Selected rotational level lifetimes and singlet-triplet coupling in the S1 state of glyoxal

Chemitztl Physics 42 (I 979) 3 I j-323 0 Ndrth-Holland Publishing Company

Y

SELECTED ROTATIONAL LEVEL LIFETIMES AND SINGLET-TRIPLET IN THE S, STATE OF GLYOXAL

COUPLING

C. MICHEL and A. TRAMER Laborrttoirr de Photoplrysique Molckoluire - C.N.R.S.. UtkcrsitL; Puris-Sd.

91405 Orsuy, Fror1ce Received 16 February 1979

The lluorescence collision-free lifetimes were measured for a few rotational levels of the 0” S, state of glyoxal using a single-mode Ar* laser. Decays are exponential over 5-6 lifetimes 2nd variation of ~~~ does not exceed j’x,. The higher limit of singlet-triplet mixing coeficient 1)’ 4 3 x IO-’ is deduced from the lifetime measurements. The efliciency of collision induced intersystem crossing and its relation with (/?‘) value is discussed. ISC is absent in collision-free

conditions

for deuterated

glyoxal

as it is known

to be for protonated

glyoxal.

1. introduction

where in the weak coupling limit:

Since the early work by Anderson et al. [l] it is known that the S,-T, coupling in glyoxal corresponds to the small-molecule weak-coupling limit. The absence of the intersystem crossing in collisionfree condition [ 1,2], and of detectable spectral perturbations in the S, t SOabsorption (at least for the 0: band) [3] is consistent with this mode!. On the other hand, the $,-So and the T,-So coupling may be well described in terms of the statistical-limit model [l]. Evidence is given by high internal conversion yield in glyoxal-h2 (qi, > 0.75 [4]), strong deuteration effect on S, state [s] and on T, state [6] lifetimes, as well as by the lack of the inert-gas pressure effect on triplet lifetime and yield [ 1,6]. The behavior of the excited system may thus be discribed in terms of the”exacf‘ molecular states IS> and 1;) resulting from the coupling between a pair of pure spin zero order states Is, o, JKM) and

(un>

If, u’, J‘X’M’)

p rovided

with a non-radiative

/Y’ z V:/@E: + 4ui), where USl= (s( H,” It> 6,,.6,,.6 .I,,,f’_t

non-radiative widths y:’ B 7;‘. Therefore yi = azys + pZy, z azys; yyd z aryyd, y; = /Fr, + a’y, z flzys;

Ii, o’, J’ICM’)

width

perturbations were not detected [3]. We will

a2 + /I” = 1,

attempt thus to estimate the average value of (u,,> ? in an indirect way.

+ ,!llt.d,J’K’M’),

= -fiI s, u, JKM)

(3)

yl”” zz fi’y;“d.

The values of the us, coupling constants and Q, /I mixing coeficients may be usually deduced from spectral perturbations (rovibronic level shifts from expected positions) but in the case of glyoxal such

continuum: = aIs, II, JKM)

(2)

We suppose as usual, that only the singlet level is provided with a radiative width yyd and that y:“d 2! 0. The coupling to the dissipative ground-state continua may be accounted for by the non-zero

due to their coupling to the ground-state quasil&u, JKh!)

4 VP 2 1~5 - E,I = SE,,,

’ Glyoxal’s shape being very close to a symmetric

-I- a(~, u’, J’K’W),

coupling different

(1) 315

top, the

between rotational levels correlated to K of the symmetrica top may be thus neglected.

316

C. Michel, A. Tramrr/L~tbrws of the S, stute of glyoxul

(1) Since the distribution of SE,, energy gaps between effectively coupled 1s) and jr) levels is completely random (the average value calculated from Haarhoff formula [7] being of the order of 1 cm- * for triplet levels isoenergetic with vibrationless S, state)T, one can expect an erratic variation of a’ and B2 mixing coefficients from one rotational level to another. The width of the distribution depends on / and that of pre-exponential factors in the case of &pulse excitation to (a’)‘/(/?‘>‘. The values of (p2> and (u,,> may be thus deduced from the deviation from a purely exponential decay [9,10]_ We thoroughly checked whether such deviations may be detected. (3) Since in the weak coupling case, no intramolecular radiationless process is expected, the phosphorescence emission from collision free glyoxal reported in recent work El l] seemed a rather surprising result. To make this point clear, we repeated pressure dependent phosphorescence intensity measurements for glyoxal-h, and -d,.

