J. Phys. Chem. 1995,99, 15642-15654
15642
Molecular Beam Study of the Collision-Induced Intramolecular Energy Transfer CO(a311 a'3Cf, d3A)
-
Ch. Ottinger* and A. F. Vilesovt Max-Planck-Institut f i r Stromungsforschung, Bunsenstrasse IO, 0-37073, Gottingen, Germany
D. D. Xu Dalian Institute of Chemical Physics, Chinese Academy of Sciences, P. 0. Box 11 0, Dalian, People's Republic of China Received: March 21, 1995; In Final Form: August 14, 1995@
The collision-induced intramolecular energy transfer from CO(a311) to CO(a'3Z+) and CO(d3A) was studied under single-collision conditions in a beadgas-cell arrangement. CO molecules were excited into the longlived a 3 n state in a dc discharge buming in the expansion region of the CO(X) supersonic beam. The relative vibrational distribution of CO(a3n) was obtained from the spontaneous beam afterglow (AG) emission spectrum of the CO(a X) Cameron bands. Additional emission of the CO(a'3Z+) and CO(d3A) states was observed to result from collisions with a target gas (He, Ne, Ar,Kr, and Xe) in a cell. This collision-induced afterglow (CIAG) is due to near-resonant intramolecular energy transfer CO(a a', d). From the CIAG spectra absolute state-to-state cross sections for populating various vibrational states in both CO(a') and CO(d) were deduced. They were obtained by normalizing the emission intensities of the product CO(a') and CO(d) levels to those of the CO(a) reactant levels. Spectral overlaps of the d3A and a'3Z+ emissions were deconvoluted by means of computer simulation. The role of the energy gap between the reactant and the product states in the intramolecular transfer processes is discussed. The CO(d,v=2) level is populated to a large extent via perturbations with the CO(a,v,=9) level, according to the gateway mechanism. As a result, the emission from this particular level exhibits a very irregular band contour, with intense superimposed spikes marking the perturbed rotational states.
-
-
I. Introduction Recently there has been great interest in collision-induced intramolecular coupling between different electronic states, especially in the cases of CN,'-4 NO,5and N2.6-8 In the former, rotationally resolved state-to-state transfer cross sections from CN(A) to CN(X) were measured with the optical-optical double resonance (OODR) technique. It was found that, despite significantly different energy mismatch in various vibrational pairs, the cross sections are of comparable magnit~de.~ These detailed results have stimulated much conesponding theoretical r e s e a r ~ h . ~In , ' ~this laboratory, collisional energy transfer CN(A X) has recently been studied with various collision partners, and their relative efficiencies were determined.' In the case of N2,637the energy transfer among the three low-lying triplet states Nz(A, B, W) has been investigated at the vibrational-state-to-state level. By means of time-of-flight6and laser-labeling techniques,' absolute cross sections were obtained. Here the energy defect in the transfer processes was found to be of paramount importance. Conclusions could be drawn about the shape of the interaction potentials N2(A, B, W) M. Very recently, by using isotopic labeling we could distinguish between the inter- and intramolecular processes when N2 itself was used as collision partner with Nz(A, W).8 All of these results are very helpful in understanding to what degree the relevant parameters such as energy gap, Franck-Condon factors, and perturbations affect the state coupling. Compared to these well advanced investigations of Nz, there are for the isoelectronic species CO very few corresponding
-
+
On leave from the Institute of Physics, St Petersburg State University. St Petersburg, 198904, Russia Abstract published in Advance ACS Abstrucrs, October 1, 1995 A
@
0022-365419512099-15642$09.OOIO
studies of collisional coupling between the low-lying triplet states (a311, a ' 3 F , d3A, or others). One somewhat indirect example is the measurement of fast vibrational relaxation of CO(d,v=4), ascribed to intermediate transfer to CO(e3Z-).I2On the other hand, from purely spectroscopic work, very detailed information has been obtained on the perturbation of the lowlying triplet statesl3-I6 and between the triplet states and the singlet state A'l-I.'7-20 The deperturbed molecular constants and perturbation parameters were obtained by means of matrix diagonalizati~n.'~-'~ It was concluded that the observed forbidden transitions of the Cameron bands (a311-X'E) and the d3AX'I: bands were due to the interactions between the A'II and the a311 and d3A states, respe~tively.'~,'~ Radiative lifetimes of individual rotational fine structure levels of A'IIZo and of neighboring triplet state^'^^^^ have also yielded the perturbation parameters. Figure 1, adapted from ref,'* shows the potential curves for several CO electronic states. In this work we report on the collision-induced coupling of the CO triplet state a311to the triplet states af3Z+and d3A. This is the first such study under single-collision conditions. It is closely related to the investigation of collisional coupling within the nitrogen triplet manifold, done earlier in this laboratory.6 One could expect that the intramolecular transfer behavior of the isoelectronic systems N2 and CO is similar. However, the ordering of states is considerably different: In N2 the lowest and hence metastable triplet state has 3Z+ symmetry, and the next higher, radiating state is 311. In CO, the reverse is the case. Also, in CO the 3A state can radiate into the lowest (a311) triplet state and is short-lived, while the 3A state in N2 is longlived. Correspondingly, in the earlier studies there were two reactant states, A(3&+) and W(3Au),which were collisionally coupled to the single product state B(317,), N2(A, W B),
-
0 1995 American Chemical Society
Intramolecular Energy Transfer CO(a3n
-
a’3Zf, d3A)
J. Phys. Chem., Vol. 99, No. 42, 1995 15643 75000
d3A
3
a n
a’
3Et
70000
h
7
E
65000
v
h
M 0 I
I
I
1
OB
12
16
20
C
0
60000
Internuctear Distance&)
Figure 1. CO potential curves for some low-lying states as indicated, taken from ref 18. The energy scale is given with respect to the u = 0 level of the X’X+ ground state, which is also shown, with its own energy scale on the right.
-
while, in the present case, i.e. CO(a d, a’), there are two product states and only one reactant state. Moreover the reactant state a 3 n can here be directly detected via its long-lived a X emission. This is a considerable advantage compared to the case of N2, where the strongly metastable A 3 Z + state can only be detected via laser-induced fluorescence, and the W3A, state only indirectly via the W B A cascade. Thus in the present work the reactant a 3 n concentration was monitored directly by the “Wbeam afterglow” Cameron band emission a X. This yielded its vibrational state distribution in the low levels, up to ua = 9. For the higher levels, which were not directly observable, the distribution could be extrapolated with an exponential function. Interaction of the metastable CO(a) molecules in the beam with target rare gas atoms caused intramolecular energy transfer into the radiating CO a’ and d states, and the ensuing collision-induced a‘ a and d a emission spectra were observed (the so-called “collision-induced aftefflow”, abbreviated below as CIAG). When the emission intensities of the a‘ a and d a transitions were compared with that of the a X UV beam afterglow, absolute cross sections were obtained for collisional population of a range of vibrational levels in the a’ and d states and for all five rare gases. Since the a‘ a and d a bands in the visible and near IR on the one hand and the a X bands in the UV on the other hand were detected using two different gratings, the relative sensitivity of the apparatus in these two spectral regions had to be established. Figure 2 shows the vibrational levels of the a, a’, and d triplet states in the relevant energy region. Similar to the case of N2,6 the energy resonance between the reactant and product vibrational levels is expected to be important in the intramolecular transfer processes. The role of spectroscopic perturbations in these processes is discussed in detail. For the perturbed CO(d,u=2) level, it has dramatic consequences for the observed emission band contour.
-
--
-
-
-
-
-
--
55000
--
11. Experiment The experimental arrangement used in this work has been described in detail in refs 6, 7, 11, and 21. It is essentially the same as in refs 6 and 11, as far as the CIAG detection technique is concerned. For the present work, a collimated beam containing CO(a) molecules was generated by expansion of pure CO gas. The metastable CO(a) molecules were produced by means of a dc discharge burning in the beam expansion region.
50000
1 0 -
Figure 2. Vibrational energy level diagram for the CO(a, a’, and d) states, calculated from molecular constants given in ref 24. The energy scale refers to the minimum of the CO(XIZ+)potential energy curve. Energy differences between closest-to-resonant vibrational level pairs are indicated (in cm-I). Negative AE indicates exothermic transfer from the a-state to the a’- or d-state.
The discharge conditions were similar to those used in refs 6, 7, 11, and 21. The stagnation pressure at the 1 mm diameter nozzle orifice was about 60 mbar. The main problem, as in ref 11, was the formation of a solid carbon deposit which clogged the nozzle orifice within about 1 h. The method for removing it has been described in ref 11. The stability of the beam was checked every time after the cleaning operation was performed. This ensured that the signal was constant to better than 10%. Passing the beam through a target gas cell, collision-induced emission from the cell was observed. The cell was placed quite far (53 cm) from the source, since at shorter distances the background due to scattered light from the discharge is a problem. The pressure in the cell was controlled by two needle values and measured by a Baratron model 127 pressure gauge. It was in the range 0.3-10 mTorr. A high-performance liquid-nitrogen-cooled charge-coupled device (CCD) detection system was used for the spectral measurements. Details of this detector have been communicated earlier.22 Light emanating from the cell was conducted to a 0.25 m spectrograph by a high-grade W quartz fiber bundle and then dispersed on the CCD chip, of which 550 x 360 pixels were used. Two different gratings were used, one with 2400 lines/”, blazed at 250 nm, and another with 1200 lines/mm, blazed at 500 nm. The parameters used for recording the spectra are given in the figure captions.
