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An investigation of the solvent dependence on the ultrafast intersystem crossing kinetics of xanthone
13 September 1996
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 259 (1996) 495-502
An investigation of the solvent dependence on the ultrafast intersystem crossing kinetics of xanthone Joseph J. Cavaleri, Katherine Prater, Robert M. Bowman * Department of Chemistry, University of Kansas, Lawrence, KS 66045, USA
Received 30 April 1996; in final form 21 June 1996
Abstract
The photophysics of xanthone in solution are measured using femtosecond pump-probe techniques. A kinetic model which includes intersystem crossing from both the ~TrTr* and ln~r * electronic states accurately represents the non-single exponential growth of the triplet-triplet absorption after excitation into the ~zrzr * state at 310 nm. The inters~'stem crossing rate constants are consistent with an 'inverse' gap effect due to solvent polarity induced shifts in the electronic states. The branching between intersystem crossing from the Jzmr * and tnzr * electronic states is also solvent dependent and is determined by the rate constant for internal conversion in the singlet electronic state.
1. I n t r o d u c t i o n
In contrast to most aromatic molecules, intersystem crossing (ISC) in aromatic carbonyl compounds is kinetically competitive with other radiative and non-radiative photophysical processes, and in many cases dominates [1,2]. The increase in the rate constant for ISC is due to the proximity o f the nzr * electronic state, created by the promotion of a nonbonded electron from the oxygen to the antibonding 7r * state, with respect to the zr~r * state. The nonradiative channels for relaxation can be enhanced by the vibronic coupling of the nTr * and 7rzr * states induced by out-of-plane bending modes [3]. This results in intersystem crossing on a picosecond time
* Corresponding author.
scale, as has been observed in several aromatic carbonyl compounds [4-14]. It is well known that the polarity of a solvent greatly influences the energies o f the electronic states in carbonyl systems [2]. An increase in solvent polarity results in stabilization of states of 7r~" * character and a blue shift of n ~ ~- * transitions as evidenced by a shift in the position o f the absorption maxima. Similar shifts have been observed in the triplet energy levels as a function o f solvent polarity. In many cases, aromatic carbonyl compounds fluoresce in polar solvents and exhibit no fluorescence in nonpolar solvents [2]. This indicates that the fluorescent 1 7rTr * state is the lowest excited singlet state in polar solvents, while in non-polar solvents, the nTr * state, which has little or no oscillator strength, is lowest in energy. The aromatic carbonyl chosen for study is xanthone. Xanthone is a rigid molecule which is planar
0009-2614/96/$12.00 Copyright © 1996 Elsevier Science B.V. All fights reserved. PH S0009-261 4(96)00782-8
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J.J. Cavaleri et a l . / Chemical Physics Letters 259 (1996) 495-502
except for the carbonyl oxygen which is slightly out of plane by 0.13 ,~ [15]. o H
Thus, the molecule has approximate C2v symmetry. Due to the rigidity of the system, any experimentally measured kinetics can be assigned to photophysical processes, and not to significant changes of structure in the excited state [16] or photochemical processes, such as isomerization reactions, which could have a dependence on solvent friction [17]. In addition, planar, rigid molecules have larger rate constants for intersystem crossing than their non-planar counterparts [18]. The quantum yield for ISC in xanthone at room temperature is 0.97 [19]. These properties make it an ideal probe of the solvent influence on the intersystem crossing kinetics. Numerous spectroscopic and kinetic studies on xanthone have been performed [7,8,19-24]. These studies revealed that the 3nTr * and the 3 ~ r * are very close in energy and the singlet-triplet energy gap is small [19-21,25]. Xanthone has a strong triplet-triplet absorption (TTA) in the 600-660 nm range [19,22]. The maximum of the TTA is seen to shift with solvent polarity going from 615 nm in 2-propanol to 655 nm in C C I 4 [19]. This observation as well as the reactivity of the triplet state on the microsecond time scale lead to the conclusion that the ordering of the 3n~-* state and the 37rzr * state changes upon going from a non-polar solvent to a polar solvent, with the 377"7/" * moving to lower energy as the solvent polarity increased [19]. The stabilization of the triplet is on the order of 1000-1500 c m - ~. This change of ordering of the triplet states as a function of solvent polarity was also invoked to explain the phosphorescent behavior of xanthone in glasses at 77 K [20]. Another study of xanthone in a crystal matrix at 1.2 K determined the energetics of the singlet and triplet states as well as the symmetries under the C2v point group [21]. Two time-resolved studies on the intersystem crossing kinetics of xanthone at room temperature have been presented in the literature [7,8]. Scott and
coworkers [7] tabulated picosecond measurements on the growth of the TTA of xanthone in benzene, p-dioxane, and ethanol, and found that the buildup in all three solvents was 8 ps. They report that the ISC kinetics are relatively insensitive to solvent polarity. Hochstrasser and coworkers [8] performed transient absorption measurements on xanthone in benzene using 8 ps pulses and found the rise time of the TTA at 650 nm to be --- 13 ps. In all cases single exponential rises were reported. There have been several ultrafast studies on the ISC crossing kinetics of benzophenone, a non-rigid molecule similar to xanthone. Mataga and coworkers [10] report almost a factor of two increase in the ISC time from 9 _+ 2 ps to 16 + 2 ps, on going from acetonitrile to isooctane. Turro and coworkers [14] report that within experimental error the ISC rate constants in both solvents are the same, but do report the same trend with solvent polarity, i.e., the growth of the TTA was 13 + 4 ps in acetonitrile and 18 + 4 ps in isooctane. A slight solvent dependence of the ISC dynamics of benzophenone were reported by Tamai et al. [12] using femtosecond transient grating spectroscopy. They found that the single exponential rise time of the triplet absorption increased from 9.6 + 0.9 ps to 11.6 + 0.9 ps on going from acetonitrile to CCI 4- No conclusive explanation was given for the observed solvent dependence in these studies. A system where a quantifiable solvent dependence on ISC kinetics has been observed is the diphenylcarbene system. Eisenthal and coworkers [26,27] have investigated the effects of solvent polarity on the singlet-triplet energy gap, ZlEsT, and the subsequent influence on the ISC of the chemical intermediates, diphenylcarbenes. They were able to change AEsT, by altering the molecular structure a n d / o r by changing the solvent polarity. They report that the rate constant for ISC decreases as AEsT decreases when the singlet and triplet electronic energies are close. These experimental results were successfully explained by noting that the coupling between the singlet and triplet manifolds was dominated by the density of triplet vibronic states isoenergetic with the singlet state. As the AEsT decreases, the density of triplet vibronic states decreases, resulting in a reduction of the ISC rate constant, a so-called 'inverse' gap effect. This behavior has not been seen in the ISC kinetics of any other system.
