DECAY OF EXCITED MOLECULAR STATES

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DECAY OF EXCITED MOLECULAR STATES

A. Tramer

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 7 , Tome 39, Juillet 1978, page C4-51

DECAY OF EXCITED MOLECULAR STATES

A. TRAMER

Laboratoire de Photophysique Moleculaire, C.N.R.S., UniversitC Paris-Sud, 91405 Orsay, France

Rhsumh. - Differentes methodes de mesures de la duree de vie des etats excites (excitation par impulsions lumineuses et impact electronique, detection par les techniques d'echantillonnage de fluorescence et de l'impulsion-sopde) sont passees en revue. Nous proposons un schema pour la description de la desactivation de 1'Ctat excite tenant compte du caractbre du couplage intramolk- culaire et des conditions d'excitation. Ce schema est illustre par quelques resultats experimentaux obtenus pour de petites molt.cules en phase gazeuse.

Abstract. - The methods of lifetime measurements involving the light or electron pulse excitation, and fluorescence sampling or probe-pulse detection are reviewed. A general schema of radiative

decay paths dependent on intramolecular coupling and excitation conditions is proposed. This schema is illustrated by a discussion of experimental data for a few small molecules.

1 . Introduction. - The experimental studies of the population decay rate from excited moleculai levels is one of the principal sources of information about the nature of electronically excited states. As it will be shown in the following, the data obtained' in this way may serve for a more accurate determination of electronic wavefunctions of molecules as well as in the study of the coupling between a discrete molecular state and other (discrete or continuous) manifolds. The interest of decay studies was recognized since a long time but the amount of the experimental work in this field was very limited, The reasons for this underdevelopment were - as we believe - the absence of experimental techniques allowing a precise determination of the decay form of well defined excited levels and, on the other hand, the absence of a unified theory describing the nature and time evolution of states prepared by a given excitation technique.

It seems that recent progress in both experimental techniques and theory offer new and extended possi- bilities. In the following we will first review experimental methods which have been applied (or may be applied today or in the nearest future) in the molecular kinetics studies. Then we will give the outlines of the theoretical description of the evolution of an excited state based on the theory of radiationless transitions and turn at last to a few examples of applications of decay experiments in the study of excited molecular systems. We will be mainly interested by the case of small (diatomic and small polyatomic) molecules in the gas phase under gas pressure low enough to reduce the probability of a . collision

during a lifetime of the excited state to a negligible value. Among the experimental techniques we will discuss in more detail those, which may be applied for excitation of high molecular levels corresponding to the VUV transitions.

2. Experimental techniques. - Historically, the first exact method of the excited state lifetime measure- ment was the phase fluorimetry [ l ] . The fluorescence decay time is here deduced from the modulation depth and phase shift. of the fluorescence excited by the light (or electron) beam the intensity of which is modulated with a frequency of the order of the fluorescence decay rate 117. This method, still useful in many particular cases [2], is in fact limited to purely exponential decays and it fails in the case of more complex decay paths. During last years, pulse methods and related techniques. have been widely developed, this development being essentially due to a progress in the short (light and electron) pulse generation and in the time-resolved fluorescence detection.

The experiment consists in :

(i) creation of the 'well defined excited molecular state :

(e.g. single rovibronic level of the small molecule) at the time t = to f 6t/2 where 6t indicates the uncertainty of the excitation time (usually the width of the exciting pulse) and

(ii) monitoring of the time evolution of the popu-

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lation of the excited level (or of other levels populated may be hardly reduced below about 200 ps for a by the intra- or inter-molecular relaxation processes) single-photon response of best photomultipliers. with a time resolution of 6t'.