111. Results
-
-
A. Spontaneous and Collision-Induced Emission a‘ a and d a. Figure 3 shows the collision-induced spectra in the range from 490 to 900 nm for the five gases as indicated.
Ottinger et al.
15644 J. Phys. Chem., Vol. 99, No. 42, 1995 4500
I
I
1
-
a’
I
I
a(v,=O) 5
6
7
4
3500
v a t = 12
v.= 7
10
11
9
4
6
i
1
I
5
6
7
8
2
3
v1
4
1500
-
1000
-
500
-
d
w
AG
0 -
-
’
... .
-
..
.......
~
700
800
500
....
800
......
~
900
(nm) Figure 3. Overview spectra of the collision-induced afterglow emission CO(a’ a, d a) taken at a distance of 53 cm from the discharge source, uncorrected for the spectral sensitivity curve, which is also shown in the figure. The 1200 lines/” grating and a 150pm slit were used (resolution of 0.5 nm fwhm). Each spectrum is a composite of 16 separately recorded sections; each has a total exposure time of 6 x 100 s and covers about 25 nm. The collision gases are indicated for each spectrum. The pressures are 9.0, 7.0, 4.8,4.0, and 2.9 mTorr for He, Ne, Ar, Kr, and Xe, respectively. The bottom trace is the beam afterglow (AG) measured with an empty collision cell. The bands in this spectrum can also be assigned to the above two transitions (see the text). Vibrational levels in the a’- and d-states are indicated by u,‘ and ud, respectively, and those in the a-state, by ua. The strong spike in the Kr spectrum (arrow) is a Kr line at 760.2 nm, which is from the 2p6 ’P2 transition. The reaction which produces this line is not yet clear. It must be a very closely resonant reaction, since there are neither other Kr lines in this spectrum nor similar Xe or Ar lines in the respective spectra. Wavelength
-
-
-
The spectra are uncorrected for the spectral sensitivity. The sensitivity curve in this region was obtained by means of a standard tungsten ribbon lamp and is also given in Figure 3. The spectrum shown at the bottom was recorded without any collision gas in the cell. It is due to spontaneous emission from the beam particles and is termed the (visible) beam afterglow (AG) spectrum. The collision-induced spectra were assigned to two electronic transitions, d a and a’ a, according to ref,23 as c o n f i i e d by calculations of band origins using molecular constants from ref 24. Interestingly, the bands in the background AG spectrum can also be assigned to these two emission systems, mainly in the a‘ a (4,0),(5,0), (6,O)and d a (2,O)bands. The lifetimes of the d and a’ states are less than 20 ps,I8 corresponding to a flight distance of about 2 cm at a velocity of 1000 d s . The observed emission from the d and a’ state levels at much greater distances from the source must then be due to some long-lived precursor level, which feeds the levels in question via slow, unobserved (probably IR) radiative transitions. This is similar to the case of the spontaneous beam afterglow in a nitrogen beam which is due to the Nz(W B A) cascade.25 With CO, measurements of the intensity falloff along the beam in the a’ a (4,0),(5,0), and (6,O)bands showed effective lifetimes of 250-160 A possible precursor state might here be the a-state itself in its high vibrational levels. The CO afterglow would then be due to intrasystem cascades “a(high v)” “a’ and d” “a(1ow u)”. CO(a,v,) lifetimes have only been measured for low (or sometimes poorly specified) v, level^,^'-^' which can only radiate into the ground state. The experimental, as well as some theoretical,” results are all in the greater than millisecond range. This is clearly too long to explain the intensity falloff observed in ref 26. However, for the high vibrational levels present in our beam, there are the additional radiative pathways into CO-
-
-
-
-
- -
-
-
-
(a’ and d). These may shorten the CO(a, high v ) lifetimes sufficiently to be consistent with fhe above interpretation of the visible CO afterglow. The Franck-Condon factors for transitions from the a, v, = 10-14 levels into a‘, v = 4-6 and from a, v, = 8 and 9 into d, v = 2 are, in fact, all quite large (>O.l). CO beam afterglow spectra extending as far as 400 nm have been reported on in ref 26. A revised identification of the bands in the 600-400 nm region, as being due to very high vibrational levels in the a’ state ( v I20), has been given in ref 32. In the wavelength region ?, > 700 nm, Figure 3 shows a continuous background underlying the spectrum of the spontaneous afterglow (bottom trace). It is due to residual scattered light of the discharge source. This stray light background has already been subtracted from the CIAG spectra for the five gases. In addition, the CIAG spectra were corrected for the AG contribution (see below). From Figure 3 it can be seen that the emission intensity increases dramatically from the AG background level when a collision gas is admitted to the cell. The relative band intensities are also significantly different from those in the spontaneous AG emission spectrum. The enhanced afterglow intensity is attributed to the collision-induced intramolecular energy transfer from the metastable state CO(a) to the emitting states CO(a’) and CO(d), CO(a,v,)
+ M - CO(a’,u,,) + M - CO(d,v,) + M
(1)
(2)
M is one of the rare gases used in the cell: He, Ne, Ar, Kr, and Xe. The identification of CO(a) as the reactant species responsible for the CIAG emission rests on the following observations. In
Intramolecular Energy Transfer CO(a311
-
a'3X+, d3A)
J. Phys. Chem., Vol. 99, No. 42, I995 15645
the case of the product level CO(d,v=2) the energy transfer occurs definitely from the nearly isoenergetic level CO(a,v,=9). This is clearly demonstrated by the analysis of the perturbations between these two levels; see section N . A . For all other product states, the propensity of near-resonant da', d level pairs (see Figures 11 and 12) strongly supports the assumed mechanism (reactions 1 and 2). The only conceivable alternatives would be collisional population from very high-lying vibrational levels of the CO(XIZ+)ground state or from the CO(DIA)state, since the CO molecule does not possess any other long-lived electronic states in this energy regime. From similar observations in the case of a CN beam," the presence of highly vibrationally excited ground state CO molecules in the beam is certainly a possibility, while nothing is known about any CO(D' A) beam component. However, the collisional energy transfer CN(X2Z+ A 2 n , B2Z+) observed in ref 11 did not involve a spin change. Spin-changing collision-induced intramolecular transitions are much less likely, provided the collision partner itself does not possess any spin. This has been demonstrated very clearly for the case of NO quartet-doublet transitions5 Apart from perturbed levels, these were found to be negligible in collisions with light rare gas atoms, very weak with Xe, but strong with NO(X211) and 02(X3Z,-). By analogy, in the present case we can rule out any CO(X or D a', d) singlet triplet transitions. Figure 3 shows that generally there is some overlap between the d a and a' a emission bands. State selective emission intensities were obtained as follows: (1) d,l a,O with a',7 a,l: These two bands overlap heavily. But the a',7 a,O band is free from overlap, and its intensity can be taken as the band integral. The a',7 a, 1 band intensity was then calculated from the (sensitivity-corrected) intensity of the a',7 a,O band and the Franck-Condon factors for these two bands and was subtracted from the total integral intensity under the d,l a,O transition so as to obtain the true integral intensity of the d,l a,O band. In fact, the a',7 a,l contribution to this band amounts to only about 10%. (2) d,2 a,O with a',8 a,l: The former band was computer-simulated with molecular constants from ref 24. The main attention was paid to obtaining a good fit in the left half of the overlapped bands, since this part belongs purely to d a emission. The intensity of the d,2 a,O band was then taken as the integral of the corresponding simulated band, and the remainder of the total intensity of the overlapped bands was attributed to the a',8 a,l transition. The levels vd = 5 and 6 were treated in the same way as ud = 2. They have overlaps with a',ll and a',12 emissions, respectively. By means of subtraction of the simulated vd = 5 and 6 band contours, the intensities of the va' = 11 and 12 levels were determined at the same time. The rotational temperatures used in the simulation were Trot= 350 K for He and 550 K for Xe, as obtained from the high-resolution spectra; see below. Trot= 550 K was also used for Ne, Ar, and Kr, because the band contour is here essentially the same as with Xe. (3) d,3 a,O with a',9 a,l: Nominally, there is also an overlap between these two bands. However, the high-resolution spectra given in Figure 4b show that the intensity in this region arises totally from the former transition. Also, the a',9 a,O band in Figure 3 is undetectable even in the spectrum for Xe. In the case of the overlap of d,4 a,O with a',10 a,l, the situation is similar to that for the d,3 level (cf. Figure 4a), and we consider that the a',10 emission does not contribute either. Since the Franck-Condon factors for both the a',9 a,l and the a',10 a,l emissions are not much smaller (about half) than those for the d,3 a,O and d,4 a,O bands, respectively,
-
-
- - - -
-
-
+
-
-
-
-
-
-
-
-
-..
-
-
-
-
-
-
-..