2. Experimental

Glyoxal-hz was prepared by heating glyoxal polymer in presence of P,O,, glyoxal-d, by oxidation of ethylen-& by a SeOz + P,O, mixture. Products were purified by a trap-to-trap distillation in vacua, the receiver being cooled by liquid Nz or dry ice-acetone mixture. All spectroscopic measurements were carried out ’ A more exact Stein-Rabinovitch formula yields 1.2 levels/cm - ’ according to ref. [22]. This estimation is confirmed by a direct experiment involving s-f level crossing in strong magnetic fields [23].

in flowing gas in order to avoid the effects due to photochemical products, the gas pressure was controlled by a system ofmicrovalves and measured by means of a Pirani gauge calibrated with an MKS baratron. Cylindrical cell of 30 mm diameter was used for fluorescence measurements and a spherical one of 120 mm diameter in the phosphorescence studies, both equipped with plane windows and a black horn. Glyoxal was excited by the 454.5 nm line of an argon-ion laser (Coherent Radiation CR-12 Model) working either in multimode or single-mode regime. In the latter case, the intracavity etalon was driven by a stepping motor, allowing a slow scanning across the argon line, controlled by means of a Spectra-Physics spectrum analyser. A Jobin-Yvon HRS3 monochtomator, a cooled EMI 9658 photomultiplier and a photon-counting system were used for detection_ Fluorescence spectra were recorded with 1.4 cm-’ spectral resolution, while for fluorescence lifetime measurements the monochromator with 70 cm-’ spectral slit was set up at the peak of the 8: + 47 band. The laser beam was slightly defocused in order to minimize the effects due to diffusion of excited molecules out of the zone viewed by the detecting system. Square light pulses of variable (30 ns to 6 ,us) length at a repetition rate of 30 kHz and with the extinction ratio of 1: 100 were obtained by means of an electro optic Gsanger LMOZO P5W modulator combined with Glan prisms. Decay curves were recorded by the single-photon-counting technique. For phosphorescence intensity measurements under a multimode excitation, the laser beam was modulated with a 1 kHz mechanical chopper, the detecting system being equipped with a linear gate rejecting light signals recorded during the opening period of the chopper. The phosphorescence intensity in the 0: and 27 bands was recorded as a function of the glyoxal pressure, the optical detection system being modified in such a way that the whole volume of the cell was viewed by the detector.

317

3. Results 3.1. Single rotationallevel lifetimes The assignment of rotational levels excited by modes of the Ari laser 454.5 nm line was performed by Parmenter and Rordorf [12]. The resolution being limited by the Doppler width, e pure single-rotational level excitation is impossible but by a suitable choice of the exciting mode, the major part of the absorbed intensity corresponds to the pumping of a determined rotational level. The technique described in ref. [13] has been used: the monochromator with narrow slits was first set up at one of the rotational features of the lluorescence spectrum and the excitation spectrum was recorded (fig. 1). Then the excitation conditions were fixed and lifetime measurements were ready to be performed. In order to obtain reasonable counting rate, the spectral bandwidth at the detection side was chosen in such a way that the major part of the O”-state emission was collected, while the emission from 12’ and 7’ rotational levels pumped in overlapping 12: and 7: “hot” bands [ 1l] was rejected. We record obviously the fluorescence of a few rotational levels but (as it can be deduced from the data of ref. [ 131 confirmed by our own measurements) 80-90 “/, of the total intensity originates from a single rotational level (underlined in table 1) at each excitation wavelength. The results are summarized in table 2. The glyoxal pressures being varied between 2 and 8 mTorr, the collision-free lifetimes TV and apparent quenching constants k, are derived from SternVolmer plots. In view of the limited pressure range the accuracy of the kg measurements is low and the physical meaning of it - in our detection conditions - not well-established: the variation of lifetimes with increasing gas pressure is mainly due to the electronic quenching and vibrational up-relaxation. However, considering the limited detection spectral width, the observed quenching rates may be affected also by rotational relaxation, the importance of which is different for different initially excited levels. Nevertheless, lifetimes values extrapolated to zero pressure (rO) retain all their physical meaning. Our value 7. observed under the multimode excitation coincides - within the error limits - with previous data [2]. This value is somewhat larger different

4

SGHZ

___)

Fig 1. Excitation spectra corresponding to different observation wavelengths. Letters indicate the excitation wavelength chosen for single rotational level lifetime measurements.

