J . Phys. Chem. 1984,88, 3407-3411 approximations, and the true renaissance did not begin until the mid 1970s. Naturally, it coincided with the modern revolution in statistical mechanics-the discovery of the renormalization group procedure,29 the development of efficient Monte Carlo schemes,30and the wide availability of computers with which to perform these calculations. These techniques provide a variety of methods by which one can for the first time successfully treat nonlinear classical statistical-mechanics problems. By exploiting the isomorphism which arises from the path integral formulation, the new techniques provide methods for approaching classes of quantum phenomena that could not be treated before. Physicists have begun applying the path integral methods with Monte Carlo and renormalization group calculations to solve a number of problems in particle physics.” Progressing in a different direction, the recent research reviewed herein has exploited the advances in the modern statistical-mechanical theories of the liquid state5 and has extended Feynman’s classical isomorphism in ways which make the methodology particularly useful to chemistry. Along with the work we have explicitly reviewed, the recent literature contains many more applications, and we list here a few of them: Thirumalai and Berne32have described the analytic continuation of Monte Carlo simulation results to obtain time correlation functions, and they have tested it on some simple one-dimensional systems. Behrman et al.33 have presented a method for direct Monte Carlo evaluation of time correlation functions, and they have applied it to the simple two-state tunneling model described above. This application attempts to grapple with the fact that the weight functionals are not always positive for (29) K. G.Wilson, Rev. Mod. Phys., 55, 584 (1983),and references cited therein. (30)K. Binder, Ed., “Monte Carlo Methods in Statistical Physics”, Springer-Verlag, New York, 1979. K. Binder, Ed.‘Applications of the Monte Carlo Method in Statistical Physics”, Springer-Verlag, New York, 1984. (31) J. B. Kogut, Rev. Mod. Phys., 51,659 (1979). (32) D. Thirumalai and B. J. Berne, J . Chem. Phys., 79, 5029 (1983). (33) E.C. Behrman, G. A. Jongeward, and P. G. Wolynes, J. Chem. Phys., 79, 6277 (1983).
3407
paths in real time (as opposed to the imaginary time iph encountered in equilibrium calculations). The feature of nonpositive weights is frequently referred to as the “alternating-weights problem”, which is also a stumbling block in treating by these methods many-body systems composed of fermions. This problem is thus present when considering condensed-phase effects on chemical bonding of many-electron molecules. A Monte Carlo method for handling such phenomena has been proposed by Chiles et al.,34and they illustrated their method with a primitive model for an influence functional. It remains to be seen whether their particular scheme will be useful with more realistic and quantitative treatments of the solvent and solvent-solute interactions. Finally, we note that Logan35 has extended the quantum theory of the Drude oscillator solvent to include quadrupoles as well as dipoles. The extension provides a theory for collisional-induced dipolar spectra, but no test of the theory has yet been made. Thus, the applications are still at an early stage, but it is already clear that in the hands of an experienced practitioner of classical equilibrium statistical mechanics, the isomorphism provides a powerful tool for solving condensed-matter quantum problems. We may also anticipate that the isomorphism coupled with renormalization group-Monte Carlo techniques will soon alter the way we think about the electronic structure of molecules and provide sorely needed insights into the nature of chemical bonding. Acknowledgment. This article is based upon a series of lectures I delivered in February 1983 while visiting the Australian National University in Canberra, Australia. I am grateful to the students and faculty in Canberra for their generous hospitality. I am also grateful to Peter Wolynes for working with me on much of the path integral research reviewed herein and for providing helpful advice on the first draft of this manuscript. This research has been supported by grants from the National Science Foundation. (34) R. A. Chiles, G. A. Jongeward, M. A. Bolton, and P. G. Wolynes, preprint, 1984. (35) D. E. Logan, Mol. Phys., in press.