J.l. Cavaleri et al. / Chemical Physics" Letters 259 (1996) 495-502
The investigations reported here detail the ISC dynamics of xanthone after excitation into the ~zrTr * electronic state in three solvents: methanol, nbutyronitrile, and hexane. The growth of the T T A of xanthone in all solvents displays non-single exponential behavior which depends strongly on the solvent polarity. A model incorporating two pathways for ISC, one originating from the 17rTr * state and the other from the ~n~r * state explains the observed kinetics if E1-Sayed's propensity rules for ISC are considered [1]. As the solvent polarity is increased, the rate constant for ISC from the ~TrTr* state decreases, and from the l nTr * increases. These experimental observations can be explained by the 'inverse' gap effect seen in the ISC kinetics of diphenylcarbene systems. The change of the density of vibronic triplet states, as a result of the concurrent stabilization of 7rTr * states and destabilization of the nTr * states as solvent polarity is increased, is consistent with the observed changes in the rate constants. The branching ratio between the two pathways is determined by a competition between the internal conversion between the ~'~r * state and the ~nzr * state and the intersystem crossing from the ~TrTr* state.
"~
1.2
120o
I.O
~ 8c~
0.8
~
!
32 36 40 44
0.4
--1
t"
0.6
"~
"
48
52
C
0.2 0.0 300
320
340
360
380
Wavelength (nm) Fig. 1. The absorption spectrum of 1 mM xanthone in (A) hexane, (B) n-butyronitrile, and (C) methanol. The arrow indicates the
pump wavelength of 310 nm. The inset displays the shift in cmof the first absorption peak as a function of the solvent polarity parameter, E.r(30). The peak shifts are relative to the peak maximum in hexane.
497
2. Experimental The experiments were performed on an amplified colliding-pulse mode-locked laser system which has been described previously [28]. The output is a 30 Hz train of < 100 fs pulses with a central wavelength of 620 nm and pulse energy of 0.5-1.0 mJ. The 310 nm pump pulse is generated by frequency doubling in a 0.5 m m KDP crystal. All transient absorptions were measured at the magic angle. The sample, 5 mM xanthone (Aldrich), was flowed in a 1 mm path length quartz cell with a peristaltic pump. The solvents hexane, n-butyronitrile, and methanol (Fisher Scientific) were reagent grade and used as purchased. Absorption spectra were measured with a Kontron Instruments Uvikon model 9410 U V - V I S spectrophotometer.
3. Results and discussion
3.1. UV-VIS absorption spectra The absorption spectra of 1.0 mM xanthone in hexane, n-butyronitrile, and methanol are shown in Fig. 1. The excitation energy of 32260 c m - J for the pump probe experiments is shown by an arrow. A red shift in the onset of absorption as a function of solvent polarity is evident as well as slight differences in the overall absorption line shape. The inset in Fig. 1 shows that the spectral shift of the absorption maxima in wavenumbers as a function of the polarity parameter ET(30) [29] is approximately linear. The absorption maxima were determined from fitting the spectra to a sum of Gaussians; the low energy peak is chosen for comparison. The origin of the shift is attributed to stabilization of the lerTr* state, commonly observed in aromatic carbonyl compounds[2]. The stabilization of the 17rzr * in going from hexane to methanol is -- 1000 cm -~. As mentioned previously [19], a similar stabilization of approximately the same magnitude, i.e., 1000-1500 cm -1, has been observed in the 371"7/"* state of xanthone. We see no evidence of the 'forbidden' n ~ ~-* transition within the sensitivity limits of our apparatus so it was not possible to quantify the predicted shift in the ~nTr * state. An increase in energy of the i nrr in benzophenone of = 800 c m -
498
J.l. Cavaleri et al. / Chemical Physics Letters 259 (1996) 495-502
has been observed on going from cyclohexane to ethanol [1]. We use this value as an approximation of the destabilization of the n~r * electronic states due to polar solvents in both the singlet and triplet manifolds. Thus, an increase in polarity appears to produce a concomitant stabilization in both the singlet and triplet electronic states of ~'Tr" character and destabilization of the states of nrr" character. Fig. 2 shows the energies, symmetries, and assignments of the states involved in the photophysics of xanthone in a non-polar solvent (hexane) and a polar solvent (methanol) using our results as well as previous experimental results [19-21]. The direction but not the magnitude of the shifts of energies of the nTr * states are shown in Fig. 2 since no quantitative measurements are available for the expected destabilization in polar solvents in xanthone.
0.6 0.4 0.2 0.0 /-"~ 0.8 ~
0.4
~
0.2
b
~1~ 0.0
~Z 08[-
c
06I 0.4 02 0.0
1 ~:
-
-2
r-._-
I
*
0
I
,
2
I
4
,
I
6
Time (ps) Fig. 3. Six picosecond scans of the transient absorption at 620 nm following an excitation at 310 nm of 5 mM xanthone in (a) hexane, (b) n-butyronitrile, and (c) methanol. The solid lines are fits to the kinetic model described in the text.
3.2. Femtosecond pump-probe experiments Fig. 3 shows 6 ps scans of the transient absorption at 620 nm following an excitation pulse of 310 nm of xanthone in hexane, n-butyronitrile, and methanol. Fig. 4 shows a 100 ps scan of xanthone in nbutyronitrile, indicating that the kinetics are complete on that time scale. The early time scans are each normalized to the asymptotes of the long time scans and scaled to one for comparison. As stated earlier, absorption between 600-660 nm is assigned to the well-known triplet-triplet absorption in xanthone. The transient absorption at 620 nm is assigned to the absorption from the electronic triplet state and therefore the growth of the signal is indicative of the formation of the triplet ground state, i.e., the inter-
system crossing photophysics. The growth kinetics cannot be fit by a single exponential rise or a sequential A ~ B ~ C model. The experimental data can be fit to a biexponential, but no definitive assignments of the rate constants and amplitudes can be made.
