Radiative and nonradiative decay rates of state selected H–(C≡C)–2H+, D–(C≡C)–2D+,Ã2Π u , determined by a photoelectron–photon coincidence techniqueJohn P. Maier and Fritz Thommen Citation: The Journal of Chemical Physics 73, 5616 (1980); doi: 10.1063/1.440083 View online: http://dx.doi.org/10.1063/1.440083 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/73/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Near ultraviolet photolysis of C2H2: A precise determination of D 0(HCC−H) J. Chem. Phys. 101, 2630 (1994); 10.1063/1.467635 Photoionpair formation and photoelectroninduced dissociative attachment in C2H2: D 0(HCC–H) J. Chem. Phys. 93, 5586 (1990); 10.1063/1.459629 Photoelectron–photon coincidence studies of halobenzene cations in their excited electronic states J. Chem. Phys. 77, 4427 (1982); 10.1063/1.444444 Emission spectra of alkyl substituted diacetylene radical cations: CH3–C≡C–C≡C–R+ with R=H, D, CH3, andCD3; CD3–C≡C–C≡C–R+ with R=H, D, CD3 and C2H5–C≡C–C≡C–R+ with R=H and C2H5. Competition of theradiative à (π−1) → X̃ (π−1) and fragmentation decay of their à (π−1) states J. Chem. Phys. 72, 701 (1980); 10.1063/1.438905 Studies of the metastable c 3Π u state of H2: Towards a twophoton amplifier J. Chem. Phys. 69, 2076 (1978); 10.1063/1.436806

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Radiative and non radiative decay rates of state selected H-(C C)-2H+, D-(C C)-2D+, A 2Hu , determined by a photoelectron-photon coincidence technique

John P. Maier and Fritz Thommen

Physikalisch-chemisches Institut der Universitiit Basel. Klingelbergstrasse 80. CH-4056 Basel. Switzerland (Received 31 july 1980; accepted 14 August 1980)

Fluorescence quantum yields and cascade-free lifetimes of diacetylene and dideuterodiacetylene cations in selected vibrational levels in the A'll. state have been measured. This was accomplished by the detection of coincidences between energy selected electrons and undispersed photons following ionization by He(Ia) photons. The radiative and nonradiative rate constants of such state selected cations under collision­free conditions are therefore directly obtained. The fluorescence quantum yields are high, but not unity. and decrease as do the lifetimes on increasing the internal energy in the A'll. state. These first results are used to illustrate the decay behavior of open-shell organic cations for which only the 2:4 .... 21 internal conversion process completes with the 2:4 .... 21 radiative relaxation.

I. INTRODUCTION

Radiationless transitions in isolated molecules have been the subject of much experimental and theoretical work.1,2 However, in the determinations of the absolute rates for the decay channels, two main obstacles are en­countered. Firstly, the absolute determinations of the fluorescence quantum yields are problematic as they rely on suitable standards for comparison and on care­ful apparative calibrations. 3 Thus they are often marked with uncertainty. Secondly, the evaluation of the rate constants of the individual nonradiative pathways are ambiguous because of concurrent processes; for ex­ample in the case of the S("'N""SO internal conversion, the SI ~ To intersystem crossing is always a competing pro­cess. 2

The study of the internal conversion process is Simpler with open-shell polyatomic organic cations because there is usually no state of higher multiplicity (i. e. ,4 ii) lying below the lowest excited doublet state (2...1) in energy to provide a decay channel. Thus, such radical cations in the lowest excited doublet state relax, under collision­free conditions, either radiatively (2,4 - 2X), or by in­ternal conversion (2,4 -vvv- 2 X), if fragmentation is ener­getically not accessible.

In order to probe quantitatively the decay pathways, the radiative relaxation has to be evident. This has been the objective of our past studies and by now the emission spectra (2JJ, or 2,4 - 2X) of around hundred organic radi­cal cations have been discovered. 4 One of the conse­quences of this is that, among the smaller polyatomic cations in particular, the frequencies of many of the totally symmetric vibrational fundamentals have been inferred for the ground (2X) cationic states from the emission spectra4 and are now being obtained for the ex­cited (2,4") state from laser induced excitation spectra in the gaseous and matrix states. 5 Thus, the frequencies of these modes in both the states of concern in the inter­nal conversion process are known. Furthermore, among these radical cations there are even examples where the electronically excited cations fragment (2,4 ~ F;, F;, ... ) as well as relaxing radiatively e,4" - 2X). 4