ARTICLES Photoselection Studies of Transition-Metal Complexes. 3. Chromium( I I I ) Complexes S. Michael Angel and M. Keith DeArmond* Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204 (Received: August 3, 1983; In Final Form: December 5, 1983) Luminescence spectra and photoselection spectra have been measured for a series of Cr(II1) complexes having molecular D3 and C, symmetries including [Cr(bpy)$+, [Cr(en),13+,[Cr(~-hist)J+, and [Cr(IDA)J. The photoselection data indicate involves a second-orderspin-orbit coupling that the intensity mechanism for emission of [Cr(en)3]z(S04)3and [Cr(~-hist)~]NO~ mechanism.
Introduction Previous from this lab have emphasized the use of the luminescence photoselection technique for the imine chelates of d6 metal ions of Rh(III), Ir(III), Ru(II), and Os(I1). The (1) DeArmond, M. K.; Huang, W. L.; Carlin, C. M. Inorg. Chem. 1978, 18, 3388. (2) DeArmond, M.K.;Carlin, C. M.; Huang, W. L.Inorg. Chem. 1980, 19, 62. (3) Carlin, C. M.; DeArmond, M. K. Chem. Phys. Left. 1982, 89, 297.
0022-3654/84/2088-3407$01.50/0
emission at low temperature (77 K) for these complexes has generally been idet~tified~.~ as mr* or d?r* type, thus characteristic of multiatom ligand orbitals and typically evidencing ligand vibrational structure. The emission photoselection spectra for these systems indicate that totally symmetric modes dominate the emission, thus implying that first-order spin-orbit effects are (4) DeArmond, M. K.Acc. Chem. Res. 1974, 7, 309. (5) Crosby, G.A. Acc. Chem. Res. 1975, 8, 231.
0 1984 American Chemical Society
3408
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
predominant in the relaxation of the excited state unlike that situation that occurs for planar nitrogen-containing aromatics where the photoselection method has been used to identify asymmetric out-of-plane bending modes participating in the nonradiative relaxation6 However, high-resolution photoselection data for the frozen solution [Ru(bpy),12+ and the monomer [Ru(bpy)(py),] *+ have been used as evidence for the localization of the luminescence excited state on a single chelate ring of the m ~ l e c u l e .Thus, ~ [Ru(bpy),12+ and its analogues are “spatially isolated orbital” emitters consistent with the multiple-state spatially isolated emission first identified7 for [ R h ( b p ~ ) ~ p h e n ]and ~+ [Rh(phen)zbpy]3+and later postulated for [ R ~ ( b p y ) ~ ] Such ~+. emission obviously must result from a unique vibronic coupling and is, in part, the motivation for this photoselection study of the Cr(II1) emitters. The emission from Cr(I1I) complexes is complementary to that of the d6 complexes since the emission is now localized primarily on the metal atom with the ligand atoms contributing a lesser amount to the emitter orbital. The most common emission is the ZE 4A2phosphorescence which, because it occurs from an approximately vertical potential surface, results in relatively narrow line structured emission8-l1 with vibrational structure. Less that, because it occurs common is the 4Tz 4A2flu~re~cences from displaced potential surfaces, is broad, shifted from the corresponding absorption band, and structureless. In some few cases, both fluorescence and phosphorescence emission bands have been observed. In one case, the tris(dithi0carbamate) complex of Cr(III), [Cr(dtc),], a unique emission that may be a hybrid fluorescence-phosphorescence has been observed.10J2 Thus, the initiation of the photoselection method with Cr(II1) complexes has three main purposes: (1) to assess the sensitivity of the photoselection method to vibronic coupling in ”metal-localized” emitters, (2) to compare and contrast the vibronic coupling in metal-atom-localized emitters to that of d6 charge-transfer emitters by using photoselection as the probe method, and (3) to attempt to assess the effect of the potential surface displacement and thus the “spatial isolation” upon the vibronic coupling between excited states. This paper will be concerned primarily with the first two purposes while a later paper will be concerned with the third purpose, in particular that situation occurring for the unique emission of the Cr(dtc), complex. -+