3.3. Kinetic model of appearance of triplet-triplet absorption A biexponential growth which cannot be represented by an A ~ B ~ C model is indicative of at least two pathways to the final product, in this case the absorbing triplet state. A Jablonski-type diagram
Nonpolar solvent
Polar solvent
~n*(lA1)
29,450 cm-t~.........._~
nn*QA2)
27,700 em-l
nn*QAt)
~*(3AI) n~*(3A2)
_ _ - -
n~*0A2) 25,900 cm-I 25,400 cm "I ~ " ~
28,450 cm-I ?
27,700cm"1 ? nTt*(3A2)
- ~ * ( 3 A t )
25,400 cm-l 24,400 cm -l
Fig. 2. Energy level diagram for the singletand tripletelectronicstatesin a nonpolar solvent (hexane) and a polar solvent (methanoD. The energies and symmetry assignments given are taken from the absorption data presented here and Refs. [1,19-21]. The arrows on the ln~" * and 3nor electronic states represent the expected blue shifts in a polar solvent. Values for the destabilization energies of the nor ° states in xanthone have not been reported in the literature.
499
J.l. Cavaleri et aL / Chemical Physics Letters 259 (1996) 495-502 1.0
. "s~.'~t-urZ
....
:2--.~'~..~-.,,:.~
0.8 0.6 "~
0.4
r~
0.2
0.0
.,2,¢,.'~
Time (ps) Fig. 4. One hundred picosecond scan of the transient absorption at 620 nm following excitation at 310 nm of 5 mM xanthone in n-butyronitrile. The solid line is a fit to the kinetic model described in the text.
310 n m we are exciting into the vibrationally excited IA t ¢rTr* state. E1-Sayed's rules state that the allowed transitions for intersystem crossing are o f the type nTr * ~ ¢rcr* [1]. The two pathways for intersystem crossing, which obey E l - S a y e d ' s rules, originating from the 1A l wTr * electronic state are: (a) intersystem crossing from 1AI TrTr* to 3 A 2 n w * electronic state (rate constant = kisc(i)) followed b y relaxation in the triplet m a n i f o l d (rate constant = kr~), and (b) internal conversion from the IA I ~'/r* to the ~A 2 n~r * (rate constant= kic), followed by intersystem crossing to the 3A~ ~-~ * state (rate cons t a n t = kisc(ii)) and subsequent relaxation in the triplet electronic manifold. A n exact solution to the proposed model is shown below: S i g n a l ( t ) = p * ( 1 - e -k~'0i)') + q * ( 1 - e -k~,t)
of the states potentially i n v o l v e d in the intersystem crossing are s h o w n in Fig. 5. These states form the basis o f an e l e m e n t a r y kinetic m o d e l of the photophysics of xanthone used to interpret our results. A t
S1 E l e c t r o n i c M a n i f o l d IA 2 nx*
+ r *(1 - e -(k,c +kiS~O))t)
where p, q, and r are functions o f the four rate
T1 E l e c t r o n i c
1A 1 7ut*
(l)
3A 2 nx*
Manifold
3A 1 7t7~*
kic kisc(i) ~
~
kisc(ii)
krel
= Shift of 7trt* electronic state with increasing solvent polarity
Fig. 5. A diagram showing the kinetic processes and rate constant designations considered in the kinetic modelling of the experimental data. The relative energies are similar to those given in Fig. 2 for the nonpolar solvent. The downward arrows represent the stabilization of the ,rrr * states as the solvent polarity is increased.
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J.l. Cavaleri et a l . / Chemical Physics" Letters 259 (1996) 495-502
Table 1 Time constants for the internal conversion and intersystem crossing kinetics of xanthone Solvent
E T (30) (kcal/mol)
zic (ps) I1rzr * ~ tnTr *
7"isc(i) (ps) lzrzr * ~ 3n'n" *
7isc(ii) (ps) Inzr * ~ 3~'7r *
hexane n-butyronitrile methanol
30.9 43.3 51.9
2.3 + 0.1 1.1 ± 0.1 0.90 ± 0.05
0.70 ± 0.05 1.4 + 0.1 1.4 ± 0.!
10.0 ± 0.5 7.1 -4- 0.3 4.3 ± 0.2
constants as shown below; they are not freely floating amplitude factors. kic
p=
kic + kisc(i ) - kisc(ii ) ' q=
ki~c(i) kic + k ~ ( i )
- k~
'
1
kic kisc(ii )
ki~ + ki~c(i)
ki~(ii) - kic - kis~(i )
r
k~c(i) k~.~ kre I -
kic - kisc(i )
This equation has the same number of parameters, four, as a biexponential fit where the amplitudes are freely floating. Thus, this model does not introduce more parameters than a biexponential fitting function. Since the transient absorption is observed in polar and non-polar solvents, it is not clear from earlier studies the nature of the electronic state responsible for the triplet-triplet absorption. Therefore, the assumption is made that relaxation in the triplet manifold, k ~ , is not the rate limiting step, i.e., it is assumed to be on the order of or faster than all of the other rate constants. The validity of this assumption will be tested in the interpretation of the abstracted rate constants as a function of solvent polarity. 3.4. Interpretation o f solvent-dependent rate constants
The solid lines on the experimental data in Figs. 3 and 4 are fits to Eq. (1) fixing k~l to be less than 250 fs, convolved with a Gaussian response function representing our pulse. This procedure has been described in detail previously [30]. The results of the fitting are shown in Table 1. There are several
interesting trends in the abstracted rate constants with polarity. The smallest rate constant, kisc(ii), increases with solvent polarity. This yields formation times of 10.0, 7.1, and 4.3 ps for xanthone in hexane, n-butyronitrile, and methanol, respectively, for the intersystem crossing times from the l nTr * state. The number reported by Hochstrasser and coworkers [8] for the growth of the triplet absorption was -- 13 ps in benzene, a non-polar solvent, which is consistent with our results. Earlier time-resolved studies [7,8] on the photophysics of xanthone did not report biexponential behavior in their results. This could have been due to either the larger pulse widths used in the experiments, or the fact that their excitation energy of 28300 cm-~ is not energetic enough to access the lzrzr * state directly, therefore only the ISC channel originating from the ~nrr* state is possible. Thus, these results are not inconsistent with the findings presented here. The increase in the intersystem crossing rate constant with polarity can be understood in the following manner. El-Sayed's rule[l] asserts that the electronic state to which the I nTr * state intersystem crosses is the 3zrer * state. The energy separation between the 1A 2 nzr* and t h e 3A 1 71"/'/'* is on the order of 1800 cm - l in a non-polar matrix [21], which is in the small gap limit for intersystem crossing. As discussed earlier, the 3A l zrTr * state of xanthone is lowered by -- 1000 c m - i in going from hexane to methanol. This value for the change in the energy gap is only a lower limit since we have not included the expected blue shift of the nTr * state due to solvent polarity since it has not been experimentally quantified. Thus the energy gap increases as the polarity of the solvent increases. An increase in the intersystem crossing rate constant with increasing singlet-triplet energy separation merely reflects the effect of the increase in the density of vibronic states in the triplet manifold isoenergetic (or