Table I Assignment of excitedrotational levels with corresponding excitation position in the excitation spectra, fig. 1; underlined levels refer to preponderant

ones

Excited levels

Excitation position

K’=6.J’=13 K’ = 5. J’ = 18; 5,46 K’ = 5, J’ = 18; 5,46;w K’=8.J =49;m K’ = 8, J’ = 49; 6.12; 8.25

A B C D E

Table 2 Quenching constents and collision free lifetimes of several rotational levels obtained by Stern-Voimer plot in pressure ran_ee of 2 to 8 mTorr. The average error on k, is of the order of 15 x,_ J..R

Excitation position

k, x IO6 (s-’ Torr-‘)

;;s,

A B C D

8.6 8.6 7.8 7.3

2.34 2.29 2.27 2.31

E

5.1

2.24 & 0.07

multimode

5.5 + 1.5

r0 = 2.37 * 0.02

Beyer data [z]

6.3 i 0.35

q, = 2.41 + 0.06

+ 0.07 + 0.07 & 0.07 t 0.07

than the average of the lifetimes ra.K) measured under a single mode excitation, but this is not surprising: multimode excitation concerns a much

larger number of rotational levels than those live particular ones we attained: pumping of high rotational levels leads to the excitation of weak rotational lines forming a quasi-continuous background. T:.“) values show slight variations of about 5 % hardly exceeding the error limits of t 3 %_ Each decay is purely exponential over three lifetimes: this

means that even if we excite more than one level their lifetimes must be closely the same (a simultaneous excitation of 2-3 levels with lifetimes

differing by z 10% gives a detectable deviation from the pure exponential). The lifetimes of individual rotational levels do not show any clear dependence on the level energy, J and K quantum numbers etc. Their variation may be explained either by fluctuations in the singlettriplet coupling due to a random distribution of the 8E,, spacing between effectively coupled zero-order [s) and It) levels or to the fluctuations in the excited singlet-ground singlet interaction, resulting from not entirely smooth character of the Se quasicontinuum. In order to decide between those alternatives, precise quantum yield measurements would be necessary: in the first case, the coupling to the discrete T, manifold modifies lifetimes but not the quantum yields, while in the latter one lifetimes and yields depend in the same way on the coupling to the dissipative Se quasi-continuum. Parmenter [ 121 measured the variation of fluorescence quantum

yield relative to different rotational levels to be within 30’;/,; more precise measures would be necessary. Thus, if the observed variation on T:."' is considered as real and entirely due to the Sr-T, interactions, it shows the absence of any important perturbations, i.e. of a particularly strong (or weak) coupling between a given pair of Is> and It> states. 3.2. Scorch of a long component ofjlrlorescetrce As mentioned above, the excitation of a perturbated molecular state in the weak-coupling case is equivalent to an independent (incoherent) but simultaneous population of strongly radiative {?i} states giving origin to an intense,prompt fluorescence and of weakly radiative {r} states responsible for a weak, slow emission. The decay times and pre-exponential factors depend in well defined excitation conditions on average values of mixing coefficients a’ and p’_ The exponential form of the decay of glyoxal fluorescence (re z 2.4~s) is well known [2, 143 and corresponds obviously to the prompt component. However, no attempt to evidence possible deviations from a single-exponential behavior has been reported. In order to estimate
by collisions; if the quenching constant for the longlived state is equal to that of the rotational relaxation in the singlet manifold, i.e. 2 x IO7 s-’ Torr-’ [15], its decay time at p = 6 mTorr would be thus of the order of 8 pts. From the computer simulation of the decay curves taking into account background and statistical noise, we may conclude that a nonexponential character of a two-component decay with T, = 2.35 ps and T? z 8 ps will clearly appear if the initial ratio of pre-exponential factors AZ/A, exceeds l/200. From this estimation of the higher limit for the ratio of initial fluorescence intensities: &IA,