The probe-pulse techniques ar2 free of these The time resolution of a decay experiment At is limitations. If only the initially excited state commu- given by the convolution of excitation and detection nicates radiatively with one of higher energy levels j

functions : its population may be probed by detection of the

probe-pulse attenuation (the most general but also At = E(t) X D(t)

--

J 6 t 2

+

atr2 . ₍₁₎ _{the less sensitive technicwe), of the induced fluores-}

* S.

cence (if the j-state decays by emission j -, i or j + O),

Elaborated deconvolution techniques allow the mea- _{of the ion production (if the j-state is pre-ionized), etc.} surements of the decay times of the order of 0.2 _{The time} _resolution_{is limited only by the widths} to 0.3 in At units [3, 41. _{of exciting and probe pulses and it may attain one}

Natural limits of the time and energy resolution _piCOsecond_{limit [71.} are obviously given by the Heisenberg relation. It

means that

in

an ideal decay time measurement the we must,

time resolution At is limited by the energy an excited-level population high enough to assure resolution

m

necessary for selective excitation of a satisfactory signal-to-noise ratio. This condition a given molecular state and for a selective detection is fundamenta1 for low :

of its emission. in order to measure decay times of isolated molecules, The excitation is usually carried out by means free from collision and radiation-trapping effects,

of light or electron pulses (to corresponds then to We are to with low gas pressures the

the of fie exciting pulse intensity) but order of 10-3-10-4 torr. On the other hand, high cw sources may be equally used if the signal sync.,ronic densities of the excitation energy must be avoided with the creation of the excited state may be detected. because the possibility processes For instance when the gas is excited by a mono- (step excitation to higher states, two-photon absorp- chromatic cw electron beam this signal is given by tion, etc. [S]). The best excitation conditions will detection of a scattered electron with an energy be thus attained with a train of light or electron loss E, - Ei = ho,,, where W,, is the frequency pulses with a moderate peak power and a high repeti-

of transition from the ground to the i-th excited tion rate. But even in this case, it is usually impossible molecular state [51. In a similar way, the lifetimes to attain simultaneously a necessary energy resolution of molecular ions may be measured under a mono- and a good accuracy in the decay-time determination. chromatic cw optical excitation by taking as to the In VUV spectral region we dispose actually of signal from a photoelectron (or ion) with a well- two types of excitation Sources : pulsed electron determined energy [6]. beams and pulsed light sources from classical light The population of the excited level may be rnoni- sources : discharge lamps and synchrotron radiation. tored by passive or active techniques. In the first The decay-time measurements are usually performed case, the time dependence of the spontaneous emission either under a narrow-band, selective excitation, but intensity from the excited level : with a low or none resolution at the detection side

or under unselective excitation and selective detection.

= k:ad Ni(t) Such a procedure may be applied without limitations only in the case where the excited level is populated (where k,,, is i -, 0 radiative rate) is detected by uniquely by direct excitation and decays uniquely sampling or correlated single-photon counting tech- by the emission to the ground state. Unfortunately, niques. In the latter one, a weak probe pulse is sent in most cases we cannot neglect cascade processes :

at the excited sample with a variable delay with even in absence of collisional relaxation, the i-th respect to excitation; the population of the excited state may be populated by radiative transitions from level is deduced from the system response to the higher levels and decay by emission not only to the probe pulse. ground state but also to intermediary lower states, fluorescence monitoring by correlated single- which decay in turn radiatively. In absence of a suffi- photon counting is actually the most sensitive tech- ciently high spectral resolution as well in excitation nique but suffers of severe limitations : as in detection, the recorded decay curve is affected

by cascade processes (Fig. l).

(i) It fails when the radiative rate of the i-state _us _{from this point of view the results} decay to the ground (or other lower lying electronic _{of two experimental works tending to determine} states) ktad is small as compared to the total decay _{the lifetimes of single-vibronic-fluorescence from} rate ki. This is generally the case of lowest triplet _{low-lying electronic states}_of_{NO. In the first one [g]} states with a strongly forbidden i + 0 transition. _NO _was _{excited with}_a₅ _{kev electron beam}

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DECAY OF EXCITED MOLECULAR STATES C4- 5 3

/

-,

+-T~me -

FIG. 2. - Decay curve of the fluorescence detected under selective F,c, I - Schematic representation of cascade processes and of excitation of the v = 0 level of the D state of NO : directly their effect on the decay curves in the case of unselective excitation Observed and corrected for the emission background (from

(a) and unselective detection (b). Ref. [l@]).

tored, in the latter one [10], the narrow band excitation by synchrotron radiation was applied and the decay of the total fluorescence measured (Table I).