J.l. Cavaleri et a l . / Chemical Physics Letters 259 (1996) 495-502
nearly isoenergetic) with the l nTr * state. This so called 'inverse' gap effect has been seen previously in carbene systems by Eisenthal and coworkers [26,27]. It should be noted that the increase in rate constant for the ISC kinetics of benzophenone as solvent polarity increases [10,12,14] can also be explained in this fashion. The rate constant for intersystem crossing from the 17rTr * state, kisc(i), shows the opposite trend as discussed above. The triplet appearance times increase from 700 fs to 1.4 ps upon going from hexane to methanol. The energy separation, 17rTr*-3nTr ~, in non-polar solvents is -- 4500 c m - ~, still in the small gap limit. The change in intersystem crossing time with solvent polarity also reflects the 'inverse' gap effect [26,27]. In this case the ~TrTr * and 3n~" * state move closer as the ~7r~r * state is stabilized and the 3 nTr * state is destabilized in polar solvents. Therefore, the energy gap is decreased, lowering the density of vibronic triplet states isoenergetic with the l 7rTr * state, reducing the rate constant for intersystem crossing. The intersystem crossing time is faster from the ~TrTr* state as compared to the ~nTr * due to the larger inherent gap between electronic states, i.e., E(~TrTr * ) - E ( 3 n T r *) is greater in all solvents versus E(lnTr * ) - E(37rTr * ). The rate constant for internal conversion, kic, in the excited singlet manifold appears to also be solvent dependent. The internal conversion (IC) time decreases from 2.3 ps to 900 fs between hexane and methanol. These times are consistent with the internal conversion time of benzophenone of -- 1 ps for the ~-1r~ ~ ~nTr* transition [1]. As the solvent polarity increased the difference in energy between the ~TrTr* state and the ~n~-* state decreased and the rate constant for internal conversion is observed to increase. This is consistent with the sensitivity of IC to the energy gap between the electronic states [1]. A decrease in the energy gap would result in higher Franck-Condon factors of the participating vibrational states and increase the rate constant for internal conversion. The branching ratio between intersystem crossing from the ~TrTr* state versus the I nTr * state will be determined by the relative magnitude of the rate constants k~sc(ii) and kic. This can be seen clearly in Fig. 3 where the kinetics are dominated by the fast intersystem crossing process in the • non-polar solvent and the slow ISC in the polar
501
solvents. Therefore, the intersystem crossing from the 17rTr * state effectively competes with the rapid process of internal conversion and in fact dominates in non-polar solvents.
4. Conclusions The rigid structure of xanthone makes it an ideal probe of the photophysical processes independent of any concurrent structural changes that could be influenced by solvent friction. The results presented here shed new light on the influence of solvent on the intramolecular relaxation processes, i.e. the effect of the shifts of tile electronic energy levels on the photophysics as a function of solvent polarity of aromatic carbonyl molecules in solution. Both intersystem crossing and internal conversion are controlled by the influence of solvent polarity on the relative energies of the ~-Tr * electronic states. The experimental data can be explained by two competing pathways for the intersystem crossing, the kinetics of which display an 'inverse' gap effect dominated by changes in the density of vibronic states as a function of solvent polarity. The branching ratio between the two channels for intersystem crossing are also influenced by the red shift of the rrTr * electronic states as well as a blue shift in the n~r* states, resulting in an increase in the rate constant for internal conversion as the 1~7r *-~n~r* energy gap is decreased. This work serves as another step toward a better understanding of photophysical processes in excited molecules.
Acknowledgements We gratefully acknowledge Dr. David Benson and his group for their assistance and use of their spectrophotometer in measuring the U V - V I S absorption spectra. We would also like to thank Professor Carey Johnson for numerous helpful discussions on this project. This work was supported by the Cottrell Scholars Award from the Research Corporation, and the National Science Foundation EPSCoR program.
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References [1] N. Turro, in: Modem molecular photochemistry (BenjaminCummings, Menlo Park, CA, 1978). [2] J.A. Barltrop and J.D. Coyle, in: Excited states in organic chemistry (John Wiley and Sons, London, 1975). [3] E.C. Lira, in: Excited states, Vol. III, ed. E.C. Lira (Academic Press, New York, 1977). [4] P.M. Rentzepis, Science 169 (1970) 239. [5] R.M. Hochstrasser, H. Lutz and G.W. Scott, Chem. Phys. Lett. 24 (1974) 162. [6] R.W. Anderson Jr., R.M. Hochstrasser, H. Lutz and G.W. Scott, Chem. Phys. Left. 28 (1974) 153. [7] D.E. Damschen, C.D. Merritt, D.L. Perry, G.W. Scott and L.D. Talley, J. Phys. Chem. 82 (1978) 2268. [8] B.I. Greene, R.M. Hochstrasser and R.B. Weisman, J. Chem. Phys. 70 (1979) 1247. [9] H. Miyasaka and N. Mataga, Bull. Chem. Soc. Jpn. 63
(1990) 131. [10] H. Miyasaka, K. Morita, K. Kamada and N. Mataga, Bull. Chem. Soc. Jpn. 63 (1990) 3385. [11] H. Miyasaka, K. Morita, K. Karnada, T. Nagata, M. Kiri and N. Mataga, Bull. Chem. Soc. Jpn. 64 (1991) 3229. [12] N. Tamai, T. Asahi and H. Masuhara, Chem. Phys. Lett. 198 (1992) 413. [13] K.S. Peters and J. Lee, J. Phys. Chem. 97 (1993) 3761. [14] P.F. McGarry, C.E. Doubleday Jr., C.-H. Wu, H.A. Staab and N.J. Turro, J. Photochem. Photobiol. A: Chem. 77 (1994) 109.
