this case), then the chemical shift of a hypothetical isolated H F molecule in water is +20.5 ppm to high field, the HF,- ion is $36.3 ppm 10 high field, and the chemical shift in anhydrous liquid H F is +76,1 pprn.I3 If, as seems reasonable, we assume that the chemical shift becomes diamagnetic monotonically as the hydrogen bond strength to a fluorine atom increases, then this indicates hydrogen bond strengths in the order: (HF),(anhydrous liquid) > HF2-(H20), > HF(H20), > F-(1320)z. The subscripts n, x, y , and z can be regarded as unknown solvation numbers. (13) J. A. Pople, W. G. Schneider, and H. J. Bernstein, “High-Resolution Nuclear Magnetic Resonance,” McGraw-Hill Book Co., Inc., New York, N. Y . , 1959.
Intensities of Forbidden Transitions in Octahedral Complexes Richard F. Fenske Contribution f r o m the Department of Chemistry, University of Wisconsin, Madison, Wisconsin. Received August 8, 1966 Abstract: This work concerns the relative intensities of Laporte forbidden ligand field transitions of octahedrally coordinated transition metal complexes in which the charge-transfer transitions are from the ligand to the metal. Within the framework of a one-electron approximation, it is shown from theoretical considerations that the ligand field transitions in such complexes vibronically mix with those ligand-to-metaltransitions in which the final states involve the egand not the tfgorbital of the metal. Relative intensities of ligand field transitions within a complex are correlated with the observed ligand-to-e, transition. Correlations of intensities between corresponding transitions for analogous chloro and bromo complexes are also obtained.
I
t has long been recognized’ that the portions of the absorption spectra of octahedral transition metal complexes associated with the ligand field transitions are Laporte forbidden since both the ground and excited states are of the same parity (g -+ g). That weak absorptions are actually observed has been attributed to vibrational perturbations which ‘‘mix’’ electronic states of even and odd parity. The forbidden dipole transition is said to “borrow” intensity from an allowed g + u transition. Early explanations2,3 of the Laporte forbidden transitions in metal complexes were carried out in the framework of a crystal-field model. Consequently, the state of odd parity was presumed to be the metal p orbital above the partially filled d orbitals, e.g., the 4p level for the first transition row. Englman4 was the first to attempt a calculation on the basis of a molecular (1) C. J. Ballhausen, “Introduction to Ligand Field Theory,” McGraw-Hill Book Co., Inc., New York, N. Y., 1962, and references therein. (2) C. J. Ballhausen and A. D. Liehr, Mol. Phys., 2, 123 (1959). (3) S. Koide and M. H. L. Pryce, Phil. Mug., 3, 607 (1959). (4) R. Englman, Mol. Phys., 3, 48 (1960).
Journal of the American Chemical Society
orbital (MO) model in which the g + u transition involved a “charge transfer,” that is, the molecular orbitals of even and odd parities were primarily associated with the metal and ligand atomic orbitals, respectively. Although Englman concluded that the allowed transitions in aquo complexes were from the metal to the ligand, there is substantial agreement that in complexes with electron-donor ligands it is the ligandto-metal transitions which give rise to the observed absorptions. One can say only that his correlation of ligand field transitions with the edge of the first intense absorption band was possibly fortuitous. In this connection, it should be noted that in Englman’s tabulation, he presumes that all first observed transitions occur from the 2tZgmetalorbital which is not reasonable for those ions, Fe+* through Cuf2, in which the 2eg metal orbital is occupied (see Figure 1). It is worthwhile to reexamine Englman’s postulates in the light of ligand-to-metal charge-transfer transitions involving electron. donor ligands. According to first-order perturbation theory, the contribution of odd parity states, C,, to the even parity ground and excited
89:2 / January 18, 1967
253 METAL ORBITALS
MOLECULRR
LIGAND ORBITALS
ORBITALS
were Xv is the part of the vibrational perturbation Hamiltonian which is odd in the electronic coordinates; EA, E*, and Eci are the energies of the respective states. For the present purposes, we can ignore the explicit dependence on the vibrational quantum numbers. The matrix element of the transition probability can then be written as
aLg, eg, tlu) I?
It lU
’4
,/’A 1;‘
la
/
/’
/
/
/
le
g
/
/
Figure 1. Octahedral energy levels for electron-donor complexes. The diagram is qualitative only. A dashed line connects an atomic orbital to that molecular orbital in which it has the greatest participation.