-
Experimental Section
Tris(ethylenediamine)chromium(III) sulfate, [Cr(en)3]2(S04)3, and tris(2,2’-bipyridine)chromium(III) perchlorate hemihydrate, [Cr(bpy),] (c104)3-1.5Hz0, were prepared according to literature procedures13 and recrystallized from water. Dissolved in water, both compounds eluted as a single band on a cation-exchange column (Sephadex C-25). The solid samples were stored in the dark a t 266 K until ready for use and no decomposition was observed after several weeks. Sodium cis-bis(iminodiacetato)chromate(III), cis-Na[Cr(1DA)J.I .5H20, was prepared by a literature p r ~ c e d u r e and ’~ was recrystallized from water, washed with ethanol-water, and air-dried. Further purification was obtained by eluting on an anion-exchange column (Sephadex A-25). Elution with water yielded a violet band which was not luminescent at wavelengths longer than 600 nm. A red band remained at the top of the column and was eluted with 0.5 M NaCl as a narrow red band. Excess salt was removed by using a column packed with Sephadex LH-20 before recrystallization of the red band. (6) Lim, E. C. “Excited States”; Academic Press: New York, 1977; Vol. 3. (7) Halper, W.; DeArmond, M. K. J . Lumin. 1972, 5, 225. (8) Forster, L. S. “Transition Metal Chemistry, A Series of Advances”; Marcel Dekker: New York, 1969. (9) DeArmond, M. K.; Forster, L. S. Spectrochim. Acta 1963, 19, 1687. (10) Mitchell, W. J.; DeArmond, M. K. J . Mol. Spectrosc. 1972, 41, 33. (11) Flint, C. D. Chem. Phys. Lett. 1968, 2, 661. (12) DeArmond, M. K.; Mitchell, W. J. Inorg. Chem. 1972, 11, 181. (13) Rollinson, C. L.; Bailar, J. C., Jr. Inorg. Synth. 1946, 2, 196. (14) Weyh, J. A.; Hamm, R. E. Inorg. Chem. 1968, 7, 2431.
Angel and DeArmond TABLE I: Emission and Absorption Maxima of [Cr(en)3]2(S04),and [Cr(bpy)dC104)3 at 80 K absorpn emission 10-3pmax, cm-’ 29.0 22.5
30.0 29.0 27.9 25.0 23.4 21.9
10-3vmax,
assnt 4TI
--
4T2
4TI
-
cm-I
assnt
I , arb units
[Cr(en)3ldS04)3 4A2 14.9 2E-4A2 4A2 14.83 14.69 14.48 14.26
1 0.17 0.12 0.04 0.05
[Cr(b~~)3l(C104)3 13.76 2E-,4A2 4A2 13.6 13.4
1 0.17 0.08
4T2-4A2
Bis(L-histidinato)chromium(III) nitrate, [ C r ( ~ - h i s t )(NO,), ~] was prepared following the procedure of Hoggard.I5 The reaction mixture was filtered and the red crystals washed with ethanolwater and recrystallized from alcohol-water mixtures. Dissolved in water, the solid eluted as more than one band on a cationexchange column (Sephadex C-25) and on a column packed with Sephadex LH-20. All data were taken on crystals grown over a period of several days from water at room temperature and air-dried. This technique yields the pure trans (imidazole) isomer. Anal. Calcd for [Cr(C6H8N302)2](N03):C, 34.1; H, 3.8; N, 23.2. Found: C, 33.8; H, 3.7; N, 23.5. Sodium bis(aspartato)chromate(III), Na[Cr(~-asp),], was prepared following a procedure similar to that used to make other chromium(II1) compounds. The solid was recrystallized from alcohol-water solution. Emission spectra of the recrystallized solid were found to be dependent on the excitation wavelength and two emitting species appeared to be present. Further purification was attempted by using an ion-exchange column (Sephadex A-25). Elution using 1%, 3%, and 10% NaCl solutions yielded three bands. Excess salt was removed by eluting with water on a column packed with Sephadex LH-20. Spectra run on each fraction were also dependent on excitation wavelength and showed different mixtures of the two emitting species to be present. The best spectra were obtained by using the reaction filtrate. This was eluted with methanol on a column packed with Sephadex LH-20 in methanol giving three