In this article we present the results of the direct mea­surements of fluorescence quantum yields and cascade free lifetimes of diacetylene and dideuterodiacetylene cations in selected vibrational levels of their A 2nu state. The technique necessary for these determinations relies on the detection of coincidences between energy selected photoelectrons (e 1<. E.l and undispersed photons following photoionization with He(Ia) radiation6 ; i. e. ,

Hle,e),H =t HIT:::"~:;'I'j'1

H~C=C~2H @ X2ng

The absolute fluorescence quantum yield can be ob­tained because each energy selected electron detected defines the formation of one cation with specific internal energy, and the true coincidences are monitored. 7 As the cascade-free lifetimes are obtained from the coin­cidence decay curves as well, the absolute rate con­stants of the radiative and nonradiative decay pathways are obtained for the state selected cations. In these measurements on the diacetylene cations, excess inter­nal energy in the,4 2nu state of up to'" 2500 cm-1 could be reached.

The fluorescence quantum yields and lifetimes can be usually determined with an uncertainty of 5%. The limi­tation of the method is, however, that the accumulation times are long, usually about a day per measurement. This places stringent demands on apparative stability. The other constraint is that the energy resolution de­fining the excited state is determined by the electron analyzer, which also sets the time resolution as a re­sult of the spread in flight times of the photoelectrons. Thus a compromise was reached for the apparatus con­structed, namely 50 meV and 15 ns for 5 eV electrons.

II. EXPERIMENTAL

The experimental details of the photoelectron-photon coincidence apparatus, the design considerations and its calibration have been fully described. 7 In the latter work

5616 J. Chem. Phys. 73(11), 1 Dec. 1980 0021-9606/80/235616-04$01.00 © 1980 American Institute of Physics This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

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J. P. Maier and F. Thommen: Radiative and nonradiative decay rates 5617

10

hv-e COINCIDENCES

1200 ~ .~ ;'t

600 \ 200n5

~r~ 0-'------­

TIME

o-c=c-c=c-o@

11 12

<D

13 eV

FIG. 1. Photoelectron-photon coincidence curve for the 0° level of the .. Frru state of dideuterodiacetylene cation; N e = 240 Hz, Nhv 3.1 kHz, Nt 0.49 Hz, toe 15 h, and the low ionization energy part of the He (Ia) photoelectron spectrum. The arrows and the bars indicate the internal energies and resolution, re­spectively, selected in the measurements.

the performance of the instrument was illustrated by the measurements of cascade-free lifetimes and fluorescence quantum yields of COa, COS., CS;, and N20+ in selected vibrational levels of their excited electronic states.

The essence of the measurements is to record delayed coincidences between electrons and photons. The rate of detection of energy selected electrons Ne is Ndeg, where N j is the ionization rate, fe the collection efficiency for electrons, and g is the He 58.4 nm branching ratio for the state v'. The rate of true coincidences (Nt) is

Nt = Ndefhvg1; F(V') ,

where fhV is the collection efficiency of photons and 1; F(V') is the fluorescence quantum yield of the cation in the vibrational state v' (defined by the energy of the electrons). Nt is evaluated from the coincidence curve by subtracting the uniform background due to false coin­cidences (cf. Fig. 1). As N. is measured during the ac­cumulation period (and corrected if necessary for stray electrons), the fluorescence quantum yield, 1; F(V') is obtained from

Nt/Ne = fhV 1; F(V') ,

as fhv has been absolutely determined by calibration with N;(iPL.:v'=O), N20+( .. 42I:+oO), and CO;Vi2nuOO) for which 1; F(V' = 0) are unity. 7 The relative quantum effi­ciency of the photomultiplier was evaluated using a standard lamp and a monochromator. A further internal standard used was hexafluorobenzene cation (13 2Aau 0°) because its emission band system is around 500 nm as is the case with diacetylene cation, and for which 1; F(O°) = 1. OO± o. 05 was established using three independently calibrated photomultipliers. 8 All these calibrations were found to be consistent within a few percent and the 1; F(V') values evaluated are given with an uncertainty of 5%. The absolute values of f. and fhv were both found to be around 2x 10-3 •

The typical counting rates and accumulation periods (tac) in the coincidence measurements for the diacetylene cations are given in the legend to Fig. 1. Because Nhv

(rate of detected photons) exceeded Ne by an order of magnitude, the electron events were used as the start for the time-to-amplitude conversion process and the artifically delayed photon events as the stop. For both diacetylene and dideuterodiacetylene cations, indepen­dent data were accumulated at least twice for a particu­lar vibrational state and the 1; F(V') values were found to be reproducible within a few percent.

