Vibrational energy transfer from CO to O2 in rare gas matrices.

Chemical Physics ELSEVIER

Chemical Physics 189 ( 1994) 179-204

Vibrational energy transfer from CO to O2 in rare gas matrices. I. Vibrational excitation and relaxation of O2 (X, v = 4-20) Akil Salloum, Hem-i Dubost Labnrutoire

de Photophysique

Molkculuire

CNRS, Britiment 213, Universit6 de Paris-&d,

91405 Orsay Cedex, France

Received 8 August 1994

Abstract Vibrationally excited oxygen Oz(u) is produced in matrix isolated CO-O2 mixtures by IR laser excitation of ‘3C’80. The quenching of the CO vibrational fluorescence by both 1602 and 1802 shows that energy transfer preferentially occurs from the high levels of CO. Laser probing of the vibrational energy contents of O2 confirms that a fraction of the energy initially deposited in CO is actually being converted into vibrational excitation of Oz. Excitation spectra of the A’ + X LIF reveal the existence of a broad O,( o) distribution extending from u = 4 to 20. Time resolvedmeasurements show an extremely slow vibrational relaxation in Oz. The 250 s lifetime of u = 4 is the longest value ever reported for a molecular vibration in solids. The u-dependence of the decay rates and their sensitivity to matrix change suggest that while vibrational relaxation of the lower levels is radiative in both Kr and Ar hosts, the upper levels are depopulated in the latter by radiationless multiphonon processes. Interstate cascading between O,( 6) and the nearby vibronic levels of the singlet manifolds is a negligible process. Quadrupolar effects are found to be important for both radiative relaxation and non-radiative energy transfer. The energy flow between the CO and O2 vibrational reservoirs is controlled by long-range dipole-quadrupole interactions. Vibrational up-pumping in 0, occurs through a sequence of CO(u) + 02( u’) transfer processes. In concentrated matrices back transfer from O,(v) to ground state CO as well as quadrupole-quadrupole mediated fusion of Oz(ti = 1) excitations compete with vibrational relaxation.

1. Introduction

In recent years, highly vibrationally excited diatomic molecules have attracted considerable attention [ 1,2]. The subject is of clear chemical importance as chemical reactions often involve vibrational excitation of either the reactants or the products. In particular vibrationally excited O2 molecules play an important role in atmospheric chemistry. Up to now two techniques have been employed for the production of 02( u) in the gas phase. Wodtke and coworkers [ 31 have used stimulated emission pumping to prepare O2 molecules in a selected high vibrational level of the ground electronic state. Park and Slanger [4] have generated a broad O,(u) 0301.0104/94/$07,00 0 1994 Elsevier Science B.V. All rights reserved SSDIO301-0104(94)00297-S

distribution extending to L’= 22 from the photodissociation of ozone at 248 nm. Another technique, based on the addition of vibrational quanta induced by intermolecular vibration to vibration (V-V) transfer processes, is well known to produce broad distributions of highly vibrationally excited molecules. Owing to the fundamental role played by the molecular anharmonicity in the energy accumulation process, this phenomenon is often referred to as anharmonic V-V pumping. In the gas phase the subject is well documented for NO and CO [S-9]. High vibrational excitation of CO also occurs in cryogenic liquids [ 10,111 and solids [ 12-141. In solids the pumping process is called fusion of vibrational excitations by analogy to the triplet-triplet fusion

IS0

A. Sdloum,

H. Dubost / Chemical Physics I %9 (I 994) 179-204

giving rise to delayed fluorescence in organic crystals. The most recently studied cryogenic systems include CN- in alkali halide hosts [ 151, CO physisorbed on NaCl surfaces [ 161 and NO in rare gas matrices [ 17191. Matrix isolated CO constitutes the prototypical example of vibrational up pumping in cryogenic systems [ 13,14,20]. Optical excitation in either the fundamental or the first overtone absorption band gives rise to a strong vibrational fluorescence. Vibrational energy relaxation is purely radiative. The energy deposited into the L’ = 1 or c’= 2 level is redistributed to the upper levels owing to intermolecular V-V transfer processes which are fast compared to the radiative relaxation. The vibrational energy contents of the strongest excited molecules is pretty high and amounts to 8 eV for c’= 41, the topmost detected level [ 14 J . While vibrational relaxation and energy transfer processes in matrix isolated CO are now well characterized and at least qualitatively understood, almost nothing is known about the vibrational dynamics of matrix isolated O2 in its ground electronic state. However from our knowledge about vibrational relaxation of other matrix isolated diatomics [ 2 11, the vibrational lifetime of O2 is expected to be very long. In addition the vibrational relaxation of O2 (X “C, ) in liquid Ar doped with high concentrations of oxygen has been investigated by Maier and coworkers [ 22,231. At the lowest concentration used in their experiments (30% CL) these authors found a relaxation rate of 60 s- ’ w-hich was probably controlled by 0,-O, interactions. Vibrational energy transfer from CO (1: = 1) to 0, ( I: = 1) has been thoroughly studied in both the gas and liquid phases [ 24-261. The transfer rate constants at liquid N2 temperatures are approximately equal in the two phases. The deactivation of ‘3C1G0 by O2 has also been studied in solid argon at T= 8 K [ 2 11. The transfer rate constant in the solid is quite comparable to that found in the liquid. The low quenching efficiency of the CO (u = 1) fhtorescence by the various isotopic species of oxygen should be related to the large difference between the CO and 0, vibrational quanta ( - 500 cm ~-’ ) . Energy transfer from high vibrational levels of CO to ground state 0, is expected to be much more efficient because the energy defect is considerably reduced. Spectroscopy and dynamics of the excited electronic states of matrix isolated 0, have been studied in much

greater details than vibration. All the possible transitions among the six lowest electronic states which correlate to the first dissociation limit are forbidden. However the optical selection rules are partially broken in a solid matrix. Optical excitation of O2 at any energy above 5 eV gives rise to a strong A’ 3AU+X ‘C, fluorescence in Ar and Kr matrices. The c ‘2; + a ‘A, [29,301, b’C,f +X”SC, and a’A,+X’Z:, ]31] emissions have been observed upon optical excitation. Vibrational relaxation was found to be extremely slow in both the b and a states. An intense a + X phosphorescence has also been observed from matrix isolated discharged oxygen [ 321. A few years ago an amazing property of the matrix isolated CO-O2 system was discovered. The irradiation of a rare gas matrix codoped with oxygen and carbon monoxide by an IR laser resonant with the vibrational absorption of CO was found to induce very strong a-+X,b-+XandA’-,XemissionsofO, [33-3.5l.h is evident that the emitting electronic states of oxygen are populated by efficient energy transfer from highly vibrationally excited CO. It has been speculated that the electronic excitation could result from near resonant exchange of vibrational energy from CO to Oz followed by internal energy redistribution in oxygen [ 34,201. The CO-O, mixture constitutes a unique system of energy reservoirs which are coupled together and to the radiation field and the thermal bath as well. It is the wealth of dynamical processes which makes this system an attractive one to study. The aim of the present work is to disentangle all these processes and to identify the mechanisms by which the vibrational excitation of CO is converted into electronic energy of Oz. This paper is devoted to the study of vibrational excitation and relaxation of 0, in its ground electronic state. The transfer processes responsible for electronic excitation and dissociation of O2 are left for a subsequent paper. The 0, vibrational lifetime is extremely long and it has probably the longest value ever reported for a molecular vibration in a solid. While the radiative process is completely dominant for the lowest vibrational levels, the non-radiative decay makes an important contribution to the inverse lifetime of the upper levels and can be conveniently measured. The radiationless relaxation of IR active molecules with large vibrational spacings and small rotational energies is usually masked by the much faster radiative decay. Therefore vibrationally excited O2 thus constitutes a

A. Salloum,

H. Dubost/

Chemical

unique system for testing the theories of multiphonon relaxation. While dipole-dipole vibrational transfer is standard in matrix isolated molecules, processes mediated by other types of interaction have not been clearly observed. As a matter of fact dipolar interactions are generally expected to dominate in systems characterized by allowed electric dipole radiative transitions. Although the radiative transitions among the vibrational levels of matrix isolated O2 are also electric dipole in nature, they are much weaker (by a factor of IO-‘) than vibrational transitions in IR-active molecules. As a result quadrupolar processes become of greater importance. In addition the relevant molecular parameters such as the O2 transition quadrupole moment for the O2 vibration are known from gas phase measurements. The fact that they are not significantly altered in the solid matrix allows for a quantitative estimate of the transfer probabilities. This is of great interest because in solids quadrupole radiative transitions are usually too weak to be observable and in most cases it has been possible to make only crude estimates of quadrupole effects. The rest of this paper is organized in the following format. In Section 2 we describe our experimental methods. In Section 3 the results are divided into two subsections, each representing a different way of observing the vibrational energy transfer from CO to OZ. The time evolution of the 0, vibrational populations at the cutoff of the pump laser is described in Section 3.2. The discussion in Section 4 is divided into two subsections. Section 4.1 is dealing with radiative and radiationless vibrational relaxation of OZ. The various energy transfer processes taking place among CO and 0, are described in Section 4.2. Summary and concluding remarks are presented in Section 5.

2. Experimental Premixed samples of CO and O2 in 25 mmol of the rare gas were deposited through a cold trap filled with liquid nitrogen or dry ice onto a gold coated copper mirror attached to the bottom of a variable temperature liquid helium cryostat (SMC, France) equipped with a temperature controller (Lake Shore Cryotronics DRCROC). The CO gas was isotopically enriched (CEA, ORIS) and contained 99% carbon 13 and 41%

Physics

I89 (1994)

179-204

181

oxygen 18. Natural oxygen (purity grade 99.998%) was supplied by Messergrieshem (Germany). Isotopically enriched oxygen containing 98% “0 was from ORIS (France). Argon (99.996%)) krypton (99.99% ) and xenon (99.99%) were supplied by the company L’Air Liquide (France). All gases were used without further purification. The ‘3C’s0 molecules were optically pumped into the u = 2 vibrational level using the IR radiation of our home-built color center laser (CCL). This laser has been improved to allow operation in the true CW mode (obviating the need to use a mechanical chopper to modulate the 647 nm pump beam). The KC1:Li colored crystals were supplied by either the Burleigh company or by the Laboratoire de Spectroscopic Atomique (Universitk de Caen) . The power obtained at the wavelength of the 0 + 2 overtone absorption band center of 13C’8O at h = 2.47 p,rn was 5-10 mW. The CCL pump beam was tightly focused onto the sample with a CaF, lens (f= 10 cm). Vibrational excitation of CO was directly monitored via fluorescence. Two different experimental procedures were used. In the first, the pump beam was chopped mechanically in the T/6 mode (repetition period T= 180 ms, aperture time T/6 = 30 ms) ; the IR emission was collected by a CaF2 lens cf= 4 cm), and detected through an InAs filter with a Au : Ge (77 K) photoconductive cell. The accessible spectra1 range extends from 3.7 to 8 pm. The signal was sent to a Brookdeal model 9454 amplifier ( X 300) and to a digitizing averaging oscilloscope (Lecroy mode1 9400). In the second method the fluorescence induced by the CW CCL pump was chopped at 600-800 Hz and focused onto the entrance slit of a 1 m monochromator (Sopra, France) equipped with a grating blazed at 4 p,rn and an InSb (77 K) photovoltaic detector. The spectral range covered by this system extends from 2 to 5.4 km and allows for sensitive detection of the entire Au = - 2 and of a portion of the Ar; = - 1 emission spectra of CO. Emission spectra were obtained by sending the signal from the detector to a lock-in amplifier (ATNE mode1 ADS2) then to the digitizing oscilloscope working in the roll mode with a time base of 1000 s and to a personal 486 computer for further processing. Time and frequency resolved experiments were performed by modulating the pump beam with the chopper as described above. The slow fluorescence