bands. The top band gave an emission spectrum that was predominantly from one species showing only a small wavelength dependence. Anal. Calcd for Na[Cr(C4H5N04)z-4Hz0:C, 23.5; H , 4.4; N, 6.8. Found: C, 24.2; H, 4.1; N, 6.5. Instrumentation A low-temperature cryostat made in this lab was used with a Cary 14 spectrophotometer to obtain the low-temperature absorption spectra. The base line offset was not corrected and only relative intensities are shown. Emission and photoselection spectra were obtained for samples frozen in glassy solvents by using a computer-controlled instrument that has been described previously.16 Emission photoselection spectra were obtained by using a polarized excitation source and then monitoring the resultant emission with a polarizing filter. Excitation photoselection spectra were obtained in a similar way but the emission was monitored as a function of excitation wavelength. The excitation photoselection spectra were measured while monitoring the first strong emission peak. The limiting polarization (P) values obtainable with this technique are shown in Table I1 and comparison of these values to the experimentally determined values provides information about the symmetry of the excited states. Standard deviations of the polarization value ( P ) were no larger than 0.02 (1 5) Hoggard, P. E. Inorg. Chem. 1980, 20, 4 15. (16) Carlin, C. M.; DeArmond, M. K.; Hanck, K. W. Reu. Sci. Instrum. 1981, 52, 137.
Photoselection Studies of Transition-Metal Complexes
.2
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3409
Ian I
P I
\
/
\ .o*
14.4
13.8
lo3
13.2 CM-1
l
14.5
12.6
lo3
14.1 CM-~
L
13.7
13.3
/'\
W 30
25
20
103 C M - ~
Figure 1. Na[Cr(IDA)2] spectra: (a) emission and emission polarization spectra (80 K) for 21 277-cm-' (470-nm) excitation (upper) and 22 936-cm-l (436-nm) excitation (lower): (b) low-temperature absorption spectrum (83 K) and excitation polarization spectrum (80 K) for 13 423-cm-I (745-nm) emission.
and were usually less than 0.01 unless otherwise stated. Emission decay curves (measured at the wavelengths of the emission maxima) were recorded, and the lifetimes were calculated as previously described.17
Results The absorption and emission data for [Cr(en)3]2(S04)3and [Cr(bpy)J (C104)3 are summarized in Table I. [Cr(en)3]a(S04)3. The 80 K luminescence of this molecule is similar to that reported elsewhere.ls The sharp symmetrical band at 14.9 X lo3 cm-' has vibrational sidebands beyond 14.0 X lo3 cm-' and there are small but significant variations of the polarization across these vibrational bands. The polarization also increases on the high-energy side of the 14.9 X lo3 cm-' band. The 4Tls(0,) and 4Tzg(0,) bands are found at 29.0 X lo3 and 22.5 X lo3 cm-', respectively, with the lower energy band showing evidence of some splitting. The polarization is unstructured and nearly zero across the 4T1,absorption band and it is about +0.05 on the high energy side of the "T2, band, increasing to about +0.08 on the low-energy side of this band. [Cr(l~py)~](C10~),. The 80 K luminescence agrees well with that reported in the l i t e r a t ~ r e . ' ~ There * ~ ~ is a very intense sharp phosphorescence band at 13.8 X lo3 cm-I and a few vibrational bands, the most prominent being at 13.6 X lo3 and 13.4 X lo3 cm-'. The emission polarization spectrum shows no significant variations across these sidebands but the polarization increases on the high-energy side of the 13.8 X lo3 cm-' band (0-0band). At room temperature an additional luminescence band was observed a t about 14.4 X lo3 cm-'. This has been previously reported.20 (17) Huang, W. L.; Segers, D. P.; DeArmond, M. K. J. Phys. Chem. 1981, 85, 2080. (18) Flint, C. D. J . Chem. Phys. 1970, 52, 168. (19) Kane-Maguire, N. A. P.; Langford, C. H. J . Chem. SOC.,Chem. Commun. 1971, 895. (20) Kane-Maguire, N. A. P.: Conway, J.; Langford, C. H. J. Chem. Soc., Chem. Commun. 1974, 801.