The cascade-free lifetimes were extracted from a semilogarithmic plot of the coincidence curves (after subtraction of background) by a least-squares linear fit. The uncertainties are judged to be less than 5%, except in the case when the low electron count rates, e. g., 33 levels of the A 2nu state (cf. Fig. 1), cause the accumulation of sufficient data to be prohibitively long (i. e., several days). These lifetimes are associated with an uncertainty of 10%.

Diacetylene (butadiyne) was synthesized from 1,4-dichlorobutyne-2 from which subsequently dideutero­diacetylene was prepared by several isotopic exchanges of the hydrogens in a solution of NaOD in D20. The iso­topic purity was ;" 98%.

III. R ESU L TS AND DISCUSSION

A. Coincidence measurements

In Fig. 1 is shown the He(Ia) photoelectron spectrum of dideuterodiacetylene which was recorded under the conditions used in the coincidence measurements. The two lowest ionization energy bands shown correspond to the formation of the diacetylene cation in the x2n&, and A 2nu electronic states. 9 In the case of the A 2nu state, the vibrational fine structure shows that in the He(Ia) photo ionization process the v3(C-C stretching) L.; funda­mental is dominantly excited.

Photoelectron-photon coincidences were detected for diacetylene and dideuterodiacetylene cations at the four selected internal energies within the A 2nu state as in­dicated above the corresponding band in the photoelec­tron spectrum of Fig. 1. The settings of the electron energy analyzer correspond to the maxima of the vibra­tional peaks of the V3 progression and the marked bars indicate the effective resolution. Thus the measure­ments correspond to steps of around 100 meV. One of the accumulated coincidence curves is shown in the inset of Fig. 1.

Diacetylene cation was for a long time the only poly­atomic organic cation known to decay radiatively. The emission spectrum was recorded under high resolution and was shown to be the A 2nu - X 2ng band system of this cation. 10 However, nearly all the assigned vibrational bands originate from the zeroth level of the A 2nu state and only a few bands were suggested to be associated with vibrationally excited levels, i. e., 31 and 72. In the low resolution emission spectrum recorded subse­quently the very weak 3~ band was also apparent. 11

Thus, firstly the photoelectron-photon coincidence mea­surements show directly that the radiative decay also depletes higher vibrationally excited levels of the A 2nu state, i. e., up to an internal energy of '" 2500 cm-1 and associated mainly with the 3", n = 1, 2, 3 levels. The

J. Chern. Phys., Vol. 73, No. 11, 1 December 1980

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5618 J. P. Maier and F. Thommen: Radiative and nonradiative decay rates

TABLE I. Fluorescence quantum yields <PF(v I), lifetimes T (ns), radiative kr(s-t) and non radiative knr(s-t) decay constants of H-C=C-C=C-H+ and D-C=C-C=C-D+ in the ... Fnu state.

Selected ionization energy (eV) (see Fig. 1) <l>F(V') T

H-C=C-C=C-H+ 12.620 0.72±0.04 72±3 12.72 (!) 0.62 ± O. 04 62±3 12.82 (!) 0.55±0.04 59±3 12.920 0.48±0.05 56±3

D-C=C-C=C-D+ 12.620 0.80±0.04 79±4 12.72 (!) O. 72±0. 04 72±4 12.82(!) 0.65±0.04 66± 3 12.920 O. 58± O. 05 63±3

aElectron excitation. tt •12

radiative decay of these levels must therefore be mainly through their sequence transitions. In view of the vi­brational frequencies determined recently for the two diacetylene cations from the laser induced emission (for the X an, state) and excitation (for A anu) spectra in neon matrices, 13 the 3~ sequencies should lie, succes­sively by'" 60 cm-1 intervals, on the low energy side of the emission bands originating in the zeroth level of the -a A nu state.