A = . 42tlu)(2t2g)ll B = . . .(2tlu)(2eg) 9
C
D
= =
. . .(2eg)(2tzg) . . (2tzg)(2tzg)I *
(4)
(5) Both eq 4 and 5 contribute to the intensity expression, but there are several reasons to presume that, contrary to Englman’s postulates, eq 4 represents the dominant contribution. First of all, the denominator of eq 4 will be substzntially smaller than that of eq 5, the difference being the energy of the d-d transition. Furthermore, Jgrgensens has shown that charge-transfer transitions to the eg orbital are from 4 to 20 times more intense than those to the tzg orbital. Hence ((2tlu)llPl(eg)~)is much larger than ((2tlu)llP~(tzg)l). Thus, it will be assumed in what is to follow that the matrix element of the transition probability is given by
Two sets of calculations will be presented to affirm the reasonableness of the foregoing discussion: (1) relative intensities between different states for the same complex ; (2) relative intensities between the corresponding hexachloro and hexabromo complexes.
States within a Complex Unfortunately, there are few octahedral complexes in which both the ligand field and ligand-to-2eg bands are (6) C. K. Jgjrgensen, Mol. Phys., 2, 309 (1959).
Fenske I Intensities of Forbidden Transitions in Octahedral Complexes
254
observed. Consider those complexes in which the 2tZgorbital is only partly occupied. The ligand field transitions generally occur in the range of frequencies from 15 to 25 kK, where 1 kK equals 1000 cm-1. If the first charge-transfer bands, 2t1, 2tZg,are not to mask the ligand field bands, they must occur at higher frequencies, say 35 kK. But the energy of the charge-transfer transition of interest, 2tl, + 2eg, is only slightly less than the sum of the 2tl, + 2tZgand 2tzg-f 2eg transitions, 2eg band beyond the accessible which places the 2t1, ultraviolet region. When the 2tl, 2eg transition is of low enough energy for detection, the intense 2tl, + 2tZgtransitions are of energy comparable to the much weaker ligand field transitions, and the latter are either not observed or appear as slight shoulders on the intense bands. The above dilemma does not exist for those species in which the 2t2gis fully occupied. Such is the case for the cobalt,’ iridium,* and rhodium* complexes given in Table I. Each possesses a strong field d6 configuration, 2tZg6,so that the first observed charge-transfer band must be to the 2eg orbital with an energy greater than the 2t2g 2eg transition, yet still at a detectable frequency.
-
-
-
In the above “determinants,” the states are represented by the d-orbital component of the tzg “hole” (xy), and the d-orbital component of the occupied eg orbital, (xzy z ) or (zz). Thus + +
I(XY>(X2 - YZ>l =
I
’
-
-
t
+
+
. ‘ ( ~ z > ( ~ z ) ( x Y > ( x z ) ( Y-z )YZ)I (~2
In an analogous fashion, one can represent the determinants which arise from the allowed transition of an electron from the 2tlu orbital to the eg orbitalg
-
D
mix the above
Table I. Intensities to States within a Complex
Complex
State
CCJ(NH~)~+~ ‘TI
‘Tz CTd
C ~ ( e n ) ~ + ~ ‘Tl IT2
CT Co(Cz04)3
‘T1
R hC16-
‘Tz CT ’Ti IT2
a IrCI6-3
IT1 ‘T2
RhBr6-3
IrBr 6-
CT ‘Ti ‘T2 CT(1) CT(2) ’T1 ‘Tz CT(1)
CT(2)
Frequency, kK
Intensity (exptl) X lo4
21.2a 29.4 52.6 21.P 29.6 47.2 16,7m 23.8 41.1 19. 3b 24.3 39,2< 24. l b 28.1 48.5c 18. l b 22.2 30.1~ 33.9 22.4 25.8 36.8 41.1
104 104 -4000 129 132 -3000 27 30 -3000 140 130 8000 125 120 10500 250 250 2000 3000 370 320 2500 5000
f(Tl)/f(T2) Exptl Calcd 1.00
1.19
... ...
... ...
0.98
1.02
..,
...
... ...
0.90
1.06
...
...
., 1.08 . .
1.08
1.04
1.80
..
... ...
1.00
1.41
. , , .
...
1.15
1.83
.,. ..,
... ...
...
,
...
,
.,, ,
,..
.,. , ,
...
...
...
...
a Reference 7. Reference 8. Reference 6. the charge-transfer state to the 2e, orbital.
d
...
CT symbolizes
Each of the complexes of Table I displays Laporte forbidden transitions from the ’Al, ground state to lTlg and lTZgexcited states. Both states arise from the 1 . . .(tzg)5(eg)11configuration. It is possible to calculate the oscillator strengths to these excited states by consideration of only one of the wave functions associated with them and then multiply each result by three. Thus + ’Tld1) = {(XY>(XZ 2 YZ>I + + ‘TzgU) = KXY>(Z2)I (7) A. V. Kiss and D. V. Czegledy, Z . Anorg. Allgem. Chem., 235, 407 (1938). (8) C. I