600
1
I
d,4
.v)'
1
C
600
4
2
0 0
1400
v
1200
I
I
t
I
- a,O
I
605 I
d.3
-
4
I
,
610
815
620
1
l
I
a,O
1
1000
800
600
400
200
840
I
1
1
I
845
650
655
660
Wavelength
(nm)
-
Figure 4. High-resolution spectra (0.2 nm fwhm) of collision-induced CO(d a) emissions as indicated, with 7.5 mTorr of He and 3.0 mTorr and a 50 y m slit of Xe in the cell. The grating with 1200 lines/" were used. The exposure time for each spectrum was 20 x 200 s. The thin lines are computer-simulated spectra using molecular constants from ref 24. The'simulation is based on equal fine structure level populations and Boltzmann rotational distributions with T,,, = 350 K for He and 550 K for Xe.
we conclude that the populations of the va' = 9 and 10 levels, if any, must be very small. (4) The d,7 a,O band intensity was directly taken as the band integral from Figure 3, disregarding any overlap, e.g. with the a', 13 a, 1 band. Here the uncertainty may be rather large because of the poor signal-to-noise ratio. Also, the emission intensities from all observable levels were directly determined from Figure 3, with the exception of ua' = 11 and 12; see paragraph 2 above. All of the band intensities I , obtained are given in Tables 1 and 2, for the vibrational levels of the a' and d states, respectively. The contribution of the spontaneous afterglow was eliminated by subtracting 40% of the bottom spectrum in Figure 3 from each of the other five spectra. The fraction of 40% allows for the attenuation of the original AG signal, as measured with the empty cell, by elastic scattering at the target gas pressures used. This procedure is explained more fully in ref 6. For some d a bands high-resolution spectra were also taken, namely for emission from the vd = 2-4 levels with Xe as collision gas and the vd = 2 and 3 levels with He as collision gas at s = 53 cm. Figure 4a shows the experimental (thick line) and simulated (thin line) spectra for the d,4 a,O band with Xe in the cell. Figure 4b shows the spectra of d,3 a,O with He and Xe as collision gases together with the simulation (thin lines). The calculated spectrum is in very good agreement
-
-
-
- -
15646 J. Phys. Chem., Vol. 99, No. 42, 1995
Ottinger et al.
TABLE 1: Observed CO(a’,v) Emission Intensities and Cross Sections for Population of the Vibrational Level u by Collisions of CO(a,v,*) with He through Xe
1800
d.2 1600
-{
va 5
4
u,*IAEb 71197 FCF‘ 0.102
6
8
7
81-188 0.071
91-564 0.018
11
12
I/ a(u).
3952 0.12
5836 0.18
He 1100 145 340 0.04 0.005 0.03
I/
7068 0.42
3220 0.18
810 0.06
I/ a($
I/ a(@
w
4
800
190 0.02
387 0.09
150 0.04
330 0.16
e00
M
400 200
10250 6614 0.95 0.60 12287 7390 1.4 0.83
Kr 1740 400 0.23 0.06
2100
450 0.10
0.40
-
-
E
120 470 0.008 0.07
Ar 1230 253 0.13 0.03
15900 10 130 2.6 1.6
-
-
10
~
’
890
700
805
710
705
Wavelength (nm)
,
705 0.16
320 0.12
660 0.52
1070 0.30
140 0.07
450 0.40
980
430 0.28
570 0.70
Xe
:1 a($
1200
u 1000
0
2
Ne
a($
-
1400
a
91523 101137 121413 13/44 0.070 0.058 0.049 0.030
- a.0
0.38
a The observed emission bands from the a’-state levels u terminated in the a-state vibrational level 0 for u = 4-8 and in the level for v = 11 and 12. ua* is the a-state vibrational level which is closest to resonance with the product level u in the a’-state; see Figure 2. AE is the corresponding energy mismatch, in cm-l. Negative AE indicates an exothermic transfer from CO(a,ua*) to CO(a’,u). Franck-Condon factors between reactant level ua* and product level u. Observed emission intensity, in CCD detector counts and integrated over the emission band from the a’-state level u. The pressures used for each collision gas are given in the caption of Figure 3. e In units of A2.
-
Figure 5. High-resolution spectra (0.2 nm fwhm) of the d,2 a,O transition with He and Xe as marked. Some of the superimposed emission lines (“spikes”), arising from the severe perturbation between the d, u = 2 and a, ua = 9 states, are numbered (for the line identification, see Table 3). For comparison, the simulated contour of the hypothetical unperturbed d,2 a,O band is also given (thin line). a,l The right part ( I > 700 nm) of each spectrum is due to the a’$ transition (cf. Figure 3).
-
5000
-
-
Kr
TABLE 2: Observed CO(d,v) Emission Intensities and Cross Sections for Population of the Vibrational Level u by Collisions of CO(a,v.*) with He through Xe ~_____
1
2
3
4
5
I
6
ua*IAEb 81396 9/44 101-299 111-634 111437 12/92 131-245 0.075 0.139 0.177 0.167 0.0052 0.0073 0.043
FCF‘
0
He
I/
0.03
375 0.02
234 0.02
Ne 710 0.04
120
0.005
400 0.03
192 0.02
1480 4450 3415 0.20 0.32 0.23
Ar 1500 0.11
340 0.03
505 0.06
440
270 0.03
560
0.08
430 0.10
930 0.12
690 0.14
510 0.17
a($
3580 2310 0.09 0.05
:I a(u)e
465 0.04
3024 2072 0.14 0.09
I:’ (T(U)~
1030
160 0.003
565 0.03
a(u)e
0.50 0.38
3060 4160 4190 0.37
Kr 1942 0.18
I:’
4160 4620 4640 0.97 0.60 0.57
Xe 2145 0.28
I/
a($
0.08
a All observed emission bands terminated in the a-state vibrational level 0. u,* is the a-state vibrational level which is closest to resonance with the product level u in the d-state; see Figure 2. AE is the corresponding energy mismatch, in cm-I. Negative AE indicates an exothermic transfer from CO(a,u,*) to CO(d,u). Franck-Condon factors between reactant level ua* and product level u. Observed emission intensity, in CCD detector counts and integrated over the emission band from the d-state level v. The pressures used for each collision gas are given in the caption of Figure 3. e In units of A*.
with the experimental one, demonstrating the validity of the simulation. It appears that a lighter collision partner results in
2
4
Pressure
8
8
10
(mtorr)
Figure 6. Pressure dependence of CIAG intensities for d, u = 3 emission with the five rare gases as indicated. The AG contribution has been subtracted. Curves are the fits of eq 3 to the experimental points.
lower rotational temperature in the product, while a heavier partner produces a higher Trot. The same trend was also found in the case of CN(X A),” where Trotwas 2300 K for He and 3500 K for Ar. Figure 5 shows the spectra of the d,2 a,O transition, again with He and Xe as collision gases. In this band, particularly in the case of He, several striking peaks (some of them numbered 1-9) were observed. These features will be discussed in section IV. B. Relative Collisional Transfer Efficiencies of the Rare Gases. The dependence of the intensity of the collision-induced afterglow was measured for two selected product levels, d,3 and a’3. These are especially suitable, because their respective emission bands, (3,O) and (5,0), are not overlapped by any other bands. The intensity at a given pressure was obtained by integration over the emission bands. Figure 6 shows the results for the d,3 level. The lines in this figure are fits of the data points by the function
-
I = aP exp(-BP)
-
(3)
Intramolecular Energy Transfer CO(a311 5000
I
I
-
,
I
4000 C
3000 V
v
0
2
4
Pressure
J. Phys. Chem., Vol. 99, No. 42, 1995 15647
a’3Z+, d3A)
6 (mtorr)
8
10
Figure 7. Same as Figure 5 , but for a‘, v = 5 emission.