The fluorescence quantum yields and cascade-free lifetimes determined for the internal energies indicated in Fig. 1 of the diacetylene cations in the A anu state from the coincidence data are given in Table I. The quantum yields are high but not unity, and fall with in­creasing internal energy as do the lifetimes. There is good agreement for the 00 and 31 level lifetimes with the values which were measured previously by means of pulsed electron beam excitation ('" 30 eV) and optical selection of the emission bands. 11.12

In Table I are also summarized the radiative (kr ) and nonradiative (knr) rate constants for the state selected diacetylene cations inferred from the lifetime and fluo­rescence quantum yield values. The radiative rates are constant, within the error limits, over the internal en­ergy spanned in the A anu states and are the same for diacetylene and dideuterodiacetylene cations, i. e., k r '" 1.0xI07 S-l.

B. Nonradiative decay

Diacetylene cations produced in the vibronic levels of the A anu state populated in the photoionization process (cf. Fig. 1) can decay by only two relaxation pathways.ll Both these channels connect the A 2nu and X 2n, states; the radiative decay <A - X) and the internal conversion (.A ~X).

Fragmentation pathways are not accessible for these states as has been demonstrated directly by photoelec­tron-photoion coincidence measurements for the A 2nu

state of diacetylene cation.14 Only parent ions were de­tected. Nonradiative decay to a cationic state other than the X Zn, can also be excluded. The energetically lowest lying "non-Koopmans' state" (Le" state whose electronic configuration differs by two electrons from that of the

Ta kr knr

71 ±3 1.00±0.07x107 3. 89±0. 58x 106

59±3 1. 00±0.08x 107 6.13±0.71x106

9.32 ± O. 83x 106 7.63 ± 0.78 x 106

8. 57± 1. OOx 106 9. 29± 1. 02 x 106

78±4 1.01±0.07x107 2. 53± O. 52x 106

69±4 1. OO± O. 08x 107 3. 89± O. 60x 106

9.85±0.75x106 5. 30± O. 65x 106

9.21 ±O. 91x 106 6.67±0.85x106

molecular ground state and thus not populated sufficient­ly in the photoionization process) is the 4nu state. This state is described dominantly by the configuration ... • • • 11u 4111{ 211:1 and is_expected, on simple arguments, to lie well above the A 2nu adiabatic energy. In fact, ab initio calculations based on the correlated electron pair approach yield that, in the linear configuration, the 4nu

state lies above 15 eV in ionization energy. 15 In a non­linear geometry this may no longer be the case; although the nonradiative decay rate would then be expected to be rather slow. Thus only the A 2nu -"""'-x2nu internal con­version need be considered for the nonradiative decay.

The less than unity quantum yields, within the time scale of the experiment, and the exponential decay, both measured in the low pressure limit ("isolated condi­tions"), are characteristic of the decay of a molecule in the statistical limit. 1.2 At the energy corresponding to the zeroth level of the A 2nu state of diacetylene and dideuterodiacetylene cation, the densities p(X), of the X an,. state vibrational levels are estimated using Haar­hoff's formula18 (in the harmonic approximation) to be 4 x 106/cm-1 and 2 x 107/cm-t, respectively. The vibra­tional frequencies used were the known ones for the X2n,. state from the emission spectrum (i. e., VI' 1.12,

1.13 , and 1.17),10 together with the ground molecular values for the other modes. 17 Thus, the p(X) density of levels is sufficiently large that the relationship T« I'Cp for ir­reversible decay is satisfied (T'" 10-7 s), especially as inclusion of anharmonicity would increase p(X). The nonradiative decay rate kDr to the manifold of the X Zn,

- - - 2 levels is then given by1.2 knr = (211/1'i) p(X) v(X,A) (i. e., Fermi's golden rule expression), where v(X,A) is the parameter representing the effective coupling between the X and A states. According to this expression, the v(X,A) coupling parameter is'" 1 X 10-8 cm-1

• However, this is probably a lower limit as the effective number of X states which can couple with the A state levels is re­stricted due to the high symmetry (D .. h) of the species. Similar conclusions were drawn in the study of the cor­responding X-A nonradiative coupling of dichloroacetyl­ene cation, for which the interaction parameters were estimated to be 10-4 _10-5 cm-1•

18

The nonradiative rate for electronically excited spe­cies in the statistical limit has been shown to decrease

J. Chern. Phys., Vol. 73, No. 11, 1 December 1980

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J. P. Maier and F. Thommen: Radiative and nonradiative decay rates 5619

exponentially as function of the energy gap aE, i. e., the difference between the zero-point levels of the two states. 1.2 In the case of diacetylene and dideutero­diacetylene cations, aE(X,A) is 2.45 eV. In addition, on deuteration there is a decrease in the A~X non­radiative rate because more quanta of the ll(C-D) strech­ing mode are required to absorb the energy and this re­sults in a decrease in the Franck-Condon factors. In­deed, the determined nonradiative rate constant ratio (cf. Table I) for the dihydro- and dideuterodiacetylene cations, k~,./k~r is :::; 1. 5. For aromatic hydrocarbons it has been established that the high frequency CH strech­ing vibrations are the accepting modesl ,2 and this also appears to be the case for the electronically excited diacetylene cation.