The agreement is relatively good for the lowest, long-living A 2C + state. This state. decays uniquely by emission to the ground state at a time scale long enough as compared to decays of higher states, recombination processes, etc. Its decay is thus unaf- fected, at least in its final part by cascade effects

in the case of a non-selective excitation. The total fluorescence decay recorded under a monochromatic light excitation of single vibronic levels of higher C 211 and D 'C+ states is clearly non-exponential and contains a long component due the A-X emission from different levels of the A state populated by the C-A (or D-A) transition. This component may be substracted but such a treatment introduces necessarily systematic errors (Fig. 2). On the other hand, in the case of unselective electron-pulse excitation, the recorded decay time of populations depends not only on the rate of transitions to lower states but also

on all processes increasing its population by emission from higher states, recombination. etc. The differences between z determined by both methods exceed clearly the error limits.

The example of NO may be considered as a good illustration of difficulties and uncertainties encounter- ed actually in the VUV decay time studies. We may, however, reasonably expect that an essential progress will be made in the next few years as result of development of V W tunable lasers and of higher-harmonics- generation techniques.

Different types of tunable dye lasers available today in the limited spectral regions of visible and near UV yield average powers of the order of milli- watts in form of light pulses with transform-limited time and energy widths. The scale is extended from St = 2 X 10-13 S (SE = 50 cm-') for passively lockedcw dyelacer [g to St = 10-8 S AE = 10F2 cm-' for N, laser-pumped oscillator-amplifier system [l l] and to St = 3 X 10-7 S, AE = 10-4 cm-' f o r cw dye lasers chopped by the extra-cavity or mode-

Fluorescence lcetimes of low-lying electronic states of NO, measured under dflerent excitation conditions. Exc. Technique Electron beam (Ref.

PI)

Spectral resolution in excitation none in detection 2 A

pressure range torr (1-5) 1 0 - ~

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I

- 5 0 5 10 15

D e l a y tlme tD(sIx 10-l2

jump techniques [12]. The light intensity is high enough to allow a narrow-band excitation of single vibronic levels of a polyatomic molecule followed by the detection of the time resolved emission in a single vibronic transition from the directly excited level (see e.g. [ l k ] ) . In the work in course, we excite single rotational levels of glyoxal by an extra-cavity chopped argon laser and detect their decay in absence of rotational relaxation [12b]. Moreover, the number of photons per pulse is generally sufficient to allow the application of the probe-pulse techniques and to extend in this way the decay studies to the case of very short-living and/or non-radiating excited states. The study of the lifetime of high vibrational ground- state levels of an isolated large molecule (coumarine) decaying rapidly by a non-radiative path may serve as example [13]. The molecules are pumped by a monochromatic infrared picosecond pulse from a parametric generator; the population of the excited level is monitored by a probe visible picosecond pulse transfering the molecule to the first excited electronic singlet state which cannot, be attained from the vibrationless ground-state level. The intensity of fluorescence induced in this way plotted against the delay between the pump and probe pulses served to determine the depopulation rate of the level amounting in this case to 4 f ps (Fig. 3).

The actual state and perspectives of laser sources

in VUV region are discussed .in more detail in two subsequent papers [14, 151. It is, however interesting to point out that even, now relatively high-lying molecular states may be excited by means of conven- tional dye lasers by one of the .following methods :

(i) The two-step excitation consists in the initial. creation (by a non-selective excitation) of relatively

long-living, lowest electronic states. The molecules are then excited from these levels to higher electronic states by a narrow-band laser excitation. This tech-

X

FIG. 3. - Vibrational relaxation of the 5 950 cm-' vibrational level of coumarlne 6 vapour probed by a visible pulse (from Ref. [13]).