Figure 2. [ C r ( ~ - h i s t ) ~ ] Nspectra: O~ (a) emission and emission polarization spectra (80 K) for 21 368-cm-' (468-nm) excitation; (b) low-temperature absorption spectrum (83 K) and excitation polarization spectrum (80 K) for 14286-cm-' (700-nm) emission.
The absorption spectrum shows two bands each containing three and 4T, (0,) equally spaced peaks in the regions where 4Tls(0,) bands are expected but located on the shoulder of a large charge-transfer band. The higher energy bands are separated by 950 cm-' and the lower energy bands are separated by 1550 cm-I. The polarization spectrum shows little structure. The polarization value is about -0.07 in the 4T1gregion and rises slowly to about -0.05 in the 4T2sregion where it remains flat to about 23.0 X lo3 cm-'. N ~ [ c r ( l D A ) ~ The l . 80 K luminescence of this complex agrees with that reported in the literature2' with a broad asymmetric fluorescence band centered around 13.5 X lo3cm-' and a much less intense sharp phosphorescence band a t 14.4 X lo3 cm-'. The polarization spectrum obtained with 436-nm excitation is shown in Figure l a (lower curve). At this excitation wavelength the polarization is near zero across the fluorescence band but it reaches a maximum value of about +0.10 at the phosphorescence band maximum. Structure is seen across the fluorescence band with 470-nm excitation (upper curve) but reliable polarization data could not be obtained across the phosphorescence band at this excitation wavelength. The low-temperature absorption and excitation polarization spectra are shown in Figure lb. The absorption spectrum shows two bands at 25.8 X lo3 and 19.3 X lo3 cm-' corresponding to 4Tl, (0,) and 4T2p(Oh), respectively. The lower energy band is split with maxima at 19.7 X 10' and 18.9 X lo3 cm-I. The higher energy (4TI,) band shows evidence of a low-energy shoulder which corresponds to a change in the polarization spectrum across this region. The excitation polarization spectrum is very complex with polarization decreasing from -0.07 on the high-energy side of the 4TI, band to a minimum value of -0.15 at the band maximum. (21) Hoggard, P. E.; Schmidtke, H. H. Ber. Bunsenges. Phys. Chem. 1972,
76, 1013.