where P is the pressure in the cell and /3 is, apart from a geometry factor, the integral cross section for scattering of CO(a,va) molecules out of the area viewed by the detector. The parameter a is proportional to the rate constants k( va,) and k( Vd) for population by reactions 1 and 2 of the specified product levels, summed over all contributing reactant levels va. The linear onset indicates that the collision-induced luminescence observed here is a first-order process. The spectra shown in this work were taken in the range from 3 mTorr for Xe to 9 mTorr for He. Although this is beyond the initial, linear portion of the pressure plots, it was verified that the spectral distribution is the same withh experimental error as that measured at 1 mTorr. Thus the leveling-off of the intensity with pressure is not caused by secondary collisions of the products but only by elastic scattering of the CO(a) molecules out of the beam before reaching the observation zone in the center of the cell. The spectra reflect therefore the truly nascent rovibrational product level population. From the fits in Figure 6, the rate constants for the vd = 3 level were found to be in the ratio 1.0:1.8:2.7:4.3:6.7 for the five gases. Similarly, Figure 7 shows the experimental data and fits of the pressure dependence for the vat = 5 level. The fits gave here relative rate constants in the ratio 1.3:1.0:1.6: 2.4:3.0 for He to Xe, respectively. The standard deviations of the fits are all 5% or less. For Ne through Xe, the relative rate constants are quite similar in the two data sets. He, however, behaves anomalously in the latter case. Its relative rate constant is here more than twice as large as in the former set and even greater than that of Ne. Neither in N26 nor in CN” was a similar behavior found. The effect is not yet understood, but it is certainly real; the experiments were done in the order from He to Xe, and the nozzle was purged after each gas change. This strange phenomenon can also be appreciated visually in Figure 3. Comparing the band intensities of vat = 4 and va’ = 5, one can see that, in the spectrum for He, I5 > 4; in the spectra for the other four gases, 15 < 14. Detailed measurements of the pressure dependence were only made for the vd = 3 and vat = 5 levels (Figures 5 and 6). However, an inspection of Figure 3 shows that the emission intensities in most other bands follow a smooth trend in going from one collision gas to the next; quantitatively this is evident from the cross section data presented below. There is only one other obvious irregularity: The vd = 1 emission (with a small contribution from va’ = 7) in Figure 3 is anomalously weak with Ne and He. In principle, of course, one should not expect perfect scaling of the entire set of band intensities with the collision partner. Each level ua’
or vd, together with a collision gas, characterizes a particular energy transfer process of its own, and there is no a priori reason why different product levels should scale similarly upon changing the collision gas. The relative cross sections u(va,)and u(vd) corresponding to the rate constants k( vat) and k( Vd) for the different collision gases are obtained from the relationship u = k&l, where Ere1 is the mean relative collision velocity. was not measured in this work but was assumed to be the same as in our earlier Nz study (Table I11 in ref 7). The values are &el = 1660.0, 1130.0, 1045.0, 1000.0, and 980.0 m/s for M = He, Ne, Ar, Kr, and Xe, respectively. The relative cross sections are then obtained as 1.0:2.6:4.3:7.1:11.4 for d, v = 3 and 1.0:1.1:2.0:3.1:3.9 for a’, v = 5. C. CO(a,v,) Population Distribution. Figure 8 shows the spectrum of the spontaneous beam afterglow in the W, consisting of the CO(a) Cameron band a X emission. Also shown in Figure 8 is the spectral response curve of the detection system with the particular grating used. The CO(a X) spectrum as given is uncorrected for the spectral sensitivity variation. The assignment of the Av sequences was done according to ref 23 and confirmed by calculation based on molecular constants from ref 24. All peaks of the spectrum could unambiguously be assigned to the a X transition. This means that, after a flight time of about 500 pus (assuming a beam velocity % 1000 d s , as in the case of Nz6), the only species which radiates in this spectral region with detectable intensity is CO(a). CO(a’) and CO(d) molecules are also present in the beam at this position (see section IILA), but they do not contribute in this spectral region through their forbidden transitions to the X state, since transitions back to low-lying a-state levels are much more probable. The sensitivity curve shown in Figure 8 was obtained by using the NO(A X) y band33and NO(B X) /3 band34 spectra of NO and the CO(a X) spectrum itself. A y band spectrum was produced from the energy transfer reaction: N2(A) NO(X) Nz(X) NO(A). A /3 band spectrum was generated by the “gateway-type” intramolecular process NO(a) M NO(B) M.5 The CO(a X) spectrum was for this purpose taken at a distance of 23 cm from the source, where the emission intensity is much stronger (about 3.5 times) than at 53 cm. The three band systems exhibit several interlaced v“ progressions. The Einstein coefficients for the various (u’J’’) transitions from a given u’ level are known in the case of NO;33-34 for CO they were calculated (see the Appendix). The relative spectral sensitivity was then obtained from the ratio of the measured ( v ‘ , ~ ’ ’ )band intensities within each progression to the corresponding Einstein coefficients. The vibrational population of CO(a), N(va), was calculated according to
-
-
-
-
+
- +
-
-
+
+
-
Here Z(van) is the integral intensity of the Cameron band indicated, the dimensionless constant c describes the transmission of the detector optics, V is the observation volume, and q is the spectral sensitivity at the wavelength of the ( v a n ) band. The Einstein coefficients A( v a n ) were calculated as described in the Appendix. The factor of l/3 arises because the total reactant population N(va) is distributed (equally, we assume) among the three CO(a) sublevels 311~, 311~, and 3112, of which, however, only one-third (at low J , only 311~) can radiate into the X state (for details, see the Appendix). The other two-thirds of the populated reactant levels do not contribute to the emission
Ottinger et al.
15648 J. Phys. Chem., VoE. 99, No. 42, 1995 5000
I
I
I
-
I
1
Av=-1
0
4000
2
4-
Av=-2
0
CO(a-
X)
2
h
m
E
Cr
3000
u v h
5
2000
$ .+ fi
e (
1000 0
0
2
4
6
8
r
200
220
260
240
Wavelength
280
300
(nm)
Figure 8. Spectrum of metastable CO(a) Cameron bands taken at a distance of 53 cm from the source with an empty collision cell. The grating used here has 2400 lines/”, and the slit was 150 pm, corresponding to a resolution of 0.3 nm. The spectrum is a composite of eight separate sections, each of which covers about 15 nm and has a total exposure time of 10 x 200 s. The dashed curve gives the relative spectral sensitivity of the detection system, measured as described in the text. ov=O AV=-2 Av=-3 Av=-4 Av=-5
1
1.04
v
m
d
+
sequence sequence sequence sequence sequence
E
O 0.0 0.2
0
.
2
4
6
*
8 1 0 1 2 1 4
Vibrational Level va
Figure 9. Vibrational population of the CO(a) state obtained from Figure 8. Filled symbols: relative population derived from several different Au sequences. Open circles: Average of the filled data points. Curve: Exponential fit of the open circles: see the text for more details.
intensity Z(V,Q), although they do participate (equally, it is assumed) in the collisional energy transfer studied here. When eq 4 is applied in turn to the different observed Av sequences, several values of N(va)can be obtained for the same va, especially at low v,. The agreement between them was very satisfactory; see Figure 9. The average N(ua) distribution is shown in Figure 9 as open circles. The highest level whose population can be determined directly from Figure 8 is u, = 9. The line in Figure 9 is an exponential fit to the average N(va) as a function of the vibrational term values of the CO(a) state, G(va) = we(ua l/2) - wde(va ’/#:
+
N(ua) = constant exp( -G( u,)/kTvib)
+
(5)
Tvib is a fit parameter, the vibrational temperature. The fit yields Tvib = 6400 3~ 240 K. It is seen that the data points can be
described very well by a Boltzmann distribution. The experimentally determined relative population for the levels ua 5 9 and its extrapolation according to eq 5 for va > 9 are the basis for the determination of the cross sections for the energy transfer of CO(a,va);see section m.D. Circumstantial evidence supports the exponential extrapolation. A quasi-Boltzmann vibrational population profile was also found in LIF experiments on a beam of metastable N 2 ( A 3 x + ) produced by the same discharge source.*’ Although the complex formation mechanisms of forming N2(A) and CO(a>in the discharge region may be quite different, the vibrational temperature of the N 2 ( A ) distribution, Tvib = 6900 K? was very similar to the value found here for CO(a).~ Furthermore, the vibrational distribution of long-lived N2(W3Au)molecules in the beam was found to be monotonically d e c r e a ~ i n gcorresponding ,~~ closely to a vibrational temperature of Tvib = 12 000 K in the source region. Finally, the assumption of a smoothly decreasing vibrational population was also found to be consistent with the observations in the case of a CN(X) beam generated in the same apparatus with the same discharge conditions.” D. Cross Sections for Collisional Transfer CO(a) CO(a’,d). In the following we describe the method of obtaining absolute cross sections for populating a given vibrational product level through reactions 1 and 2. As in ref 6 the assumption was made that only that vibrational level va* of the CO(a) state is important for the population of a particular ua’ and Ud level which has the smallest energy mismatch for the reaction, cf. Figure 2 and Tables 1 and 2. The steady-state condition for the number density N(v) of a given vibrational product level u (where u stands for ua’ and ud) requires that
-
dN(v)/dt = E,,,[M]cJ( v) N( va*) - N( v ) c A (vu,) = 0 (6) UP
The first term is the rate of collisional population of the level is the relative velocity of the v by reactions 1 and 2. Here collision partners given above, and [MI is the rare gas number density in the cell (see caption of Figure 3). a(v) is the cross section for collisional population of the level v in question, and
-
Intramolecular Energy Transfer CO(a311
a’3Z+, d3A)
J. Phys. Chem., Vol. 99, No. 42, 1995 15649
is the number density of reactant CO(a) molecules in the quasi-resonant level va*, assumed to be solely responsible for the collisional population of the level v. The second term in eq 6 is the total radiative depopulation rate of the product level v by emission into low-lying levels of CO(a), summed over all final state levels va. The Einstein coefficients A(vva) for these transitions were obtained according to the FranckCondon approximation
N(Va*)
(7) The Franck-Condon factors q( VVa) were calculated using molecular constants from ref 24 and a program by The relative number densities N(v) and N(va*) of products and reactants, respectively, are obtained from the observed intensities of suitably chosen emission bands. Thus the number densities in the product CO(a’) or CO(d) levels v are related to the collision-induced a’ a and d a visible emission intensities (Figure 3) by
-
-
Z(vva) = cVv(vva)A(vva)N(v)
(8)
where q(vva) is the spectral sensitivity of the detection system (cf. Figure 3), taken at the band enter. The analogous eq 4 relates the number density in the reactant level va* to the intensity Z(va*a) of the spontaneous CO(a X) emission from the beam in the W (Figure 8). The resulting N(va*) distribution has been discussed above (Figure 9). In eq 8 Va designates the CO(a) levels v, = 0 and 1 into which emission from the CO(a’ and d) states was observed; see Figure 3. From eqs 4, 6, and 8 we obtain
-
a(y)
1 =-----
I(vva) V(va*vx) A(va*vx)
1
3 E r e i [ M l I(va*vx) q(vvJ
A(vvJ
D ( v v a ) (9) ua
The intensities Z(vva) and Z(va*m) were measured using different gratings (1200 Umm for the visible/IR and 2400 Umm for the W, respectively); therefore the corresponding sensitivity functions q(vva) and q(va*a) have to be normalized to each other. This was accomplished by measuring with both gratings the intensity of the d a, 13-1 and 15-2 bands in the AG emission at 418 nm, where the two sensitivity curves overlap (not shown in Figures 3 and 8). At this particular wavelength, ~ 2 4 0 0 / ~ 1 2 0 0 = 0.39 was obtained. The intensities Z(vVa) obtained from the spectra shown in Figure 3 are given in Tables 1 and 2 as Z” (the subscript v, for the terminal level has been dropped here, because v, is zero in all but two cases; see footnote a of Table 1). The intensity Z ( v a * ~ )used in eq 9 was taken as 40% of that measured in the spontaneous W afterglow spectrum shown in Figure 8, to allow for the CO(a) beam attenuation when the scattering cell was filled with the collision gas at the respective pressures, yielding the maximum CIAG intensity (cf. ref 6). These pressures are given in Figure 3. The intensity ratio appearing in eq 9 was of course also corrected for the different CCD exposure times used in recording the data of Figures 3 and 8. The absolute magnitudes of the a’ a and d a emission Einstein coefficients, i.e. the constants Ca’,d-a in eq 7, cancel out in eq 9. The a X Einstein coefficient is given in absolute units by the calculations outlined in the Appendix; therefore, eq 9 yields absolute cross sections. For the highest reactant levels, va* = 10-13, the band intensities Z(va*m)could not be directly measured, because they are too weak (Figure 8). However, these missing data could be generated from eq 4,using the exponentially extrapolated portion (eq 5 ) of the N( va*) distribution. The factor cV in eq 4
-
-
-
-
for these “artificial” intensities was obtained by normalization using “true” intensities at lower Va. All cross section results are listed in Tables 1 and 2 for the a’ and d states, respectively.
