Absolute photolysis cross-sections for NaHCO₃ , NaOH, NaO, NaO₂ and NaO₃ : implications for sodium chemistry in the upper mesosphere

Abstract

The compounds NaHCO₃ , NaOH, NaO and NaO₂ are formed from meteor-ablated Na in the upper mesosphere. This paper reports the absolute photolysis cross-sections of these species at selected wavelengths between 193 and 423 nm, measured by laser photofragment spectroscopy. The sodium species were produced in both a slow flow reactor and a fast flow tube, by the addition of appropriate reagents to a flow of atomic Na from a heat-pipe oven. The pulsed photolysis source was either a Raman-shifted excimer laser or a Nd:YAG laser, and the resulting Na atoms were probed by laser induced fluorescence at 589.0 nm (Na(3 ²P_3/2–²S_1/2)). Measurements are reported at 200 and 300 K. A limited set of cross-sections for NaO₃ was also obtained at 300 K. In the case of NaHCO₃ , NaOH and NaO, the onset of photolysis is close to the thermodynamic threshold calculated from quantum theory. Calculations using the CI-singles method predict excited states whose relative energies are in sensible accord with the bands in the experimental spectra, but which are too high in energy with respect to their respective ground states. Photodissociation coefficients are then derived which are appropriate for modelling sodium chemistry in the upper mesosphere. Photolysis of the major sodium reservoir species, NaHCO₃ , is shown to be an important route for recycling this compound, and is also predicted to produce the HCO₃ radical, which should be stable under mesospheric conditions.

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Introduction

The layer of Na atoms that occurs globally between 80 and 105 km is formed by the ablation of sodium from the approximately 120 tons of interplanetary dust that enters the atmosphere each day.^1,2Fig. 1 is a schematic diagram of the chemistry that is believed to control the layer.³ Ion–molecule chemistry is important above the peak of the layer at about 90 km, whereas below this altitude Na is oxidised to form a number of neutral species including NaO, NaO₂ , NaOH and NaHCO₃ . A recent laboratory study of the reaction between NaHCO₃ and H has confirmed that the bicarbonate is the most stable reservoir for sodium immediately beneath the layer.⁴ Recent models of the Na layer, using rate coefficients that have all now been measured individually under conditions appropriate to the mesosphere, produce excellent agreement with the observed seasonal and latitudinal variations of the layer.^3,5

Fig. 1 The gas-phase chemistry of sodium in the upper atmosphere (adapted from ref. 3). Minor constituents such as NaCO₃ and NaO₃ have been omitted for clarity.

However, these observations were almost exclusively of the night-time Na layer. Recent advances in lidar technology permit fully diurnal measurements of the layer to be made on a routine basis, yielding both Na density and temperature (from the broadening of the hyperfine structure of the D₂ line at 589.0 nm).⁶ In order to explain the complex diurnal variability of the Na density profile, several coupled factors need to be taken into account. First, there is the effect of tidal dynamics on the layer. Indeed, the amplitudes and phases of the diurnal and semi-diurnal tides have been obtained from analysis of the Na temperature record.⁶ Second, the odd oxygen and hydrogen chemistry, which controls the underside of the Na layer (Fig. 1), exhibits a large diurnal variation below 82 km where the concentrations of O and H vary by orders of magnitude. Finally, the sodium compounds themselves may photolyse significantly during daytime, contributing a further diurnal oscillation. This is the subject of the present study.

In this paper we will describe measurements of the absolute photolysis cross-sections (to yield atomic Na) of the neutral Na-containing molecules in Fig. 1, using a laser photofragmentation method. Ab initio quantum calculations will then be employed to interpret the results, before calculating photodissociation coefficients suitable for use in mesospheric models. These sodium compounds have very large dipole moments and therefore readily cluster with water, particularly at the low temperatures of the upper mesosphere during summer.⁷ The effect of this on the photolysis cross-sections will also be examined.