E

-

₀ r. LL \

-

₀ + L m e F m W U C W U m ?! 0 3 L L 10-l

nique has been applied to the detection of extremely weak emissions from higher singlet states of polyatomic molecules [16]. It may be equally applied in order to excite diatomic molecules from their metastable lowest triplet state to higher triplet states. For example, a number of vibronic levels of the e 3C -,

d 3A and a' 3 C f states of CO may be excited by usual visible dye lasers after a preliminary excitation of the metastable a 31Z state.

1 -

-

(ii) It is possible actually to excite directly the molecular levels for

A

>

1 400

A

by the two-photon absorption. A particular interest of the technique involving the superposition of a direct and reflected laser beam consists in the possibility of a selective excitation of the fine-structure components within the Doppler width of the spectral line [l71 but even in the simple two-photon technique it is possible to attain a high resolution and a good signal-to-noise ratio. We give here as an example (Fig. 4) the excitation spectrum of the NO fluorescence in a crowded spectral region in the vicinity of the

FIG. 4. - Excitation spectrum of NOA ' Z + ( v = 2) band head (from Ref. [18]).

band head [18]. The results of the lifetime measurements obtained in this way are compared to previous results in table I. The accuracy is increased and the variation of lifetimes with v is clearly evidenced. Still more important is the possibility of selective excitation of individual rotational levels (in the present case, there lifetimes are practically the same within a vibronic band).

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DECAY OF EXCITED MOLECULAR STATES C4-55

following treatment will be limited to the case of optical excitation but may be easily generalized). Each molecular system may be described by means of two equivalent basic sets 1191 :

(i) Eigen-states of the zero-order hamiltonian X, neglecting spin-orbit .coupling, deviations from the

B 0 approximation and second-order effects. The optical excitation of these zero-order states is governed by strict selection rules (AS = 0, AA = 0, f 1, etc.). They may be thus divided into radiative (i.e. commu- nicating radiatively with the vibrationless level of the ground electronic state) and non-radiative states, denoted usually as { s ) and { l ) states. Zero-order states are not the eigenstates of the exact molecular hamiltonian X = X,

+ X'

because of the presence of off-diagonal terms : v,, representing spin-orbit or vibronic coupling :

(we may consider that ( s ) and { l ) manifolds are prediagonalized).

(ii) Quasi-stationary states { n ) are eigenstates of the exact molecular hamiltonian X and may be determined by diagonalization of the matrix (2). Both sets are related by a linear transformation :

and it is useful to express the s and l character of a mixed

l

n

>

level

(3

and

L )

by its projections on the S and L subspaces :

Because of the conservation of the angular momentum of an isolated molecular system, only the states with the same overall angular momentum (i.e. with the same rotational quantum number J) may be coupled together. The energy spacings

E ~ ~ = E ~ - E ~ - ; E ~ = E ~ + ~ - E ~ and

E,, = E,+ 1 - E"

correspond thus to the energy differences between corresponding rotational levels belonging to different vibronic states of ( s ) and { l ) manifolds. The coupling with dissipative (radiative and non- radiative) continua is introduced by assigning to each level its total width ys, y, and its radiative width

r,-gnd-F, = 0: In small molecules one can consider

that non-dissociative states may decay in absence of environment effects only by the radiative way. We have thus :

ys = Ts ; y1 = Tl = 0 ; y, =

1

a:s

rs

.

( S )

S

The character of initially prepared state depends not only on the molecular parameters but also on those of the excitation process. In the case of the optical excitation, the essential parameter of the light source is its coherence time - t,,, determining the uncertainty in the energy of a single photon emitted by the source (the photon width - 6v) :

The coherence time cannot be obviously longer than the light-pulse duration but may be much shorter in the case of non-totally coherent sources (gas discharge, multimode lasers, etc.).

