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Calculated vibrational populations of O2 Herzberg states in the mixture of CO2, CO, N2, O2 gases
Chemical Physics Letters 603 (2014) 89–94
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Calculated vibrational populations of O2 Herzberg states in the mixture of CO2, CO, N2, O2 gases A.S. Kirillov ⇑ Polar Geophysical Institute of Russian Academy of Sciences, Academytown, 26A, Apatity, Murmansk Region 184209, Russia
a r t i c l e
i n f o
Article history: Received 30 January 2014 In final form 17 April 2014 Available online 24 April 2014
a b s t r a c t Calculated in (Kirillov, 2014) constants are applied for simulations of vibrational populations of Herzberg states in mixtures of O2 with CO2, CO, N2 gases for laboratory conditions. Results show very important role of electronic-vibrational processes in redistribution of electronic excitation energy among vibrational levels. It is shown that the interaction between O2(A0 3Du) and O2 causes effective production 03 O2(c1R u ,v = 0) observed in laboratory conditions. The inclusion of the interaction between O2(A Du) and CO2 molecules may explain high intensities of Herzberg II system observed in laboratory experiments with high CO2 concentrations and registered in the nightglow of Venusian atmosphere. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Lawrence et al. in the laboratory experiment [1] have produced oxygen atoms by pumping an oxygen–helium mixture through a microwave discharge. Downstream of the discharge, carbon dioxide CO2 was added to the stream of oxygen atoms. The principal emissions from the oxygen–helium–carbon dioxide afterglow were a progression of the Herzberg II bands from the lowest vibrational level (v = 0) of the c1Ru state of molecular oxygen:
X X O2 c1 u ; v ! O2 X3 g ; v 0 þ hv HII :
O2 ðA03 Du ; v Þ ! O2 ða1 Dg ; v 0 Þ þ hv Ch ð1Þ
Therefore Lawrence et al. [1] have hypothesized that the excitation mechanism of O2(c1R u ,v = 0) in the laboratory afterglow is due to the recombination of oxygen atoms in the presence of carbon dioxide molecules. Slanger [2] has set up a conventional fast flow system, in which also oxygen atoms were formed in a microwave discharge in a He– O2 mixture. When CO2 was added directly into a downstream cell in the experiment, the Herzberg II emission bands (1) appeared in the spectra, the same 0v0 progression that Lawrence et al. [1] reported. Moreover, Slanger [2] has also shown that without CO2 the Herzberg II bands starting from v = 0 become weaker, though are the still discernible. So, this observation was the first indication that the effect of CO2 was not only one, and that the He–O2 system alone would also give the emissions from lowest vibrational level of the c1R u state. ⇑ Fax: +7 (81555) 74339. E-mail address: [email protected] http://dx.doi.org/10.1016/j.cplett.2014.04.029 0009-2614/Ó 2014 Elsevier B.V. All rights reserved.
The two experiments [1,2] have demonstrated that it is possible to generate in laboratory relatively intense spectra of the Herzberg II 0v0 bands, the same system that appears in the Venus nightglow and was observed by Krasnopolsky et al. [3] using spectral instruments of the Venera 9 and Venera 10 spacecrafts. Slanger and Black [4] also made an inspection of the Venusian nightglow spectrum by Krasnopolsky et al. [3] and have identified the Chamberlain bands
ð2Þ
in the progression 0 v0 = 4–8. The same 0 v0 progression of the Chamberlain bands was observed in the laboratory in the He–O2 mixture by Slanger [2]. It is known that the O2 Herzberg states c1Ru, A0 3Du, A3R+u are formed by oxygen atom recombination [5], however, a problem arises as to why the oxygen nightglows in the atmospheres of Earth (mainly N2 and O2 gases) and Venus (mainly CO2) are so different. In the terrestrial nightglow there is a dominance of the Herzberg I system
Xþ X O2 A3 u ; v ! O2 X3 g ; v 0 þ hv HI
ð3Þ
with v = 3–8 and some contribution of the Chamberlain bands (2) [5,6]. In the Venusian nightglow only the Herzberg II system (1) is identified [3,5] and a very small contribution of the Chamberlain system (2) [4,5]. Recently, the quenching rate coefficients of the Herzberg states c1Ru(m = 0–16), A0 3Du(m = 0–11), A3R+u(m = 0–10) by molecular components CO2, CO, N2, O2 have been calculated by Kirillov [7]. The calculation has included intramolecular electron energy
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transfers with and without vibrational excitation of target molecules (EV- and E-processes) and intermolecular processes (EE-processes). Here we apply the quenching constants for our simulation of vibrational populations of the O2 Herzberg states for laboratory conditions in the mixture of electronically excited molecular oxygen with CO2, CO, N2 and O2 gases.
E (103 cm-1)
40
35
3
1
+ g,
1
u,
2
FðEÞ exp½ðE E0 Þ =a ;
ð5Þ
Here E is the energy of vibrational levels for the three states Y = A3Ru+, A0 3Du, c1Ru and a and E0 are fitting parameters. The experimental data on the vibrational populations have been analysed by using a least-squares fitting technique which showed that the best agreement between the experimental data and the results of the calculations occurs for a = 1500 cm1 and E0 = 40 000 cm1. The scheme of the vibrational levels of the c1Ru(v = 0–16), A0 3Du (v = 0–11), A3R+u(v = 0–10) states and the quantum yields of the Herzberg states produced in three-body collisions (4) and calculated from Eq. (5) are plotted in Figure 1. To calculate populations of the vibrational levels of the O2 Herzberg states in a mixture of O2⁄ with CO2, CO, N2 and O2 gases we need a system of steady-state balance equations for the vibrational level populations of the c1Ru, A0 3Du, A3Ru+ electronic states where collisions with all the molecular components are taken into account. Using the results of calculations for the rates of removal of the Herzberg states for spin-allowed transitions in collisions with all the four molecules, one can write the steady-state balance equations for the above electronic states of molecular oxygen in the following form:
Q cv þ
X
Yc
kv 0 v ½O2 NYv 0
0
Y¼A ;A;v 0
8
X Y¼X;a;b;A0 ;A;v
cY
9 =
kvv 0 ½O2 Ncv ; 0
ð6Þ
A'3
0
A3
u
3
A
+ u
10-3
5 þ u,
2
3
+ u
30
3
where Y = X R a Dg, b R c R A Du, A Pg. Theoretical studies by Wraight [8] and Smith [9] predict that the quantum yields to seven electronic states in the process (4) do not depend on a third body (N2 and O2 in terrestrial atmosphere and CO2 in the atmospheres of Venus and Mars). Here we use the branching ratios of the Herzberg c1Ru, A0 3Du, A3R+u states fc = 0.03, fA0 =0.18, fA = 0.06 applied by Kirillov [10] in his study of the Earth’s nightglow. Kirillov [10] has presented a model of kinetics of the electronically excited molecules O2(c1Ru,v P 0), O2(A0 3Du,v P 0), O2(A3Ru+,v P 0) at the heights of the terrestrial lower thermosphere and mesosphere, where the emission of the Herzberg I (3) and Chamberlain (2) bands occurs, which dominate the spectrum of the nighttime upper atmosphere at the wavelength interval of 250–500 nm [5,6]. In that analysis of the experimental results by Stegman and Murtagh [11] and Slanger et al. [12] for the vibrational populations of the O2(A3Ru+) and O2(A0 3Du) molecules derived from the Herzberg I and Chamberlain band emissions, Kirillov [10] estimated a distribution function F for the of Y,v states excited in the process (4)
7
0
10-1
ð4Þ 03
u
Quantum yields
1
7
0
It is known [5] that the major source of electronically excited O2 molecules in the conditions of laboratory experiments [1,2] and in the atmospheres of terrestrial planets at altitudes of the oxygen nightglow is the recombination of two oxygen atoms in a collision with a third body
g,
11
10
3
c1
3
11
7
2. Vibrational populations of the Herzberg states in the mixture of O2, N2 and CO
O 3 P þ O 3 P þ M ! O2 ðY; v Þ þ M;
16
A'3
u
c1
u
10-5
10-7 0
2
4 6 8 10 12 14 16 Vibrational levels
Figure 1. The scheme of vibrational levels of the c1Ru, A0 3Du, A3R+u states and the quantum yields of the Herzberg states in three-body collisions (dashed, solid, dashdotted lines, respectively).