IV. Discussion
-
A. Perturbation-Mediated Population of CO(d,v=2). The high-resolution spectra for the d, v = 2 a, va = 0 transition (Figure 5) show some conspicuous peaks compared with Figure 4 for the d, v = 3 and 4 levels. It is known that the d, v = 2 level is severely perturbed by the level a, va = 9.13J5 This suggests that the strange spikes are produced with the assistance of the perturbations, in a type of intramolecular process referred to as a “gateway” mechanism. It has been discussed in detail in refs 5 and 36. In brief, this mechanism can operate whenever a specific rotational level of a metastable state and one of a radiating state are coupled in the isolated molecule, for example by spin-orbit interaction. The perturbed level of the metastable state will then be (weakly) allowed to radiate. Consequently, its population is depleted while that of the adjacent, unperturbed rotational levels remains unaffected. In the presence of collisions, rotational relaxation within the metastable state will then replenish the population of the perturbed level, and emission of a sharp line from this level will ensue. Very clear examples of this mechanism have recently been found in NOS and N2.36 In both cases the coupled states have different multiplicity, and the gateway mechanism is the only way of transferring population between them. In the case of a spin-allowed collisional transfer such as the present one, however, any possible gateway contribution will generally be overwhelmed by the much stronger, “direct” collisional transfer, which is not restricted to the few spectroscopicallyperturbed levels but can couple levels which are far apart. Examples of the direct mechanism are the collisional transfer processes N2(A3Eu+,W3Au B311,)6,7and CN(X2Z+ A211),” where only broad product emission bands were seen, masking any possibly underlying gateway-type spikes. Even a spin-allowedprocess can, however, exhibit pure gateway characteristics. This is true of the collisional transfer between CO+(A211,v=O) and CO+(X2Z+,v=10).37The authors attributed here the absence of a direct transfer to the very small Franck-Condon factor (4 x between these two states. The present case appears to be intermediate: The broad emission from the a’ and d levels is all due to the direct process (see section IV.B). With the exception of d, v = 2, these levels are not perturbed by the a-state, or the perturbations occur at high rotational levels, which are very weakly populated in our beam (e.g., at J around 20 for a‘, v = 4 and 8, see ref 13, Table I). The d, v = 2 emission, on the other hand, shows many gateway-type spikes in addition to the underlying broad emission; see Figure 5. Another, early example of coexisting gateway and direct processes is the collisional transfer in CN from A211, v = 10 to B2Z+, v = 0.3s Most of the prominent spikes in Figure 5 could be spectroscopically identified with known perturbations of individual rotational levels by corresponding levels of the a, va = 9 state. This analysis was based on very-high-resolution near-IR diode laser absorption measurements of the CO(d,v=2 a,v=l) band.I5 In that work, over 500 lines corresponding to transitions into the heavily perturbed d, v = 2/a, ua = 9 complex were assigned. It tumed out that the majority of lines corresponded to transitions into levels of predominant 3A character (ref 15, Table I), but in addition numerous lines were found whose upper levels had to be described as predominantly 311 in character. This was quantified by the eigenvectors, obtained from a simultaneous fit of all ( ‘ I 3 A ’ and “3rI”)lines to the eigenvalues of the 6 x 6 (3A plus 31-1)Hamiltonian. It is remarkable that
-
-
-
Ottinger et al.
15650 J. Phys. Chem., Vol. 99, No. 42, 1995
TABLE 3: Identification of the Spikes Numbered in Figure 5, top v-1715 spike v vc,d line upper n0.O (cm-l)b (cm-I) assignmentC state (cm-I) 12 753 1
2
14468 14448 14423
5 6 7 8 9
14412 14389 14 363 14357 14344 14333
x
f r o m pressure dependence
.
0
from Tables I a n d II
-
[AZ] 0.a
r
d
I
RQ2~(7)
d
12733
I1
’Q31(6) QPZI(8)
a
I
12708 12697 12674 12 648 12642 12629 12618
12699 (12673) (12647) 12643 (12631) 12617
I1 I1 I1 I
I1 I
d
RR22(6) RQ21(6) RR22(5)
QQ33(6) ‘Q23(7) pP33(8) OQ13(6)
He
a a a d a d
See Figure 5 for the number of the spike. * Wavenumbers obtained in the present work (Figure 5 ) . Wavenumbers from ref 15, Tables I and 11, as indicated, averaged over “e” and “f’ levels and rounded to the nearest integer. Lines which should be weak according to ref 39 are given in parentheses.
-
--
-
in this nominal d3A a311 (2 1) band there are so many lines which are of the type of an a311 a311 (9 1) overtone “vibrational” transition (which, however, derives its oscillator strength from the interacting 3A state). Earlier experiments with lower resolution on the vacuum W transition CO(d3A/a311 X’X)(2/9 O)I3 had already shown precisely the same division into upper state levels with less than 50% and more than 50% 311-character (Table I11 in ref 13). Since the present data refer to emission into CO(a,v=O), while ref 15 lists absorption transitions out of CO(a,v=l), the measured wavenumbers of the spikes in Figure 5 were translated to the scale of ref 15 by subtraction of the purely vibrational term difference, AG112 = G(l) - G(0) = 1715 cm-’ (calculated from the molecular constants given in ref 24). The result lies in each case within 1-2 cm-’ of one or at most two lines listed and identified in ref 15; see Table 3. This agreement is consistent with the 0.2 nm fwhm resolution of the present experiment. In some cases a few other lines from ref 15 fall within the 1-2 cm-’ margin, but they correspond to relatively high J values ( 2 10). They were ignored, because at the expected rotational temperature of our beam of 140 K (by analogy with an N2(A) beam)2 the most populated level is low, Jmax= 5 . Some of the identified lines listed in Table 3 have small transition probabilities, according to published London-Honl factors for an intermediate case (a)/(b) 3A-311 t r a n ~ i t i o n .This, ~ ~ too, is in agreement with the observation, cf. Figure 5, peaks 3, 5, and 9. With the transitions responsible for the spike emission from d, z, = 2 (and a, u, = 9) identified, the important point to note is that the upper states of these transitions are just those levels which both refs 13 and 15 indicate as being the most strongly perturbed ones: In ref 13, Table I shows that, in the low-J regime, the strongest perturbations of the d-state occur in the F1 level (Le. 3A3) at J = 6 and in the F2 level (i.e. 3A2) at J = 6 and 7. This is documented by Table III in ref 13, which shows an almost 50% ll-character for these levels. Similarly, Figure 3 in ref 15 indicates at J = 6 and 7 a strong irregularity of the d3A2 rotational levels, and Table V of ref 15, giving the eigenvectors, substantiates the profound state mixing at these same J and C2 values. The excellent agreement of the spectroscopically known perturbations with the collisionally induced spike emissions demonstrates impressively the importance of the quantum mechanical state mixing for the kinetic behavior, i.e. the gateway
-
-
12733
( 12 709)
4
.