(22) Krishnamurthy, R.; Schoap, W. B.; Perumareddi, J. R. Inorg. Chem. 1338. (23) Schaffer, C. E.; Jorgensen, C. K. K.Dan. Vidensk. Selsk. Mat.-Fys. Medd. 1965, 34, No. 13. 1967, 6,
3410 The Journal of Physical Chemistry, Vol. 88, No. 16, 1984
The polarization increases across the low-energy side of this band, reaching a value of +0.14 at the 4Tzeband and reaching a maximum value of +0.20 at 17.8 X lo3 cm-' where it begins to decrease again toward lower energy. [Cr(~-hist),]NO,. Luminescence and polarization spectra were obtained for the trans (imidazole) isomer of this compound. The 80 K luminescence was similar to that reported by Hoggard.Is There is a sharp phosphorescence peak at 14.3 X lo3 cm-' (700 nm) with sidebands a t lower energy. We have measured the lifetime at this peak and found it to be 157 f 5 p. Emission and emission polarization spectra are shown in Figure 2a. The polarization varies substantially across the main (0-0) phosphorescence band but it is nearly flat across the low-energy vibrational bands except for a small increase across the second vibrational band a t about 13.9 X lo3 cm-l. Figure 2b shows the low-temperature absorption and excitation polarization spectra. The absorption spectrum shows two peaks at 28.0 X lo3 and 20.5 X lo3 cm-' corresponding to the 4T~,(4) and 4T2g(oh)bands, respectively. There is no evidence of splitting of the absorption bands but the 4T1,band does have a shoulder at high energy and the polarization does change across this band as well as the 4Tzgband. In the 4T1,region the polarization is below zero and is unstructured but it decreases from about 0.00 to -0.05, going from the high-energy side to the low-energy side of the band. There is a distinct transition between the two bands band. The polarization to +0.14 on the high-energy side of the increases to about +0.22 at 21 X lo3 cm-', where there is an inflection and the polarization increases more sharply. The polarization reaches a maximum of about +0.45 at 18.1 X lo3 cm-' and then decreases very rapidly toward the red edge of this band. As a check against a possible "red-edge" effect,24 an emission spectrum was run exciting in this region (18.1 X lo3 cm-'). The emission spectrum obtained was not shifted from that shown (Figure 2a). Na[Cr(~-asp),]. Luminescence data were obtained for this compound at 80 K and were similar to those of [Cr(~-hist),]NO,. The emission spectrum obtained for the compound recrystallized from water solution shows a sharp phosphorescence peak at 14.4 X lo3 cm-' with sidebands at lower energy which are partially obscured by another emitting species around 14.1 X lo3 cm-'. No spectra could be obtained for this compound which showed emission from a single species due to incomplete separation on the exchange columns (see Experimental Section).
Discussion D3 Molecules. The [Cr(en),I2(SO4), and [Cr(bpy),] (C104), complexes both have D3 symmetry. Thus, the 4T, (Oh) state is split, giving states of 4E and 4A, symmetry both of which are formally allowed in absorption and are polarized (x,y) and z, state is split in D3 giving states 4E respectively. The 4T, (0,) and 4A2but only the fE state is allowed and is polarized ( x J ) . Emission from the ,E state is a spin-forbidden process; thus, it must gain intensity by coupling of the ,E state to the quartet states. This may be via a first-order spin-orbit coupling mechanism or through a second-order spin-vibronic mechanism. The latter type of mechanism can be distinguished experimentally by a vibronic band in the emission spectrum that is polarized differently from the 0-0 band.6 Since the 2E state can couple to all of the formally allowed quartet states, for a first-order mechanism an emission oscillator is expected which has components in the (x,y) and z directions. This would give values of P near zero if the (x,y) and z emission oscillator components are nearly the same. The [Cr(en)3]z(S04)3complex shows a variation of the polarization across the vibronic sidebands in the emission spectrum and a decrease across the strong phosphorescence band (0-0 band) at 14.9 X lo3 cm-'. This is evidence of nontotally symmetric modes and indicates that a portion of the emission intensity derives from a second-order spin-vibronic coupling mechanism. The (24) Galley, W. C.; Purkey, R.M. Proc. Natl. Acad. Sci. U.S.A. 1970, 65, 823.
Angel and DeArmond
-4A 2, Oh
- --- - - ---
-
4~~
C2"
Figure 3. C,, energy-level diagram as derived from Oh.
polarization decrease across the 14.9 X lo3 cm-' band could be caused by splitting of the 2Estate by spin-orbit coupling or it may be due to unresolved vibronic bands.2s The near-zero excitation polarization s p t r u m obtained while monitoring this peak suggests a nearly spherical emission oscillator with more z component than (X,Y).