Experimental measurements

The absolute photolysis cross-sections of NaHCO₃ , NaOH, NaO, NaO₂ and NaO₃ were determined by the technique of pulsed laser photolysis followed by laser-induced fluorescence (LIF) of the resulting Na atoms. This photofragmentation technique has been used previously by Silver et al.⁸ and Rajasekhar et al.⁹ to study the photolysis of NaCl and NaO₂ , respectively. The sodium compound NaX (where X = HCO₃ , OH, O, O₂ or O₃) is produced in situ by essentially complete conversion of a flow of Na atoms entering the reactor from an oven, following the addition of appropriate reagents in large excess:If the resulting flow of NaX is subjected to a laser pulse of fluence I₀(λ) at wavelength λ, then in the limit of low light absorption the concentration of nascent Na atoms created by the pulse is given bywhere σ(λ) is the absolute photolysis cross-section at λ to yield Na+X. Note that we assume here that the photolysis quantum yield following absorption of a photon is unity. This will be justified below. The Na atoms will give rise to a measured LIF signal, I_fp , when the probe laser is triggered immediately afterwards. In the absence of reagents, the LIF signal (I_f0) will be proportional to the total Na atom concentration. This is equivalent to [NaX] when reagents are added, after making a small correction for differences in the rates of diffusion of Na and NaX (see below). Since I_fp and I_f0 are measured with the same geometrical light collection factor and detection sensitivity, thenThus, σ(λ) can be determined absolutely by measuring the ratio I_fp/I_f0 , and monitoring I₀(λ).

Two experimental systems were used in this study. The first, illustrated schematically in Fig. 2, employed a stainless steel slow flow reactor that has been described in detail elsewhere.⁹ The central chamber of this reactor is at the intersection of two sets of side-arms that cross orthogonally. One set of arms provides the optical coupling of the lasers to the central chamber, as well as the means by which the flows of the reagents enter the chamber. A third side-arm was independently heated (520–555 K) to provide a source of Na atoms. A spiral of stainless steel mesh (gauge 150) was inserted into this heat pipe, along with solid Na spheres. Upon heating the mesh became wetted with molten Na, thereby greatly increasing the surface area exposed to the flow of N₂ gas that entrained the Na vapour into the central chamber. This feature, together with accurate control of the heat pipe temperature (±1 K), ensured a stable flow of Na atoms during the experiments.

Fig. 2 Schematic diagram of the slow flow reactor used to measure the absolute photolysis cross-sections of Na-containing molecules by photofragment spectroscopy: F₁ , flow of N₂ through the sodium oven; F₂ , flow of reagents into the central chamber; PMT, photomultiplier tube.

The central chamber is enclosed in an insulated compartment that can be filled with dry ice to cool it to about 200 K. The temperature of the gas flow in the chamber is monitored by a thermocouple permanently inserted about 1 cm below the path of the laser beams. Once in the chamber, the atomic Na was mixed with the reagent flows at a total pressure of about 3 Torr. The synthesis of NaHCO₃via reactions (R1)–(R3) required some care. On the one hand, sufficient CO₂ had to be added to ensure that all the NaOH produced by (R2) was converted to NaHCO₃ ; on the other, competition for NaO from the reaction

had to be minimised. A full kinetic model⁴ was employed to optimise the reagent mixing ratios: at 300 K the reagents N₂O/H₂/CO₂/N₂ were typically added in the ratio 5 : 20 : 0.3 : 74.7 (at 200 K, [N₂O] was increased because reaction (1) has a significant activation energy¹⁰).

Photolysis was carried out over a range of wavelengths from 193 to 423 nm, using a Raman-shifted excimer laser (Questek Model 2010, with unstable resonator optics) operating at 193 nm (ArF) or 248 nm (KrF). The Raman shifter (Lambda Physik, model RS75) was filled with H₂ (Air Products, 99.9999%) or D₂ (Messer, 99.7%) to between 2.2 and 10 bar. The output beams were separated spatially using a Pellin–Broca prism. The fluences of the Raman-shifted beams were measured before and after the reactor using a Molectron J-25 Joulemeter (5 mm diameter circular element, calibrated to a recent factory reference) and a quartz beamsplitter. The fluence in the central chamber was then computed as the geometric mean of the two measurements. The Raman-shifted wavelengths and typical laser fluences in the reactor are listed in Table 1.

Table 1 Typical Raman-shifted excimer laser fluences in the reactor^a

	H2 in Raman shifter		D2 in Raman shifter
	λ/nm	Fluence/mJ cm^−2	λ/nm	Fluence/mJ cm^−2
a An = Anti-Stokes, shifted n times, Sn = Stokes, P = primary.
KrF
A2	205.9	0.04	216.3	0.3
A1	225.2	2	231.2	2
P	248.4	20	248.4	40
S1	277.0	8	268.3	7.5
S2	313.0	6	291.8	5
S3	359.8	3.5	319.6	3.5
S4	423.0	0.7	353.4	1.5
S5	513.2	0.05	395.2	0.3
S6	652.3	0.005	448.2	Unstable
ArF
P	193.4	5	193.4	3
S1	210.3	3	205.3	1.2
S2	230.4	2.5	218.7	0.9
S3	254.8	1.5	234.0	0.6
S4	285.0	0.3	251.6	0.3

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The relative atomic Na concentration was measured by pumping one of the Na D-lines at 589.0 nm [Na(3 ²P_3/2–3 ²S_1/2)] using a N₂-pumped dye laser, and observing non-resonant LIF at 589.6 nm through a narrowband interference filter (Janos Corp., FWHM = 0.2 nm). A vertical side arm on the chamber provided the optical coupling to the photomultiplier tube (Thorn EMI Gencom, model 9816QB). The signal was captured by a gated integrator after pre-amplification (Stanford Research Systems, model SR445, 300 MHz). The linearity of the measured LIF signal with the Na atom density was regularly checked.