’Rzi(6)
(12 755) 12734 ( 12 709)
3
2.5
RQ2~(6)
I
12753
[A2]
-
Ne
Ar
Kr
Xe
He
Ne
Ar
Kr
Xe
Figure 10. Comparison of the dependence of cross sections for the collision-induced transfer CO(a’,v=5) and CO(d,v=3) on the collision partner. Circles: Absolute data, from normalization of the product emission to the reactant CO(a) emission intensity, making the assumption of nearest-to-resonance transfer only. Crosses: Relative data, from direct pressure dependent intensity measurements, with unspecified reactant level (normalized to the circles at Ar). mechanism, of the CO(a,va=9/d,v=2) system. Compared to our previous studies of gateway coupling in NO5 and N2,36the present system is much more complicated, on account of the large spin-orbit coupling matrix element. Largely due to the good vibrational wave function overlap (z,,Iud) (see ref 15, Figure 4), the coupling parameter Hso(va\u~) amounts to as much as e9 This will allow a great many levels to interact, and in fact the mixing coefficients listed in refs 13 and 15 show that the perturbation is by no means restricted to the J = 6 and 7 levels; it is weaker but still present throughout the range J < 6 and extends to at least J = lO.I5 Also, higher than secondorder perturbations contribute, allowing ASZ = 2 mixing.I5 Overall, this complex coupling pattern results in the chaotic intensity distribution seen in Figure 5. It is interesting to observe that in Figure 5 the spikes are much more pronounced with He than with Xe. This is typical: The direct mechanism has a much smaller cross section with He than with Xe (see Table 2), while the gateway mechanism involves collisions only via intrastate relaxation, which is less dependent on the collision partner. Therefore the “spikes” are relatively more prominent with He. A similar situation was observed in the case of N2,36although here the spikes and the background resulted from coupling between two different state pairs (the spikes from B3rII,/At5Cg+gateway coupling, the background from B311,/A3X,,+direct coupling). B. Direct Collisional Energy Transfer. The smooth contours of all other bands except the CO(d,v=2) emission (Figures 3 and 4) show that these are not affected by perturbations to any observable extent. Here the mechanism of populating the upper state levels is a nonadiabatic transition between the potential energy surfaces which describe the entrance and exit channels, CO(a) M and CO(a’,d) M. For the two product levels a’, z, = 5 and d, z, = 3 the cross section dependence on the rare gas as determined from the variation with pressure has been given in section 1II.B. These data can be compared with the results given in Table 1, third column, and Table 2, fourth column, respectively. A graphical presentation of this comparison is given in Figure 10, where the relative data from the pressure dependence have been normalized to the absolute values (Tables 1 and 2) for M = argon. Despite the very different experimental methods, based on eqs 3 and 9, respectively, the agreement in the M-dependence is very satisfactory, particularly in the d, u = 3 case. Since the determination via the pressure dependence is effectively an average over several independent measurements (see Figures 6 and 7), these results are considered to be more accurate. The
+
+
Intramolecular Energy Transfer CO(a311
-
at3Z+, d3A) 5 -
-
4
-
He
--
Ne
__
Ar
__
L r 3 0
-3
0
Kr
__
--.
Xe
-
-
200 400 600 200 400 800 200 400 800 200 400 800 200 400 800
IAEI (cm-')
2
1 b
o
3-1 -2 -3
-4
-5
-8 0
200 400 800 200 400 800 200 400 800 200 400 800 200 400 800
IAEI (cm-')
-
Figure 11. Cross sections 0 (in units of A2) for collisional coupling a a' as a function of energy defects IAEI. The lines are the fits of data points using eq 1 0 (a) with FCF; (b) without FCF. The circled points are excluded in the fit; see the text.
200400800
200400800
200400600
200400600
200400800
I A E I (em-')
Figure 12. Same as Figure 11, but for a (b) without FCF in the fit.
-
d coupling: (a) with FCF;
Tables 1 and 2 show together the a-state vibrational levels deviations of the other set of data in Figure 12, derived from the spectra at only one fixed pressure, are then indicative of the expected overall statistical accuracy of the majority of the cross sections, where detailed pressure dependence measurements have not been made. Conceivably there could be a systematic source of discrepancy between the two types of results: Since in eq 9 explicit reference is made to the assumption of near-resonant energy transfer, any collision-gas dependent violation of this assumption would show up in Figure 10 in the comparison with the results from the pressure dependence, which do not rest on any assumption. In particular, if with Xe the quasi-resonance hypothesis should be less well fulfilled than with He, then the absolute Xe cross section derived from eq 9 will be too large. The fit lines of Figures 11 and 12, especially the latter, do indicate that with Xe the resonance condition might be less critical than with the lighter gases. However, the effect is too small to be relevant for Figure 10. Note that the proportionality of the two data sets demonstrated in Figure 10 cannot prove the validity of the resonance condition as such but only that, to whatever degree this condition is valid, it holds equally well for all five gases. In related experiments on N2 and CN the efficiencies of different collision partners in inducing intramolecular transfer have also been studied. For rare gases, they increase strongly from He to Xe. The same general trend has been observed in the present work on CO, with few exceptions, as discussed in section II1.C. The rather universal increase toward the heavier collision partners may partly be due to the different relative collision energies, which have the same trend in our series of experiments, conducted at a fixed (laboratory system) kinetic energy with each metastable species. With higher energy the collision pair can reach the region of higher potential at a closer distance between the collision partners, where the magnitude of the mixing potential is expected to be larger. In addition, the stronger van der Waals attraction of the heavier rare gas atoms will lower both the entrance and exit channel potentials. This will further help to bring the effective coupling region within reach of the relative collision energy.
va*, which are closest-to-resonant with the corresponding
product levels v, and the energy defects between the two. Comparing the cross section values a(v) in these two tables, one can find the following: (1) The exothermic process is generally favored. In the case of the a'-state (Table l), population of the v = 5 level is 188 cm-l exothermic, and its cross section is the second largest among all the product levels for every collision gas. It is even larger than that of the very closely resonant but endothermic level v = 12 (AE = 44 cm-I). Comparing v = 6 (AE = -564 cm-I) with v = 7 (AE = 523 cm-I) and with v = 11 (AE = 413 cm-I), one can see this exothermic-favored trend more clearly. In the case of the d-state, the same rule is found. v = 3 (AE = -299 cm-I) has a greater cross section than the v = 6 level (endothermic by only 92 cm-I). (2) When the cross sections for exothermic and endothermic reactions within each group are compared, it is found that the absolute magnitude of the energy defect is an important factor. The intramolecular coupling is most efficient for level pairs which are in good energy resonance, just as was found earlier in this laboratory for the case of N2.6-8 From Table 1 one can see that a,=12(AE = 44 cm-I) > aF8 (AE = 137 cm-I) > a,=ll (AE = 413 cm-I) > aF7 (AE = 523 cm-') and au=5 (AE = -188 cm-1) > ( 5 ~ 4(AE = -564 cm-I) for each collision gas. Similarly in the d-state, one finds av=2(AE = 44 cm-I) > au=6(AE = 92 cm-I) > aF5 (AE = 437 cm-I) and au=3(AE = -299 cm-I) > uu=4(AE = -634 cm-I). But there are also some exceptions. For example, contrary to rule 1, in the a'-state u,=4 (AE = 197 cm-') > oU=5( A E = - 188 cm-I) except in He. Only with He as collision gas, a,=5 > a v = 4 is found in accordance with rule 1. Possibly the cross section for formation of a', v = 4 increases more strongly with increasing collision energy than that for the a', v = 5 level. Exceptions to rule 2 are as follows: For the d-state, au=6(AE = 92 cm-I) < (AE = 396 cm-I) for each gas used but especially for the heavier gases. Furthermore, 0,=2 (AE = 44 cm-I) < (AE= 396 cm-') in collisions with Kr and Xe. Thus, for every close energy resonance (in the examples given,
15652 J. Phys. Chem., Vol. 99, No. 42, 1995
Ottinger et al.
within less than 100 cm-I), the cross section is smaller than that for not quite so resonant level pairs. This is reminiscent of a recent study in this laboratory of the collisional energy transfer Xe* 14,15N2.40 In the I5N2case, with AE = 220 cm-I, the cross section is only about one-third of that for the corresponding but less resonant (AE= 480 cm-I) level of I4N2. In the highly resonant case the entrance and exit channel potentials for the collision pair cross at such a large atommolecule distance that the matrix element for the nonadiabatic coupling is small at the crossing point. A similar mechanism may be operative in the present case, although the process concemed is now intramolecular energy transfer. Interestingly, the inversion of the expected ordering of the cross section magnitudes appears to occur preferentially with heavy collision partners, i.e. for those which should produce potential crossings at longer range than light atoms would. It was found in refs 6 and 7 that the relationship between cross section u and energy gap AE could be expressed approximately by a simple exponential function u FZ exp(-AE/ EO) for the N2(A, W B) processes. Thus, instead of the traditional (kT)-' term in the exponent, an adjustable parameter EOwas used which characterizes the energy specificity of the process. For the A B transfer EO was found to be substantially smaller than that for the W B process. In addition, the Franck-Condon factor between the initial and final molecular states may play a role. Its effect has recently been studied for the case of the collision-induced intermolecular electronic energy transfer in the system Xe* N2.41 The principal conclusion was that the cross section is proportional to the Franck-Condon factor if and only if the time zc characteristic of the nonadiabatic transition is short compared to a typical vibrational period, Zvlb. zc depends on the radial relative velocity of the two collision partners at the potential crossing but also on other parameters of the crossing (nonadiabatic coupling matrix element and the difference of the radial forces before and after the transition, as in the well-known Landau-Zener formula). These parameters can vary widely and cannot be predicted unless the topology of the potential surface crossing is well-known, which is hardly ever the case. For this reason we are presenting the cross section results of this work both with and without including the Franck-Condon factors. Figure l l a shows the cross section for the a'-state plotted against the energy defects IAEl. The points are experimental data, and the lines are the fits of the points with the expression
+
+
-
-
+
u = 0, FCF exp( - I AEIIE,)
(10)
where 00 and EO have the same meaning as in refs 6 and 7. FCF is the Franck-Condon factor for the particular level pair in which the intramolecular energy transfer takes place; see Table 1. The circled data points for the exceptionally large exothermicity of AE = 564 cm-I for the v = 6 level were excluded from the fit. As Figure 2 shows, the a',6 level lies almost midway between a,9 and a,8. Both these reactant levels may therefore contribute about equally to the population of a',6 (the somewhat larger energy deficit from a,8 compared to a,9 will be at least partially offset by the x1.4 times higher population of the former level). Dividing this anomalously large cross section by 2, to allow for the two contributing reactant levels, brings the circled data points into much better agreement with the others. In Figure 1l b another fit of the same data points is shown, obtained from an exponential expression as in eq 10 but now without the FCF. This fit is not as close as that in Figure l l a .
