J. Phys. Chem. 1992, 96, 3605-3609
I
1-
Neat Pyrrole
750
4
800 Wavelength (nm)
Figure 8. Liquid overtone spectrum of the u = 4 N-H transition of pyrrole diluted in CC14.
The other absorptions shown in Figura 2 and 3 involve the N-H stretching motion which, similar to the C-H oscilator in CX3H,lZ interacts with the bend, causing new absorptions to appear. The general pattern is a strong peak accompanied by two or three weaker peaks to lower energy. For instance, the 13 305-cm-’ band in pyrrole (assigned to the 4-0 N-H transition) has three weaker transitions 103, 191, and 309 cm-’ to the red. The corresponding transition in pyrrolidine a t 12 551 cm-’ has three weaker peaks shifted to the red by 82, 197, and 325 cm-I. The 5 - 0 N-H transitions lie a t 16 316 and 15 298 cm-’ for pyrrole and pyrrolidine, respectively. The transitions for pyrrole are blue-shifted due to aromaticity, while those in pyrrolidine are typical of other amines. For example, the N-H(5) level in ammonia and methylamine lies a t 15 4505 and 15 325 cm-’,* respectively. The spectrum of pyrrole-d4 confirms the assignments of the N-H multiple transitions. The normal and deuterated samples have the same two transitions with similar intensity ratio at the first overtone level. The three strongest peaks in the normal third overtone spectrum are also found in the same relative intensities in the spectrum of pyrrole-d4. It is clear that the peaks common
3605
to both spectra must be due to N-H transitions and not due to overtones and combinations of the C-H stretches. Changes in band intensities and transition wavenumbers are expected since the vibrational mode responsible for the coupling (possibly the N-H: C-H bend) is altered by the deuteration. This could account for the disappearance of the two peaks in the third overtone spectrum of pyrrole-d,. Further evidence that these multiple absorption belong to intramolecular vibrational coupling in the N-H comes from the liquid spectra. The 4-0 N-H transition in the neat pyrrole spectrum shown in Figure 7 is shifted 500 cm-I to the red from the gaseous value. However, upon dilution in CC14 this broad red-shifted peak shows structure reminiscent of the gaseous spectrum (Figure 8). Specifically, the splittings of 85, 186, and 303 cm-l appear in the dilution spectra while the splittings in the gaseous spectrum are 103, 191, and 309 cm-’. These numbers are in excellent agreement since the liquid spectra were recorded on a conventional absorption spectrometer at 1 nm (above 20 cm-I) resolution. The intensity at the red side of the broad peak in neat pyrrole decreases at higher dilution and is probably due to inhomogeneous absorption of hydrogen-bonded N-H oscillators. The values in the last column in Table I1 indicate that the entire N-H absorption at the v = 4 level shifts about 200 cm-l in the liquid 10% dilution. In contrast, the C-H v = 4 and 5 levels only shift about 100 cm-I. For pyrrolidine neat liquid the 4-0 N-H transition is split. The comparison of dilution splittings to those of the gas for pyrrolidine is not as good as for the case of pyrrole but does show the same trend.
Conclusion The vibrational overtone spectra of gaseous and liquid-phase pyrrole and pyrrolidine have been observed in the near-infrared and visible regions of the spectrum. The first, second, third, and fourth N-H stretch overtone transitions were observed. It is clear that the N-H stretch is coupled to some other vibrational mode and that the vibrational coupling pattern is similar for pyrrole and pyrrolidine. Several C-H stretch overtones for pyrrole and pyrrolidine were also observed. The C-H overtone spectra are simple and reflect the aromaticity of pyrrole and the boat conformation possible in pyrrolidine. Acknowledgment. This work was funded in part by the Office of Naval Research and the Keck Foundation. We thank Shannon Tansey for taking the 0.125-cm-’ pyrrole-d4 spectrum. Registry No. Pyrrole, 109-97-7; pyrrolidine, 123-75-1.