The [Cr(bpy),] (C104), complex has an emission spectrum similar to [Cr(en)3]z(S04)3but the emission polarization spectrum shows no significant structure across the vibronic sidebands, indicating that these are totally symmetric modes. However, the polarization does change across the strong 13.8 X lo3 cm-' band (0-0 band), implying the presence of hidden structure. The 2,2'-bipyridine ligand has low-lying a* orbitals and the dd* absorption bands for the complex appear on the shoulder of an intense charge-transfer (da*) band. Absorption is mainly into the charge-transfer band; thus, it is polarized in the plane of the molecule ( x y ) leading to little variation in the polarization value across most of the absorption region. This is consistent with the flat excitation polarization spectrum observed and the polarization value of about -0.07 means that the emission oscillator has more z component than (x,y). At lower energy some structure appears in the excitation polarization spectrum, growing in as the charge-transfer band decreases in intensity and the d-d band begins to dominate the absorption. The higher values for the polarization at low energy are consistent with an emission oscillator which has a larger z component . C, Molecules. [Cr(~-hist),](NO,) and cis-Na[Cr(IDA),] both have C, symmetry considering only the atoms that are coordinated directly to the metal. The energy-level diagram for C, symmetry is shown in Figure 3. The 4T2g(Oh) state is split in C,,into three states 4A1,4B1,and 4B, but only the 4A, and 4Bl states are formally allowed in absorption and are polarized x and z, respectively. The 4T1g(0,) state is also split in C,,into three states 4Az, 4B1,and 4Bz with transitions to the 4Azand 4B1states allowed and polarized y and z, respectively. The symmetry of the lowest doublet state is not known and the ,E (Oh)and ,T1, (oh)components are probably mixed. Figure 4 shows how the various doublet states may gain intensity by coupling to the quartet ground state (4B1)through the various quartet excited states. The emission oscillator may be linear, planar, or spherical depending on the doublet state involved in emission and the amount of coupling of this doublet state to each of the quartet excited states. That this results in a much more complicated polarization spectrum than for the D, symmetry molecules is verified by the polarization spectrum of [Cr(Lhist),](NO,). [ Cr(~-hist),](NO,). The emission polarization spectrum for this complex changes across at least one of the low-energy sidebands showing a peak corresponding to the band at 14.0 X lo3 cm-' (Figure 2a). This is evidence that this band does not correspond to a totally symmetric mode. Across the main peak ( 0 4 band) at 14.3 X lo3 cm-' the polarization changes about 0.20 ( 2 5 ) Flint, Colin D.; Matthews, Anthony P. J . Chem. SOC., Faraday Tram. 2 1974, 70, 1307.
The Journal of Physical Chemistry, Vol. 88, No. 16, 1984 3411
Photoselection Studies of Transition-Metal Complexes
Figure 4. Spin-orbit coupling of doublet states (right of arrows) to quartet ground state (left of arrows) through quartet excited states (above the arrows). The polarization of the excited states is indicated by lower case x, y , or z . TABLE II: Photoselection Limits abs osc em osc P 2
z
z
X
Z
[z,x] [x,Y]
Z
0.50 -0.33 0.14 -0.33
abs osc [x,y]
[
any
~
em osc z
l [x,YI [x,y,z]
P
-0.33 0.14 0.00
polarization unit, indicating hidden structure, perhaps vibronic bands (such a small vibrational spacing is observed for similar Cr(II1) complexeszs), or alternatively indicating that the emission is occurring from two close-lying doublet states. Crystal field and angular overlap model calculations have shown that the ZA2and ZBzstates are accidentally degenerate zz,z3 therefore, it is reasonable to assume that these two states are close in energy. The excitation polarization spectrum is shown in Figure 2b. The interpretation of the negative polarization values (P)in the 4T1,(4)region and the very high polarization values in the 4T2, (0,) region is that the emission oscillator has x and z components but with one component larger than the other. There is no y component in the emission oscillator since this would