As can be easily shown [20, 211, the optical excitation prepares in general a non-stationary molecular state which may be represented as a coherent linear combination of all ( n ) states, contained in the energy band 6v :

ICl(0) =

1

A,

I

n ) ( 7 )

n

where A, coefficients depend on the radiative widths of { n ) states. The further evolution of the system (in absence of environment effects) is described by its wavefunction :

and that of its fluorescence intensity (due totally to its S-character) by :

If the photon width - 6v is smaller than the spacing between neighbour

I

n ) states E,,, the excitation prepares directly one

I

n ) state yielding a simple exponential decay. In the case of a broad band excitation, many ( n ) states are simultaneously but independently excited and the overall decay is non- exponential but may be represented as a sum of exponentials. On the other hand, when 6v > E,,

a coherent excitation of a number of ( n ) states results in interference effects due to the cross terms in equations (8) and (9) (see below).

We will limit our discussion to a few specific cases of a real interest for the study of small (diatomic, triatomic) molecules :

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and we expect a slow variation of t, with rotational and vibrational quantum numbers v and J due to a dependence of the electronic transition moment on the rotational and vibrational motion.

2. The { s } states are coupled to a discrete manifold of { l } states (this corresponds to a perturbation of a radiative state by another non-dissociative state) (we are mainly interested by non-radiative e.g. triplet perturbing states). It is convenient to treat separately the weak-coupling and strong- coupling limits defined as :

1. v,,

-

but vSl 4 811

and

2. vsl

-

&,I and v,, 9

.

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In the first case, one

I

s ) level is efficiently mixed with one

1

l ) level only giving origin to a pair of { n )

levels :

with radiative widths :

where a = b in the case of resonance between zero- order states.

We expect then :

(i) A large spread of lifetimes of individual levels :

those of { nl } levels varying between t, for a 2 -+ 1 and 2 T, for a 2 + 0.5 while those of { n2 } levels vary between infinity for aZ + 1 and 2 z, for a2 -+ 0.5. In any way, the interaction leads to a lengthening of the decay time (Fig. 5).

(ii) A rapid variation of lifetimes with quantum numbers v and J.

FIG. 5.

-

Dependence of decay times of mixed levels on the mixing coefficient a.

Such a behaviour is typical for perturbed vibronic levels of diatomic molecules.

In the strong coupling limit, one

/

s ) level is mixed with N { I ) levels giving origin to N

+

1 { n }

levels with an average width of :

Molecular states are characterized by decay times anomalously long as compared to the pure singlet lifetime deduced from integrated absorption measurements. Such a behaviour was observed for the first time by Douglas [22] in a few triatomic molecules (NO,, SO,, CS,) with exceptionally strong coupling between electronic states and then in a number of small polyatomic molecules (pyrazine [23], biacetyl [24]. etc.) and in small polyatomic ions [25].

3. The coupling of a discrete

I

s ) state to { I }

states forming a true continuum (as in the case of predissociated or pre-ionized states) or a dense quasi-continuum (in the case of a molecule in the rigid matrix) may be described as providing an additional non-radiative width of the level :

Y n = Ts

+

Ynr

.

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The line conserves its lorentzian shape (i.e. the decay remains strictly exponential) but the lifetime is shortened and the fluorescence yield reduced from 1 to T,/y,. The variation of lifetimes with v and J may be more or less rapid (as in the case of the coupling between discrete manifolds) but the interaction leads in this case to the shortening of the decay cimes.

4. Informations from lifetime experiments. -

4.1 PURE RADIATIVE STATES. - Determination of decay times for individual vibronic levels of a pure radiative state is an important source of information about electronic wave-functions of molecules.