0
Q Av þ
X AA0 X YA0 kv 0 v ½M NAv 0 þ kv 0 v ½O2 NYv 0 v0
Y¼c;A;v 0
( X A0 X X A0 a X A0 Y ¼ Avv 0 þ Avv 0 þ kvv 0 ½M þ v0
v0
Y¼X;A;v 0
X
A0 Y
Y¼X;a;b;c;A;v
)
0
kvv 0 ½O2 NAv 0
ð7Þ Q Av þ
X A0 A X YA 0 kv 0 v ½M N Av 0 þ kv 0 v ½O2 NYv 0 v0
Y¼c;A0 ;v 0
( X AY X AX ¼ Avv 0 þ kvv 0 ½M þ v0
Y¼X;A0 ;v 0
X Y¼X;a;b;c;A0 ;v 0
)
ð8Þ
AY
kvv 0 ½O2 NAv
where Q Yv and NYv are the quantum yield of the process (4) and the population of the vibrational level v of the Y state, AYZ vv 0 – the sponYZ taneous transition probability for the transition Y,v ? Z,v0 , kvv 0 and YZ kvv 0 are the rate coefficients for the collisions with M (CO2, CO, N2) and O2 molecules, respectively, with quenching of Y,v and production of Z,v0 . Einstein coefficients for spontaneous radiative tran3 0 1 3 + 0 03 03 0 sitions c1Ru,v ? X3R g ,v , A Du,v ? X Rg ,v , A Du,v ? a Dg,v , A Ru, v ? X3Rg,v0 are taken according to [13]. Rates of depopulation of 3 + 03 the c1R u , A Du, A Ru states and quantum yields in inelastic collisions with CO2, CO, N2, O2 molecules are taken according to [7]. In Figure 2 we present the calculated vibrational populations of the three Herzberg states at a pressure of 101 Pa in a mixture of N2 and O2 gases with the mixing ratio [N2]/[O2] = 4. The populations of all vibrational levels of the three Herzberg states are normalized to the population of O2(A0 3Du,v = 7). Altitude profiles of the main atmospheric constituents N2 and O2 at the heights of 80–100 km in the lower thermosphere and mesosphere, according to Rodrigo et al. [14], show a variation in the mixing ratio [N2]/[O2] between 3.8 and 4.5. Therefore the calculated populations in Figure 2 correspond to the altitude of 95 km in the Earth’s atmosphere where the intensity maxima of the Herzberg I (3) and Chamberlain (2) bands are observed [5] and the air pressure is about 101 Pa. The calculated vibrational populations of the c1Ru, A0 3Du, A3Ru+ states in the pressure interval of 101–103 Pa with the mixing ratio of [N2]/[O2] = 4 does not show any principle change in the relative
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103
Relative population
Relative population
101 100 10-1 10-2 10-3 0
102 101
2 1
2
100 1
1
2
4 6 8 10 12 14 16 Vibrational levels
2
10-1 0
2
4 6 8 Vibrational levels
10
Figure 2. The calculated relative vibrational populations of the c1Ru , A0 3Du, A3R+u states (dashed, solid, dash-dotted lines, respectively) at pressure 101 Pa for [N2]/ [O2] = 4.
Figure 4. The calculated relative vibrational populations of the c1Ru , A0 3Du, A3R+u states (dashed, solid, dash-dotted lines, respectively) at pressures 101 and 103 Pa (lines 1 and 2, respectively) for [N2]/[O2] = 300.
populations and significant increases in the c1Ru, v = 0 and A0 3Du,v = 0 populations as observed by Slanger [2] for laboratory conditions. Therefore, one of our aims is a simulation of vibrational populations for different values of the ratio [N2]/[O2] and pressures. The calculated relative vibrational populations of the Herzberg states at the pressure of 101 Pa in pure O2 with the ratio [N2]/ [O2] = 0 are presented in Figure 3. As in the case of [N2]/[O2] = 4 the calculation of the populations of the Herzberg states in the pressure interval of 101–103 Pa in pure O2 does not show any principle change in the relative populations. The comparison of results presented in Figures 2 and 3 shows that the increase of N2 content in the mixture enhances the populations of the lowest levels of the c1Ru and A0 3Du states. Lawrence et al. [1] made their laboratory experiment at a total pressure of 3103 Pa in a 0.3 percent oxygen–helium mixture. Slanger [2] followed the prescription of Lawrence et al. [1] using a microwave discharge at the same total pressure and pO2/pHe = 1.5103. To show the effect of the content of molecular oxygen in a mixture of N2 and O2 on vibrational populations of the Herzbeg states we have calculated vibrational populations of the three Herzberg states for the three cases: pN2/pO2 = 30, 300, 3000. The calculated vibrational populations of the c1Ru, A0 3Du, A3Ru+ states at pressures of 101 and 103 Pa in a mixture with a mixing ratio [N2]/[O2] = 300 are plotted in Figure 4. Here the effect of pressure on the populations of the lowest vibrational levels of the c1Ru and A0 3Du states is evident. The pressure increase causes the rise of the c1Ru, v = 0 and A0 3Du,v = 0 populations and of the ratio [c1Ru,v = 0]/[A0 3Du, v = 0]. This dependence of the c1Ru,v and A0 3Du,v populations on the O2 content and pressure can be explained by higher removal rates by molecular oxygen calculated by Kirillov [7]. Therefore O2 molecules stabilize the relative distributions depending on a vibrational level.
Results of the calculation of the quenching rate coefficients for the A0 3Du state in collisions with CO2, CO, N2, O2 molecules by Kirillov [7] demonstrated the importance of the EV-processes
Relative population
101 100 10-1 10-2 10-3 10-4 0
2
4 6 8 10 12 14 16 Vibrational levels
Figure 3. The calculated relative vibrational populations of the c1Ru, A0 3Du, A3Ru+ states (dashed, solid, dash-dotted lines, respectively) at pressure 101 Pa in pure O2.