182

A. Salbum.

H. Dubost/

Chemical Physics 189 (1994) 179-204

intensity changes were also analyzed by blocking the laser beam manually. Vibrational excitation of OZ in its ground electronic state was monitored using a pump-probe technique based on the detection of laser induced electronic fluorescence. The CCL was used as the pump for the COO2 system while a pulsed dye laser (Lambda Physik FL2002) pumped by a KrF excimer (Lumonics Hyperex 400) operating at a repetition rate between 1 and 40 Hz was used to probe the 0, vibrational excitation. Both laser beams were focused in coincidence onto the sample. Using the commercially available dyes, the probe laser was operated from 320 to 850 nm with a few discontinuities [ 361. Scanning the probe wavelength through the tuning range of each of these dyes was found to induce the A’-X fluorescence of O2 in the UV-visible region. The emitted light was dispersed by a Jobin Yvon HRS monochromator equipped with a grating blazed at 600 nm and detected using a cooled ( - 30°C) GaAs photomultiplier. The resolution of the monochromator with its slits fully open (2 mm) was sufficient to detect single O2 vibronic lines. The signal from the photomultiplier was sent to a boxcar integrator (SRS model 250) with a temporal gate appropriate for the A’-X fluorescence lifetime (80 ps for IhO, and 31 ps for 1802 in solid argon). Excitation spectra of selected A’ ‘A, -+ X ‘xi (0, u) bands were obtained by scanning the probe laser wavelength and recorded in the same manner as the CO vibrational fluorescence spectra. The time evolution of the O2 vibrational populations after blocking the pump laser was obtained by monitoring the A’ + X fluorescence intensity induced by the probe laser tuned into resonance with a particular excitation line.

3. Results -1.I. Quenching of the CO vibrationalfiuorescence

by

02 While the vibrational population distribution in rare gas matrices doped with pure CO is well characterized previously, in the mixed CO-O2 samples we expect energy transfer to modify this distribution. This set of measurements is aimed at characterizing the efficiency of the CO fluorescence quenching by O2 as well as the modified CO vibrational distribution.

The energy of the pump laser deposited into I: = 1 or u = 2 level of ‘3C’80 is redistributed to the higher levels of the same isotopic species. The mechanisms responsible for anharmonic V-V pumping in matrix isolated CO have been described previously [ 14,201. Phonon assisted intermolecular V-V transfer processes, ‘“c’*o(u=

1) + 1”c’80(u>2)

+ ‘.lC’XO( u = 0) + ‘3c’80( cl+ 1) +AE=u(24

cm-‘)

,

(1)

populate the lower levels of the vibrational ladder quite efficiently because they involve the delocalized u = 1 excitation. However the energy defect AE which is involved in these processes increases linearly with the vibrational quantum number of the acceptor, leading to a corresponding decrease in the V-V transfer probability. The excitation of the upper levels takes place according to the reaction ‘aC’sO( u) + ‘3C’80( G”= u) -+ ‘3c’*o(L; - 1) + 13C80( u’ + 1) +AE=24

cm-’

,

(2)

which describes a one phonon assisted V-V exchange between two CO molecules both excited to nearly the same vibrational level. Infrared emission spectra of matrix isolated CO excited by the CCL tuned into resonance with the 0 -+ 2 absorption line of ‘3C180 are shown in Fig. 1. These spectra consist of the Au = - 2 sequence of ‘C”O, without any evidence for the presence of lines originating from other isotopic species, in spite of the fact that the enriched CO used in these experiments contains 60% of 13C160 molecules. This fact should be related to the endothermic nature of energy transfer from ‘3C180 to lighter isotopic species which makes such processes completely inefficient. The intensity distribution of the Au = -2 sequence exhibits a bimodal character with a main maximum at I,’= 12 and a secondary maximum around G’= 34. The distribution terminates abruptly at u = 38. The corresponding distribution for Kr and Xe matrices is similar to that observed for solid argon, except for the fact that the intensity of the lines originating from the upper levels decreases from Ar to Xe. Several factors contribute to the reduced efficiency of up-pumping in solid Kr and Xe. These are: (a) the decrease of the CO radiative lifetime [ 371 from Ar to Xe; (b) the decrease

183

A. Salloum, H. Dubost / Chemical Physics 189 (1994) 179-204

3

co/k-:

1%

CO,‘Kr:

4000

1%

3000

3500 Energy

(cm-

Fig. 1. Vibrational Au = - 2 emission spectra of “C”O and Xe matrices at T= 7 K.

1) in Ar, Kr

in phonon assisted V-V transfer resulting from a reduction in the Debye limit; (c) the fact that intermolecular distances are larger in heavier matrices. The addition of O2 to the CO/rare gas samples results in the quenching of the 13C’80 vibrational fluorescence. In the presence of oxygen, the intensity of the total (non-dispersed) fluorescence is decreased by a factor 3 to 5 at 0.2% 02, 5 to 10 at 0.5% and 15 to 20 at 3%. In contrast the CO fluorescence decay is practically unchanged in the presence of O2 at concentrations up to 0.5%. At higher O2 concentrations the decay time is only slightly reduced as shown in Fig. 2. More interesting is the effect of O2 upon the CO fluorescence spectra. For O2 concentrations smaller than 0.1% the intensity distribution of the Au = - 2 emission lines is practically unaltered. When the 0, concentration is increased, the lines emanating from the upper levels disappear successively as shown in Fig. 3. At 0.2% 02, the v -+ v - 2 lines with v B 24 are missing while the intensity distribution of the lines emitted from the lower levels is nearly identical to that observed for oxygen free CO/Ar samples. The quenching effect becomes more pronounced at 0.5% O2 where a cut-off in the fluorescence spectrum is observed at v = 18. The addition of 3% O2 results in a strong

160dCO/Ar

”

=!

&

b

2b

4b

I

60

:(

d 80

Time (ms) Fig. 2. Vibrational fluorescence decay of I % CO in solid argon at T= 7 K. (a) Without oxygen; (b) in presence of 3% natural O2 (the intensity is decreased by a factor 15).

Fig, 3. First overtone vibrational fluorescence spectra of 1% CO (0.4% “C’“0) in solid argon at T= 7 K codoped with natural oxygen at various concentrations.

184

A. Sullourn, H. Dubosr / Chemical Physics 189 (1994) 179-204

quenching of the CO fluorescence. The cut-off occurs at I‘ = 15 and the intensities of the remaining lines are reduced to 10% of their values in the absence of OZ. Isotopic substitution in 0, does not significantly change the quenching of the total fluorescence. However, the intensity distribution is modified. Fig. 4 shows the effect resulting from the addition of i802 to the CO/ Ar samples. The quenching of the CO fluorescence by ‘“02 and by i802 are similar except for the fact that in the presence of the heavier isotopic species the cut-off in the intensity distribution is shifted upward by 2 to 4 vibrational levels. The highest detected level is u = 28 at 0.2%, u = 22 at 0.5% and u = 17 at 3% of “0,. The time development of the intensity of the individual fluorescence lines emitted from the lowest vibrational levels of ‘3C’80 upon a squared pulse excitation is displayed in Fig. 5. In the absence of oxygen the intensity decay of the successive u + u - 2 lines is identical within a factor of 2 (Fig. 5a). Addition of natural oxygen results in a u-dependent shortening of the fluorescence decay time (Fig. 5b). For instance at 3% natural O?, the lifetime of u = 4 is practically unchanged while the emission from u = 14 follows the laser pulse.

Laser

Time (ms)

4-2 5-3 6-4

3.2. Probing of the vibrational energy contents of 0, The results of the previous section show that the CO fluorescence is strongly quenched and that the vibrational distribution is modified by the presence of oxy-

18OdCOlAr

I

n 4000

&

1

-12

A.

3500 Wavenumbers

3/l/100 3000 (cm-l)

Fig 4. First overtone vibrational fluorescence spectra of 1% CO (0.4% “C”O) in solid at T=7 K codoped with “Oz at various concentrations.

Fig. 5. Time dependence of the intensity of AIS= 2 fluorescence lines of “C”O in solid argon at T=7 K. (a) At 1% CO and without oxygen; (b) at I % CO and 3% natural Oz.

gen. In this section we describe experiments aimed at interrogating the vibrational energy contents of 0,. Steady state measurements described in Section 3.2.1 are intended for demonstrating the occurrence of V-V transfer from CO to O2 and characterizing the O2 vibrational distribution. In addition kinetics of the O2 populations can provide further information about specific channels of population flow. This is the aim of rise and fall measurements presented in Section 3.2.2. 3.2.1. Excitation spectra of the A’ -+XJIuorescence The vibrational excitation of 02(X ‘I;, ) is probed by laser induced fluorescence using the pulsed dye laser. For probe wavelengths shorter than 500 nm, the

A. Salloum, H. Dubost/

Chemical Physics I89 (1994) 179-204

three nested states c ‘CL, A’ “A” and A “XC,+are energetically accessible from the high vibrational levels of the ground electronic state. The excitation spectra of the A’ -+X fluorescence of O2 in solid Ar have been recorded by Goodman and Brus [27] and in greater details by Salloum et al. [38]. In the 245-290 nm region, the spectrum consists of a vibronic progression of triplets assigned to the A’ 3A, + X “XL ( u’, 0) transitions from L” = 1 to v’ = 9. Each triplet component consists of a rather broad band with a FWHM of N 20 cm-’ accompanied by a weaker feature on the high frequency side at 40 cm - ’ from the main peak which could be a phonon sideband. There is no clear evidence for a contribution from the A+X transition to the excitation of the A’ -+X fluorescence. Therefore the excitation spectra of vibrationally hot O2 are expected to consist mostly of the A’ + X progressions. A portion of the excitation spectrum of the A’ --)X emission of 0, in presence of vibrationally excited CO is shown in Fig. 6. The six main peaks accompanied by a weaker sideband are clearly identified with the ( 1, 15) and (2, 16) members of the A’ 3Au +X ‘2; triplet progression. This result demonstrates that V-V transfer occurs from CO(o) and populates the high vibrational states of 0,. Since the vibrational energies in the ground state are approximately twice the values in the A’ 3A, state, the frequencies of the (u’, u”) transitions coincide with those of (G” + 2, U”+ 1) . The assignment of the exci-

(2, 16)

710

720

730

740

Wavelength (run) Fig. 6. Excitation spectrum of the A’ +X( 0,7) fluorescence of “0, (h,,=421.2 nm) in solid argon doped with 1% CO and 0.2% Oz at T= 7 K obtained with the pyridine 2 dye (not corrected for the dye laser intensity).