= l,,,,(t,)ll,,,,,,(t,)

< 5 x lo- 3,

(4)

we may estimate the higher limit of the /?‘/a” ratio. As it can be easily shown, in the case of excitation of {SI}and (i) levels by square light pulse (0, fo) (the probability of excitation being assumed as proportional to the level radiative width $” and y:_‘“)the initial intensity ratio is given by: ~sl&$prompt(fO) = VdWG+YdNr(to), where IV&,) and N&J

(5)

are initial populations:

IV@,) = Z0[l - exp(-kr,)]k’“‘/k,

(6)

k is the overall decay rate = -#I. By assuming as previously the linear dependence of the total decay rate on the gas pressure: ki(p) = kj(0) + kip;

kdp) = ki(O) + I@),

where ki = 2 x lo6 s-’ Torr-’ and ki = 2 x lo7 s- ’ Torr-’ and using eq. (3), we obtain for r, = 5 ps and p = 6 x 10m3Torr: Islaa(fo)/lprompl(fo)= WV.

(7)

Hence pz < 4 x lo-’ for all exciting wavelengths. If supposed that {$ levels are randomly distributed with respect to {i} levels, we may expect still higher N$Nj ratios when excitation is carried out at wavelengths corresponding to the minimum of the SI + S, absorption, i.e. when NAO) is reduced by a factor of ten. If this correction is taken into account, the higher limit for j?’ will be reduced to about 1 x lo-‘.

It is well known that radiationless transitions in isolated molecules occur uniquely in the case, when one of interacting manifolds may be considered at the time scale of the experiment as a dissipative continuum. The S,-T, coupling in glyoxal low vibronic states corresponds obviously to an interaction between discrete manifolds and intersystem crossing in collision-free conditions does not lit into general scheme of the small-molecule weakcoupling limit. In a recent work, Kuttner et al. [l I] have reported a non-negligible rate of the intramolecular intersystem crossing, evidence being given by a non-

zero phosphorescence yield in collision-free glyoxal~1~.This observation, if confirmed, would necessitate a quite direrent approach to the problem of the S,-T, coupling in glyoxal. For this reason, the measurements of the pressure dependence of the phosphorescence intensity for glyoxal-hl and 4, were repeated. The main difference with respect to Kuttner’s et al. experiment consisted in: (i) Large dimensions of the gas cell. Considering the 9.6 p.s lifetime of glyoxal-d,, the probability of collisions with the cell walls is not negligible (about 1 “/,) even if the laser beam is focused in the center of a 30 mm diameter cell. Such collisions induce very efficiently the S-T crossing, while the triplet quench-

ing is much less efficient. The collisions with cell walls may, however, be neglected for glyoxal-It2 (even for R = I.5cm) and for glyoxal-d, sufficiently large (R = 6 cm) cell.

in a

(ii) Careful elimination of the fluorescence background by both time- and energy-resolution. (iii) Low power of the cw laser, reducing the possibility of a subsequent two-photon excitation. A further difference in experimental conditions, is our use of multimode llser line, which gives

relatively narrow excitation band and restricted excitation spectral range, but this does not seem very important. Results are given in fig. 2. The phosphorescence intensity normalized to the number of absorbed photons I&)/p is plotted as a function of pressure in the 0.5-20 mTorr range for both glyoxal-h, and glyoxal-dz. The expected pressure dependence of

C. Michel, A. Tramer/Lifetimesofthe S, state ofglyoxal

320

I

*phIpUp

p 0

- iphipl

20

30

BO

I p

ptmtorrl

> 9 0 O0 /, 2

10

C

Fig. 2. Phosphorescence intensity normalized to the number of absorbed glyoxal-d,.