X O2 A03 Du ; v þ O2 X 3 g ; v ¼ 0 X X ! O2 c1 u ; v 0 þ O2 X3 g ; v ¼ 1
ð9Þ
for the lowest vibrational levels of the state only in collisions with O2 molecules. The calculation of the removal rates for the process (9) showed the dominance of the transitions A0 3Du,v ? c1Ru,v0 = v and production of O2(X3R g ,v = 1) in spin-allowed collisions. The author of [7] has emphasized the preliminary character of the estimations of the rate coefficients for the EV-processes. The normalizing factors for the processes were taken from the comparison of the calculated quenching rate coefficients of the singlet molecular oxygen O2(b1R+g) by molecular components with experimental data made in [15]. Also Schmidt and co-authors [16–18] paid special attention to the radiationless deactivation of the two singlet states, b1Rg+ and a1Dg, of molecular oxygen by different quenchers in a gas and liquid phases. They have pointed out quantitatively on the dominance of the EV energy transfers in deactivation of the electronically excited states of O2. To show the important role of the processes (9) in kinetics of the two states, A0 3Du and c1Ru, we calculated the vibrational populations assuming the removal rates for the process (9) to be k9 = kEV and k9 = kEV/10, where kEV stands for the constants estimated by Kirillov [7] for the EV-process O2(A0 3Du)+O2(X3R g ). The calculated ratios of the concentrations [c1Ru,v = 0]/[A0 3Du, v = 0] for [N2]/[O2] = 30, 300, 3000; k9 = kEV, kEV/10 and at pressures of 102–103 Pa are plotted in Figure 5. The results presented in Figure 5 show that a decrease in the O2 content and in rates of the process (9) cause accumulation of the excitation energy on the lowest vibrational level of the A0 3Du state. These results can be applied for estimation of the efficiency of the EV-process (9) in quenching of the A0 3Du state. For example, Slanger [2] observed in his measurements of intensities (I) of the Herzberg II (1) and Chamberlain (2) bands emitted from the lowest vibrational levels v = 0 of the c1Ru and A0 3Du states that IHII (0–9) ICh(0–5) and IHII(0–10) ICh(0–6) (see Figure 2 in that paper). Taking into account the Einstein coefficients, AHII (0–9) = 0.044 c1, AHII(0–10) = 0.031 c1, ACh(0–5) = 0.045 c1 and ACh(0–6) = 0.072 c1 according to Bates [13], we can estimate that [c1Ru,v = 0]/[A0 3Du,v = 0] (0.045 + 0.072)/(0.044 + 0.031) = 1.6 in the experiment by Slanger [2]. On the other hand, our calculations show that the ratio [c1Ru,v = 0]/[A0 3Du,v = 0] = 2.4 and 0.24 for k9 = kEV and k9 = kEV/10, respectively, for the ratio pO2/pN2 = 1.5 103. The same ratio was used in the experiment by Slanger [2] but for a mixture of O2 and He. Therefore, to obtain agreement with
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101 Nc(0)/NA'(0) 100 10-1
1
2
1 2
3
3
10-2 10-3
N2,O2
10-4 101 Nc(0)/NA'(0) 100 10-1
1
2
1
3
2 3
10-2 10-3
CO,O2
-4
10
10-1
100 101 102 Pressure (Pa)
103
Figure 5. Calculated ratios of the concentrations [c1Ru ,v = 0]/[A0 3Du,v = 0] for [N2]/ [O2] = 30, 300, 3000 (lines 1,2,3, respectively); k9 = kEV, kEV/10 (solid and dashed lines, respectively) at pressures of 102–103 Pa. The same results for the mixture of CO and O2 are on the lower panel.
the results of Slanger [2], we have to reduce the coefficient kEV by the factor 0.67. However, Slanger [2] obtained his data for the He– O2 mixture, so we have to take into account also the rates of intramolecular electron energy transfer processes between the Herzberg states in inelastic collisions with He atoms. By the way, we have obtained [c1Ru,v = 0]/[A0 3Du,v = 0]104 in the case when k9 = 0 cm3 s1. In Figure 5 are also shown the calculated ratios of the concentrations [c1Ru,v = 0]/[A0 3Du,v = 0] for a mixture of CO and O2 with [CO]/[O2] = 30, 300, 3000; k9 = kEV, kEV/10 at pressures of 102– 103 Pa. We can see that the effect of the isoelectronic CO and N2 molecules on the populations of the lowest vibrational levels of these two states of molecular oxygen is similar. This similar behaviour of the kinetics of the Herzberg states in the N2–O2 and CO–O2 mixtures can be explained by the close values of the removal rates of the states calculated by Kirillov [7]. The N2 and CO molecules in the ground states X1R+g and X1R+ have close values of 2330 and 2143 cm1 for vibrational quanta [19], therefore similar contributions of the EV-processes to the quenching of the lowest vibrational levels of the c1Ru state for these two molecules follows from the constants calculated in [7]. The removal of the A0 3Du state is related to intramolecular processes and any difference in the removal rates by N2 and CO can be explained only by the normalizing factors applied by Kirillov [7].
3. Vibrational populations of the Herzberg states in the mixture of O2 and CO2 In the laboratory experiment by Lawrence et al. [1] oxygen atoms produced in oxygen–helium mixture through a microwave discharge were added downstream by carbon dioxide CO2 with a partial pressure pCO2 1.3103 Pa. A comparison of the Herzberg II bands (1), as produced in the laboratory by Lawrence et al. [1], and the Venus nightglow bands, as observed by Venera 9 and Venera 10 spacecrafts by Krasnopolsky et al. [3], has allowed to identify spectral emissions of the Venus nightglow as the 0 – v0 progression of the Herzberg II system. This was a very interesting
discovery since CO2 is the major constituent of the atmosphere of Venus. Also Slanger [2] has shown clearly that the addition of CO2 to the He–O2 flowing afterglow enhances emission from the c1R u (v = 0) state, and this fact explains why the Herzberg II emissions (1) are so intense in the Venus nightglow. The measurements by Slanger [2] were made both for 16O2 and for 18O2 molecules. Recently, Gerard et al. [20] and Migliorini et al. [21] have reported the detection of eight bands 0 – v0 (v0 = 6–13) of the Herzberg II system (1) and three bands 0–v0 (v0 = 6–8) of the Chamberlain system (2) in the visible spectral range, observed by the VIRTIS spectrometer on board the Venus Express spacecraft. The Herzberg II and Chamberlain bands are too weak to be measured at nadir from the spacecraft. Therefore, Gerard et al. [20] and Migliorini et al. [21] used only the limb intensities to quantify the altitude brightness of these two emissions. They estimated that the Herzberg II and Chamberlain emission peaks are located at the heights of about 96 and 100 km in the Venusian atmosphere, respectively. Also Gerard et al. [20] and Migliorini et al. [21] have estimated the mean total intensities of these two band systems to be IHII = 149 kR and ICh = 53 kR, as observed at the limb of the Venusian atmosphere (1 Rayleigh = 106 photon cm2 s1). Taking into account the Einstein coefficients, AHII(0v0 ) = 0.29 c1 and ACh(0v0 ) = 0.49 c1 according to Bates [13], we can estimate a mean value of the ratio [c1Ru,v = 0]/[A0 3Du,v = 0] = (149/53)(0.49/ 0.29) = 4.8 in the atmosphere of Venus. This value is three time higher than our estimate for the value of the ratio [c1Ru,v = 0]/ [A0 3Du,v = 0] for conditions in the microwave discharge in the He–O2 mixture studied by Slanger [2]. The pressure in the atmosphere of Venus at the altitudes 96– 100 km is a few Pa. Our calculations of the ratio [c1Ru,v = 0]/ [A0 3Du,v = 0] for the mixtures of N2–O2 and CO–O2 at pressures of 102–103 Pa show the same character of the dependence on the rates of the process (9). The calculated in [7] quenching rate coefficients of the A0 3Du state by the CO2, CO, N2 molecules have similar behaviour in the dependence on vibrational level. The removal rates by all the three molecules are related to intramolecular processes in an electronically excited oxygen molecule. Therefore the consideration of the spin-allowed processes suggested by Kirillov [7] does not change principally the ratio [c1Ru,v = 0]/[A0 3Du,v = 0] for the mixture of the CO2 and O2 gases in comparison with the N2– O2 and CO–O2 mixtures and it is necessary to include a new mechanism in the consideration responsible for the increase of the ratio in the presence of CO2 molecules. To improve an agreement with the experimental data of [1,2] we included the spin-forbidden EV-interaction