185

tation has been done according to the following procedure. We have calculated the A’ ‘A,, +- X “xi ((I’, G”‘)transition frequencies by combining the values of the A’ ‘A, +X “xi (u’, 0) measured in Bonn [ 381 to the ground state vibrational frequencies obtained using the molecular constants given by Becker et al. [ 3 11 (for the low u” levels) or to the A’ “Au-+ X ‘xi (0, u”) emission frequencies measured by Rossetti and Brus [ 281 (for the high L,”levels). In addition we have calculated the FranckkCondon factors (FCF) of the A’ +X(v’, u”) transitions up to u”= 20 using the gas phase RKR potential given by Krupenie [ 391 for the X “C; state and the molecular constants given by Coquart and Ramsay [40] for A’ ‘A,. The substantial difference in the FCF allows in general to decide which transition should be expected for a given triplet. In this way the vibronic bands present in the A’ -+ X excitation spectra have been unambiguously assigned. The agreement between experimental and calculated values is less than 0.2 nm. As the probe wavelength is shortened, while the A’ 3Au state can still be reached from the lower vibrational levels of the ground state, transitions from the high u levels to the B ‘2; state become energetically accessible. As is well known, the excitation of vibrationally cold 0, through the Schumann-Runge absorption band gives rise to emission from the lower state manifold around 30000 cm-‘, mostly from A’ 3Au and to a lesser extent from c ‘2; [28-301. This is due to the strong predissociation of the B “xi (u’ > 0) state which results in dissociative excitation of the lower states. Consequently the excitation spectrum of the hot A’ +X ffuorescence emanating from vibrationally excited O2 becomes more complicated in the near UV than in the red region because strong B +X lines are superimposed on the A’ +X triplet progressions. This is illustrated by Fig. 7 which depicts the A’ -+X excitation spectrum from 360 to 400 nm. The main A’ + X triplet progression (0,5), ( 1,6), (2,7) and the weaker one (2, 6)) (3, 7)) (4, 8) are blended with the B +- X progression (3, 18), (4, 19), (5, 20) and (3, 19). However the B +X lines can be distinguished from their dependence upon the excitation density which differs significantly from that of the A’ +X triplets. As a matter of fact the CO population distribution is strongly dependent upon the CCL energy density [ 141. The excitation of the upper CO levels requires a sharp focusing of the laser. On the contrary, an increase in

A. Salloum, H. Dubost/ Chemical Physics 189 (1994) 179-204

186

I(a.u.

be accessible by probing in the visible region through the B + X transition. In fact only the levels U”= 13, 14, 15, 18, 20 f 1 have been detected at h < 400 nm with a substantial increase in sensitivity resulting from the large oscillator strength of the Schumann-Runge band. The absence of B +X lines in the excitation spectra at h > 400 nm shows that the O2 vibrational levels with u” 2 21 are not populated. A semi-quantitative estimate of the vibrational population distribution can be obtained by comparing the intensity of the A’ +X fluorescence induced by the successive probe transitions. The population ratio of two vibrational levels v’,’ and u; of the X “S; state is proportional to the fluorescence intensity ratio corrected for the Franck-Condon factors and for the change in probe laser intensity: rrobe

rrobe

370

380 Wavelength

390 (nm)

Fig. 7. Excitation spectra of the A’ +X(0, 9) fluorescence of “0, in solid argon doped with 1% CO and 0.2% O2 at T= 7 K obtained with the QUI dye. Upper spectrum: the CCL pump laser is sharply focused onto the sample (spot size = 100 km). Lower spectrum: the spot size of the pump laser is increased by a factor 10.

the CCL spot size onto the sample produces a significant shift of the population distribution toward the lower levels. The selective quenching of the high u levels of CO by the presence of O2 has suggested that V-V transfer to oxygen occurs preferentially from the high levels of CO. Therefore a decrease in excitation density should result in a decrease of the vibrational energy available for oxygen and a shift of the O2 population distribution toward the lower levels. Fig. 7 shows the effect of increasing the laser spot size by one order of magnitude. The intensity decrease of the B +- X lines is 2 to 3 times larger than that of the A’ +X lines. We have calculated the B 3c; +X “2, (u’, u”) values using the B “c; +-X ‘c, (u’, 0) absorption frequencies measured by Fugol et al. [ 411. However the accuracy is not sufficient for precise assignments. The identification of the “xi (u”) level is within one or two vibrations. The vibrational excitation of oxygen has been probed in the three systems Ar/1602, Kr/“02 and Ar/180,. The measured wavelengths of the observed excitation lines are listed in Table 1 together with their assignment. In the Ar/r60, system vibrational levels v”=4 to 19 have been observed through the A’ +X probe transition. The detection of levels u<3 requires an excitation wavelength Aprobe< 320 nm while levels u > 20 are expected to appear at Aprobe> 850 nm. In spite of the fact that the lowest u levels are probably strongly populated they could not be observed in the present experiments. In contrast the upper levels should

No; -= N,,;

Zn(u;, u’,‘) FCF(u;,

u;) Zl”&

Zn( u;, u;) FCF(u;,

~7) Iprobe ’

(3)

The calculation of the population ratio rests on the assumption that the gas phase FCF are not substantially changed in the matrix. Experimentally we have found that the intensity ratio of the fluorescence induced by excitation lines originating from the same u” level corrected for the probe intensity agrees with the gas phase FCF ratio to better than a factor of 2. The relative population distribution of i602 in Ar host is shown in Fig. 8 together with the r3C”0 distributions of pure CO and in CO-Q mixtures. The rather high uncertainty for the high u levels results from the fact that the NJN, ratios are not directly measured. Their values are obtained by multiplying the successive N,,, , /N,, ratios calculated using Eq. (3) from the same excitation spectrum. Under the assumption that the quantum yield of A’ -+ X fluorescence induced by excitation into the B %; state is close to unity, the comparison between the intensities of B +X and A’ +-X lines appearing in the same spectrum leads to the ratios N4/N,4= lo4 and N6/N2,,= 10’. On average the O2 vibrational populations are decreased by one order of magnitude as u is increased by 3 units. The other two systems have also been studied but less extensively than natural O2 in argon. Probing of the vibrational levels of r602 in solid krypton through the A’ +-X transitions has allowed for the detection of u”=4 to 14 while u”= 12, 13, 14, 15 and 17 have been observed using the B +-X excitation lines. The distri-

187

A. Sulloum, H. Dubost/ Chemical Physics 189 (1994) 179-204 Table 1 Observed excitation wavelengths (nm in vacuum) for the A’ ?A” + X ‘Cs and B ?Z; +X ‘Z; Ar at T= 7 K. In each case the A’ + X( 0, U) fluorescence is monitored “O,/Ar A’ IA ,I

VII

v’

B ‘2, 0

h,,,x

1:’

(nm) 4

2

5

0

6

2

6

1

7

2

8

1

8

0

9

0

‘sOJAr

‘“O,/Kr

x “H,

1 2 3 1 2 3 1 2 3

1 2 3 1 2 3 1 2 3 1 2 3

I 2 3

V’

R

(nm)

11’

3

1 2 3

I 2 3

3

I

1 2 3 1 2 3 1 2 3 1 2 3

h B-X

2

1

382.3 384.0 386.2

379.9 383.5 385.6

I1

0

12

4

12

1

13

0

14

1

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

501.2 505.0 508.5 537.0 541.3 545.9 492.0 495.3 498.9 552.2 556.6 561.3 623.8 629.4 635.4 641.9 647.8 654.2

0

1 2

0

448.4 470.5 473.6 477.0

1

502.5 506.1

2

2

4

0

327.8

1

336.4

1

1 2 3

1 2 3

A*,-,

1 2 3

V’

x B-x

(nm)

330.0 332.2 334.1

1 2 3 1 2 3 1 2 3

375.0 377.3 384.8 386.6 389.3 382.3 384.2 386.6

1 2 3 1 2 3

428.9 431.7 434.4 439.4 442.2 445.1 454.2 457.2 460.4 450.3 453.2 456.4 475.9 478.2 481.8 469.8 473.2 477.4

429.75

0

0

n

(nm)

336.4 338.8

9

10

01

(nm)

(nm) 2

333.9 335.8 337.4 371.8 373.0 375.4 369.7 371.2 373.2 380.5 382.6 384.8 390.2 392.3 394.6 426.2 428.9 431.7 441.3 444.1 447.1 469.7 472.8 476.3

h,,-x

B ‘2;

A’ 3A”

B %;

A’ 3A” h,-x

systems of 1602 in Ar, ‘“0, in Kr and ‘so2 in

4

493.6 496.7 500.2

647.4 652.5 657.9

0

320.8

0

329.4

2

328.2

I 2 3 1 2 3 1 2 3 1 2 3

(continued on next page)

I88

A. Sallourn, H. Dubost / Chemical Physim 189 (I 994) 179-204

Table 1 (continued) ‘“OJAr x 1s &P

A’ ‘A II

(”

0

1s

2

R

I 2 1 2 3

1

16

2

1

17

2

2 3 3

18

3

19

5

7

A’ ?A”

B ‘8,;

15

20

“OJAr

‘602/Kr

1 2 3

I 2 3 1 2

h*,-x (nm) 661.5 661.1 697.2 704.6 711.9 719.5 727.0 735.2 805.4

820.4 830.7 840.6 805.4 814.5 824.0 805.0 810.9

li

2

I

3

A,-, (nm)

11’

A13A ”

B ‘Z; R

A*,-, (nm)

L’)

(nm) 3 2

339.2

h DCX

I>’

B ‘6 n

h.4f-X (nm)

VI

hrJ+x (nm)