[15] S. Onuma, K. lijima and I. Oonishi, Acta. CrystaUogr. C46 (1990) 1725. [16] V.D. Vachev and J.H. Frederick, Chem. Phys. Lett. 249 (1996) 476. [17] D.H. Waldeck, Chem. Rev. 91 (1991) 415. [18] N.I. Nijegorodov and W.S. Downey, J. Phys. Chem. 98
(1994) 5639. [19] J.C. Scaiano, J. Am. Chem. Soc. 102 (1980) 7747. [20] H.J. Pownall and J.R. Huber, J. Am. Chem. Soc. 93 (1971) 6429. [21] A. Chakrabarti and N. Hirota, J. Phys. Chem. 80 (1976) 2966. [22] A. Garner and F. Wilkinson, J. Chem. Soc., Faraday Trans. 2 72 (1976) 1010. [23] M. Koyanagi, T. Terada and K. Nakashima, J. Chem. Phys. 89 (1988) 7349. [24] M. Barra, C. Bohne and J.C. Scaiano, J. Am. Chem. Soc. 112 (1990) 8075. [25] M. Szymanski, A. Maciejewski and R.P. Steer, J. Photochem. Photobioi. A: Chem. 57 (1991) 405. [26] E.V. Sitzmann, J.G. Langan, D Griller, and K.B. Eisenthal, Chem. Phys. Lett. 161 (1989) 353. [27] J.G. Langan, E.V. Sitzmann and K.B. Eisenthal, Chem. Phys. Lett. 110 (1984) 521. [28] D.P. Colombo Jr., K.A. Roussel, J. Saeh, D.E. Skinner, J.J. Cavaleri and R.M. Bowman, Chem. Phys. Lett. 232 (1995) 207. [29] C. Reichardt, Angew. Chem. Int. Ed. Engl. 4 (1965) 29. [30] D.E. Skinner, D.P. Colombo Jr., JJ. Cavaleri and R.M. Bowman, J. Phys. Chem. 99 (1995) 7853.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 259 (1996) 495-502
An investigation of the solvent dependence on the ultrafast intersystem crossing kinetics of xanthone Joseph J. Cavaleri, Katherine Prater, Robert M. Bowman * Department of Chemistry, University of Kansas, Lawrence, KS 66045, USA
Received 30 April 1996; in final form 21 June 1996
Abstract
The photophysics of xanthone in solution are measured using femtosecond pump-probe techniques. A kinetic model which includes intersystem crossing from both the ~TrTr* and ln~r * electronic states accurately represents the non-single exponential growth of the triplet-triplet absorption after excitation into the ~zrzr * state at 310 nm. The inters~'stem crossing rate constants are consistent with an 'inverse' gap effect due to solvent polarity induced shifts in the electronic states. The branching between intersystem crossing from the Jzmr * and tnzr * electronic states is also solvent dependent and is determined by the rate constant for internal conversion in the singlet electronic state.
1. I n t r o d u c t i o n
In contrast to most aromatic molecules, intersystem crossing (ISC) in aromatic carbonyl compounds is kinetically competitive with other radiative and non-radiative photophysical processes, and in many cases dominates [1,2]. The increase in the rate constant for ISC is due to the proximity o f the nzr * electronic state, created by the promotion of a nonbonded electron from the oxygen to the antibonding 7r * state, with respect to the zr~r * state. The nonradiative channels for relaxation can be enhanced by the vibronic coupling of the nTr * and 7rzr * states induced by out-of-plane bending modes [3]. This results in intersystem crossing on a picosecond time
* Corresponding author.
scale, as has been observed in several aromatic carbonyl compounds [4-14]. It is well known that the polarity of a solvent greatly influences the energies o f the electronic states in carbonyl systems [2]. An increase in solvent polarity results in stabilization of states of 7r~" * character and a blue shift of n ~ ~- * transitions as evidenced by a shift in the position o f the absorption maxima. Similar shifts have been observed in the triplet energy levels as a function o f solvent polarity. In many cases, aromatic carbonyl compounds fluoresce in polar solvents and exhibit no fluorescence in nonpolar solvents [2]. This indicates that the fluorescent 1 7rTr * state is the lowest excited singlet state in polar solvents, while in non-polar solvents, the nTr * state, which has little or no oscillator strength, is lowest in energy. The aromatic carbonyl chosen for study is xanthone. Xanthone is a rigid molecule which is planar
0009-2614/96/$12.00 Copyright © 1996 Elsevier Science B.V. All fights reserved. PH S0009-261 4(96)00782-8
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J.J. Cavaleri et a l . / Chemical Physics Letters 259 (1996) 495-502
except for the carbonyl oxygen which is slightly out of plane by 0.13 ,~ [15]. o H
Thus, the molecule has approximate C2v symmetry. Due to the rigidity of the system, any experimentally measured kinetics can be assigned to photophysical processes, and not to significant changes of structure in the excited state [16] or photochemical processes, such as isomerization reactions, which could have a dependence on solvent friction [17]. In addition, planar, rigid molecules have larger rate constants for intersystem crossing than their non-planar counterparts [18]. The quantum yield for ISC in xanthone at room temperature is 0.97 [19]. These properties make it an ideal probe of the solvent influence on the intersystem crossing kinetics. Numerous spectroscopic and kinetic studies on xanthone have been performed [7,8,19-24]. These studies revealed that the 3nTr * and the 3 ~ r * are very close in energy and the singlet-triplet energy gap is small [19-21,25]. Xanthone has a strong triplet-triplet absorption (TTA) in the 600-660 nm range [19,22]. The maximum of the TTA is seen to shift with solvent polarity going from 615 nm in 2-propanol to 655 nm in C C I 4 [19]. This observation as well as the reactivity of the triplet state on the microsecond time scale lead to the conclusion that the ordering of the 3n~-* state and the 37rzr * state changes upon going from a non-polar solvent to a polar solvent, with the 377"7/" * moving to lower energy as the solvent polarity increased [19]. The stabilization of the triplet is on the order of 1000-1500 c m - ~. This change of ordering of the triplet states as a function of solvent polarity was also invoked to explain the phosphorescent behavior of xanthone in glasses at 77 K [20]. Another study of xanthone in a crystal matrix at 1.2 K determined the energetics of the singlet and triplet states as well as the symmetries under the C2v point group [21]. Two time-resolved studies on the intersystem crossing kinetics of xanthone at room temperature have been presented in the literature [7,8]. Scott and