X O2 A03 Du ; v þ CO2 ð0; 0; 0Þ ! O2 c1 u ; v 0 ¼ v þ CO2 ð1; 0; 0Þ ð10Þ where the symmetric stretch mode of the carbon dioxide molecule is excited. It is worth to note that Schmidt and co-authors [16–18] have shown that experimental data for the O2(b1Rg+) and O2(a1Dg) removal by different quenchers can be fitted by similar analytical expressions by including normalizing factors CR and CD, respectively. They considered the EV-processes O2(b1R+g ? a1Dg) and O2(a1Dg ? X3R g ) with vibrational excitation of different target molecules. The normalizing factors CR and CD are dependent on the electronic factors fSS (singlet–singlet) and fST (singlet–triplet) of transitions in an electronically excited O2 molecule. Schmidt and co-authors [16–18] in their quantitative analysis of liquidphase and gas-phase constants for the O2(b1R+g) and O2(a1Dg) molecules have obtained the ratio of CR/CD 104 for spin-allowed and spin-forbidden processes. Also Kirillov [22] divided the normalizing amplitude factor estimated for spin-allowed processes by the value of 50 to obtain the magnitude of an experimental rate constant for
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the vibrational level v = 0 of the singlet state a0 1R u of N2 in spin-forbidden processes of energy transfer to triplet states. Therefore we calculated the removal rates for the spin-forbidden process (10) with the normalizing parameters multiplied by the factors f1 = 101, f2 = 102, f3 = 103, f4 = 104 in comparison with the spin-allowed EV-process considered in [7]. The calculated quenching rate coefficients for the EV-process (10) using the values f1–f4 are compared with the total removal constants of the A0 3Du state by a CO2 molecule presented by Kirillov [7] in Figure 6. It should be noted that the calculations in [7] showed the dominance of the transitions A0 3Du(v = 0) ? A3Ru+(v0 = 0) and of the inverse processes in inelastic collisions with the N2, CO, CO2 molecules. Therefore, there is some equilibrium between the lowest vibrational levels of these two states in laboratory conditions and the removal of the A0 3Du(v = 0) level is related mainly with the transition to the triplet ground state X3R g in spin-allowed processes. For example, the intramolecular transfer to the X3R g state without vibrational excitation of a target-molecule CO2 has very small rate constant of 1017 cm3 s1 [7]. The concentration of carbon dioxide at the altitudes of 95– 100 km in the Venusian atmosphere are higher by about 4000 times than the concentration of molecular oxygen, therefore in Figure 7 we show the calculated ratios of the concentrations [c1Ru,v = 0]/[A0 3Du,v = 0] at pressures 102–103 Pa for a mixture of CO2 and O2 with [CO2]/[O2] = 4000, k9 = kEV and without and with the inclusion of the EV-processes (10) for the four values of decreasing factors f1–f4. It can be seen from the figure that the increase of the factors causes the rise of the O2(c1Ru,v = 0) population in comparison with the O2(A0 3Du,v = 0) population. For example, the application of the factor f3 = 103 leads to the increase of the ratio [c1Ru,v = 0]/[A0 3Du,v = 0] of 2.8 times. To show the effect of both the (9) and (10) EV-processes on the calculated O2(c1Ru,v = 0) and O2(A0 3Du,v = 0) populations we plotted the ratios of [c1Ru,v = 0]/[A0 3Du,v = 0] at pressures of 102–103 Pa for the mixture of CO2 and O2 with [CO2]/[O2] = 300, k9 = kEV and k9 = kEV/10 for the process (9), without and with the inclusion of the EV-process (10) for the four values of decreasing factors f1–f4 in Figure 8. The calculations show that the decrease in the rates of both processes (9) and (10) results in lower popula03 tion of O2(c1R u ,v = 0) in comparison with the O2(A Du,v = 0) population in our simulation. However, experimental results by Slanger [2] obtained for laboratory conditions and intensities of emissions registered by the VIRTIS spectrometer on board the Venus Express spacecraft in [20,21] are not sufficient to estimate the rates of the processes (9) and (10). Therefore, more detailed measurements of the intensity ratios of the Herzberg II (1) and Chamberlain (2) emissions in different mixtures of molecular oxygen with N2, CO, CO2, etc. gases
10-10 k, cm3s-1
10-12 1 2
10-14
3 4
10-16 0
2
A'3
4 6 8 10 Vibrational levels
u
12
Figure 6. The calculated quenching rate coefficients for the EV-processes (10) with the values f1–f4 (dashed lines 1–4, respectively) are compared with total removal constants of the A0 3Du state by CO2 molecule presented by Kirillov [7] (solid line).
102 Nc(0)/NA'(0)
1 2
101
3 4
100 10-1 10-2 -3
10
k9=kEV 10-1
103
100 101 102 Pressure (Pa)
Figure 7. The calculated ratios of the concentrations [c1Ru,v = 0]/[A0 3Du,v = 0] at pressures of 102–103 Pa for [CO2]/[O2] = 4000, k9 = kEV (solid line) and with inclusion of the EV-processes (10) for factors f1–f4. (dashed lines 1–4, respectively).
102 Nc(0)/NA'(0)
1
101
2 3
100 10-1
k9=kEV
10-2 101 Nc(0)/NA'(0)
2
100
3 4
10-1 10-2 10-3
k9=kEV/10 10-1
100 101 102 Pressure (Pa)
103
Figure 8. The calculated ratios of the concentrations [c1Ru ,v = 0]/[A0 3Du,v = 0] at pressures of 102–103 Pa for [CO2]/[O2] = 300, k9 = kEV or k9 = kEV/10 (solid lines) and with inclusion of the EV-processes (10) for factors f1–f4. (dashed lines 1–4, respectively).
and at different pressures should be used for the estimation of the removal rates of the EV-processes of the Herzberg states. 4. Conclusions The calculated in [7] quenching rate constants of the c1Ru, A0 3Du, A3R+u states of O2 by other molecules are applied for simulation of the vibrational populations of the Herzberg states in a mixture of molecular oxygen with CO2, CO, N2 gases for laboratory conditions. The main results of this paper are as follows. 1. The calculations for a mixture of N2 and O2 (CO and O2) gases show that the effect of the pressure (p = 102–103 Pa) on the populations of the lowest vibrational levels of the c1Ru and A0 3Du states is apparent in the cases of a small content of molecular oxygen in the mixture. The pressure increase causes a rise of the c1Ru,v = 0 and A0 3Du,v = 0 populations and of the ratio [c1Ru, v = 0]/[A0 3Du,v = 0]. We also point out the important role of the EV-process (9) in kinetics of two states, A0 3Du and c1Ru. It can be seen from the calculation that mainly the spin-allowed EV-process 1 0 O2(A0 3Du,v) + O2(X3R g ) with the production of O2(c Ru ,v = v) + O2 3 (X Rg ,v = 1) are responsible for effective emission of the Herzberg II bands (1) clearly observed by Slanger in his laboratory experiment in a He–O2 mixture [2].
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2. The same calculations for a mixture of CO2 and O2 gases show that the inclusion of the spin-forbidden EV-interaction of O2(A0 3Du,v) + CO2 molecules (10) in the simulation can explain the high intensities of the Herzberg II band system (1) observed in laboratory experiments [1,2] with high CO2 concentrations. The spin-forbidden process (10) could be a possible important mechanism for production of high intensities of the Herzberg II bands (1) registered by spectrometers in the nightglow of the Venus atmosphere from Venera 9 and Venera 10 [3] and Venus-Express [19,20] spacecraft. Acknowledgements This research is supported by the Programs of Presidium of RAS No 4, 22. Author thanks Dr. Yu. N. Kulikov for his help in the correct writing of the Letter. References [1] G.M. Lawrence, C.A. Barth, V. Argabright, Science 195 (1977) 573.