During photolysis experiments, the dye laser triggered 8.7 µs after the photolysis pulse. During this period an insignificant fraction of the nascent Na atoms would have reacted with the oxidant (N₂O or O₂) in the chamber. When the Na concentration in the absence of reagents was being measured (i.e.I_f0), the total flow and pressure in the central chamber were maintained by increasing the N₂ flow through the side-arms. In order to make a measurement of σ(λ), I_fp and I_f0 were obtained by averaging a minimum of 200 data points in each case. A background (zero) signal was also obtained by measuring the LIF signal with the reagents flowing through the reactor but the photolysis laser off.

A limited number of experiments were performed using a second experimental system. This was a fast flow tube, described recently by Cox et al.,⁴ which operated at a pressure of 1.5 Torr with flow velocities of 12–24 m s⁻¹. Photolysis cross-sections were determined using the same photolysis/LIF technique. Na vapour was produced in an oven at the upstream end of the tube, entrained in N₂ and then mixed in the flow tube with reagents that were added sequentially to produce the same compounds as before. Photolysis cross-sections were determined using a frequency tripled or quadrupled Nd:YAG laser (Continuum Minilite). The beam energy was determined with a calibrated Molectron J-50 Joulemeter, and the beam area measured with photosensitive paper. This yielded fluences of 170 mJ cm⁻² at 354.6 nm and 110 mJ cm⁻² at 265.9 nm.

The cross-section measurements with both experimental systems were performed with a total Na concentration less than 1 × 10⁹ molecule cm⁻³ in the photolysis region. This is important in order to avoid the clustering of Na compounds to form dimers and higher polymers. Polymerisation should be a fast process because of the strong intermolecular forces resulting from the large dipole moments of these species (see below). The absolute Na concentration was determined in a separate experiment where it was measured in the absence of reactants by the resonance absorption of the radiation from a Na hollow cathode lamp directed transversely to the flow. An absorption cross section of 1.85 × 10⁻¹¹ cm² for the [Na(3 ²P_J–3 ²S_1/2)] transition was assumed.¹¹

Materials

N₂ (BOC, 99.9999% pure), N₂O (Air Products, 99.99% pure), CO₂ (Air Products, 99.995% pure), H₂ (Air Products, 99.9999% pure) and O₂ (Air Products, 99.995% pure) were used without further purification. Sodium metal spheres (3–8 mm, Aldrich Chem. Co., Inc.) were cleaned with solvent before insertion into the heat-pipe ovens.

Results

The photolysis cross-sections, σ(λ), were determined using eqn. (II). Measurements of the NaHCO₃ , NaOH, NaO and NaO₂ cross-sections were made at both 300 and 200 K, since the lower temperature is representative of the upper mesosphere. The photolysis of NaO₃ , which is a less important mesospheric species,³ was only studied at 300 K. Diffusion corrections to σ(λ) were made in the following way. For the slow flow reactor (Fig. 1), the flow of Na atoms from the heat pipe into the central chamber is balanced by diffusion to the chamber walls of Na (in the absence of reagents) or of NaX. As we have shown previously for this reactor,¹² the steady-state concentration of Na is given by F_Na/k_diff(Na), where F_Na is the flow rate of Na into the chamber from the heat pipe, and k_diff(Na) is the first-order loss of Na to the walls of the chamber, which closely approximates to a cylinder of radius r = 3 cm and length l = 6 cm. k_diff(Na) is given bywhere D(Na) is the diffusion coefficient for Na in N₂ , at the pressure and temperature of the central chamber. When reagents are added to the same flow of Na from the heat pipe, the steady-state concentration of NaX is by analogy F_Na/k_diff(NaX). Hence, the cross-section σ(λ) needs to be corrected by the factor k_diff(Na)/k_diff(NaX) ≈ D(Na)/D(NaX). The diffusion coefficients used to make this correction are listed in Table 2. When correcting the 200 K data, it was assumed that the diffusion coefficients of Na and NaX had the same temperature dependences.