1

329.9

3

330.4

335.7 342.1

377.5 387.0 373.0 373.0 390.2

4 3

380.7 390.2

5

375.5

S

387.0

7 6 7

373.1 382.3 389.5

21

butions of vibrational populations in solid Ar and Kr are quite similar. A few levels higher than those observed are certainly populated in the Kr matrix. We have not attempted to probe the lh02/Kr system in the red region. A significant difference results from the substitution of 1802 to 1602. The probe signals detected for the 1802/ Ar in general are one order of magnitude smaller than their counterparts for ‘“O,/Ar. The topmost level which has been detected through A’ +X is U”= 12. Only two lines belonging to the Schumann-Runge system are observed. They are assigned to the B ‘2; +X’C; (1, 15) and (3, 16) transitions. The intensity of these lines is reduced by a factor of 15 in comparison to ihO*. The B +X excitation lines observed for 1602 in the 365400 nm region are missing in the case of “Oz. These observations indicate that the vibrational excitation of the heavier isotopic species is considerably weaker than that of the lighter one. 3.2.2. Decay of the 0, vibrationalpopulations We have measured the time dependence

of the

A’ -+X fluorescence intensity excited by the probe laser after the cutoff of the IR pump. The experimental procedure is as follows. The sample was irradiated with the CW CCL for a time long enough to establish a steady state population of the O2 (X ‘xi, u”) levels. A particular vibrational level was probed through the most appropriate A’ ‘AU+X ‘XL (u’, u”) transition. The steady state intensity I( u”) of the induced fluorescence signal is proportional to the equilibrium value of N,“. At time t = 0 the pump beam was blocked while keeping the probe onto the sample. The resulting time evolution of the fluorescence intensity Z( u”, t) is shown in Fig. 9 for selected levels. The time necessary to the lowest observed level u”=4 for reaching the thermal equilibrium is strikingly long ( > 15 min). On such a long timescale the probe laser itself operating at a repetition rate of a few Hz could perturb the population of the probed level. We have checked that it was actually not the case by decreasing the dye laser intensity. The time evolution was insensitive to a change by a factor of 50 in the probe intensity. In addition we have care-

A. Sullourn, H. Dubost/

I

CO/Ar

I

Chemical Physics 189 (1994) 179-204

described by the kinetic equation

:l/lOO

0 #Zo/Ar

:0.2/l/100

lo

N ,(CWWO)

I

15 20 III

1200

1400

1x9

1600 1800 Energy(cm-I)

2000

Fig. 8. Relative vibrational population distributions of ‘3C’80 and 1602 versus single L;+ o - 1quantum energy represented on different arbitrary scales. The standard distribution for 1% CO in solid argon at T= 7 K is sketched in the upper panel. The effect of doping by 0.2% natural oxygen is described in the lower two panels which show the quenching of the upper levels of CO and the corresponding population distribution of Oz.

fully controlled the long term stability of the probe intensity. A second remarkable feature of the signals from the lower levels appearing in Fig. 9 is constituted by their initial increase in intensity at the pump laser cut-off. Such a behaviour is characteristic of a relaxation cascade in which the upper levels decay at a rate faster than the lower levels. Assuming that single quantum transitions are dominant in the relaxation process the time dependence of the population N,,,,of level c”’is

where k,.!!_ ,,‘,_ , is the relaxation rate of level c,“. However, provided that the relaxation rate of level U”+ 1 is significantly larger than the rate of level L”’and that NIZr, + , is substantially smaller than N,,., the longtime evolution is dominated by the first term of Eq. (4). This is precisely what happens in the case of vibrationally excited OZ. A semilog plot of I( v”, t) is shown in Fig. 10 for u” = 4. The intensity decay is perturbed by the relaxation cascade from the upper levels in the time interval 80< t< 250 s. In contrast the decay is almost perfectly exponential at times t > 250 s, indicating that the cascading effect becomes negligible. The values of the decay time of the observed levels of l6O2 in solid Ar for different CO and O2 concentrations are listed in Table 2. It can be seen that they exhibit a strong v’ dependence as they are decreased by 3 orders of magnitude from L’’ = 4 to 19. The lifetimes of the upper levels are independent of both the CO and 0, concentrations. For example the value of 3.5 s for u” = 14 should be considered as the intrinsic relaxation time of this level. In contrast, the lifetimes of the lower levels are concentration dependent. For instance the decay time of the L”’= 4 level increases from 290 to 380 s as the CO concentration is decreased by a factor of 10. This fact suggests that the O2 vibrational excitation is weakly quenched by CO at the highest concentration. More surprising is the decay time shortening which results from a decrease in the O2 concentration. Such an effect should be related to the interaction between O2 molecules. The 250 s lifetime measured at 0.02% O2 and 0.1% CO is taken as the closest to the intrinsic value of the u” = 4 vibrational relaxation time. At 0.2% O2 and 1% CO the decay of u = 9 is markedly non-exponential. For this reason it has been characterized by the two different asymptotic time constants which are reported in Fig. 9 and Table 2. Upon a decrease on the CO concentration the faster component of the decay tends to disappear. This is illustrated in Fig. II. At 0.1% CO the decay curve for v = 9 is similar to that of the lower levels. The decay is exponential in a large time interval while the bump characteristic of the radiative cascade is more clearly observed. The vibrational decay times of “0, in Ar and lhOZ in Kr are also listed in Table 2. The lifetimes of the

190

A. Salloum. H. Dubost/

Chemical Physics 189 (1994) 179-204

r--1 v=6

I\

-

c=5”8s T=15 s

r=150s

0

5=5 s

v=13

v=8

I\

i” d

r=3.5s

x=2&

v=14

0

I

200

/

I

600

4dO

800

0

20

Time (s)

I

40 Time (s)

I

60

1

80

Fig. 9. Time evolution of the 1602 (A’ -+X) fluorescence intensity induced by the probe laser at the cutoff of the CCL pump. The probe wavelength is tuned into resonance with the most appropriate A ’ c X transition for each vibrational level of ground state oxygen. The T value indicated in the figure is the time constant of the exponential portion of the decay. The non exponentialdecay of the L’=9 level is characterized by initial and final asymptotic time constants.

lowest levels are virtually unaltered by isotopic substitution in OZ. The L”‘= 15 lifetime is shorter for the heavier isotope by a factor of 3 to 4. In contrast there is a strong matrix effect on the vibrational dependence

I--

I

4. Discussion

t

I-

of the lifetime. While the lifetimes of u”=4 and 6 are similar in the three systems, the value found for the higher levels is 10 times longer in Kr than in Ar. Moreover in the ‘hO,lKr system the lifetimes of the upper levels are significantly increased upon a decrease in the CO concentration. Finally we have measured the temperature dependence of the decay time for levels ~“=4, 6 and 15 of 1602. A weak shortening of the lifetimes, not exceeding 20% of the value at T=7 K, is observed upon a temperature increase up to 20 K in solid argon and 40 K in solid krypton.

4.1. Vibrational relaxation of matrix isolated 0, 400

600

800

Time (s) Fig. 10. Semilog plot of the A’ + X fluorescence intensity decay proportional to the ‘6O2 (u =4) population. In the time interval 80 < t < 250 s the decay is perturbed by the relaxation cascade from the upper levels. At times 1> 250 s, this effect becomes negligible and the observed decay is almost perfectly exponential.

The results presented in Section 3.2.2 suggest that the vibrational relaxation of the lower levels of O2 could be radiative while the strong v-dependence of the lifetime of the upper levels together with the matrix effect give evidence for the occurrence of radiationless processes. The aim of Section 4.1.1 is to calculate the rate of vibrational relaxation by spontaneous emission. The

A. Salloum, H. Dubnst/ ChemicalPhysics 189 (1994) 179-204

191

Table 2 Experimental decay times (s) of the vibrational populations of l6O2 in Ar and Kr hosts and of ‘*02 in Ar at T= 7 K. The probe laser is tuned either on the B + X (starred values) or on the A ’ t X transition. The A’ G-X fluorescence is monitored in each case ‘60,/CO/Ar 0.2/1/100

‘60,/CO/Ar 0.2/0.1/100

‘60,/CO/Ar 0.02/1/100

‘60Z/CO/Ar

“OJCO/Ar

0.02/0.1/100

0.2/l/100

4 6 8 9

290 150 28 5/18

370-400

220-240

250

10 11 12 13 14 15 16 17 18 19

15 12 10 5

120 40 28

26160 21 13

3.5(3.4*) 1.7( 1.9*) 1(1.2*) 0.6 0.7 0.4

3.5* 2.8

3.8*

‘“O,/CO/Kr 0.2/0.1/100

350400

250-300 160 57

350-550

60

3.5* 0.8*

_I1(u.a.)

L

I

50

‘6OJCOlKr 0.2/l/100

18 8

u = 1 radiative lifetime is first deduced from absorption intensity measurements. Then we derive a simple model in order to make an estimate of the dipole moment induced by the 0, quadrupole in the nearest neighbour rare gas atoms. In Section 4.1.2 the O2 non

0

“O,/CO/Ar 0.2/0.1/100

100

150

Time (s) Fig. Il. Influence of the CO concentration upon the time evolution of the 1602 (o = 9) vibrational population monitored through A’ + X LIF. (a) Solid argon doped with 0.2% natural 0, and 1% CO. The fast decay results from the quenching of Oz by CO. (b) The matrix contains 0.2% O2 and 0.1% CO. The quenching by CO is considerably weaker. The time evolution of LI= 9 looks more similar to that of the lower levels. The effect of the relaxation cascade is clearly observed whereas it was totally masked at 1% CO by the O2 + CO transfer.

221120

46* 32* 26(26*) 22*

80(50*) 42* 40* 31*

11*

25*

radiative rates are calculated using the standard models of vibrational multiphonon relaxation. 4.1.1. Radiative relaxation of the u = I level The radiative lifetime of u = 1 is the inverse of the Einstein coefficient for spontaneous emission from the initial state u = 1 to the final state u = 0. It can be written in the form [ 421

The first term of Eq. (5) describes the usual electric dipole radiation while the second term stands for the next higher order contribution from the electric quadrupole. In this expression vl,, is the vibrational frequency of the 1 * 0 transition in Hz, (11 p IO) is the matrix element of the dipole moment p and (1 I Q I 0) is the transition quadrupole matrix element. The last factor which depends on the refractive index n is a correction for the effect of a solid environment. For instance in solid argon, II = 1.27 and n[ ( n2 + 2) / 3]2=1.84. The dipole moment for purely vibrational transitions of free oxygen is zero and the radiative lifetime is completely controlled by the quadrupole term. The transition quadrupole moment is a key parameter not

192

A. Sallourn, H. Dubost / Chemical Physic.s 189 (I 994) 179-204

only for radiative relaxation but also for V-V transfer processes between CO and Oz. Several values of the transition quadrupole moment can be found in the literature. However they are somewhat scattered and need to be discussed in detail. The most accurate experimental determination of the transition-quadrupole matrix element has been reported by Reid et al. [43]. These authors have measured the integrated intensity of the u = 0 + u = I absorption band of 1602 using a tunable diode laser and a 40 m path of low pressure oxygen. They obtained the value ( I( Q ] 0) = ( 1.45 f 0.026) X lo-” esu cm*. Shapiro and Gush [44] had previously determined Q,, the rate of change of the quadrupole moment with internuclear distance, from intensity measurements of the collision-induced 1 +O band at high 0, pressure. Approximating the O2 quadrupole moment by a first order expansion

Q=Q, +Q,x, the transition

(6a) quadrupole

moment can be written as

(~lQlo>=Q,(1I~lO).

(6b)

In the harmonic approximation, the matrix element of the internal coordinate is expressed as a function of the O2 reduced mass m and of the 1 + 0 angular frequency o=27ruas

c*IxlO) =

($J

=3.683x10-‘“cm.