[2] T.G. Slanger, J. Chem. Phys. 69 (1978) 4779. [3] V.A. Krasnopolsky, A.A. Krysko, Y.N. Pogashev, Y.A. Parshev, Cosmic Res. 14 (1977) 687. [4] T.G. Slanger, G. Black, Geophys. Res. Lett. 5 (1978) 947. [5] T.G. Slanger, R.A. Copeland, Chem. Rev. 103 (2003) 4731. [6] A.L. Broadfoot, K.R. Kendall, J. Geophys. Res. 73 (1968) 426. [7] A.S. Kirillov, Chem. Phys. Lett. 592 (2014) 103. [8] P.C. Wraight, Planet. Space Sci. 30 (1982) 251. [9] J.W.M. Smith, Int. J. Chem. Kinet. 16 (1984) 423. [10] A.S. Kirillov, Geomag. Aeron. 52 (2012) 242. [11] J. Stegman, D.P. Murtagh, Planet. Space Sci. 36 (1988) 927. [12] T.G. Slanger, P.C. Cosby, D.L. Huestis, A.M. Widhalm, Ann. Geophys. 22 (2004) 3305. [13] D.R. Bates, Planet. Space Sci. 37 (1989) 881. [14] R. Rodrigo, J.J. Lopez-Moreno, M. Lopez-Puertas, F. Moreno, A. Molina, Planet. Space Sci. 34 (1986) 723. [15] A.S. Kirillov, Chem. Phys. 410 (2013) 103. [16] R. Schmidt, Ber. Bunsenges. Phys. Chem. 96 (1992) 794. [17] R. Schmidt, M. Bodesheim, J. Phys. Chem. 102 (1998) 4769. [18] C. Schweitzer, R. Schmidt, Chem. Rev. 103 (2003) 1685. [19] K.P. Huber, G. Herzberg, Molecular spectra and molecular structure. IV. Constants of diatomic molecules, VNR Company, New York, 1979. [20] J.-C. Gerard, L. Soret, A. Migliorini, G. Piccioni, Icarus 223 (2013) 602. [21] A. Migliorini et al., Icarus 223 (2013) 609. [22] A.S. Kirillov, J. Quant. Spect. Rad. Trans. 112 (2011) 2164.
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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
Calculated vibrational populations of O2 Herzberg states in the mixture of CO2, CO, N2, O2 gases A.S. Kirillov ⇑ Polar Geophysical Institute of Russian Academy of Sciences, Academytown, 26A, Apatity, Murmansk Region 184209, Russia
a r t i c l e
i n f o
Article history: Received 30 January 2014 In final form 17 April 2014 Available online 24 April 2014
a b s t r a c t Calculated in (Kirillov, 2014) constants are applied for simulations of vibrational populations of Herzberg states in mixtures of O2 with CO2, CO, N2 gases for laboratory conditions. Results show very important role of electronic-vibrational processes in redistribution of electronic excitation energy among vibrational levels. It is shown that the interaction between O2(A0 3Du) and O2 causes effective production 03 O2(c1R u ,v = 0) observed in laboratory conditions. The inclusion of the interaction between O2(A Du) and CO2 molecules may explain high intensities of Herzberg II system observed in laboratory experiments with high CO2 concentrations and registered in the nightglow of Venusian atmosphere. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction Lawrence et al. in the laboratory experiment [1] have produced oxygen atoms by pumping an oxygen–helium mixture through a microwave discharge. Downstream of the discharge, carbon dioxide CO2 was added to the stream of oxygen atoms. The principal emissions from the oxygen–helium–carbon dioxide afterglow were a progression of the Herzberg II bands from the lowest vibrational level (v = 0) of the c1Ru state of molecular oxygen:
X X O2 c1 u ; v ! O2 X3 g ; v 0 þ hv HII :
O2 ðA03 Du ; v Þ ! O2 ða1 Dg ; v 0 Þ þ hv Ch ð1Þ
Therefore Lawrence et al. [1] have hypothesized that the excitation mechanism of O2(c1R u ,v = 0) in the laboratory afterglow is due to the recombination of oxygen atoms in the presence of carbon dioxide molecules. Slanger [2] has set up a conventional fast flow system, in which also oxygen atoms were formed in a microwave discharge in a He– O2 mixture. When CO2 was added directly into a downstream cell in the experiment, the Herzberg II emission bands (1) appeared in the spectra, the same 0v0 progression that Lawrence et al. [1] reported. Moreover, Slanger [2] has also shown that without CO2 the Herzberg II bands starting from v = 0 become weaker, though are the still discernible. So, this observation was the first indication that the effect of CO2 was not only one, and that the He–O2 system alone would also give the emissions from lowest vibrational level of the c1R u state. ⇑ Fax: +7 (81555) 74339. E-mail address: [email protected] http://dx.doi.org/10.1016/j.cplett.2014.04.029 0009-2614/Ó 2014 Elsevier B.V. All rights reserved.
The two experiments [1,2] have demonstrated that it is possible to generate in laboratory relatively intense spectra of the Herzberg II 0v0 bands, the same system that appears in the Venus nightglow and was observed by Krasnopolsky et al. [3] using spectral instruments of the Venera 9 and Venera 10 spacecrafts. Slanger and Black [4] also made an inspection of the Venusian nightglow spectrum by Krasnopolsky et al. [3] and have identified the Chamberlain bands
ð2Þ
in the progression 0 v0 = 4–8. The same 0 v0 progression of the Chamberlain bands was observed in the laboratory in the He–O2 mixture by Slanger [2]. It is known that the O2 Herzberg states c1Ru, A0 3Du, A3R+u are formed by oxygen atom recombination [5], however, a problem arises as to why the oxygen nightglows in the atmospheres of Earth (mainly N2 and O2 gases) and Venus (mainly CO2) are so different. In the terrestrial nightglow there is a dominance of the Herzberg I system
Xþ X O2 A3 u ; v ! O2 X3 g ; v 0 þ hv HI
ð3Þ
with v = 3–8 and some contribution of the Chamberlain bands (2) [5,6]. In the Venusian nightglow only the Herzberg II system (1) is identified [3,5] and a very small contribution of the Chamberlain system (2) [4,5]. Recently, the quenching rate coefficients of the Herzberg states c1Ru(m = 0–16), A0 3Du(m = 0–11), A3R+u(m = 0–10) by molecular components CO2, CO, N2, O2 have been calculated by Kirillov [7]. The calculation has included intramolecular electron energy
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transfers with and without vibrational excitation of target molecules (EV- and E-processes) and intermolecular processes (EE-processes). Here we apply the quenching constants for our simulation of vibrational populations of the O2 Herzberg states for laboratory conditions in the mixture of electronically excited molecular oxygen with CO2, CO, N2 and O2 gases.
E (103 cm-1)
40
35
3
1
+ g,
1
u,
2
FðEÞ exp½ðE E0 Þ =a ;
ð5Þ
Here E is the energy of vibrational levels for the three states Y = A3Ru+, A0 3Du, c1Ru and a and E0 are fitting parameters. The experimental data on the vibrational populations have been analysed by using a least-squares fitting technique which showed that the best agreement between the experimental data and the results of the calculations occurs for a = 1500 cm1 and E0 = 40 000 cm1. The scheme of the vibrational levels of the c1Ru(v = 0–16), A0 3Du (v = 0–11), A3R+u(v = 0–10) states and the quantum yields of the Herzberg states produced in three-body collisions (4) and calculated from Eq. (5) are plotted in Figure 1. To calculate populations of the vibrational levels of the O2 Herzberg states in a mixture of O2⁄ with CO2, CO, N2 and O2 gases we need a system of steady-state balance equations for the vibrational level populations of the c1Ru, A0 3Du, A3Ru+ electronic states where collisions with all the molecular components are taken into account. Using the results of calculations for the rates of removal of the Herzberg states for spin-allowed transitions in collisions with all the four molecules, one can write the steady-state balance equations for the above electronic states of molecular oxygen in the following form:
Q cv þ
X
Yc
kv 0 v ½O2 NYv 0
0
Y¼A ;A;v 0
8
X Y¼X;a;b;A0 ;A;v
cY
9 =
kvv 0 ½O2 Ncv ; 0
ð6Þ
A'3
0
A3
u
3
A
+ u
10-3
5 þ u,
2
3
+ u
30
3
where Y = X R a Dg, b R c R A Du, A Pg. Theoretical studies by Wraight [8] and Smith [9] predict that the quantum yields to seven electronic states in the process (4) do not depend on a third body (N2 and O2 in terrestrial atmosphere and CO2 in the atmospheres of Venus and Mars). Here we use the branching ratios of the Herzberg c1Ru, A0 3Du, A3R+u states fc = 0.03, fA0 =0.18, fA = 0.06 applied by Kirillov [10] in his study of the Earth’s nightglow. Kirillov [10] has presented a model of kinetics of the electronically excited molecules O2(c1Ru,v P 0), O2(A0 3Du,v P 0), O2(A3Ru+,v P 0) at the heights of the terrestrial lower thermosphere and mesosphere, where the emission of the Herzberg I (3) and Chamberlain (2) bands occurs, which dominate the spectrum of the nighttime upper atmosphere at the wavelength interval of 250–500 nm [5,6]. In that analysis of the experimental results by Stegman and Murtagh [11] and Slanger et al. [12] for the vibrational populations of the O2(A3Ru+) and O2(A0 3Du) molecules derived from the Herzberg I and Chamberlain band emissions, Kirillov [10] estimated a distribution function F for the of Y,v states excited in the process (4)
7
0
10-1
ð4Þ 03
u
Quantum yields
1
7
0
It is known [5] that the major source of electronically excited O2 molecules in the conditions of laboratory experiments [1,2] and in the atmospheres of terrestrial planets at altitudes of the oxygen nightglow is the recombination of two oxygen atoms in a collision with a third body
g,
11
10
3
c1
3
11
7
2. Vibrational populations of the Herzberg states in the mixture of O2, N2 and CO
O 3 P þ O 3 P þ M ! O2 ðY; v Þ þ M;
16
A'3
u
c1
u
10-5
10-7 0
2
4 6 8 10 12 14 16 Vibrational levels
Figure 1. The scheme of vibrational levels of the c1Ru, A0 3Du, A3R+u states and the quantum yields of the Herzberg states in three-body collisions (dashed, solid, dashdotted lines, respectively).