IO

I mtorrl

photons

for (a) glyoxal-h,,

and for(b)

Zph’p”p = A (kj + k:;i + k,-p) (k, + k,,p)’

I 15

plm torrl 1

Fig. 3. (a) Computed 1,&p)/(p) versus p with rate constants taken from ret [l l] for intramolecular IX rate k’,, = 0, 1 x 104s-’ and 2 x lo4 s-’ (ref. [l 11): upper curve. (b) Experimental data (000) compared to same computed expression 1,&)/p versus pressure but fork, B k,,p; lower curve k;, = 0; upper curve k;, = 2 x lo4 s-’ (ref.[I I]). (Curves are normalised at 45 mTorr for (a), and at highest pressure data point for(b).)

p 2 10 mTorr and the maximum of the curve is attained at 50(35)mTorr. Our experimental data

ZJp)/p in_presence of intramolecular.ISC rate kf (corresponding to k, of ref. [l 11)is given by: k;;p + k;

5

(8)

If ki, the intrinsic decay rate of thermaly equilibrated triplet state, is supposed to be 164 s- I [6] and if ICY,,, the rate constant for triplet quenching by ground

state glyoxal molecules, is equal to 3.1 x lo3 s-’ Torr-l [6] (or 6.9 x lo3 s-’ Torr-’ [ll]) the slope of 1,&)/p versus p (lig. 3a) decreases rapidly for

show only a slight deviation from the linearity. This is probably due to a deactivation of long-living triplet molecules on the cell walls; if such deactivation has an efficiency exceeding lo-* per collision, one can assume k, 9 k,,,p for p G 20 mTorr. In fig. 3b, the experimental data are compared to Z,,(p)/p computed for &, + k,,,p z constant, and different values of kg,. In the low pressure range ZJp)/p shows a linear dependence on the gas

C. Michel, A. Tramer/Lijidtnes ofthe S, stcrreof gl_roml

pressure with an intersection point close to zero excluding k~i 2 lo3 S-‘. On the other hand, it must be pointed out that the slope of 1,&)/p reported in ref. [I l] cannot be explained by k$ # 0 and must be due to residual collisions of S, state molecules (probably with the cell walls) inducing an efficient S + T transfer.

4. Discussion The results of the present work are negative in this sense that no direct determination of c1and fi coefficients (or of v,, and E,, values) for a given pair of levels could be done. On the other hand, in the limited spectral range given by the Ar’ laser width the number of rotational levels is too low to allow a statistical treatment. The way to deduce information from experimental data consists in a probabilistic approach. Obviously, both parameters u, and 6E,, vary in a random way for different pairs of states; nevertheless, in absence of correlation between u,, and SE,,, the average value (u,,) may be estimated by assuming o,, to be constant. The probability to find a given value of fl* will then depend only on the probability of a corresponding 6E,, value, and may be expressed for a completely random distribution of triplet levels, by [ 171: P(bE,) d@E,,) = 2p, e-zpcdEs~d@E,,),

(9)

where p, is the average triplet-level density. Therefrom P(jl*) dfl and integrated probability to find fl* in the (0, j&J range may be easily deduced. The experimental data (single-rotational level lifetimes as well as the weakness of the slow fluorescence) show that for five accidentally chosen rotational levels the 8’ values are contained in the (0, 0.4). If the average density of triplet levels pl is supposed to be I/cm-‘, such a narrow distribution will be highly improbable for u,, > 3.10-* cm-‘. This estimation is strongly corroborated by the absence of strong perturbations in the rotational structure of the 0; band, where about 2000 rotational frequencies have been measured by Ramsay and Paldus [3], with the accuracy of 3 x 10m3 cm-’ and Doppler-limited resolution. For u,, exceeding the Doppler width of 3 x lo-* cm-‘, the perturbation

321

is easily detactable when 6E,, < usl. From eq. (9), the probability of such a close spacing for u = , cm-’ and p, = t/cm -’ is of6 x IO- 2 . ;hls_ ~~:~~’ would correspond to a large number 0; strong perturbations. Thus u,~must be smaller than 3 x lo-* cm-‘, but for a more precise evaluation of u,, from spectroscopic data, Doppler-free absorption (or excitation) spectra are needed. At last, an indirect argument may be deduced from the van der Werff et al. study of biacetyl [lS]_ The electronic matrix element for the s-t coupling is of the same order of magnitude for biacetyl and glyoxal, and uzp, is expected to be constant when the coupling is redistributed between a larger number of vibronic levels. Since u:p, = 4.10M5 with pr = 105/cm-’ for biacetyl, we obtain usr = 6.10e3 cm-’ in the case of glyoxal. All the data argue in favor of u,, values of the order of 10e2 cm-’ (corresponding to f12 < lo-*). Such low values of the coupling and mixing parameters seem to be contradictory with a high efficiency of the collision induced intersystem crossing: it is well known that the cross section for CI ISC a,, is about l/10 of that of the total (vibrational and rotational) relaxation within the singlet manifold G,O,[19]. L=5 0.1 was deduced from this ratio through the first order perturbation treatment [19]_ The first-order treatment cannot be, however, applied to the case of glyoxal. The basic assumption of the Freed CI ISC theory [IO] is the collisional mixing of rotational levels, inducing a coupling between close lying I$ J) and It, J’) levels with the coupling matrix element VU.‘J’ = PKJ.SJ~I