Under the assumption that the multipolar moments of oxygen are those of the free molecule, the radiative quadrupolar lifetime of O2 ( u = 1) given by the second term of Eq. ( 1) is rraad=3.1X107s;=lyear.Thecorresponding IR absorption of a matrix sample would be impossible to detect. Actually the IR activity of symmetric molecules dispersed in rare gas crystals results from the appearance of a dipole moment induced by the solid environment. The induced infrared absorption of Hz, D, and N, in solid argon or krypton at liquid nitrogen temperatures has been observed a long time ago by Welsh and coworkers [ 47-491. The 02-rare gas systems do not seem to have been studied. Therefore we have looked for the O-+ 1 induced absorption band of O2 in an argon matrix at T=7 K. A weak absorption band with a FWHM of N 0.5 cm- ’ could be observed, in spite of the fact that the thickness of our matrix samples was 2 orders of magnitude smaller than the length of the crystals prepared by Welsh et al. [ 47-491. This is certainly due to the significant spectral narrowing at low temperature and also to the high sensitivity of the FTIR spectrometer (Bruker 120) that we employed for our measurements. For a sample thickness I= 1 mm and a concentration of 1% O2 in solid argon, the integrated intensity of the 0 --) 1 band was found to be S = 0.0055 cm- ‘. The radiative lifetime is connected to the absorption intensity through the expression

(6~)

N,cl Li =

The value Q, = 1.6 e a, = 4.07 X lo- ” esu cm is equivalent to a quadrupole matrix element (11 Q]O) = 1.50X 10p2’ esu cm*. The agreement with the value given by Reid et al. [43] is excellent although it may be considered fortuitous. A somewhat smaller Q, value can be found in two recent papers by Millot et al. [ 451 and by Billing and Kolesnik [46]. From the reported value of the first order derivative of the quadrupole moment with respect to the reduced internal coordinate: dQ/dt= - 2Qo, where t= (r- re) Ire =x/r,, r, is the equilibrium internuclear distance and Q. is the permanent quadrupole moment, the quadrupole transition matrix element can be deduced. Using the values Qc,=0.39X lO-2h esu cm2 and r,= 1.207X lo-‘cm, one finds (11 Q ]0) = 2.38 X 1O-28 esu cm*, i.e. 6 times smaller than the value of Reid et al. However the authors do not comment on the determination of this low value and we will retain the higher one.

8rrz&n*S

(7)

Here No is the number density of O2 molecules in the v = 0 level in units of cm ‘, 1 the sample thickness in cm, vro the O+ 1 vibrational frequency in Hz, n the refractive index of the solid matrix and S the integrated intensity in cm- i. The induced radiative lifetime of O2 (c’= 1) based on the IR absorption and Eq. (7)) is rrad = 1650 s in Ar, i.e. five orders of magnitude smaller than the quadrupolar lifetime. Pressure induced infrared absorption of symmetric molecules in the gas phase has been extensively studied. Van Kranendonck [ 501 has developed the socalled exp-4 model, in which the dipole moment resulting from the interaction with a perturber is found to be a sum of two contributions. One results from the dipole moment induced in the perturber by the molecule while the other arises from short range interaction.

A. Salloum, H. Dubost/

Let us consider for instance 0, perturbed by a rare gas. The dipole moment induced in 0, by collision with a rare gas atom is written P(R

(8a)

r, 0) = I*~(R, 0) (r-r,)

and /J,(R

0) = 5

+ pexp(

-R/p)

%,.Q,(3 ,

cos*o-

193

Chemical Physics 189 (1994) 179-204

I) (8b)

where R is the O,-rare gas distance, (Y,.~,the polarisability of the rare gas atom, Q, the rate of change of the O2 quadrupole moment with respect to the internuclear distance, 0 the angle between the molecular axis and the line joining the O2 molecule and the rare gas atom, p and pare constants characterizing the dipole resulting from the overlap of electron clouds (magnitude and range, respectively). Shapiro and Gush [44] have studied the collision induced fundamental band of oxygen in gaseous mixtures with argon at pressures of a few tens of atmospheres. They have calculated the band intensity profile resulting from the quadrupole contribution. They find a good agreement between the experimental and calculated synthetic quadrupole spectrum, suggesting that the overlap contribution is not very important, even in the Q-branch region. For intermolecular separations of the order of the nearest neighbour distance in solid argon, the repulsive contribution should be still smaller. In order to make an estimate of the 0, dipole moment induced by the solid rare gas environment we will make the assumption that the contribution resulting from the repulsive forces can be neglected. We will assume that OZ molecules occupy a single substitutional site and that they are oriented along the [ 1001 axis of the fee crystal. In such a geometry, four among the twelve nearest neighbours are located at each end of the molecule and for these atoms 0 = 45”. The induced dipole moment resulting from the interaction between O2 and a single end neighbour atom is

Using for the rare gas polarizabilities and nearestneighbour distances the values crAr= 1.64 A3, CY~= 2.48 A’ [ 5 I], R,, = 3.76 A, R,, = 4.00 A and for the 0, quadrupole moment Q1 =3.94X 1O-‘8 esu cm, we get

p,(O*-Ar) =2.42X lo-‘* esu and p,(02-Kr) = 2.86 X lo-” esu. For a static solid the contributions of individual atoms cancel each other and the induced dipole moment is zero. The situation is different for a vibrating solid provided that the displacement of the guest molecule is different from that of the surrounding atoms. Since the O2 molecule is lighter than the Ar or Kr atoms of the host lattice, the localized O2 oscillation is expected to have an amplitude larger than that of the neighbouring rare gas atoms. In the case of matrix isolated CO a localized mode has been found to appear with a frequency of 80 cm - ’ in solid argon and 70 cm- ’ in solid krypton [ 521. Assuming that for matrix isolated O2 a localized mode occurs with a frequency similar to that of CO and neglecting the motion of rare gas atoms, the mean square value of the O2 displacement associated with the zero point motion at T= 0 K, (AX*) = 3h.l 2Mw is 1.97 X lo-‘* cm* in solid argon and 2.25 X 10-i’ cm* in solid krypton. For a localized motion taking place along the [ 1001 direction the mean square change in the intermolecular distance is (AR*) = ( AX2 cos*0) = f (AX*). The corresponding ratio of the root mean square change in R to the equilibrium value R,,s, is (AR*)‘/‘/ R,,, = 2.64 X lo-* in solid Ar and 2.65 X lop2 in krypton. Therms value of the O2 dipole induced by the eight effective neighbours is then given by

(A,u2)“==16~5 PI(K,,~

( AR2)‘12 R

‘_&.

(10)

and the resulting values are 1.45 X 10 _ ‘* esu in argon and 1.7 1 X lO_ I2 esu in krypton. The radiative lifetime associated with the induced dipole moment is obtained using the first term in Eq. (5). We find T,,~==1630 s for 1602 in Ar, 1160 s for 1602 in Kr and 2210 s for “O2 in Ar. The excellent agreement with the value deduced from absorption measurements should be considered as fortuitous. The important conclusion is that the radiative transition is controlled by the dipole moment induced in the neighbouring rare gas atoms by the O2 quadrupole. 4.1.2. Radiationless relaxation This subsection is devoted to radiationless vibrational relaxation. Because of the low rotational energy of 02, the direct relaxation by multiphonon emission is necessarily the dominating process. In addition only

194

A. Salloum, H. Dubost / Chemical Physics I89 (1994) 179-204

relaxation in AU = 1 steps is possible due to the strong dependence of the non radiative rate upon the number of emitted phonons. From the comparison between the calculated and experimental decay rates it should be possible to determine the nature of the dominant relaxation process for each step of the O2 vibrational ladder. The theory of vibrational multiphonon relaxation of matrix isolated molecules has been worked out by several groups [53-561. According to Nitzan et al. [54] the rate of non-radiative relaxation of the u = 1 level is given by k l-O=

k,-O(O)F(T)

7

where k, +o(O) corresponds T=O K:

k, -+0(O)= and F(T)

(lla)

to the relaxation

fJ$ ,(1,x,0),*$ h2

is the temperature

F(T) = (1 +r$Ne2S”.

rate at

tllb)

coefficient: (llc)

Here vi+, is the phonon frequency, (1 ]x IO) = (A/ 2mw ) I” is the matrix element of the internuclear coordinate, S the average vibration phonon coupling strength, N= v,,/Y,, the number of phonons emitted in the non-radiative process and ?i = [ exp( h v,,/kT) - I] -’ is the phonon occupation number. The coupling parameter C = Z( dVo/&x),_o is the rate of change of the isotropic interaction potential V. between the molecule and a rare gas atom with respect to the molecular internuclear distance times Z, the number of effective neighbours. As in the foregoing discussion the O2 molecular axis is assumed to point along the [ 1001 direction and Z = 8. The O,-argon interaction has been studied by several authors [ 57-591. Pirani and Vecchiocattivi [ 591 have calculated an (O,-Ar) potential energy surface from a multiproperty analysis. The isotropic part of the interaction is described by an exponential-spline-Morsespline-van der Waals (ESMSV) potential whose analytical form valid for 3.20 A < R < 4.09 A is V,,(R)=E(e~*“‘“-“-2e-P’“~l’),

(12a)

where E= 1.84X lOI erg, p=6.45 andx= R/R, with R,,,=3.72 A. In order to calculate (~3V,,ldx),,, we make the assumption that a change in the internuclear coordinate axis is equivalent to a displacement i & of the molecule along the internuclear axis and results in

a change dR = f dx cos 8 in the intermolecular Then

distance.

t

12b)

At the distance R=R,,=3.76 A, (dVo/dx),=,,= - 1.96X 10d6 erg/cm and ] C] = 1.568 X lo-’ erg/ cm. The resulting 1 + 0 relaxation rate is t

134

where crphis the phonon wavenumber in cm- ‘. Following Nitzan et al. [54] the relaxation rate of vibrational levels u > 1 can be estimated by taking into account the effect of molecular anharmonicity upon the vibrational energy while keeping the harmonic oscillator approximation for the vibrational matrix elements, i.e. J(u~x~u-1)~2=o~(1~x~O)~2. Assuming for matrix isolated O2 an average vibration-phonon coupling strength S = 1, the rate of the u + v - 1 process involving the emission of N localized phonons with a wavenumber a,,, = 75 & 5 cm- ’ is given as ku+,>-,(O)

=

1 15 x 10” ” .

N!

.