0
Q Av þ
X AA0 X YA0 kv 0 v ½M NAv 0 þ kv 0 v ½O2 NYv 0 v0
Y¼c;A;v 0
( X A0 X X A0 a X A0 Y ¼ Avv 0 þ Avv 0 þ kvv 0 ½M þ v0
v0
Y¼X;A;v 0
X
A0 Y
Y¼X;a;b;c;A;v
)
0
kvv 0 ½O2 NAv 0
ð7Þ Q Av þ
X A0 A X YA 0 kv 0 v ½M N Av 0 þ kv 0 v ½O2 NYv 0 v0
Y¼c;A0 ;v 0
( X AY X AX ¼ Avv 0 þ kvv 0 ½M þ v0
Y¼X;A0 ;v 0
X Y¼X;a;b;c;A0 ;v 0
)
ð8Þ
AY
kvv 0 ½O2 NAv
where Q Yv and NYv are the quantum yield of the process (4) and the population of the vibrational level v of the Y state, AYZ vv 0 – the sponYZ taneous transition probability for the transition Y,v ? Z,v0 , kvv 0 and YZ kvv 0 are the rate coefficients for the collisions with M (CO2, CO, N2) and O2 molecules, respectively, with quenching of Y,v and production of Z,v0 . Einstein coefficients for spontaneous radiative tran3 0 1 3 + 0 03 03 0 sitions c1Ru,v ? X3R g ,v , A Du,v ? X Rg ,v , A Du,v ? a Dg,v , A Ru, v ? X3Rg,v0 are taken according to [13]. Rates of depopulation of 3 + 03 the c1R u , A Du, A Ru states and quantum yields in inelastic collisions with CO2, CO, N2, O2 molecules are taken according to [7]. In Figure 2 we present the calculated vibrational populations of the three Herzberg states at a pressure of 101 Pa in a mixture of N2 and O2 gases with the mixing ratio [N2]/[O2] = 4. The populations of all vibrational levels of the three Herzberg states are normalized to the population of O2(A0 3Du,v = 7). Altitude profiles of the main atmospheric constituents N2 and O2 at the heights of 80–100 km in the lower thermosphere and mesosphere, according to Rodrigo et al. [14], show a variation in the mixing ratio [N2]/[O2] between 3.8 and 4.5. Therefore the calculated populations in Figure 2 correspond to the altitude of 95 km in the Earth’s atmosphere where the intensity maxima of the Herzberg I (3) and Chamberlain (2) bands are observed [5] and the air pressure is about 101 Pa. The calculated vibrational populations of the c1Ru, A0 3Du, A3Ru+ states in the pressure interval of 101–103 Pa with the mixing ratio of [N2]/[O2] = 4 does not show any principle change in the relative
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103
Relative population
Relative population
101 100 10-1 10-2 10-3 0
102 101
2 1
2
100 1
1
2
4 6 8 10 12 14 16 Vibrational levels
2
10-1 0
2
4 6 8 Vibrational levels
10
Figure 2. The calculated relative vibrational populations of the c1Ru , A0 3Du, A3R+u states (dashed, solid, dash-dotted lines, respectively) at pressure 101 Pa for [N2]/ [O2] = 4.
Figure 4. The calculated relative vibrational populations of the c1Ru , A0 3Du, A3R+u states (dashed, solid, dash-dotted lines, respectively) at pressures 101 and 103 Pa (lines 1 and 2, respectively) for [N2]/[O2] = 300.
populations and significant increases in the c1Ru, v = 0 and A0 3Du,v = 0 populations as observed by Slanger [2] for laboratory conditions. Therefore, one of our aims is a simulation of vibrational populations for different values of the ratio [N2]/[O2] and pressures. The calculated relative vibrational populations of the Herzberg states at the pressure of 101 Pa in pure O2 with the ratio [N2]/ [O2] = 0 are presented in Figure 3. As in the case of [N2]/[O2] = 4 the calculation of the populations of the Herzberg states in the pressure interval of 101–103 Pa in pure O2 does not show any principle change in the relative populations. The comparison of results presented in Figures 2 and 3 shows that the increase of N2 content in the mixture enhances the populations of the lowest levels of the c1Ru and A0 3Du states. Lawrence et al. [1] made their laboratory experiment at a total pressure of 3103 Pa in a 0.3 percent oxygen–helium mixture. Slanger [2] followed the prescription of Lawrence et al. [1] using a microwave discharge at the same total pressure and pO2/pHe = 1.5103. To show the effect of the content of molecular oxygen in a mixture of N2 and O2 on vibrational populations of the Herzbeg states we have calculated vibrational populations of the three Herzberg states for the three cases: pN2/pO2 = 30, 300, 3000. The calculated vibrational populations of the c1Ru, A0 3Du, A3Ru+ states at pressures of 101 and 103 Pa in a mixture with a mixing ratio [N2]/[O2] = 300 are plotted in Figure 4. Here the effect of pressure on the populations of the lowest vibrational levels of the c1Ru and A0 3Du states is evident. The pressure increase causes the rise of the c1Ru, v = 0 and A0 3Du,v = 0 populations and of the ratio [c1Ru,v = 0]/[A0 3Du, v = 0]. This dependence of the c1Ru,v and A0 3Du,v populations on the O2 content and pressure can be explained by higher removal rates by molecular oxygen calculated by Kirillov [7]. Therefore O2 molecules stabilize the relative distributions depending on a vibrational level.
Results of the calculation of the quenching rate coefficients for the A0 3Du state in collisions with CO2, CO, N2, O2 molecules by Kirillov [7] demonstrated the importance of the EV-processes
Relative population
101 100 10-1 10-2 10-3 10-4 0
2
4 6 8 10 12 14 16 Vibrational levels
Figure 3. The calculated relative vibrational populations of the c1Ru, A0 3Du, A3Ru+ states (dashed, solid, dash-dotted lines, respectively) at pressure 101 Pa in pure O2.