The probabilities of electronic transitions are usually treated in the rough approximation (crude Born-Oppenheimer approximation, CBO), where the electronic wave-function is considered as indepen- dent of small changes of nuclear coordinates R

resulting from vibration and rotation, and the electronic transition moment P does. not depend on R :

The transition rate between i-th vibronic level of the excited state and j-th vibronic level of the ground state is then given by :

where

64 7r4

A = -

(8)

and the total decay rate of the i-th level by :

The decay rate (corrected for the frequency distribution in the emission spectrum) would be thus the same for all vibronic levels. In the more refined Born-Oppenheimer approximation (BO), the electronic transition moment is a function of R and this dependence may be expressed by the dependence of P on R-centroid of a vibronic transition i -+ j [26] :

p(Xij) = P,(I

+

aEij

+

bXt), where

K j =

( i J R J j ) . (18) The radiative decay time of the i level will be :

and if vibrational wave functions of both electronic states are known, the P(R) functional dependence may be deduced from lifetimes of excited vibronic levels.

We dispose now of an important amount of data concerning decay times of individual vibronic levels of small molecules. In some cases, the lifetime is surprisingly constant for an extended set of v-values (Fig. 6); such a behaviour has been observed for

FIG. 6. - Fluorescence decay time plotted against U' vibrational quantum number of excited state for Na, BA' (a) and N,B 317, (b).

(Data from Refs. [27] and [29].)

A 'C, state of Na, [27l and the d 3Cg state of C, [28].

On the other hand a relatively important variation of z(v) was found for the B 3ZIg state of N, [29] and A I l l state of CO [30]. In the classical Jeunehomme's

work on NZ [29], the a and b coefficients in equation (18) have been determined :

a =

-

5 f 0.4A-l and b = 25.5 $- 2 A W 2 and in the case of CO [30] :

a = 1.8

+

0.3A-l and b < 2 k 2 .

By the variation it is possible to check validity of proposed electronic wave functions of excited molecular states.

4.2 DISCRETE-DISCRETE COUPLING. WEAK-COUPLING CASE. - Let us discuss first the case of incoherent

excitation of individual molecular states (Sv

<

E,,,

see above).

In general the perturbation leads to a lengthening of the lifetime of radiative states for which the mixing coefficient a2 is sufficiently different from one and appearance of long-living -states (essentially non- radiative but borrowing the oscillator strength pro- portional to b2 from s-levels) corresponding to the extra-lines in the spectra of perturbed transitions. Since the mixing coefficients may be calculated from the level shift determined by the high-resolution spectroscopy, the variation of lifetimes of individual ro-vibronic levels may be predicted. On the other hand, the perturbations may be easily detected and estimated by lifetime measurements in the case of complex spectra, where the spectral resolution is not sufficient for the rotational analysis.

If individual rotational levels may be selectively excited (or detected), a localized perturbation will appear as a sudden increase of decay times as in the case of the v = 1 level of the N l B 'C: state (Fig. 7) [2]. In the case of broad-band excitation, the decay is apparently non-exponential, contains a long component and its from changes on scanning across a vibronic band envelope. This is the case for strongly perturbed (v = 0, 1 and 6) vibronic levels of the A

'n

state of CO [30]. The excitation in the (0, 0) band head (corresponding to a pumping of a group of ( nl } levels with an average mixing coefficient of ( a 2 ) z 0.9 overlapping ( n2 ) levels with

<

b2 ) X 0.1) yields a strongly non-exponential decay

which may be roughly represented as a superposition of two quasi-exponential components with respective decay times of 10.8 and

-

100 ns. The excitation of the high-frequency wing of the (0, 0) band results in a quasi-exponential decay with z

--

200 ns in a

A

I 6 0 - ~

A

A A A

~

A

~

A

l I I I l : l l c l / I, I / 1; li 6 ,E l0 'J2 13 l4 ,15 l 6 1,8 N L225 L22 0 4215 4210 Wavelength ( A )

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good agreement with a calculated ( b2 ) value of excited ( n2 ) levels of about 0.05 (Fig. 8). On the other hand, the variation of lifetimes of individual vibronic levels measured under a broad-band excitation is no longer regular : the lifetimes of perturbed levels are anomalously long (Fig. 9). The deperturbed lifetimes of these levels may be easily estimated if

( a 2 ) value is known :

As may be seen, the deperturbed lifetimes show a quite regular dependence on the vibrational quantum number.