(13b)

The radiationless relaxation rates calculated with the above formula are compared to the experimental values for the vibrational levels from u = 4 to 19 of 1602 in solid argon in Table 3. The values measured for levels u = 4 to 6 are much larger than the calculated non-radiative rates. In contrast they are close to the inverse radiative lifetimes which can be deduced from the k, +. value of Section 4.1.1 using the harmonic approximation (k,, + I,~, = uk, _o). The conclusion that vibrational relaxation of the lower levels of O2 is purely radiative is further supported by the fact that the experimental rates are similar for the three systems which we have studied. The reverse is true for the upper levels U”= 9 to 19 of 1602 in Ar host. The experimental values are in quite good agreement with the calculated non-radiative rates, whereas they are significantly larger than those expected for the radiative process. In addition both the strong matrix effect observed when krypton is substituted with argon and the weak isotopic effect are accounted for by the theories of multiphonon relaxation. We conclude that while in solid argon the vibra-

A. Sulloum, H. Dubost / Chemical Physics 189 (1994) 179-204

tional relaxation of the upper levels of O2 is non-radiative and controlled by high frequency localized phonons, in solid krypton the radiative channel is dominant for all the observed levels. If we accept the idea that the induced dipole moment and the non radiative relaxation in O2 are controlled by high frequency localized phonon modes, both radiative and radiationless processes are expected to show a weak temperature dependence. The foregoing analysis rests on the implicit assumption that the X3Cg levels do not interfere with the vibronic levels of excited states. In fact O2 (X, u”) is the same region of energy as 0, (a, u’) and 0, (b, u’). While the X-levels with ~1"< 5 lie below the singlet states, a more complex situation prevails for the upper levels due to the overlap of the X and a or b vibrational manifolds. In addition to direct vibrational relaxation, the X-levels may undergo a radiationless transition to the next lower vibronic level of either of the singlet states. Intersystem crossing to the a state is energetically possible from levels U”> 6. This process involves energy gaps which are considerably larger in 1602 (AE= 1000 cm-‘) than in “02 (AE=SOO cm-‘). Table 3 Comparison of the experimental decay rates k:‘“Y,_ , (in s - ‘) of ‘“02 ( r = 6- I9 ) with the values k”,’ / _, _I predicted by the theory of vibrational multiphonon relaxation (Eq. (13b)) under the assumption that a single local phonon mode with an energy of 75 cm-’ is participating to the radiationless process. N is the number of local phonons necessary to dissipate the energy cr,,_,._ , of a single quantum. The vibrational energies of “Oz (X ‘C; ) have been calculated using the molecular constants given in Ref. 131 I. 1!

o;+,-I (cm-‘)

N

k=r o-11 (s-1)

I 6 8 9 10 II 12 13 14 1.5 16 17 1x 19 22

I556 1436 1391 I369 I348 1327 1307 1286 1267 1247 1228 1210 1192 1174 1124

21 19 19 I8 1X 18 1X 17 17 17 17 17 16 16 1.5

6.7X <3.6X 1.7x 4.8X 8.3X 7.7x 2.0x 2.9x 3.6~ 8.3 x 1.4 1.7 2.5 -

I

k”.’ /-
10-r IO-’ lo-z lo-’ IO_’ IO_’ lo-’ 10-l IO-’ IO- ’

2.2 x lo-’ 5.8X 1o-4 7.7 x lo-” 1.6X IO-’ 1.8X lo-’ 2.0x IO_? 2.2x lo-2 4.2X 10-l 4,5x10-’ 4.8X 10-i 5.1 x10-r 5.4x IO_’ 9.9 10.4 2x102

19s

The rate of phonon assisted intramolecular transfer is expected to be steeply dependent on the energy gap [ 201. Therefore the a +- X crossing should be strongly favoured in the heavier isotope. Radiationless crossing to the b state is only possible from X-state levels u” > 9 in 1602 and U”> 10 in “OZ. While this process is almost perfectly resonant in IhO (AE= 20-40 cm- ’ for u” = 9), a much larger energy gap is involved in ‘“0, ( AE = 600 cm- ’ for u” = 10). The b + X rate should be larger in i602 than “0, by orders of magnitude. Actually neither of the expected strong isotopic effects is observed. The experimental decay rates of levels u” = 4 to 15 are nearly identical for both isotopes. Moreover the vibrational dependence of the rates is smooth and shows no abrupt increase which could be related to the overlap of the vibrational manifolds. We conclude that in matrix isolated O2 interstate cascading does not significantly contribute to the relaxation of the ground state vibrational manifold. How the multiphonon relaxation of ground state O2 does compare with that of similar nonhydride diatomics such as CO, NO or NZ? It is reasonable to assume that the vibration phonon coupling is not very different from one molecule to another. From the extrapolation of the present data, the radiationless decay of the u = 23 level of 160, in Ar involving the dissipation of a vibrational energy of 1100 cm - ’ occurs at a rate of 5 X 10’ s _ ’ . The single quantum transitions 42 -+ 41 in “C’80 and 27 + 26 in i4N’h0 are isoenergetic with 23 + 22 in 1602. The upper levels of these transitions are precisely the topmost levels which have been found to be populated by anharmonic V-V pumping [ 14,171. Therefore the vibrational dependence of the 0, relaxation rate gives strong support to the idea that vibrational relaxation of 13C”0 and 14NL60 is controlled by spontaneous IR emission up to II = 42 and 27 respectively, while further up pumping is prevented by the onset of multiphonon relaxation. Other data are concerned with the vibrational relaxation of vibronic levels. It is generally accepted that the rates in excited electronic states can be faster than those in the ground state by several orders of magnitude. The present results are consistent with the rate of IO6 s-’ given by Goodman and Brus [60] for the 14 0 relaxation of NO (a 4H) in Ar involving an energy of 990 cm-’ and with the 14 s-’ value recently reported by Kuszner and Schwentner [ 6 1] for the dissipation of 1 + 0 quantum energy ( 1430 cm-‘)

196

A. Sailourn, H. Dubost / Chemical Physics I89 (1994) 179-204

of N2 (A ‘C,’ ) in Kr matrix. They also agree with the minute lifetime of O2 (a ‘Ag) found in solid argon by Becker et al. [ 311. In contrast they are difficult to reconcile with the value of 1.25 X lo4 reported by Rossetti and Brus [ 281 for the 750 cm- ’ 1 + 0 transition of 16-18O2 (c ‘C; ) in Ar host. 4.2. Vibrational energy transfer among matrixisolated CO and 0, While dipole-dipole vibrational energy transfer among matrix isolated molecules is standard [ 1315.170-2 1,66,67], processes induced by higher order terms in the multipole expansion have not been considered before. For instance the transfer processes which are responsible for the accumulation of vibrational energy in the upper levels of matrix isolated CO are induced by dipole-dipole [ 63-661. The free O2 molecule has no transition dipole moment and only a very small induced dipole moment due to interactions with the surrounding matrix atoms. Therefore the long range interaction which can possibly induce the transfer of vibrational excitation from CO to O2 (or from O2 to CO) should involve the transition dipole moment in CO and the transition quadrupole in OZ. Similarly VV transfer between O2 molecules could be of the quadrupole-quadrupole type. In Section 4.2.1 we give expressions for the microscopic probabilities of dipoiedipole, dipole-quadrupole and quadrupole-quadrupole transfer. From the calculated probabilities for the possible transfer processes, we should be able to identify those which are likely to occur in the CO-O, system. Section 4.2.2 is aimed at comparing theory with experiment more quantitatively in order to get a detailed picture of the energy flow among the coupled vibrational reservoirs. For this purpose it is necessary to make use of the appropriate macroscopic transfer rates. 4.2..1. Microscopic V-V transfer probabilities We wish to express the probability of energy transfer between a donor molecule D and an acceptor molecule A trapped in a solid matrix with a refractive index n and occupying sites separated by R,,. The probability for resonant transfer induced by multipolar interactions has been calculated by Fiirster [ 681 and Dexter [ 691 using first order perturbation theory. These classic results have been used to calculate the probability for resonant transfer of vibrational energy in matrix iso-

lated CO [63,66]. When the vibrational transitions involved in the transfer process are not in resonance, energy transfer requires the emission or absorption of one or several lattice phonons whose energy compensates for the energy mismatch between the two transitions and ensures the conservation of energy in the transfer process. The probability for one phonon assisted transfer of electronic excitation has been calculated by Orbach [ 70 ] and Holstein et al. [ 7 1 ] using second order perturbation theory. Miyakawa and Dexter [ 721, Wassam and Fong [ 731 have considered multiphonon-assisted transfer of electronic excitation among ions in crystals while Lin et al. [ 561 and Blumen et al. [ 661 have given a theory more specific for nonresonant vibrational energy transfer between matrix isolated molecules. (i) Dipole-dipole energy transfer. The probability for resonant transfer of vibrational energy can be written in the convenient form

(14a) Here pd= (~‘~~1~1 uid) and pd= (vfal ~1 Uia) are the transition dipole matrix elements of the donor and the acceptor,respectively. The factorF,,, = I&( ~)f,( v) d v describes the overlap between the normalized spectral lineshapes of the donor and the acceptor. It can be expressed as a function of A v& the FWHM of fd ( v) and A pa of f,(v). In the case of exact resonance between Lorentzian lines 2 F,,(

v) =

The probability written as

P,,(dd) =

(14b)

7F(AVd + Av,) ’ of non-resonant

energy transfer can be

877’j.&..L2 -g$ Fph.ass.( AE) .

3h”

da

The various theories of phonon assisted energy transfer [ 56,66,70-731 lead to significantly different expressions of the phonon contribution Fph,ass.(AE) and it is not easy to decide which theory is to be preferred. Experimental studies [ 2 1,641 of vibrational energy transfer in the Ar-CO system have shown that in this cm-‘) =5X lop3 F,,. This case Fph.ass. (AE=50 value will be taken as a reasonable estimate of Fph.ass,

197

A. Salloum, H. Dubost / Chemical Physics 189 (1994) 179-204

for all the non resonant transfer processes among CO and O2 involving the emission of a single phonon. Let us consider for example one phonon assisted processes which are responsible for the accumulation of vibrational excitation in the upper levels of matrix isolated ‘3C’80, such as ‘“c’so(u=21)

+‘“c’*o(u=21)

+ ‘3C’gO( u = 20) + ‘%‘*O( u = 22) + AE =23 cm-’

.

(15)

The transition dipole matrix elements of CO have been calculated by Zondy [ 141 according to the work by Bouanich and Brodbeck [74]. Inserting the values pd=(21 1,u]20)=4.3OX lo-l9 esu cm and pa= (22 1p 121) = 4.36 X lo- ” esu cm, and defining Cda the coefficient of microscopic probability by P,,(dd) = CdaR&, one gets the value C,, = 1.OX 1O-3’ cm6 ss’ and Pda= 10” s-’ at a distance R,,= 100 A. Even at large intermolecular distances, energy transfer between highly vibrationally excited CO molecules is still faster than radiative relaxation. This is the reason why the up-pumping described by Eq. (2) is able to populate very high CO levels. (ii) Dipole-quadrupole energy transfer. The microscopic probability for resonant energy transfer can be found in the classic paper by Dexter [69]. For the specific case of vibrational energy transfer, we use the following expression:

+‘3C’80(u-1)+02(~~=1)+AE.