X O2 A03 Du ; v þ O2 X 3 g ; v ¼ 0 X X ! O2 c1 u ; v 0 þ O2 X3 g ; v ¼ 1
ð9Þ
for the lowest vibrational levels of the state only in collisions with O2 molecules. The calculation of the removal rates for the process (9) showed the dominance of the transitions A0 3Du,v ? c1Ru,v0 = v and production of O2(X3R g ,v = 1) in spin-allowed collisions. The author of [7] has emphasized the preliminary character of the estimations of the rate coefficients for the EV-processes. The normalizing factors for the processes were taken from the comparison of the calculated quenching rate coefficients of the singlet molecular oxygen O2(b1R+g) by molecular components with experimental data made in [15]. Also Schmidt and co-authors [16–18] paid special attention to the radiationless deactivation of the two singlet states, b1Rg+ and a1Dg, of molecular oxygen by different quenchers in a gas and liquid phases. They have pointed out quantitatively on the dominance of the EV energy transfers in deactivation of the electronically excited states of O2. To show the important role of the processes (9) in kinetics of the two states, A0 3Du and c1Ru, we calculated the vibrational populations assuming the removal rates for the process (9) to be k9 = kEV and k9 = kEV/10, where kEV stands for the constants estimated by Kirillov [7] for the EV-process O2(A0 3Du)+O2(X3R g ). The calculated ratios of the concentrations [c1Ru,v = 0]/[A0 3Du, v = 0] for [N2]/[O2] = 30, 300, 3000; k9 = kEV, kEV/10 and at pressures of 102–103 Pa are plotted in Figure 5. The results presented in Figure 5 show that a decrease in the O2 content and in rates of the process (9) cause accumulation of the excitation energy on the lowest vibrational level of the A0 3Du state. These results can be applied for estimation of the efficiency of the EV-process (9) in quenching of the A0 3Du state. For example, Slanger [2] observed in his measurements of intensities (I) of the Herzberg II (1) and Chamberlain (2) bands emitted from the lowest vibrational levels v = 0 of the c1Ru and A0 3Du states that IHII (0–9) ICh(0–5) and IHII(0–10) ICh(0–6) (see Figure 2 in that paper). Taking into account the Einstein coefficients, AHII (0–9) = 0.044 c1, AHII(0–10) = 0.031 c1, ACh(0–5) = 0.045 c1 and ACh(0–6) = 0.072 c1 according to Bates [13], we can estimate that [c1Ru,v = 0]/[A0 3Du,v = 0] (0.045 + 0.072)/(0.044 + 0.031) = 1.6 in the experiment by Slanger [2]. On the other hand, our calculations show that the ratio [c1Ru,v = 0]/[A0 3Du,v = 0] = 2.4 and 0.24 for k9 = kEV and k9 = kEV/10, respectively, for the ratio pO2/pN2 = 1.5 103. The same ratio was used in the experiment by Slanger [2] but for a mixture of O2 and He. Therefore, to obtain agreement with
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101 Nc(0)/NA'(0) 100 10-1
1
2
1 2
3
3
10-2 10-3
N2,O2
10-4 101 Nc(0)/NA'(0) 100 10-1
1
2
1
3
2 3
10-2 10-3
CO,O2
-4
10
10-1
100 101 102 Pressure (Pa)
103
Figure 5. Calculated ratios of the concentrations [c1Ru ,v = 0]/[A0 3Du,v = 0] for [N2]/ [O2] = 30, 300, 3000 (lines 1,2,3, respectively); k9 = kEV, kEV/10 (solid and dashed lines, respectively) at pressures of 102–103 Pa. The same results for the mixture of CO and O2 are on the lower panel.
the results of Slanger [2], we have to reduce the coefficient kEV by the factor 0.67. However, Slanger [2] obtained his data for the He– O2 mixture, so we have to take into account also the rates of intramolecular electron energy transfer processes between the Herzberg states in inelastic collisions with He atoms. By the way, we have obtained [c1Ru,v = 0]/[A0 3Du,v = 0]104 in the case when k9 = 0 cm3 s1. In Figure 5 are also shown the calculated ratios of the concentrations [c1Ru,v = 0]/[A0 3Du,v = 0] for a mixture of CO and O2 with [CO]/[O2] = 30, 300, 3000; k9 = kEV, kEV/10 at pressures of 102– 103 Pa. We can see that the effect of the isoelectronic CO and N2 molecules on the populations of the lowest vibrational levels of these two states of molecular oxygen is similar. This similar behaviour of the kinetics of the Herzberg states in the N2–O2 and CO–O2 mixtures can be explained by the close values of the removal rates of the states calculated by Kirillov [7]. The N2 and CO molecules in the ground states X1R+g and X1R+ have close values of 2330 and 2143 cm1 for vibrational quanta [19], therefore similar contributions of the EV-processes to the quenching of the lowest vibrational levels of the c1Ru state for these two molecules follows from the constants calculated in [7]. The removal of the A0 3Du state is related to intramolecular processes and any difference in the removal rates by N2 and CO can be explained only by the normalizing factors applied by Kirillov [7].
3. Vibrational populations of the Herzberg states in the mixture of O2 and CO2 In the laboratory experiment by Lawrence et al. [1] oxygen atoms produced in oxygen–helium mixture through a microwave discharge were added downstream by carbon dioxide CO2 with a partial pressure pCO2 1.3103 Pa. A comparison of the Herzberg II bands (1), as produced in the laboratory by Lawrence et al. [1], and the Venus nightglow bands, as observed by Venera 9 and Venera 10 spacecrafts by Krasnopolsky et al. [3], has allowed to identify spectral emissions of the Venus nightglow as the 0 – v0 progression of the Herzberg II system. This was a very interesting
discovery since CO2 is the major constituent of the atmosphere of Venus. Also Slanger [2] has shown clearly that the addition of CO2 to the He–O2 flowing afterglow enhances emission from the c1R u (v = 0) state, and this fact explains why the Herzberg II emissions (1) are so intense in the Venus nightglow. The measurements by Slanger [2] were made both for 16O2 and for 18O2 molecules. Recently, Gerard et al. [20] and Migliorini et al. [21] have reported the detection of eight bands 0 – v0 (v0 = 6–13) of the Herzberg II system (1) and three bands 0–v0 (v0 = 6–8) of the Chamberlain system (2) in the visible spectral range, observed by the VIRTIS spectrometer on board the Venus Express spacecraft. The Herzberg II and Chamberlain bands are too weak to be measured at nadir from the spacecraft. Therefore, Gerard et al. [20] and Migliorini et al. [21] used only the limb intensities to quantify the altitude brightness of these two emissions. They estimated that the Herzberg II and Chamberlain emission peaks are located at the heights of about 96 and 100 km in the Venusian atmosphere, respectively. Also Gerard et al. [20] and Migliorini et al. [21] have estimated the mean total intensities of these two band systems to be IHII = 149 kR and ICh = 53 kR, as observed at the limb of the Venusian atmosphere (1 Rayleigh = 106 photon cm2 s1). Taking into account the Einstein coefficients, AHII(0v0 ) = 0.29 c1 and ACh(0v0 ) = 0.49 c1 according to Bates [13], we can estimate a mean value of the ratio [c1Ru,v = 0]/[A0 3Du,v = 0] = (149/53)(0.49/ 0.29) = 4.8 in the atmosphere of Venus. This value is three time higher than our estimate for the value of the ratio [c1Ru,v = 0]/ [A0 3Du,v = 0] for conditions in the microwave discharge in the He–O2 mixture studied by Slanger [2]. The pressure in the atmosphere of Venus at the altitudes 96– 100 km is a few Pa. Our calculations of the ratio [c1Ru,v = 0]/ [A0 3Du,v = 0] for the mixtures of N2–O2 and CO–O2 at pressures of 102–103 Pa show the same character of the dependence on the rates of the process (9). The calculated in [7] quenching rate coefficients of the A0 3Du state by the CO2, CO, N2 molecules have similar behaviour in the dependence on vibrational level. The removal rates by all the three molecules are related to intramolecular processes in an electronically excited oxygen molecule. Therefore the consideration of the spin-allowed processes suggested by Kirillov [7] does not change principally the ratio [c1Ru,v = 0]/[A0 3Du,v = 0] for the mixture of the CO2 and O2 gases in comparison with the N2– O2 and CO–O2 mixtures and it is necessary to include a new mechanism in the consideration responsible for the increase of the ratio in the presence of CO2 molecules. To improve an agreement with the experimental data of [1,2] we included the spin-forbidden EV-interaction