The nonradiative rate increases approximately linear­lyon increasing the internal vibrational energy (up to '" 2500 cm- I

) of the diacetylene cations in the A 2n" state (cf. Table I). Although the absolute values of knr are uncertain to about 15% due to the errors in the fluores­cence quantum yields and lifetimes, assuming that the radiative rate is constant over the measured internal energy range (c!. Table I), the relative rates should be accurate to within a few percent. Such an increase (lin­ear or exponential) in the nonradiative rate has often been observed in molecular systems and is usually at­tributed to the increasing ease with which the vibration­al modes optically excited can change their quantum numbers in the coupling process. 1,2 In the present in­stance the mode primarily excited appears to be the 113(C-C stretching) fundamental (Fig. 1); however, the higher resolution laser excitation spectra of the diacetyl­ene cations in neon matrices show that the lI2(C=C stretching) and 111(C-H stretching) as well as the liT (bend) overtones are populated. 13 The same situation prevails for dideuterodiacetylene cation and the excess energy dependence of the nonradiative rate runs parallel to that of diacetylene cation.

In conclusion, the purpose of this study was to show how radiative and nonradiative decay rate constants can be directly obtained for state selected electronically excited open-shell organic cations. Unlike the situation

in molecular systems, the discussion of the determined radiationless rate constants is often Simpler with organic radical cations as the only accessible decay channel is to the cationic ground state manifold. These aspects are illustrated by the present data on diacetylene and dideu­terodiacetylene cations in their A 2nu state.

ACKNOWLEDGMENTS

This work is part E 29 of project No.2. 212-0. 79 of the Schweizerischer Nationalfonds zur Forderung der wissenschaftlichen Forschung (Part E 28 Ref. 19). Ciba-Geigy SA, Sandoz SA, and F. Hoffmann-La Roche & Cie. Sa Basel are thanked for financial support.

l K. F. Freed, Top. Appl. Phys. 15,23 (1976). 2p. Avouris, W. M. Gelbart, and M. A. El-Sayed, Chern.

Rev. 77, 793 (1977) and references therein. 3See for example, W. E. Howard and E. W. Schlag, Chern.

Phys. 17, 123 (1976). 4J . P. Maier in "Kinetics of Ion-Molecule Reactions," edited

by P. A. Ausloos (Plenum, New York, 1979); J. P. Maier, Chimia 34, 219 (1980) and references therein to these studies.

5T. A. Miller and V. E. Bondybey, J. Chim. Phys. 77, (1980) and references therein.

6M. Bloch and D. W. Turner, Chern. Phys. Lett. 30, 344 (1975).

TJ • P. Maier and F. Thommen, Chern. Phys. 51, (1980). 8J. P. Maier and F. Thommen (to be published). 9C. Baker and D. W. Turner, Proc. R. Soc. London, Ser.

A 308, 19 (1968). IOJ. H. Callomon, Can. J. Phys. 34, 1046 (1956). 11M. Allan, E. Kloster-Jensen, and J. P. Maier, Chern. Phys.

7, 11 (1976). 12J. P. Maier, O. Marthaler, and E. Kloster-Jensen, J. Chern.

Phys. 72, 701 (1980). 13V. E. Bondybey and J. H. English, J. Chern. Phys. 71, 777

(1979). 14J . Dannacher, E. Heilbronner, J.-P. Stadelmann, and J.

Vogt, Helv. Chim. Acta 62, 2186 (1979). 15p . Rosmus (personal communication). 16p. C. Haarhoff, Mol. Phys. 7, 101 (1963). 17J . Lamrnotte, C. Binet, and R. Romanet, J. Chim. Phys. 74,

577 (1977). 18G . Dujardin, S. Leach, G. Taieb, J. P. Maier, and W. M.

Gelbart, J. Chern. Phys. 73, 4987 (1980). 19J . P. Maier and L. Misev, Chern. Phys. 51, (1980).

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