(17)

The energy defect is AE = 17 cm-’ for 1602 and u = 21 in CO, In this case the relevant matrix elements are (21 I P)20)=4.3OX lo-l9 esu cm for CO and (01 Q] 1) = 1.45 X lo-*’ esu cm* for 02. Insertion of the above parameters into Eqs. ( 16b) and ( 16a) results in the values Cd,=1.8X10-50 cm8 s-’ and P,,(dq) = 10” s-’ at Rda=25.5 A. (iii) Quadrupole-quadrupole energy transfer. The vibrational lifetime of matrix isolated 0, is so long that energy transfer among O2 molecules induced by the quadrupole-quadrupole interaction should be considered. The microscopic probability for resonant transfer of vibrational energy between two axially symmetric molecules separated by the distance R,, is [ 36,69,75] P,,(qq)

56~~ 1 = 5h2

Q:QtF,,,.

n4R’!’ da

3

(18)

where Qd = ( ufd I Q I L’id) and Q, = ( ura I Q I Uia) are the transition quadrupole matrix elements of the donor and the acceptor, respectively. Assuming that the FWHM A(~=0.5 cm-’ of the induced infrared absorption line of O2 centered at 1551.8 cm-’ is homogeneous, the overlap integral involved in the resonant transfer process 02(u=

1) +o,(u=o)

+O,(v=O)

+o,(v=l) (19a)

4,rr2 = h2n4~8

Pd,(dq)

da

&Q:Fr,,

,

(164

where the average has been taken over all the possible molecular orientations and Q, = (L!‘~] Q ] Uia) is the transition quadrupole matrix element of the acceptor. The numerical factor of 4 in Eq. ( 16a) instead of 9a ((Y= 1.266) in Dexter’s expression is appropriate for a quadrupole moment with an axial symmetry [ 36,751. Like in the dipole-dipole case, the coefficient of microscopic probability for phonon-assisted dipole-quadrupole transfer is 4rr cda

=

4

h-n

~:Q&,.ass.< W

.

(16b)

This expression can be used to calculate the probability for one-phonon-assisted transfer from highly vibrationally excited CO to O2 described by the equation

has thevalue (vAY) -’ =4.71 X 10’“s. Theprobability coefficient calculated using Eq. (18) with d = a is Cdd=9.08X 10-6scm10 ss’ and Pdd(qq) = 10’s_’ at R,, = 19.8 A. Similarly, the fusion of two u = 1 vibrational excitations of 0, described by the reaction

+02(u=O)

+O,(u=2)

+ AE=24

cm-’ (19b)

has a probability Pda( qq) = lo3 s- ’ at R,,= 12.5 A. Here we have assumed that I(21 Q] 1) I 2=

2l(llQlO)l’. As expected the range of energy transfer decreases as the interaction responsible for the various processes is of higher order. However important conclusions can be drawn from the values of the microscopic probabil-

1%

A. Sullaurn,

H. Dubost/Chernical

ities. The CO-O2 dipole-quadrupole near resonant transfer can compete favorably with the CO vibrational rehrxation at relatively large distances. In the same way both resonant and non resonant quadrupole-quadrupole transfer among O2 molecules are faster than the vibrational relaxation of low u levels at intermolecular distances exceeding 30 A,. All these processes are expected to occur at the concentrations used in the present experiments.

4.2.2. Channels of vibrational population transfer Before going further in the analysis of vibrational energy transfer in the CO-Q system it is necessary to calculate the transfer rate from an ensemble of excited donors to an ensemble of randomly distributed acceptors. This macroscopic rate depends crucially upon the mobility of the donor excitation. In the case of a weak excitation of the donors, the u = 1 excitation migrates among the donor molecules in the ground state. Vibrational excitation u= 2 can migrate either among the molecules in the u = 1 level by resonant exchange of a single quantum h v, j 1 or among the ground state molecules by exchange of two vibrational quanta. In both cases the mobility of u = 2 is expected to be lower than that of z?= 1, due to fact that the u = 1 concentration is small and because the transition dipole moment associated with the 0+2 overtone transition is weak. Therefore the higher the vibrational excitation the stronger it is localized. (i) Vibration a 1 energyjow from CO to 02. The CO fluorescence quenching experiments described in Section 3.1 show that CO + O2 energy transfer occurs preferentially from high vibrational levels. In this case the donor excitation is strongly localized. Under the assumption of a random distribution of the molecules in the matrix, there is a variety of acceptor environments and the transfer probability should be averaged over all the possible acceptor configurations. Provided that the fraction of excited donors is small compared to the population of both unexcited donors and acceptors and that the back transfer from excited acceptors to donors is negligible, the equation governing the excited donor population, according to the original work of Fijrster [ 681 extended to higher order interactions by Inokuti and Hirayama [ 761, is written as

Physics 189 (1994) 179-204

- t

N$=N$(O)exp

XN,(

C&p

[

)

1

l-

- $r (

5 1

(20)

where rd is the intrinsic lifetime of the donor, Tis the gamma function, N, is the acceptor concentration in cme3 and C,, the coefficient of microscopic probability. The integer s = 6 for dipoledipole, 8 for dipolequadrupole, 10 for quadrupolequadrupole. Although the direct transfer cannot be described by a single macroscopic rate, it is still possible to define an average rate as the inverse of the time at which the population of initially excited donors would have decreased by e - 1..

(21) Let us consider for example the dipolequadrupole (u=21) to 1602 (r;=O) energy transfer from V80 of Eq. ( 17). The average rate, calculated using Eq. with s=8, T(5/8) =1.436, and Cda= (21) 9.7 X 10p50 cm* s-’ is Kda=2.1 X lo3 s-’ at O-05%, 8.6X lo4 s-l at 0.2% and 1.2X lo8 s-’ at 3% O2 in sohd Ar. Actually the processes described by Eq. ( 17) are in competition with both radiative relaxation and further up pumping in CO. Let us consider the case of ‘3C’s0 ( u = 2 1) in presence of 1602. The average rate constant for the V-V pumping process of Eq. (15) can be also calculated using Eq. (21) with s = 6, r( l/2) = & and Cda= lo-” cm6 s- ’ . However the acceptor concentration, i.e. the number density of CO molecules in the u = 21 level, is not accurately known. From the vibrational population distribution shown in Fig. 8, the fraction of o = 21 molecules represents 1.3% of the vibrationally excited CO. Assuming that 30% of the total number of molecules is excited, then N21 = 4.3 X lOI cmm3 at 0.4% 13C’“0 in Ar and K$Z$ = 10’ s - I. We conclude that the branching ratio is in favor of the CO-+02 transfer for a large range of O2 concentrations. Process ( 17) is near resonant at u = 21 for 1602 and at u = 25 for rxOz as shown in Table 4. For higher u levels in CO single quantum V-V transfer to O2 becomes endothermic and therefore very slow. For lower levels process ( 17) is exothermic with AE

A. Sulloum.H. ljubost / Chemical Physics 189 (1994) 179-204 Table 4 of Comparison of the a,,, ,,_ 1 transition frequencies (in cm-‘) ‘k2”O with those of “OZ and r802 in Ar host showing the energy matching between the high vibrational levels of the CO ladder and the low u of O1

I!

u,,.+,.(cm-‘)

I1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

1800 1777 1754 1730 1707 1684 1661 1638 1615 1592 1569 1547 1524 1502 1479 1457 1435 1413

I

I)

a, -,a-,

11

1 2 3 4 5 6 7 8

1556 1531 1506 1482 1459 1436 1414 1391

q>+,,-I (cm-‘)

(cm-‘)

1 2 3 4

1464 1443 1423 1402

increasing as u is decreased in CO. The microscopic transfer probability is reduced for each additional phonon necessary to match AE. For instance in the case of CO, the probability for two phonon assisted V-V transfer is 4 times smaller than that for a one-phonon process [ 641. In addition lower levels are connected by smaller dipole matrix elements than higher levels. For these reasons, vibrational energy transfer to O2 occurs selectively from the upper levels of the CO manifold, leaving the lifetime of the lower levels almost unaltered as shown in Figs. 2 and 5. While at low 0, concentrations an almost perfect resonance is necessary for process (17) to occur, the value of &, (CO +02) is still of the order of 104-105 ss’ at L;= 10, i.e. it is comparable to Z& (CO-j CO). Therefore the CO fluorescence quenching is strongly dependent upon the oxygen concentration and to a lesser extent upon the isotopic substitution in 02, in agreement with Figs. 3 and 4. Up pumping in O2 occurs through a sequential process described by the reaction

‘C ‘*O( v=21)

+‘602(u)

~‘~C’80(~=20)+‘h02(~+l)+AE.

(22)

199

The first steps of the upward cascade are illustrated in Fig. 12. The average transfer rate is given by Eq. (2 1) where N, is now the number of excited molecules O*(u). Assuming that 10% of the total number is excited to the u = 1 level, we get &,?~$$o, = 185 s _ ’ at 0.2% Oz. What are the processes limiting the 0, vibrational excitation? On one hand, the process of Eq. (22) involving lower acceptor concentrations and higher energy defects slows down considerably as v is increased in Oz. On the other hand the rate of multiphonon relaxation given by Eq. (13) is expected to increase in the upper part of the vibrational ladder. Like in the other systems for which anharmonic V-V pumping has been observed, the topmost excitation is determined by the balance of the slowing down up-pumping and of the speeding up relaxation cascades. In the case of O2 other quenching mechanisms alter the O2 vibrational populations. The first one is related to the presence of low energy electronic states in Oz. A substantial fraction of the 02(u) population is converted into O,(a) or 02( b) by further energy transfer from CO( 0). These processes are particularly efficient in “02. They

1

21 20

l5=/

IO-

b-q

-6

5-

3 o13~180

k

0

1

1602

Fig. 12. Schematic energy level diagram showing the first steps of the up-pumping process in 1602. Near resonant single quantum transfer from ‘3C’80 (~=21) to “Oz (v=O, I, 2, 3, . ..) occurs through dipolequadrupole interaction.