require values of P much lower than those observed in the 4Tz, (0,) region of the absorption spectrum. Therefore, the emitting state cannot be 'B1 or ZA,since these states gain intensity through first-order spin-orbit coupling from 4A1( x ) and 4Az(y), and from 4A2 (y) and 4B1 (z), respectively. For a first-order spin-orbit coupling of the doublet and quartet states, the polarization data would necessitate an emission oscillator that has primarily x and z components. This is consistent with an emission occurring from the 2Az or 2Bz states. NLZ[C~(ZDA)~]. The emission polarization (Figure l a ) shows structure across the fluorescence band increasing at the emission peak and showing minima on either side, indicating a vibronic coupling between the emitting state and other quartet states. The increase in P at about 14.3 X lo3 cm-' can be due to the phosphorescence band at 14.40 X lo3 cm-'. The polarization
structure does not necessarily reflect structure in the emission envelope precisely since shifts due to overlapping bands may occur. The excitation polarization spectrum is shown in Figure lb. The polarization values of +0.14 across most of the 4Tz,(0,) band indicate that the emission oscillator is planar with x and z components only, since the absorption oscillators are x and z in this region (Table 11). The negative polarization values observed in the 4T1, (0,) band are expected for a planar (x,z) emission oscillator since the absorption oscillators are y and z in this region (Figure 3). From the excitation polarization spectrum, the fluorescence emission oscillator is determined to be planar with x and z components rather than a linear oscillator; thus, coupling must occur 4B2,and 4A1 between the lowest lying quartet states, Le., the 4B1, states. Three possibilities can rationalize this: (1) Emission could occur from both states if the 4A1and 4B, states are close in energy. (2) Emission may occur from the 4A1or 4B1state which is vibronically coupled to other close-lying quartet states. This would lead to a structured emission polarization spectrum such as that shown in Figure la. (3) If the lowest state is 4B2, the symmetry-forbidden transition to the ground state could only occur through coupling to other quartet states, thus leading to a nonlinear emission oscillator. All of these possibilities would lead to similar polarization spectra; therefore, these data alone cannot be used to distinguish between them. Reliable polarization data could not be obtained across the phosphorescence emission band (see Experimental Section) but the increase in P across this band indicates that the emission oscillator for the phosphorescence state is different from that for the fluorescence state. Na[Cr(~-asp),]. The sharp line phosphorescence at 14.3 X IO3 cm-' is similar to that observed for [Cr(~-hist),]NO,. The "impurity" emission band at 14.1 X IO3 cm-l appears to be broader than typical Cr(II1) phosphorescence bands and is probably due to another isomer of this compound. Spectra for this compound were obtained from the last band eluted on an anion-exchange column (Sephadex A-25), suggesting that the phosphorescence spectrum is due to the cis isomer of this compound. The excitation polarization spectrum is similar to that seen for the C, compounds and provides additional evidence that this is the cis compound.
Conclusion The photoselection method is sufficiently sensitive to provide useful information on the vibronic coupling in Cr(II1) "metallocalized" emitters. The photoselection data require that the intensity mechanism for emission does involve a second-order spin-vibronic coupling mechanism for [Cr(en),]z(S04), and [Cr(~-hist),]NO~ and show that vibronic coupling of the emitting state to other quartet states occurs for Na[Cr(IDA),]. The photoselection spectra for [Cr(bpy),] (C104)3indicates that the predominant intensity mechanism results from the charge-transfer band overlapping the d-d bands. Acknowledgment. This research was supported by the National Science Foundation, Grant Number CHE-80-14183. Registry No. [ C r ( b ~ y ) ~ ]15276-15-0; ~+, [Cr(en),13+,15276-13-8; [Cr(~-hist)~]*, 757 14-74-8; [Cr(IDA),]-, 26534-12-3; [Na[cr(~-asp),], 60895-53-6.