X O2 A03 Du ; v þ CO2 ð0; 0; 0Þ ! O2 c1 u ; v 0 ¼ v þ CO2 ð1; 0; 0Þ ð10Þ where the symmetric stretch mode of the carbon dioxide molecule is excited. It is worth to note that Schmidt and co-authors [16–18] have shown that experimental data for the O2(b1Rg+) and O2(a1Dg) removal by different quenchers can be fitted by similar analytical expressions by including normalizing factors CR and CD, respectively. They considered the EV-processes O2(b1R+g ? a1Dg) and O2(a1Dg ? X3R g ) with vibrational excitation of different target molecules. The normalizing factors CR and CD are dependent on the electronic factors fSS (singlet–singlet) and fST (singlet–triplet) of transitions in an electronically excited O2 molecule. Schmidt and co-authors [16–18] in their quantitative analysis of liquidphase and gas-phase constants for the O2(b1R+g) and O2(a1Dg) molecules have obtained the ratio of CR/CD 104 for spin-allowed and spin-forbidden processes. Also Kirillov [22] divided the normalizing amplitude factor estimated for spin-allowed processes by the value of 50 to obtain the magnitude of an experimental rate constant for
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the vibrational level v = 0 of the singlet state a0 1R u of N2 in spin-forbidden processes of energy transfer to triplet states. Therefore we calculated the removal rates for the spin-forbidden process (10) with the normalizing parameters multiplied by the factors f1 = 101, f2 = 102, f3 = 103, f4 = 104 in comparison with the spin-allowed EV-process considered in [7]. The calculated quenching rate coefficients for the EV-process (10) using the values f1–f4 are compared with the total removal constants of the A0 3Du state by a CO2 molecule presented by Kirillov [7] in Figure 6. It should be noted that the calculations in [7] showed the dominance of the transitions A0 3Du(v = 0) ? A3Ru+(v0 = 0) and of the inverse processes in inelastic collisions with the N2, CO, CO2 molecules. Therefore, there is some equilibrium between the lowest vibrational levels of these two states in laboratory conditions and the removal of the A0 3Du(v = 0) level is related mainly with the transition to the triplet ground state X3R g in spin-allowed processes. For example, the intramolecular transfer to the X3R g state without vibrational excitation of a target-molecule CO2 has very small rate constant of 1017 cm3 s1 [7]. The concentration of carbon dioxide at the altitudes of 95– 100 km in the Venusian atmosphere are higher by about 4000 times than the concentration of molecular oxygen, therefore in Figure 7 we show the calculated ratios of the concentrations [c1Ru,v = 0]/[A0 3Du,v = 0] at pressures 102–103 Pa for a mixture of CO2 and O2 with [CO2]/[O2] = 4000, k9 = kEV and without and with the inclusion of the EV-processes (10) for the four values of decreasing factors f1–f4. It can be seen from the figure that the increase of the factors causes the rise of the O2(c1Ru,v = 0) population in comparison with the O2(A0 3Du,v = 0) population. For example, the application of the factor f3 = 103 leads to the increase of the ratio [c1Ru,v = 0]/[A0 3Du,v = 0] of 2.8 times. To show the effect of both the (9) and (10) EV-processes on the calculated O2(c1Ru,v = 0) and O2(A0 3Du,v = 0) populations we plotted the ratios of [c1Ru,v = 0]/[A0 3Du,v = 0] at pressures of 102–103 Pa for the mixture of CO2 and O2 with [CO2]/[O2] = 300, k9 = kEV and k9 = kEV/10 for the process (9), without and with the inclusion of the EV-process (10) for the four values of decreasing factors f1–f4 in Figure 8. The calculations show that the decrease in the rates of both processes (9) and (10) results in lower popula03 tion of O2(c1R u ,v = 0) in comparison with the O2(A Du,v = 0) population in our simulation. However, experimental results by Slanger [2] obtained for laboratory conditions and intensities of emissions registered by the VIRTIS spectrometer on board the Venus Express spacecraft in [20,21] are not sufficient to estimate the rates of the processes (9) and (10). Therefore, more detailed measurements of the intensity ratios of the Herzberg II (1) and Chamberlain (2) emissions in different mixtures of molecular oxygen with N2, CO, CO2, etc. gases
10-10 k, cm3s-1
10-12 1 2
10-14
3 4
10-16 0
2
A'3
4 6 8 10 Vibrational levels
u
12
Figure 6. The calculated quenching rate coefficients for the EV-processes (10) with the values f1–f4 (dashed lines 1–4, respectively) are compared with total removal constants of the A0 3Du state by CO2 molecule presented by Kirillov [7] (solid line).
102 Nc(0)/NA'(0)
1 2
101
3 4
100 10-1 10-2 -3
10
k9=kEV 10-1
103
100 101 102 Pressure (Pa)
Figure 7. The calculated ratios of the concentrations [c1Ru,v = 0]/[A0 3Du,v = 0] at pressures of 102–103 Pa for [CO2]/[O2] = 4000, k9 = kEV (solid line) and with inclusion of the EV-processes (10) for factors f1–f4. (dashed lines 1–4, respectively).
102 Nc(0)/NA'(0)
1
101
2 3
100 10-1
k9=kEV
10-2 101 Nc(0)/NA'(0)
2
100
3 4
10-1 10-2 10-3
k9=kEV/10 10-1
100 101 102 Pressure (Pa)
103
Figure 8. The calculated ratios of the concentrations [c1Ru ,v = 0]/[A0 3Du,v = 0] at pressures of 102–103 Pa for [CO2]/[O2] = 300, k9 = kEV or k9 = kEV/10 (solid lines) and with inclusion of the EV-processes (10) for factors f1–f4. (dashed lines 1–4, respectively).
and at different pressures should be used for the estimation of the removal rates of the EV-processes of the Herzberg states. 4. Conclusions The calculated in [7] quenching rate constants of the c1Ru, A0 3Du, A3R+u states of O2 by other molecules are applied for simulation of the vibrational populations of the Herzberg states in a mixture of molecular oxygen with CO2, CO, N2 gases for laboratory conditions. The main results of this paper are as follows. 1. The calculations for a mixture of N2 and O2 (CO and O2) gases show that the effect of the pressure (p = 102–103 Pa) on the populations of the lowest vibrational levels of the c1Ru and A0 3Du states is apparent in the cases of a small content of molecular oxygen in the mixture. The pressure increase causes a rise of the c1Ru,v = 0 and A0 3Du,v = 0 populations and of the ratio [c1Ru, v = 0]/[A0 3Du,v = 0]. We also point out the important role of the EV-process (9) in kinetics of two states, A0 3Du and c1Ru. It can be seen from the calculation that mainly the spin-allowed EV-process 1 0 O2(A0 3Du,v) + O2(X3R g ) with the production of O2(c Ru ,v = v) + O2 3 (X Rg ,v = 1) are responsible for effective emission of the Herzberg II bands (1) clearly observed by Slanger in his laboratory experiment in a He–O2 mixture [2].
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2. The same calculations for a mixture of CO2 and O2 gases show that the inclusion of the spin-forbidden EV-interaction of O2(A0 3Du,v) + CO2 molecules (10) in the simulation can explain the high intensities of the Herzberg II band system (1) observed in laboratory experiments [1,2] with high CO2 concentrations. The spin-forbidden process (10) could be a possible important mechanism for production of high intensities of the Herzberg II bands (1) registered by spectrometers in the nightglow of the Venus atmosphere from Venera 9 and Venera 10 [3] and Venus-Express [19,20] spacecraft. Acknowledgements This research is supported by the Programs of Presidium of RAS No 4, 22. Author thanks Dr. Yu. N. Kulikov for his help in the correct writing of the Letter. References [1] G.M. Lawrence, C.A. Barth, V. Argabright, Science 195 (1977) 573.
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