0 50

FIG. 8. - Decay curves of CO fluorescence from v = 0 level of the A 'l7 state : excitation of the band head ( a ) and of the extra-lines (b)

FIG. 9. - Perturbed (e) and deperturbed (0) Ilfetimes of individual vibronic levels of the COA 'L' state.

If the spacing between

I

nl ) and

l

n2 ) levels resulting from the S-I coupling is smaller than the coherence width of exciting radiation, the optical excitation prepares an initial state, which may described either as a non-stationary

I

s ) state or as

coherent combination of ( nl ) and

1

n2 ) states with a defined phase relation.

In this case, the fluorescence decay is not a simple sum of two exponentials but contains interference terms and its form will be (cf. Eq. (8)-(9)) :

The decay is modulated at the frequency

v12 = ( E I - E2)/fZ, the modulation depth attaining its maximum value in the pure resonance case (E, = E,, a 2 = b2, El

-

E2 = 2 v,,). Such quantum beats, well known for atomic systems (see e.g. [31]), have not yet been observed, to our knowledge, for molecular levels resulting from the S-l coupling.

The observability conditions :

where 6t and 6t' are, respectively, the time resolution in excitation and detection are not easily fulfilled in usual single-photon counting experiments (if 6t z 6 t f = 1 ns, then E, - E, 10d3 cm-'). These conditions may be realized in the case of a very weak coupling (strongly forbidden perturbation) by inducing the resonance between closely lying

I

s )

and

I

l ) levels in a magnetic field. A good example would be e.g. that of N = 13-16, 19-21, 27-30 rotational levels of the B 'C +(v = 11) state of CN weakly interacting with a quartet (probably 4Z+) state, where the level-anticrossing effects (closely related to quantum beats) have been detected [32].

4 . 3 DISCRETE-DISCRETE COUPLING. STRONG-COUPL-

ING CASE. - AS mentioned above, the oscillator strength of a single radiative state

I

s ), strongly coupled to a large number of ( I } states is diluted (redistributed between many { n ) levels resulting from the

S-I

mixing) and we observe decay times much longer than that of the zero-order ( s ) level. Such a strong mixing may occur either in small molecules with a relatively large E,, spacing but also

very large off-diagonal v,, terms or in intermediate- size molecules with a dense { l ) manifold. In the first case, the excitation prepares individual ( n )

states, while in the latter one we may expect a coherent excitation of a whole bunch of levels.

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longer and depend strongly on the excitation spectral range. For low lying levels in the 5 940

hi

range exponential decays with lifetimes varying slightly around 30 and 115 ps were observed when different spectral features are excited with a relatively broad (1 cm-') exciting band [33]. On the other hand, a narrow (I 0-4 cm- ') band excitation of individual lines coinciding with the 4 880

hi

Ar- line induces a non- exponential decay resolved into about 3 ps, 28 ps and 80 ps components. [34, 351. The NO, puzzle is still unresolved but there is no doubt about the relation between the strong mixing of electronic states and anomalously long decay time.

For intermediate-size molecules with closely spaced { I ) (and { n )) levels the description of the system in terms of average coupling constants ( v,, )

and average level densities p, = ( ) - may be applied [19]. The S-character (and oscillator strength) will be then redistributed among N states contained in the energy band

-

A , where N and A are given by the formulae :

If 6v 2 A 4 E,,, the optical excitation prepares

a strongly radiative non-stationary door-way state

I

s ).

It may be clearly seen from equations (8)-(9) that the phase coherence between coherently excited { n }

states is lost after a time of the order of h/A. If the

{ n ) levels are not equally spaced no further construc- tive interference will occur and { n } states decay independently with their characteristic decay times of the order of T,/N [36, 371. This corresponds to a quasi-biexponential decay 1381 with rate constants :

The non-exponential decay seems to be a rule for intermediate-size (about 10 atoms) molecules and has been observed in many cases, even when the l-level density is much lower than expected from equation (22), the reasons of this discrepancy being still unclear. It means, however, that a similar behaviour is not excluded even in small molecules if the

I

s ) level interacts with a relatively dense manifold { l } e.g. in the vicinity of the dissociation limit of the non-radiative state. It is interesting to note that a strongly non-exponential decay have been observed for a number of small polyatomic ions (H-C=C--Cl+ , H-&C-Br +

,

H-+C-I + )

[25] (Fig. 10) even if it is still impossible to decide whether this behaviour results from an intermediate- case s-l coupling or is due to quite different reasons.