Temperature-Dependent Emission and Lifetime Measurements of Te4+ Doped in (ethyl,N),-CIS-[ SnCI,Br,] Hans-Herbert Schmidtke,* Michael Diehl, and Joachim Degen Institut fur Theoretische Chemie, Universitat Dusseldorf, 0-4000 Dusseldorf, Federal Republic of Germany (Received: August 19, 1991; In Final Form: December 4, 1991) Temperature-dependent rise time and lifetime results by measuring the photon emission in the range 10-200 K were obtained on cis-[TeC14Br212-doped in (ethy14N)2-cis-[SnC1,Br,] with the same molecular configuration (Cb).The kinetics of energy excitation and relaxation are described by a three-level model containing transition rate constants the sizes of which are related to different symmetry selection rules between corresponding electronic levels. The occupations of the excited states do not seem to be thermally equilibrated. The results allow the determination of the symmetry and energetics of the lowest levels which arise from the excited sp electron configuration of the Te(1V) central ion. 1. Introduction Absorption and emission spectra of mono- and divalent metal ions with s2 valence electron configuration incorporated as impurities in alkali-metal halide host lattices have been widely studied.’ Ions of higher formal charges, e.g., Sb(III), Se(IV),
or Te(IV), bonded in hexachloro and hexabromo complex compounds, exhibit very similar optical properties.2” Also doped (1) Ranfagni, A.; Mugnai, D.; Bacci, M.; Viliani, G.; Fontana, M. P. Adu. phys. 1983, 32, 823.
0022-365419212096-3605%03.00/0 0 1992 American Chemical Society
3606 The Journal of Physical Chemistry, Vol. 96, No. 9, 1992
(:I)(
-Aot-i02
Am io,
AIO
I,,
-AIo-L,I
AI?
-i?o-L>)
)=(!!I
O.no Figure 1. Possible transition rates within a three-level system and corresponding rate equations. materials of these ions in oxide or chloride hosts of higher charged central metals, which avoid the charge-compensating defect, Le., Sc, Y,and La oxides or corresponding elpasolites and A2MC16 with A = K, Rb, or Cs and M = Zr or Sn, exhibit quite similar spectra which can be interpreted by the same theoretical proced u r e ~ . ~ , 'Apart from measuring the absorption and emission spectra and discussing the assignments of the peaks to electronic and vibrational levels, in some of this work also the time resolution of the emission, Le., lifetimes, kinetics of energy decay, etc., has been inve~tigated.~?~-l~ From mixed halogeno s2 compounds, only an optical investigation on (ethy14N)z[TeC1,X], (X = Br, I) has been reported so far." From time-resolved luminescence spectra, by measuring the temperature dependence of lifetimes, the electronic level splittings due to the lower symmetry (C,) could be observed, at least for some of the emitting states. These, in general, cannot be obtained from absorption spectroscopy if the low-symmetry fields due to the ligands are small giving rise to level splittings of only about 100 cm-I. The strong temperature dependence of lifetimes is given by the Boltzmann formula relating the transition rates k12and k21between the lowest excited and one of the higher states (cf. Figure 1). The kinetics can then be described by several noninteracting three-level systems which allow the lifetime data for some separate temperature intervals to be explained. In the present article we report similar results on another mixed halide complex, this time of C , symmetry, Le., cis- [TeCl4Brzl2-, incorporated in a host lattice of (ethy14N)z[SnC14Brz]with the same geometric coI@uration. Since rise time measurements could be performed as well, the complete kinetic model for occupation in a three-level model applies which is briefly summarized using different starting conditions and assuming certain relations on the decay constants which are derived from radiative and nonradiative selection rules imposed on each pair of electronic level^.^.'*'^ 2. Kinetics
The characteristic matrix of the balance equations for the level populations ni(t) of a system containing three energy levels is shown (2) Stufkens, D. J. Recl. Trau. Chim. Pays-Bus 1970, 89, 1185. (3) Wernicke, R.; Kupka, H.; Ensslin, W.; Schmidtke, H.-H. Chem. Phys. 1980, 47, 235.
(4) Oomen, E. W. J. L.; Smit, W. M. A,; Blasse, G. Chem. Phys. Leff. 1987, 138, 23. (5) Degen, J.; Schmidtke, H.-H. Chem. Phys. 1989, 129, 483. (6) Schmidtke, H.-H.; Krause, B.; Schbnherr, T. Ber. Bunsen-Ges. Phys.
Chem. 1990, 94, 700.
(7) Boulon, G.; Pednni, C.; Guidoni, M.; Pannel, C. J . Phys. 1975, 36, 267. (8) Oomen, E. W. J . L.; Smit, W. M. A,; Blasse, G. J . Phys. C 1986, 19, 3263.' (9) Donker, H.; Schaik, W. V.; Smit, W. M. A,; Blasse, G . Chem. Phys. Lefr. 1989, 158, 509. (10) Donker, H.: Smit. W. M. A.; Blasse, G.J . Phys. Chem. Solids 1989, 50,'60i. (1 1) Schmidtke, H.-H.; Basenbeck, M.; Degen, J. J . Lumin. 1989,44, 177. (12) Hughes, A. E.; Pells, G.P. Phys. Srafus. Solidi ( B ) 1975, 71, 707.