200

A. Sallourn. H. Dubosl/

Chemical Physics 189 (I 994) 179-204

-9

13C160

1602

Fig. 13.Schematic energy level diagram illustrating the quenching mechanism of 1602 (II= 9) by “C160 (II= 0). This multiquantum transfer process, in which three vibrational quanta of O2 are exchanged against two quanta of CO, is mediated by the CO-O2 dipole quadrupole interaction.

are described in details elsewhere [ 36,771. The second one resulting from the interaction between O,(U) and vibrationally cold CO is the subject of the next subsection. (ii) Back transfer from 0, to CO. The dependence of the O,( 5) lifetimes upon the CO concentration, particularly marked for l6O2 (c’ = 9) in Ar, shows that back lransfer from CO to O2 is occurring. Single quantum exchange from O2 to CO is possible only provided that the quantum energy is smaller in CO than in OZ. This could happen in the presence of vibrationally excited CO with L’ > 22. However the concentration of 13C’s0 t I! > 22) acceptors is much smaller than that of 02( u =O). The probability of single quantum back transfer to lower CO levels is much smaller than the probability of process ( 17). The one-quantum transfer from O*(U) to vibrationally cold CO is unimportant because of the large non-resonance between the Au = 1 transition in O2 ( < 1550 cm-‘) and the CO fundamental ( > 2040 cm- ‘). While single quantum transfer between O?( U) and CO is highly endothermic, the multiquantum process ‘h0*(U) +co(o=o) +‘hOZ(u-3)

two quanta of CO and is mediated by dipolequadrupole interaction. On the other hand the donor excitation is strongly localized. Therefore the population decay of 02(u) is described by Eq. (20). The microscopic probability coefficient is given by Eq. ( 16b) in which the role of the donor and of the acceptor is reversed. A fit of the theoretical expression to the experimental decay curve of the v = 9 level is shown in Fig. 14. The adjusted parameters are the intrinsic donor lifetime TV, the initial fluorescence intensity IO and the transition quadrupole moment in the donor. The fitted value T-*= 63 s coincides with the time constant of the exponential decay measured at a lower CO concentration (Fig. 9 and Table 2). The fitted value of the quadrupole moment associated with the ~1= 9 + u = 6 transition in ‘3C’60 is Qd = 4.42 X 10 ‘9 esu cm’. We believe that this is a reasonable value. Indeed the corresponding ratio (lIQ10)/(91Q16)=32.8 while in CO (11 ~lO)/(9l~l6)=27.5. The energy defect involved in process (23a) increases rapidly as u is decreased. Therefore the 0, + CO back transfer is a minor process in comparison to the CO + O2 population flow. Nevertheless the satisfactory agreement between theory and experiment provides a valuable check for the validity of the model. The process of Eq. (23a), endothermic for c’> 10 is unable to account for the CO concentration dependent quenching of the upper levels of OZ. The most probable

Time (s)

+CO(u=2)

+ AE

(23a)

isnearlyresonantatr~=10for’~C’*O(AE=54cm~’) andatL~=9for”C’hO(AE=12cm-‘).Letusrecall here that the isotopically enriched CO contains 60% of “C’“O. As illustrated by Fig. 13, this process involves the exchange of three vibrational quanta of 0, against

Fig. 14. Time decay for the “0, (I) = 9) population monitored through A’ + X LIF. The Ar matrix is doped with 1% CO (0.6% “C’“0) and 0.2% O2 at T=7 K. The solid curve is theoretical and based on Eqs. ( 16b) and (20) with pz, = 6.37 X 10ezl esu cm, s = 8 and a three-parameters fit (lo = 240, Qd = 4.42 X 1O-‘9 esu cm’ and b = 63 s). Intrinsic vibrational relaxation and l6O2 + “C’“0 dipolequadrupole energy transfer process illustrated in Fig. 13 are taken into account

A. Salloum. H. Dubost / Chemical Physics I89 (1994) 179-204

explanation for the deactivation of 0, ( u > 10) by CO is that the two-quantum process described by the reaction ‘ho*(U) +co(u=o) +i602(u-2)

1) + AE

27

r(4/3)

~0.5 N;‘0’3Cd;1

(25)

(23b)

3740 r(5/3) -

Kdn =AC;;‘°C:;‘oN:‘“N,,

In this case the

where the constant +CO(v=

resonant at u = 27 for ‘3C160 is still active in quenching O2 levels around u = 15. The two-quantum exchange of Eq. (23b) involving larger transition matrix elements in both the donor and the acceptor accomodates for energy gaps considerably larger than those which can be accepted in the three-quantum process of Eq. (23a). (iii) Migration and fusion of O2 (u = 1) excitations. The dependence of the u = 4 decay rate upon the O1 concentration suggests that energy transfer among oxygen molecules occurs to some extent. As a matter of fact the complete isolation of O2 molecules, such that communication between them via quadrupole-quadrupole interaction is slower than relaxation, requires large intermolecular separations. As shown in Section 4.2.1, this is particularly true for the resonant process of Eq. (19a) which is responsible for the hopping of excitation from one O2 molecule to another. The hopping mechanism of energy transfer in randomly distributed systems has been investigated by several authors [78-801. The average hopping time of the u = 1 excitation, calculated according to the model of Blumen et al. 1791 modified for quadrupole-quadrupole transfer, is written as 7hop =

quadrupole-quadrupole interaction. transfer rate can be written as

201

.

(24)

At 0.2% of O2 in solid Ar, r,,,,,,= IO-’ s. The hopping time of u = 1 is short compared to the vibrational lifetime. Consequently the O2 vibrational excitation is substantially delocalized. The fusion of two 0, ( LJ= 1) excitations is described by Eq. ( 19b). The range of this non resonant process is considerably extended by the hopping mechanism of Eq. ( 19a). The macroscopic rate of migration assisted transfer from a donor to an acceptor depends on the microscopic probability coefficients C,, of donordonor and C,, of donor-acceptor transfer as well as on the donor and acceptor concentrations [ 79,801. Processes of Eqs. (19a) and (19b) are both mediated by

A= (3~~~~:~:~“~~~(7,10))1013=8.5 and Nd is the concentration of unexcited donors. The fusion process of Eq. (19b) is dependent upon the concentration of excited molecules. At 0.2% O2 in Ar and assuming that 10% of the molecules is excited, Eq. (25) yields K\ Y,i = 11 s - ‘. Although the fusion process is fast compared to vibrational relaxation in OZr it is slow relatively to the up-pumping process of Eq. (22). At 0.02% KfZg=5XlO-’ ss’ while +2(02) K:, + ZO(c!O)= 2 s - ’ . Therefore in the presence of vibrationally hot CO the fusion process of Eq. (19b) is expected to bring a minor contribution to the excitation of the upper levels of 0,. In contrast, at 0, concentrations of 0.2% or more, the fusion of u = 1 excitations results in a significant lengthening of the u > 1 apparent lifetimes during the relaxation cascade which occurs at the cutoff of the pump laser where the CO energy supply is suppressed. The important conclusion of this section is that the Fiirster-Dexter model with the gas phase value of the O2 transition quadrupole moment provides a quantitative understanding of the V-V processes which occur in the CO-O,-Rg systems. Single-quantum transfer processes mediated by dipole-quadrupole interaction are found to have rates large enough to compete with up pumping and radiative relaxation in CO for a broad range of guest concentrations. The rates of multiquanturn quadrupoledipole and one-quantum quadrupolequadrupole transfer are much smaller. However in highly concentrated matrices they are still larger than the rate of O2 vibrational relaxation.

5. Summary and conclusion We have demonstrated that in IR-pumped CO-O,Rg systems efficient V-V transfer occurs from the high u levels of 13C’a0 to the O2 vibrational manifold. The observed i602(u) distribution is very broad and extends from u = 4 to u = 20. The vibrational relaxation of O2 has been investigated in solid argon and krypton.

702

A. Sallourn, H. Dubost / Chemical Physics 189 (1994) 179-204

The lifetimes of the lowest detected levels are radiative in both matrices. The experimental values agree quite well with those which can be deduced from IR absorption measurements or from the quadrupole-induced dipole in the harmonic approximation. While in krypton the lifetimes of the upper levels are also radiative, in argon they are controlled by non radiative relaxation. Phonon assisted intersystem crossing from O?(G) to nearby vibronic levels of the a ‘Ag and b ‘xi states is negligible. Therefore the direct vibrational relaxation mechanism which is usually masked in asymmetric nonhydride species by the much faster radiative decay can be readily observed in the upper levels of 0,. The order of magnitude, the vibrational dependence and the matrix effect are in satisfactory agreement with the theories of radiationless multiphonon relaxation. The CO and O2 vibrational manifolds constitute two energy reservoirs which are coupled through long range multipolar interactions. The CO reservoir, coupled to the radiation field and almost uncoupled to the phonon bath, has a characteristic lifetime in the ms range. Elnergy can be deposited into the CO vibration by optical excitation. In contrast the O2 reservoir is almost uncoupled to the radiation field and only weakly coupled to the thermal bath. Consequently it is characteriLed by an extremely long lifetime which amounts to several hundred seconds, i.e. 4 to 5 orders of magnitude longer than that of CO. Although it cannot be excited by IR radiation, the O2 vibration has the capability of storing enormous amounts of energy. Excitation transfer mediated by dipolequadrupole interaction provides a convenient access to the forbidden O2 vibrational manifold through single quantum V-V exchange. Because the O? vibrational quanta are smaller than those of the CO ladder below u = 21, the energy has the tendency to flow from CO to Oz. The reverse flow resulting from quadrupoledipole multiquantum transfer is of minor importance. However at high concentrations these processes contribute to the deactivation of O2 (u) levels, in particular of u = 9. The up-pumping processes resulting from the fusion of 0, vibrational excitations through quadrupolequadrupole interaction give rise to a significant lifetime lengthening of the lower levels at high 0, concentrations. All these processes are reasonably well described by the Forster-Dexter model using the transition quadrupole moment of O2 (u = 1 + u = 0) determined in the gas phase. In this respect van der Waals crystals undoubt-

edly present an advantage over other types of solid for which this information is generally not available. The O2 reservoir is leaking from the upper levels toward the thermal bath. Actually there are other channels by which the O2 vibrational energy is dissipated. In presence of vibrationally excited CO, a substantial fraction of the O2 vibrational energy is removed by vibrational to electronic energy transfer and is ultimately transformed into near IR or UV-visible photons. These processes are responsible for the strong dependence of the 0, vibrational populations upon isotopic substitution, All these phenomena will be described in a subsequent paper. While there is no doubt that the lower O2 levels are strongly populated, they could not be probed with the present apparatus. Experiments at shorter probe wavelengths are underway in order to measure the u = 1 lifetime which is expected to be - 1000 s. Probing of 0, (u = 0) is also of great interest in so far as it would allow for a quantitative estimate of the vibrational energy stored in the ground state manifold. Finally, besides the potential applications for energy storage, the high vibrational excitation of 0, makes accessible the low vibronic levels of the B ‘2; state which cannot be directly excited from the ground state. This would be very useful for studying the influence of the matrix environment upon the predissociation mechanisms of O,(B). Acknowledgement

This work was supported by EEC under SCIENCE program, grant number SC 1-0220-C (AM). We would like to thank Professor V.A. Apkarian for his interest in this work and for a critical reading of the manuscript. We are greatly indebted to Mrs. R. Charneau and Dr. R. Kolos for their participation in the early stages of the experiments, and to Mr. J. Lefevre for his skilful technical assistance. The help of Dr. N. Legay-Sommaire in recording FTIR absorption spectra and of Drs. C. Cossart and H. Lefebvre-Brion in calculating 0, FC factors is gratefully acknowledged. References [ 1 I X. Yang, J.M. Price, J.A. Mack, CC. Morgan, C.A. Rogaski, D. McGuire, E.H. Kim and A.M. Wodtke, J. Phys. Chem. 97 (1993) 3944.

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