coworkers [7] tabulated picosecond measurements on the growth of the TTA of xanthone in benzene, p-dioxane, and ethanol, and found that the buildup in all three solvents was 8 ps. They report that the ISC kinetics are relatively insensitive to solvent polarity. Hochstrasser and coworkers [8] performed transient absorption measurements on xanthone in benzene using 8 ps pulses and found the rise time of the TTA at 650 nm to be --- 13 ps. In all cases single exponential rises were reported. There have been several ultrafast studies on the ISC crossing kinetics of benzophenone, a non-rigid molecule similar to xanthone. Mataga and coworkers [10] report almost a factor of two increase in the ISC time from 9 _+ 2 ps to 16 + 2 ps, on going from acetonitrile to isooctane. Turro and coworkers [14] report that within experimental error the ISC rate constants in both solvents are the same, but do report the same trend with solvent polarity, i.e., the growth of the TTA was 13 + 4 ps in acetonitrile and 18 + 4 ps in isooctane. A slight solvent dependence of the ISC dynamics of benzophenone were reported by Tamai et al. [12] using femtosecond transient grating spectroscopy. They found that the single exponential rise time of the triplet absorption increased from 9.6 + 0.9 ps to 11.6 + 0.9 ps on going from acetonitrile to CCI 4- No conclusive explanation was given for the observed solvent dependence in these studies. A system where a quantifiable solvent dependence on ISC kinetics has been observed is the diphenylcarbene system. Eisenthal and coworkers [26,27] have investigated the effects of solvent polarity on the singlet-triplet energy gap, ZlEsT, and the subsequent influence on the ISC of the chemical intermediates, diphenylcarbenes. They were able to change AEsT, by altering the molecular structure a n d / o r by changing the solvent polarity. They report that the rate constant for ISC decreases as AEsT decreases when the singlet and triplet electronic energies are close. These experimental results were successfully explained by noting that the coupling between the singlet and triplet manifolds was dominated by the density of triplet vibronic states isoenergetic with the singlet state. As the AEsT decreases, the density of triplet vibronic states decreases, resulting in a reduction of the ISC rate constant, a so-called 'inverse' gap effect. This behavior has not been seen in the ISC kinetics of any other system.
J.l. Cavaleri et al. / Chemical Physics" Letters 259 (1996) 495-502
The investigations reported here detail the ISC dynamics of xanthone after excitation into the ~zrTr * electronic state in three solvents: methanol, nbutyronitrile, and hexane. The growth of the T T A of xanthone in all solvents displays non-single exponential behavior which depends strongly on the solvent polarity. A model incorporating two pathways for ISC, one originating from the 17rTr * state and the other from the ~n~r * state explains the observed kinetics if E1-Sayed's propensity rules for ISC are considered [1]. As the solvent polarity is increased, the rate constant for ISC from the ~TrTr* state decreases, and from the l nTr * increases. These experimental observations can be explained by the 'inverse' gap effect seen in the ISC kinetics of diphenylcarbene systems. The change of the density of vibronic triplet states, as a result of the concurrent stabilization of 7rTr * states and destabilization of the nTr * states as solvent polarity is increased, is consistent with the observed changes in the rate constants. The branching ratio between the two pathways is determined by a competition between the internal conversion between the ~'~r * state and the ~nzr * state and the intersystem crossing from the ~TrTr* state.
"~
1.2
120o
I.O
~ 8c~
0.8
~
!
32 36 40 44
0.4
--1
t"
0.6
"~
"
48
52
C
0.2 0.0 300
320
340
360
380
Wavelength (nm) Fig. 1. The absorption spectrum of 1 mM xanthone in (A) hexane, (B) n-butyronitrile, and (C) methanol. The arrow indicates the
pump wavelength of 310 nm. The inset displays the shift in cmof the first absorption peak as a function of the solvent polarity parameter, E.r(30). The peak shifts are relative to the peak maximum in hexane.
497
2. Experimental The experiments were performed on an amplified colliding-pulse mode-locked laser system which has been described previously [28]. The output is a 30 Hz train of < 100 fs pulses with a central wavelength of 620 nm and pulse energy of 0.5-1.0 mJ. The 310 nm pump pulse is generated by frequency doubling in a 0.5 m m KDP crystal. All transient absorptions were measured at the magic angle. The sample, 5 mM xanthone (Aldrich), was flowed in a 1 mm path length quartz cell with a peristaltic pump. The solvents hexane, n-butyronitrile, and methanol (Fisher Scientific) were reagent grade and used as purchased. Absorption spectra were measured with a Kontron Instruments Uvikon model 9410 U V - V I S spectrophotometer.
3. Results and discussion
3.1. UV-VIS absorption spectra The absorption spectra of 1.0 mM xanthone in hexane, n-butyronitrile, and methanol are shown in Fig. 1. The excitation energy of 32260 c m - J for the pump probe experiments is shown by an arrow. A red shift in the onset of absorption as a function of solvent polarity is evident as well as slight differences in the overall absorption line shape. The inset in Fig. 1 shows that the spectral shift of the absorption maxima in wavenumbers as a function of the polarity parameter ET(30) [29] is approximately linear. The absorption maxima were determined from fitting the spectra to a sum of Gaussians; the low energy peak is chosen for comparison. The origin of the shift is attributed to stabilization of the lerTr* state, commonly observed in aromatic carbonyl compounds[2]. The stabilization of the 17rzr * in going from hexane to methanol is -- 1000 cm -~. As mentioned previously [19], a similar stabilization of approximately the same magnitude, i.e., 1000-1500 cm -1, has been observed in the 371"7/"* state of xanthone. We see no evidence of the 'forbidden' n ~ ~-* transition within the sensitivity limits of our apparatus so it was not possible to quantify the predicted shift in the ~nTr * state. An increase in energy of the i nrr in benzophenone of = 800 c m -
498
J.l. Cavaleri et al. / Chemical Physics Letters 259 (1996) 495-502
has been observed on going from cyclohexane to ethanol [1]. We use this value as an approximation of the destabilization of the n~r * electronic states due to polar solvents in both the singlet and triplet manifolds. Thus, an increase in polarity appears to produce a concomitant stabilization in both the singlet and triplet electronic states of ~'Tr" character and destabilization of the states of nrr" character. Fig. 2 shows the energies, symmetries, and assignments of the states involved in the photophysics of xanthone in a non-polar solvent (hexane) and a polar solvent (methanol) using our results as well as previous experimental results [19-21]. The direction but not the magnitude of the shifts of energies of the nTr * states are shown in Fig. 2 since no quantitative measurements are available for the expected destabilization in polar solvents in xanthone.