Schmidtke et al. in Figure 1.7J3 The solution of the eigenvalue problem for rate equations when describing only the depopulation of the excited level manifold is well-known.Iel6 In this case the rate equations do not contain the excitation parameters koi,i = 1,2. In addition, some further relations have been assumed depending on particular system investigated: Hager and CrosbyI4state thermal equilibrium (Boltzmann distribution) between excited states, Le., n2(t) = n , ( t ) exp(-AElkZ') with AE being the energy difference of levels 1 and 2 (cf. Figure l ) , which remains unchanged for all times of the decay process. Patterson et a1.16 on the other hand discuss the luminescence decay within a system of three excited states assuming kzl >> k l o in the notation of Figure 1. Gliemann et al.ls studied luminescence lifetimes using the same assumption. In all cases the nonradiative rates kI2and k21between two excited states are related by the Boltzmann factor as k12 = kzl exp(-M/kZ') (1) From eq 1 and setting kzl >> kloone obtains thermally equilibrated populations ni(r), i = 1, 2, of the excited states, Le., nz(t)= n , ( t ) exp(-M/kT). In this paper we shall consider the kinetics of a three-level system where the evolution in time of the excited level populations during the excitation is induced. The effect resulting from t b different assumptions on the transition rates will be discussed, which we denominate the thermal equilibrium regimeIz and the transition probability regime.svll Since the number of molecules n is constant in time, the equations Cin,(t)= n and X i dnkt)/dt = 0 must hold. By solution of the corresponding eigenvalue problem the population numbers obtainI3 2
ni(t) =
EAij exp(-rjt) + j=
i = 0, 1, 2
1
(2)
The amplitudes A , depend on the rate constants and on the initial conditions which are different for the rise and the decay process. The time constants supplied by the eigenvalues are r1,2= 6 f (b2 f (3) kij13917
with the abbreviations 26 = kol + klo
+ ko2 + kzo + k12 + k2l
(4)
A = kIO(k21 + k02 + k2o) + kOI(k21 + k12 + k2o) +
koz(k,z + kzd + w 2 0 ( 5 ) Since, by comparison of eqs 5 with 4, b2 is always very large relative to A, the square root in eq 3 can be expanded yielding rl E 26 and rz E A/26 (6) with rl being the fast and rz the slow component. The Aid coefficients contain two integration constants13 which are given by the starting conditions nl(0)and n2(0) at time t = 0, supplying when introduced into the eq 2 ni(0) = x j = l A i jwith i = 0, 1, 2. For a rise time measurement when all molecules are in the ground state at t = 0 the starting'conditions are nl(0) = nz(0) = 0. For relatively weak intensities of incident light, when most of the molecules remain in the ground state, the excitation rates koI and b2are small compared to all other rates k,. In this case the time constants of eq 3 are rl = kl0 + k12 + kz1 + k2o k10k21 + kl2k2, + k10k20 r2 = (7) k1o + k12 + k2l
+
k20
It can be shown that the decay curves obtained from eq 2 with the parameter pattern of Figure 1 do not depend on the absolute values of kol and ko2but only on the kO1/ko2 ratio which corresponds to the observation that the intensity-time curve is largely ~
(13) Stepanov, B. I. Theory ofluminescence; Iliffe Books: London, 1968. (14) Hager, G. D.; Crosby, G. A. J . Am. Chem. SOC.1975, 97, 7031. (15) Hidvegi, I.; von Ammon, W.; Gliemann, G.J . Chem. Phys. 1982,76, 4361. (16) Viswanath, K.; Vetuskey, J.; Leighton, R.; Krogh-Jespersen, M.-B.; Patterson, H. H. Mol. Phys. 1983, 48, 567. (17) Ozin, G. A.; Vander Voet, A. J . Mol. Sfrucf.1972, 13, 435.
The Journal of Physical Chemistry, Vol. 96, NO. 9, 1992 3607
Spectra of cis-[TeC1,BrZl2-
2'
2 1
T
AE2 90cm-1 A X 332'
i
when again eq 1 is used which now refers to a detailed balance of population kinetics" between levels 1 and 2. In this case the total populations nl and n2 are not at thermal equilibrium. At zero temperature the slow component r2 of eq 10 agrees with eq 8 and the fast component rl of eq 10 and eq 8 is equal to the respective largest k , parameter depending on the rate relations which are assumed. In the particular case where experimentally only a monoexponential decay is found in an emission experiment for one of the decay curves, the luminescence intensity 1, of level i is given by Zi(t) 0: ni(t) = Ai,z exp(-r2t) Ai,3 i = 1, 2 (1 1)
+
Figure 2. Lowest energy levels arising from s2 and sp electron configuration in 0,and C2, symmetry (degeneracies in parentheses). TABLE I: Selection Rules in CsuSymmetry for Electric Dipole (Upper Right Part) and Nonradiative (Lower Left Part) Transitions' radiative
a1 a2 bl
b2
Allowed electronic transitions are indicated by (+); for vibronic transitions the active (promoting) normal modes of vibrations are given.