4.4

DISCRETE

STATE COUPLED TO A CONTINUUM. -

We will be mainly interested in the molecular predissociation. A strong predissociation may be qualita- tively evidenced by a broadening of spectral lines and by the anomalous intensity distribution (breaking- o@ in the emission spectra. It seems, however,

FIG 10. - Decay of the A Zfl state of the H-C=C--Cl+ rad~cal cation excited by electron pulse (from Ref. [25]).

that the decay-time measurements become actually a very efficient tool for a quantitative description of predissociation phenomena. Since the accuracy in decay times determination by the single-photon- counting techniques attains a few percent of the observed lifetime, a very weak predissociation, hardly competing with radiaive decay may be evidenced. On the other hand, probe-pulse techniques (never applied, to our knowledge, to a study of predissociated states) allow measurements of dissociation rates of the order of 1012 S-', where the fluorescence is too weak to be detected.

Let us give two examples of fluorescence lifetime measurements for weakly and very weakly predissociated molecular levels.

1. It is well known that the dissociation limit of the NO X 'Il ground state corresponds to the energy values higher than that of v = 0, N = 0 level but lower than v = 1 level of the C '27 state [39]. It was deduced from indirect (fluorescence yield and pressure effects in steady-state excitation conditions) measurements that the lifetime of higher rotational levels of the v = 0 state is significantly shortened [40] but this effect is not strong enough to induce an anomalous intensity distribution in the C -+ A(0, 0)

emission band [39]. Under a broad-band optical excitation of the C(v = 0) level, the observed decay is strongly non-exponential and may be roughly resolved into two z

--

20 ns and z

-

3 ns components. Under a narrow band (1.5

A)

excitation at different wavelengths within the band contour, the ratio of preexponential factors varies with A,,, and the long component is practically absent when higher rotational levels are selectively excited. This result confirms a weak predissociation for N > 5-7 and yields an estimation of the predissociation rate : z,, = 2.5 X 108 S-' [IO].

(11)

fine and rotational) effects [41]. The predissociation rate depends on v through the Franck-Condon factors for 317,,+ and

'II,,

states and the maximum rates are expected for v = 3 and v = 24 levels. The observed decay times are plotted in figure 11 vs. the vibrational quantum numbers [42], such a dependence cannot be explained by the variation of the radiative lifetime and suggests a more efficient non-

radiative decay from lower and higher vibronic levels as compared to v = 10-15. This suggestion has been confirmed by more elaborated photophysical methods [41].

5. Conclusion. - In view of a rapid development of experimental techniques, the studies of decay mecha- nisms will take an important place in the armory of photophysical methods. We listed here the main app1i;ations of lifetime measurements in the investi- gations of isolated molecules, but the time-resolved spectroscopy is equally one of the fundamental methods in the studies of vibrational and rotational ,

relaxation, of the energy transfer processes, of reactive collisions, etc. .Optical excitation using different types of tunable lasers combined with the fluorescence sampling and probe-pulse detection techniques seems to be the most adequate method allowing a simulta- neous high time- and energy-resolution.

Acknowledgments. - If this revue article contains some original ideas, they result from a long collabo-

0.5

o 10 2 o 3 o ration and numerous discussions with M. Lavollke,

FIG. 11. - Fluorescence decay times for individual vibronic levels

R.

L"pez-Delgado, B- Seep and C . Tric whom of the B

3n,,+

state of 1, molecule (from Ref. [42]). the thanks are due.

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