0.6 0.4 0.2 0.0 /-"~ 0.8 ~
0.4
~
0.2
b
~1~ 0.0
~Z 08[-
c
06I 0.4 02 0.0
1 ~:
-
-2
r-._-
I
*
0
I
,
2
I
4
,
I
6
Time (ps) Fig. 3. Six picosecond scans of the transient absorption at 620 nm following an excitation at 310 nm of 5 mM xanthone in (a) hexane, (b) n-butyronitrile, and (c) methanol. The solid lines are fits to the kinetic model described in the text.
3.2. Femtosecond pump-probe experiments Fig. 3 shows 6 ps scans of the transient absorption at 620 nm following an excitation pulse of 310 nm of xanthone in hexane, n-butyronitrile, and methanol. Fig. 4 shows a 100 ps scan of xanthone in nbutyronitrile, indicating that the kinetics are complete on that time scale. The early time scans are each normalized to the asymptotes of the long time scans and scaled to one for comparison. As stated earlier, absorption between 600-660 nm is assigned to the well-known triplet-triplet absorption in xanthone. The transient absorption at 620 nm is assigned to the absorption from the electronic triplet state and therefore the growth of the signal is indicative of the formation of the triplet ground state, i.e., the inter-
system crossing photophysics. The growth kinetics cannot be fit by a single exponential rise or a sequential A ~ B ~ C model. The experimental data can be fit to a biexponential, but no definitive assignments of the rate constants and amplitudes can be made.
3.3. Kinetic model of appearance of triplet-triplet absorption A biexponential growth which cannot be represented by an A ~ B ~ C model is indicative of at least two pathways to the final product, in this case the absorbing triplet state. A Jablonski-type diagram
Nonpolar solvent
Polar solvent
~n*(lA1)
29,450 cm-t~.........._~
nn*QA2)
27,700 em-l
nn*QAt)
~*(3AI) n~*(3A2)
_ _ - -
n~*0A2) 25,900 cm-I 25,400 cm "I ~ " ~
28,450 cm-I ?
27,700cm"1 ? nTt*(3A2)
- ~ * ( 3 A t )
25,400 cm-l 24,400 cm -l
Fig. 2. Energy level diagram for the singletand tripletelectronicstatesin a nonpolar solvent (hexane) and a polar solvent (methanoD. The energies and symmetry assignments given are taken from the absorption data presented here and Refs. [1,19-21]. The arrows on the ln~" * and 3nor electronic states represent the expected blue shifts in a polar solvent. Values for the destabilization energies of the nor ° states in xanthone have not been reported in the literature.
499
J.l. Cavaleri et aL / Chemical Physics Letters 259 (1996) 495-502 1.0
. "s~.'~t-urZ
....
:2--.~'~..~-.,,:.~
0.8 0.6 "~
0.4
r~
0.2
0.0
.,2,¢,.'~
Time (ps) Fig. 4. One hundred picosecond scan of the transient absorption at 620 nm following excitation at 310 nm of 5 mM xanthone in n-butyronitrile. The solid line is a fit to the kinetic model described in the text.
310 n m we are exciting into the vibrationally excited IA t ¢rTr* state. E1-Sayed's rules state that the allowed transitions for intersystem crossing are o f the type nTr * ~ ¢rcr* [1]. The two pathways for intersystem crossing, which obey E l - S a y e d ' s rules, originating from the 1A l wTr * electronic state are: (a) intersystem crossing from 1AI TrTr* to 3 A 2 n w * electronic state (rate constant = kisc(i)) followed b y relaxation in the triplet m a n i f o l d (rate constant = kr~), and (b) internal conversion from the IA I ~'/r* to the ~A 2 n~r * (rate constant= kic), followed by intersystem crossing to the 3A~ ~-~ * state (rate cons t a n t = kisc(ii)) and subsequent relaxation in the triplet electronic manifold. A n exact solution to the proposed model is shown below: S i g n a l ( t ) = p * ( 1 - e -k~'0i)') + q * ( 1 - e -k~,t)
of the states potentially i n v o l v e d in the intersystem crossing are s h o w n in Fig. 5. These states form the basis o f an e l e m e n t a r y kinetic m o d e l of the photophysics of xanthone used to interpret our results. A t
S1 E l e c t r o n i c M a n i f o l d IA 2 nx*
+ r *(1 - e -(k,c +kiS~O))t)
where p, q, and r are functions o f the four rate
T1 E l e c t r o n i c
1A 1 7ut*
(l)
3A 2 nx*
Manifold
3A 1 7t7~*
kic kisc(i) ~
~
kisc(ii)
krel
= Shift of 7trt* electronic state with increasing solvent polarity
Fig. 5. A diagram showing the kinetic processes and rate constant designations considered in the kinetic modelling of the experimental data. The relative energies are similar to those given in Fig. 2 for the nonpolar solvent. The downward arrows represent the stabilization of the ,rrr * states as the solvent polarity is increased.
500
J.l. Cavaleri et a l . / Chemical Physics" Letters 259 (1996) 495-502
Table 1 Time constants for the internal conversion and intersystem crossing kinetics of xanthone Solvent
E T (30) (kcal/mol)
zic (ps) I1rzr * ~ tnTr *
7"isc(i) (ps) lzrzr * ~ 3n'n" *
7isc(ii) (ps) Inzr * ~ 3~'7r *
hexane n-butyronitrile methanol
30.9 43.3 51.9
2.3 + 0.1 1.1 ± 0.1 0.90 ± 0.05
0.70 ± 0.05 1.4 + 0.1 1.4 ± 0.!