independent on the power of incident light. For further simplification one can assume a thermal equilibrium population between levels 1 and 2 (thermal equilibrium regime). In this case k21>> kzoand kI2>> klomust hold', and eqs 7 become r l = kzl(l exp(-AE/kT))
+
cf. eq 2, where it is assumed that the first term referring to the fast component vanishes due to rl > r2within the considered time scale compared to the other terms, a situation which may also result from a small amplitude Ai,l < Ai,,. These experimental conditions are actually met for the presently investigated compound. Since in C, symmetry the transition 1 0 is forbidden while 2 0 is allowed (vide supra) the transition from level 1 is slower and will be observed in a monoexponential decay. For a rise time experiment assuming k20 >> klo and experimental conditions chosen such that kzl >> k12,(Le., AE/kT in eq 1 relatively large), one obtains from the increase of the populations ni(t) with nl(0)= nz(0) = 0, the intensity
-
-
A comparison with the measured intensity would allow the determination of r l and r2, Le. both lifetimes T~ = l/rl and T~ = l/r, from the rise time curve. The experimental data ought to be, however, very accurate, since rl must be determined from the deviation of 1 in the first term of eq 8. The population numbers in Figure 1 obtained for a rise time measurement can be used as starting conditions for a decay experiment: with the occupations nl(to) and n2(to) calculated for a pulse length t = to the amplitudes Aidof n l ( t ) and nz(t)can be calculated for t > to; Le., decay curves are obtained. With the transition rate relations kzo >> klo and kzl >> kI2and kol = ko2= 0 applicable for an emission experiment, the relation of the amplitudes (A2d, = 1, 2 in eq 2) in the decay curve of level 2 is calculated workmg out the corresponding formalism to be
_ -A2,l If, on the other hand, selection rules are considered to be more important to the system (transition propability regime), the transition 1 0 (i.e,, A2 A I in C, symmetry, cf. Figure 2) being radiatively and nonradiatively forbidden, cf. Table I (only allowed by vibronic selection rules), and the transition 2 0 (in C, A , ( z ) ,B,(x), or B 2 b )- A , ) allowed (nonradiatively for BI and B2 only vibronically), then the relation klo> k21since the nonradiative transition between levels 1 and 2 is electronically forbidden but only vibronically allowed. In an octahedral environment the activating mode for this vibronic transition would be a rl, vibration which occurs only as lattice mode.s With the latter inequality, eqs 9 become rl
=
k20
r2 = klo +- k21exp(-AE/kT)
(10)
A2,2
1+--
n2(to)
n,(to)
kll
k20
+ k21
n z ( t 0 )k2o + k2l - 1
(1 3)
Therefore, it is possible, by different choices of the length to of excitation pulse, to control the relative occupation numbers n2(to)/nl(to) (vide infra) and change the amplitude relations of the biexponential decay curve according to eq 13. Since it is k21/(k20 kzl) < 1 and (kZ0+ k 2 1 ) / k 1>> 2 1 in eq 13, a decrease of the occupation ratio by an appropriate choice of pulse length, would result in an intensity increase of the fast component A2,1relative to the slow component A2,2in this transition. A corresponding formula can be worked out for the 1 0 transition; the amplitude dependence A I , I / A I on , Z the occupation ratio is, however, given by a more complicated formula. If a change of amplitudes is observed by varying the excitation pulse length, the occupations between levels 1 and 2 cannot be at thermal equilibrium because the fast kinetics of the 2 0 is predominant. By changing the excitation pulse length it can be decided which of the two assumptions on the rate relations kzl >> kZ0,kI2>> klo (thermal equilibrium regime12) or k20 >> klo, k20>> kZI(transition probability regime5-l1)apply for the particular system considered.
+
-
-
3. Experimental Section
For the spectroscopic investigations, samples of different Te content have been used. Two typical preparations are as follows.
3608 The Journal o/ Physical Chemistry, Vol. 96, No. 9, 1992
Schmidtke et al.
TzlZK
b;
""r---*
= 457.5 nm) and excitation spectra (monitoring at the emission maximum) of cis-[TeCI4Br,l2-doped in (ethyl,N),cis-[SnCI4Br2]at given temperatures. The band A corresponds to the I',+ r4-and B to I',+ I'C, r