The same process was used for the d-state, again using eq 10 with and without the FCF. The results are shown in parts a and b, respectively, of Figure 12. Again inclusion of the FCF's (Figure 12a) appears to improve the fit, but in either case the cross sections depend rather weakly on the energy gap (particularly for heavy atoms). The orbital configuration of CO(a311) is h ' R ' , while a' and d both have ...x3u2R'. The presence of a collision partner causes one electron to move from the JC orbital to the u orbital in both reactions. On this basis the different behavior of the a'- and d-states is unexpected. This situation is similar to the case of N2(A, W B),6-7where A and W also have identical electronic configurations but the energy gap dependence of the cross section is much less pronounced for the W state. The effects of energy gap AE and FCF on the rate of intramolecular electronic energy transfer have been the theme of many collision-induced transfer studies.1-4,6.7,42-45Some results support the exponential dependence of the cross section on the energy gap,6,7.42while others show that there is no such d e p e n d e n ~ e . ' - ~ ,As ~ ~regards - ~ ~ the Franck-Condon factor, refs 42 and 43 state that the cross section appears to be proportional to the FCF, while refs 1, 3,6, and 7 deny the importance of the FCF. Theoretical work"6 has also questioned the use of the FCF. It was suggested that a "distorted" Franck-Condon factor should be used, which reflects the overlap integral of the molecule in the presence of a perturber. In view of the controversial results, it is not possible to give a universal description of electronic transfer processes. Each system, molecule, or even the particular state being studied appears to have its own characteristics. This is also true of the absolute magnitude of the energy transfer cross sections measured here, which are surprisingly small in comparison with the quite analogous case of N2.637As regards the electron configurations involved, the two systems are mirror images of each other: While in the N2(A3&+,W3A, -, B317,) transfer the configuration changes from n3u2ji1 to 3t'u'7i1,the reverse change takes place in the CO(a311 a'3Cf, d3A) processes. On this basis, the cross sections would be expected to be similar. The Franck-Condon factors between initial and final states are also not very different in the two systems. The different reactivity can therefore not be explained considering only the diatomic molecule before and after the collision; it must be rooted in the triatomic nature of the collision system including the target particle. The details of the crossings of the associated potential energy hypersurfaces are apparently decisive.
-
-
V. Conclusion
-
In this work the collision-induced intramolecular state conversion of CO(a a' and d) was studied, for the first time, under single collision conditions. The vibrational population distribution of the reactant state CO(a) was obtained from its spin-forbidden Cameron band CO(a X) emission. Absolute cross sections for transfer into CO(a' and d) have been deduced from the collision-induced emission spectra for a range of vibrational levels in both product electronic states, a' and d. Two general rules were found for the transitions: (1) Exothermic processes are generally favored over endothermic ones. ( 2 ) Energy resonance is a critical condition for the transfer. These findings are in good agreement with the results of other spinallowed intramolecular coupling studies6-* For the CO(d,v=2) product level, a gateway mechanism involving perturbations with the CO(a,v,=9) reactant level was identified. This is one of the few examples of a gateway process operating between two states of the same spin.
-
Intramolecular Energy Transfer CO(a311
-
J. Phys. Chem., Vol. 99,No. 42, 1995 15653
a’3Z+, d3A)
Acknowledgment. A.V. thanks the Deutsche Forschungsgemeinschafi and the Alexander von Humboldt foundation for financial support. D.X. acknowledges gratefully a scholarship from the Max Planck Society in cooperation with the Chinese Academy of Sciences. Appendix: Einstein Coefficients of the Cameron Bands The CO(a311- X’Z+) Cameron band system is a forbidden electronic transition which “borrows” its intensity predominantly through spin-orbit coupling between the a3111 component and the A’II state.I7 The CO(A) state has a high probability for radiative transitions (“fourth positive band system”) into the ground state. Thus, at least at low J, only the a3111component has an appreciable radiative transition probability, while 3110 and 3112are “dark” states (cf. the comments following eq 4). With increasing rotational excitation, the 311~ and 3112 components mix with 3111and thereby also contribute to the emis~i0n.l~ However, it is shown in ref 17 that the total radiative transition probability is independent of J. Therefore the increased emission from 3110and 3112at higher J occurs at the expense of the 3111emission, and the overall intensity is still only onethird of what it would be if all three sublevels coupled equally with the A-state. Note, however, that the J-independence of the overall intensity stated in ref 17 holds strictly only at t = 0. Since, at any given finite J , the radiative rates for 3rIIo,2 are smaller than for 31’il,the unresolved integral intensity will decay nonexponentially, such that the share of 3 1 1 ~ , 2increases with time. In our experiment this effect is negligible, since the timeof-flight of CO(a) from the source to the observation region is %OS ms, which is small compared even to the shortest lifetimes calculated in ref 17 (i.e. z = 2.93 ms for 311~at J = 1). The CO(a/A) coupling is a classic example of perturbation of a metastable state by the entire vibrational manifold of a single remote radiative state, such as is treated at some length in the book by Lefebvre-Brion and Field (ref 47, p 284). There it is shown that, approximately, the emission branching from a given level va into the ground state level vx follows the distribution of the corresponding Franck-Condon factors, q(vavx), even though the “direct” a -.X transition is rigorously forbidden; summation over the multitude of the mediating A-state vibrational levels (eq 5.4.8 in ref 47) eliminates the A-state from the radiative distribution.
In the present context it is therefore tempting to use the Franck-Condon approximation
for use in eq 4. However, warnings are given in ref 47 that the assumptions underlying this approximation are rather drastic: The electronic (S/O-)coupling element must be r-independent; the energy spacing between the level va considered and the perturbing A-state must be so large that it can be considered as independent of VA; and the A -.X transition moment must be r-independent. Especially the second assumption is by no means justified in the present case, for most of the Va levels of interest (va 5 13), since the minimum of the A-state potential energy curve lies near va = 10. For this reason it was necessary to calculate the Einstein coefficients A(vaa) for all these Z/a levels, following the procedure used by James for va = 0 and l.I7 James shows that the transition moment of the a X band system can be expressed by products of the vibronic dipole matrix elements (square root of the band strengths) of the A X transition and the S/O vibronic coupling matrix elements, divided by the a,va - A,VAenergy spacing and summed over VA. The first factor can be calculated in the r-centroid approximation, using the known r-dependence of the A-X transition The second factor is based on the equality of the a/A S/O perturbation operator and the a-state S/O coupling constant A , the r-dependence of which is also kn0wn.4~ According to this brief outline it was possible to obtain absolute values of all Einstein coefficients important for this work. However, we depart from James work in one important respect. In his eq 19 he multiplies the measured CO(A-X) transition moment from ref 48 by d2, i.e. the Einstein coefficient A by a factor of 2, in order to allow for both A components (since the experiment of ref 48 involved only one component). The rationale is apparently that in the a311~/A111 coupling both A components are involved, “e” coupling with “e” and “f’with “f ’. While this is true, it appears erroneous to sum the radiative Einstein coefficients. Since, as James recognizes, the lifetimes and A values are the same for the two A components, the lifetime for the combined emission from both and the corresponding A values are also the same. The article by Tatum, cited by James himself, states this fact
-
-
TABLE 4: Emission Einstein CoePficients of the Forbidden Transition CO(a311
-
X W ) Bands (in s-l)
Uf
dl
0
1
2
3
4
5
6
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
132.35 135.25 60.90 15.70 2.55 0.28 0.02
172.22 5.28 47.03 72.42 34.37 8.41 1.24 0.12
127.81 41.22 56.74 1.35 46.08 43.59 15.91 3.13 0.37
72.39 108.33 0.29 57.25 9.93 15.76 39.77 22.32 5.81 0.86
35.43 113.43 37.71 25.77 24.39 30.03 0.92 27.19 25.20 8.82 1.62
16.15 82.47 92.22 1.43 46.49 2.06 35.40 2.72 12.93 23.71 11.40 2.60
7.15 49.74 104.08 43.04 8.40 39.19 3.15 24.91 12.24 3.09 18.54 12.86 3.66
7 27.47 84.14 88.06 7.28 29.20 17.69 16.11 9.84 19.84 0.00 11.65 12.71 4.63
8
57.39 99.59 50.19 0.95 37.94 2.24 25.26 0.84 20.68 2.39 5.34 11.01 5.25
9
85.58 87.93 15.72 14.15 29.43 1.21 22.99 1.52 15.33 7.09 1.29 8.34 5.25
10
98.37 57.86 0.49 28.31 13.61 9.07 12.65 8.52 7.33 10.85 0.00 5.43 4.78
11
90.39 25.56 4.70 32.13 2.64 15.33 3.05 14.91 1.45 11.19 1.25 2.13 4.07
12
64.95 4.50 16.80 22.12 0.51 16.67 2.38 16.47 0.11 8.98 3.54 0.89 3.00
13
34.62 0.39 24.42 9.10 6.01 10.88 3.50 12.41 2.68 4.93 5.65 5.82 1.97
14
21.36 0.11 5.22 0.04 10.99 2.76 6.03 2.15 7.43 0.01 6.53 0.83 1.36
15654 J. Phys. Chem., Vol. 99, No. 42, 1995
Ottinger et al.