(IO)

describes the collisional where LJ, = LJ. coupling between rotational levels responsible for the rotational relaxation within the singlet (or triplet) manifolds. It has been recently shown [IS] that a single collision may induce transitions to a large number of [sJ) levels i.e. that Vs,.s,’ S a&,

where 6E, average spacing of the singlet rotational levels is of the order of 0.1 cm-‘. On the other hand, the estimation of the overall density of rovibronic triplet levels which may be collisionally coupled to the jsJ) state is uncertain.

If the density of (t) vibronic levels is of l/cm- ‘, each of them yielding ten rotational levels per cm-’ and if the coupling is limited to those contained in the energy band of the order of kT, we obtain the density of about 103/cm-‘. If it is so, even for fi z IO-‘, we have equally:

values but it shows that for sufficiently strong collisional interactions and/& high p,/p, level density ratios, gii,, may attain large values even for a very weak s-t mixing.

5. Conclusion

that the perturbation treatment is inappropriate. As a matter of fact, the problem is to be treated in terms of a strong collisional coupling between two dense manifolds. In absence of a proper theoretical treatment, we applied tentatively to the estimation of ~,,,--a,,, ratio a simple two-level model of the collision induckd intersystem crossing [21]. The time dependent collisional perturbation mixing two states (which may be strong with respect to 6.E) is given by: so

V = $?A

e-n’bL sech ($caar),

(11)

where A and a are constants measuring strength and range ofthe interaction potential, 0 the impact parameter and II the relative velocity of colliding partners_ We calculated G,~ and Go”*by numerical integration of the equations: a(@ = (@a’) sech’(SE/hov) x

y

+

In

(&‘l’A

6E

[

s Co

CT=

-&jci

I

)I

Acknowledgement

The authors are highly indebted to Dr. C. Tric for many discussions and valuable comments and to Mr. M. Lavollde and Miss 0. Benoist d’Azy for the help in measurements and data treatment.

(12) References

Lc

u(u)P(u)c~dv/

0

_ 27$’

Spectral and collision-free lifetime measurements suggest a very weak singlet-triplet mixing for the vibrationless level of the glyoxal first excited singlet state: 8’ < IO-‘. Intramolecular intersystem crossing does not occur in both deuterated and hydrogenerated species. The S,-T, interaction is entirely consistent with the weak coupling limit in a small-molecule case. This result is not contradictory with a relatively high efticiency of the collision-induced intersystem crossing, the first order perturbation treatment being inappropriate in the case of @yoxal.

P(c) drl

(13)

s Cl

(P(U) is the Maxwell-Boltzmann distribution of velocities.) For a transition within the singlet manifold (rotational relaxation: G_,~),A was varied in the 50-250 cm-’ range and 6E = 6E,,.,. = 6E, was assumed equal to 10-l cm- * while for G,~=A is replaced by PA [ 17,2 I] with fi varying in the 10e2-3 x 10-l cm-’ range and 6E = 6EfJ., = 6 E, = lob3 cm-‘. l/(~, the van der Waals radius of the glyoxal molecule, was taken in the both cases equal to 4 A. We found that for A = ZOOcm-’ the value 0.1 of a,&,, is reached for fl” z 10e4 while for A = 50 cm- ’ we need /I’ zz 2 x 10e3. In view of these drastic approximations, this model cannot be used for any evaluation of 8’

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matrices

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D. Grimbert,

[z]

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[23] R. Jost. M. Lombardi. C. Michel and A. Tramer, to be published.