10.0 ± 0.5 7.1 -4- 0.3 4.3 ± 0.2
constants as shown below; they are not freely floating amplitude factors. kic
p=
kic + kisc(i ) - kisc(ii ) ' q=
ki~c(i) kic + k ~ ( i )
- k~
'
1
kic kisc(ii )
ki~ + ki~c(i)
ki~(ii) - kic - kis~(i )
r
k~c(i) k~.~ kre I -
kic - kisc(i )
This equation has the same number of parameters, four, as a biexponential fit where the amplitudes are freely floating. Thus, this model does not introduce more parameters than a biexponential fitting function. Since the transient absorption is observed in polar and non-polar solvents, it is not clear from earlier studies the nature of the electronic state responsible for the triplet-triplet absorption. Therefore, the assumption is made that relaxation in the triplet manifold, k ~ , is not the rate limiting step, i.e., it is assumed to be on the order of or faster than all of the other rate constants. The validity of this assumption will be tested in the interpretation of the abstracted rate constants as a function of solvent polarity. 3.4. Interpretation o f solvent-dependent rate constants
The solid lines on the experimental data in Figs. 3 and 4 are fits to Eq. (1) fixing k~l to be less than 250 fs, convolved with a Gaussian response function representing our pulse. This procedure has been described in detail previously [30]. The results of the fitting are shown in Table 1. There are several
interesting trends in the abstracted rate constants with polarity. The smallest rate constant, kisc(ii), increases with solvent polarity. This yields formation times of 10.0, 7.1, and 4.3 ps for xanthone in hexane, n-butyronitrile, and methanol, respectively, for the intersystem crossing times from the l nTr * state. The number reported by Hochstrasser and coworkers [8] for the growth of the triplet absorption was -- 13 ps in benzene, a non-polar solvent, which is consistent with our results. Earlier time-resolved studies [7,8] on the photophysics of xanthone did not report biexponential behavior in their results. This could have been due to either the larger pulse widths used in the experiments, or the fact that their excitation energy of 28300 cm-~ is not energetic enough to access the lzrzr * state directly, therefore only the ISC channel originating from the ~nrr* state is possible. Thus, these results are not inconsistent with the findings presented here. The increase in the intersystem crossing rate constant with polarity can be understood in the following manner. El-Sayed's rule[l] asserts that the electronic state to which the I nTr * state intersystem crosses is the 3zrer * state. The energy separation between the 1A 2 nzr* and t h e 3A 1 71"/'/'* is on the order of 1800 cm - l in a non-polar matrix [21], which is in the small gap limit for intersystem crossing. As discussed earlier, the 3A l zrTr * state of xanthone is lowered by -- 1000 c m - i in going from hexane to methanol. This value for the change in the energy gap is only a lower limit since we have not included the expected blue shift of the nTr * state due to solvent polarity since it has not been experimentally quantified. Thus the energy gap increases as the polarity of the solvent increases. An increase in the intersystem crossing rate constant with increasing singlet-triplet energy separation merely reflects the effect of the increase in the density of vibronic states in the triplet manifold isoenergetic (or
J.l. Cavaleri et a l . / Chemical Physics Letters 259 (1996) 495-502
nearly isoenergetic) with the l nTr * state. This so called 'inverse' gap effect has been seen previously in carbene systems by Eisenthal and coworkers [26,27]. It should be noted that the increase in rate constant for the ISC kinetics of benzophenone as solvent polarity increases [10,12,14] can also be explained in this fashion. The rate constant for intersystem crossing from the 17rTr * state, kisc(i), shows the opposite trend as discussed above. The triplet appearance times increase from 700 fs to 1.4 ps upon going from hexane to methanol. The energy separation, 17rTr*-3nTr ~, in non-polar solvents is -- 4500 c m - ~, still in the small gap limit. The change in intersystem crossing time with solvent polarity also reflects the 'inverse' gap effect [26,27]. In this case the ~TrTr * and 3n~" * state move closer as the ~7r~r * state is stabilized and the 3 nTr * state is destabilized in polar solvents. Therefore, the energy gap is decreased, lowering the density of vibronic triplet states isoenergetic with the l 7rTr * state, reducing the rate constant for intersystem crossing. The intersystem crossing time is faster from the ~TrTr* state as compared to the ~nTr * due to the larger inherent gap between electronic states, i.e., E(~TrTr * ) - E ( 3 n T r *) is greater in all solvents versus E(lnTr * ) - E(37rTr * ). The rate constant for internal conversion, kic, in the excited singlet manifold appears to also be solvent dependent. The internal conversion (IC) time decreases from 2.3 ps to 900 fs between hexane and methanol. These times are consistent with the internal conversion time of benzophenone of -- 1 ps for the ~-1r~ ~ ~nTr* transition [1]. As the solvent polarity increased the difference in energy between the ~TrTr* state and the ~n~-* state decreased and the rate constant for internal conversion is observed to increase. This is consistent with the sensitivity of IC to the energy gap between the electronic states [1]. A decrease in the energy gap would result in higher Franck-Condon factors of the participating vibrational states and increase the rate constant for internal conversion. The branching ratio between intersystem crossing from the ~TrTr* state versus the I nTr * state will be determined by the relative magnitude of the rate constants k~sc(ii) and kic. This can be seen clearly in Fig. 3 where the kinetics are dominated by the fast intersystem crossing process in the • non-polar solvent and the slow ISC in the polar
501
solvents. Therefore, the intersystem crossing from the 17rTr * state effectively competes with the rapid process of internal conversion and in fact dominates in non-polar solvents.
4. Conclusions The rigid structure of xanthone makes it an ideal probe of the photophysical processes independent of any concurrent structural changes that could be influenced by solvent friction. The results presented here shed new light on the influence of solvent on the intramolecular relaxation processes, i.e. the effect of the shifts of tile electronic energy levels on the photophysics as a function of solvent polarity of aromatic carbonyl molecules in solution. Both intersystem crossing and internal conversion are controlled by the influence of solvent polarity on the relative energies of the ~-Tr * electronic states. The experimental data can be explained by two competing pathways for the intersystem crossing, the kinetics of which display an 'inverse' gap effect dominated by changes in the density of vibronic states as a function of solvent polarity. The branching ratio between the two channels for intersystem crossing are also influenced by the red shift of the rrTr * electronic states as well as a blue shift in the n~r* states, resulting in an increase in the rate constant for internal conversion as the 1~7r *-~n~r* energy gap is decreased. This work serves as another step toward a better understanding of photophysical processes in excited molecules.
Acknowledgements We gratefully acknowledge Dr. David Benson and his group for their assistance and use of their spectrophotometer in measuring the U V - V I S absorption spectra. We would also like to thank Professor Carey Johnson for numerous helpful discussions on this project. This work was supported by the Cottrell Scholars Award from the Research Corporation, and the National Science Foundation EPSCoR program.
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J.J. Cavaleri et a l . / Chemical Physics Letters 259 (1996) 495-502
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