TABLE 5: Exact CO(a-X) Einstein Coefflcients vs Franck-Condon Approximation, A ( v . v ~ ) ~ q ( v , , v ~x) @10” ]
(4) Dagdigian, P. J.; Patel-Misra, D.; Berning, A,; Werner, H.-J.; Alexander, M. H. J . Chem. Phys. 1993, 98, 8580. (5) Ottinger, Ch.; Vilesov, A. F. J. Chem. Phys. 1994, 100, 1805 and 1815. (6) Bachmann. R.: Li. X.: Ottinser. Ch.; Vilesov, A. F. J . Chem. Phys. vx 7 9 11 13 1992, 96, 5151. (7) Bachmann. R.; Li, X.: Ottinger, 1 0.68 - Ch.; Vilesov, A. F.; Wulfmeyer, V. J. Chem. Phys. 1993, 98, 8606. 2 0.57 (8) Ottinger, Ch.; Vilesov, A. F.; Xu, D. D. J. Chem. Phys. 1995, 102, 3 0.53 0.65 1673. 4 0.63 0.58 (9) Werner, H.-J.; Follmeg, B.; Alexander, M. H. J . Chem. Phys. 1988, 5 0.38 0.64 0.65 89, 3139. 6 0.38 0.31 0.70 (IO) Werner, H.-J.; Follmeg, B.; Alexander, M. H.; Lemoine, D. J . Chem. 7 0.33 0.38 0.27 0.80 Phys. 1989, 91, 5425. 8 0.31 xx 0.39 xx (11) de Moor, M.; Ottinger, Ch.: Vilesov, A. F.; Xu, D. D. J. Chem. 9 0.28 0.31 0.59 0.34 Phvs. 1994, 101, 9506. 10 xx xx 0.27 0.38 (12) Clyne, M. A. A.; Heaven, M. C. J . Chem. SOC.,Faraday Trans. 2, 0.19 0.26 0.21 0.26 11 1981, 1375. 0.31 0.23 12 0.15 0.23 (13) Field, R. W.; Tilford, S. G,; Howard, R. A,; Simmons, J. D. J . Mol. Spectrosc. 1972, 44, 347. 0.50 13 0.11 xx xx (14) Effantin, C.; Michaud, F.; Roux, F.; D’Incan, J.; Verges, J. J. Mol. 14 0.12 0.20 0.27 Spectrosc. 1982, 92, 349. 15 0.08 xx 0.28 (15) Momona, M.; Kanamori, H.; Sakurai, K. J . Mol. Spectrosc. 1993, 16 0.11 0.17 159, 1. xx 17 0.77 (16) Yamamoto, S.; Saito, S. J . Chem. Phys. 1988, 89, 1936. (17) James, T. C. J . Chem. Phys. 1971, 55, 4118. Li Entries xx mark very small values of both A(vam)and q(v,vx), (18) Herzberg, G.; Hugo, T. J.; Tilford, S. G.; Simmons, J. D. Can. J . making their ratio numerically inaccurate. Only some va values out Phys. 1970, 48, 3004. of the range of interest, va = 7-13, have been selected, to illustrate (19) Strobl, K. H.; Vidal, C. R. J. Chem. Phys. 1987, 86, 62. the general trends. (20) le Floch, A.; Rostas, J.; Rostas, F. Chem. Phys. 1990, 142, 261. (21) Geisen, H.; Neuschafer, D.; Ottinger, Ch. J . Chem. Phys. 1990, 92, 104. explicitly (ref 50, section F): “The transition probability of a (22) Bachmann, R.; Ottinger, Ch.; Vilesov, A. F. J . Chem. Phys. 1993, line with unresolved A doubling is equal to that of each of its 99, 3262. components.” Therefore we used the expression for the (23) Pearse, R. W. B.; Gaydon, A. G. The ldent$cation of Molecular Spectra; Chapman and Hall: New York, 1976. transition moment as originally given in ref 48, and consequently (24) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular all Einstein coefficients A(v,m) should also be only half of the Structure. IV. Constants of Diatomic Molecules; Van Nostrand: New York, values obtained according to James’ prescription. Note that, 1979. when calculating the lifetimes, James corrects the error in the (25) Neuschafer, D.; Ottinger, Ch.; Sharma, A. Chem. Phys. 1987, 117, 133. A values by applying, in his eq 25, an extra factor of ‘/z. Thus (26) Geisen, H.; Neuschafer, D.; Ottinger, Ch.; Sharma, A. Acta Phys. only his A values, not his lifetimes, are incorrect. Polonica 1984, A66, 289. The Einstein coefficients A( vam)calculated in the present (27) James, T. C. J. Mol. Spectrosc. 1971, 40, 545. (28) Lawrence, G. M. Chem. Phys. Lett. 1971, 9, 575. work are given in Table 4. A comparison with the values for (29) Slanger, T. G.; Black, G. J . Chem. Phys. 1971, 55, 2164. u, = 0 and 1 given in Table 111 of ref 17 shows excellent (30) Johnson, C. E.; van Dyck, R. S., Jr. J. Chem. Phys. 1972,56, 1507. agreement, if the latter are divided by 2. (31) Burden, F. R.; Clyne, M. A. A.; Fontijn, A. Chem. Phys. 1982,65, The Franck-Condon approximation, on the other hand, is 123. (32) Kriimpelmann, T. Dissertation, Gottingen, 1987, published as clearly inappropriate. We have calculated the a-X FranckBericht 1711987, Max-Planck-Institut fur Stromungsforschung, Gottingen. Condon factors q(v,m) in the same way as the Franck-Condon (33) Piper, L. G.; Cowles, L. M. J . Chem. Phys. 1986, 85, 2419. factors q(VVa); see section 1II.D. Table 5 shows the ratio of the (34) Piper, L. G.; Tucker, T. R.; Cummings, W. P. J. Chem. Phys. 1991, exact, absolute A( u,m) and the “approximate”, relative 4 ( ~ a m ) ~ ~94, 7667. (35) Zare, R. N. Univ. Calif. Rad. Lab. Report UCRL 10925, 1963; J . transition probabilities for some selected levels in the region Ua Chem. Phys. 1964, 40, 1934. = 7-13. This ratio varies by almost one order of magnitude (36) Ottinger, Ch.; Vilesov, A. F. J . Chem. Phys. 1994, 100, 4848. across the range of interest; thus, it is imperative to use the (37) Dentamaro, A. V.; Katayama, D. H. J. Chem. Phys. 1989, 90,91. (38) Radford, H. E.; Broida, H. P. J. Chem. Phys. 1963, 38, 644. correct values of A ( u , a ) . However, comparing with Table 4, (39) Kovacs, I.; Toros, R. Acta Phys. Hung. Tom. XVIII. Fasc. 2 1965, it is seen that abrupt changes of A(u,m) (e.g. from the 7,3 to 101. the 7,4 band) are mirrored rather closely by the corresponding (40) Ottinger, Ch.; Vilesov, A. F.; Xu, D. D. Chem. Phys. 1995, 192, 49. 4 ( v , ~ ) v 3values, a remarkable fact considering that the method (41) Aauilanti. V.: Candori. R.: Pirani. F.: Ottineer. Ch. Chem. Phvs. of JamesI7 does not involve any direct calculation of alx 1994,187,’171. vibrational overlap integrals. Furthermore, for low levels va, (42) Katavama. D. H.; Miller. T. A,: Bondvbev. - . V. E. J. Chem. Phvs. such as were used in the determination of the apparatus 1979, 71, 1662. (43) Katayama, D. H.; Welsh, J. A. J. Chem. Phys. 1983, 79, 3627. sensitivity function and the vibrational population N( u,) (section (44) Katayama, D. H.; Dentamaro A. V.; Welsh, J. A. J . Chem. Phys. IU.C), the Franck-Condon approximation was found to describe 1987, 87, 6983. the relative Einstein coefficients very well. The validity criteria (45) Dentamaro, A. V.; Katayama, D. H. Phys. Rev. A 1991.43, 1306. (46) Alexander, M. H.; Corey, G. C. J . Chem. Phys. 1986, 84, 100. from ref 47 stated above are, in fact, fulfilled for these low ua (47) Lefebvre-Brion, H.; Field, R. W. Perturbations in the Spectra of levels. Diatomic Molecules; Academic Press, Orlando, FL, 1986. (48) Mumma, M. J.; Stone, E. J.; Zipf, E. C. J. Chem. Phys. 1971, 54, References and Notes 2627. (49) Stern, R. C.; Gammon, R. H.; Lesk, M. E.; Freund, R. S.; (1) Furio, N.; Ali, A,; Dagdigian, P. J. Chem. Phys. Lett. 1986, 125, Klemperer, W. A. J . Chem. Phys. 1970, 52, 3467. 561; J . Chem. Phys. 1986, 85, 3860. (50) Tatum, J. B. Astrophys. J . Suppl. No. 124 1967, 14, 21. (2) Guo,J.-H.; Ali, A.; Dagdigian, P. J. J . Chem. Phys. 1986,85,7098. (3) Ah, A,; Guo,J.-H.; Dagdigian, P. J. J . Chem. Phys. 1987,87,2045. JP950824G ~
~~~~
Y
Y