Table 2 Diffusion coefficients and thermodynamic data

Species	Diffusion coefficient at 300 K/cm^2 s^−1 Torr	Thermo-dynamic limit λ/nm	Lowest vibrational frequency/cm^−1	Ratio of v′′ = 1 populations 300 to 200 K
a Ref. 4. b Measured relative to D(Na) in the fast flow tube. c Estimated from long-range capture theory (see ref. 14). d Ref. 4 and present calculations on HCO3 . e Ref. 17. f Ref. 18. g Ref. 22. h Ref. 23.
NaHCO3	120^a	257^d	118^a	1.33
NaOH	134^b	368^e	261^e	1.87
NaO2	119^b	747^f	333^g	2.22
NaO	141^a	443^e	492^h	3.26
NaO3	110^c	581^f	—	—
Na	152^a	—	—	—

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For the fast flow tube measurements, the diffusion correction was applied by assuming uptake coefficients for Na and NaX of close to unity on the walls so that strong radial concentration gradients would have developed in the tube. The first-order loss to the walls under laminar flow conditions was then described using the approximation of Huggins and Cahn.¹³ In the case of NaOH and NaO₂ , a movable injector was used to vary the point in the flow tube at which reagents were added to produce these species from Na. By observing the apparent change in σ(λ) as the injection distance was varied, the diffusional loss to the walls of NaOH and NaO₂ was determined relative to that of Na.

The resulting σ(λ) are listed in Tables 3–7 for the five sodium species that were studied. The quoted 1σ errors are computed by combining in quadrature the statistical and systematic errors. The statistical error arises from the standard deviations in the measurement of I_f0 and I_fp (eqn. (II)). When using a strong photolysis laser line (e.g. the KrF primary) and if σ(λ) > 10⁻¹⁸ cm², this error was less than 10%. However, if σ(λ) was very small or the laser fluence was weak, then the statistical error could exceed 100%. There are two significant sources of systematic error. First is the uncertainty in the measured laser fluence. This ranged from 4% for the primary excimer lines to 20% for the highly Raman-shifted beams. The YAG fluences were estimated to have an uncertainty of 13%. The second systematic uncertainty is in the diffusion correction factor. For NaOH and NaO₂ , the diffusion coefficients relative to D(Na) were measured using the fast flow tube (see above), and D(NaO) was determined in a previous flow tube study,⁴ so the error in the diffusion correction factors for these species is better than 5%. D(NaHCO₃) and D(NaO₃) were estimated from long-range capture theory,¹⁴ using parameters calculated from quantum theory (see below); the uncertainty in their diffusion correction factors is estimated to be 12%.

Table 3 Photolysis cross-sections for NaHCO₃

Raman line^a	λ/nm	σ(λ) at 300 K/10^−18 cm^2	σ(λ) at 200K/10^−18 cm^2
a The nomenclature used to describe the photolysis line: exciplex (ArF or KrF), Raman-shifting gas (H2 or D2), An = anti-Stokes n shifts, Sn = Stokes n shifts, P = primary. Nd:YAG 3ν or 4ν = tripled or quadrupled Nd:YAG laser.
ArF P	193.4	1.13 ± 0.23	0.7.35 ± 0.237
KrF H2 A2	205.9	0.487 ± 0.358
ArF H2 S1	210.3	1.16 ± 0.36	0.947 ± 0.387
KrF D2 A2	216.3	1.20 ± 0.56
KrF H2 A1	225.2	0.773 ± 0.093	0.987 ± 0.501
ArF H2 S2+KrF D2 A1	230.9	0.547 ± 0.179	0.578 ± 0.217
KrF P	248.4	0.0401 ± 0.0054	0.0355 ± 0.0113
Nd:YAG 4ν	265.9	−0.11 ± 0.15
KrF D2 S1	268.3	0.0095 ± 0.0269
KrF H2 S1	277.0	0.0109 ± 0.0045	0.0549 ± 0.0438
Nd:YAG 3ν	354.6	−0.018 ± 0.030

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Table 4 Photolysis cross-sections for NaOH

Raman line^a	λ/nm	σ(λ) at 300 K/10^−18 cm^2	σ(λ) at 200K/10^−18 cm^2
a See Table 3.
ArF P	193.4	5.51 ± 0.43	2.92 ± 2.38
ArF D2 S1+KrF H2 A2	205.7	8.67 ± 2.74
KrF H2 A2	205.9		5.63 ± 2.52
ArF H2 S1	210.3		1.85 ± 3.28
KrF D2 A2	216.3	4.89 ± 2.60
ArF D2 S2	218.7	6.96 ± 2.79	3.76 ± 5.12
KrF H2 A1	225.2	14.3 ± 1.3	10.5 ± 1.5
ArF H2 S2+KrF D2 A1	230.6	18.2 ± 0.18	7.66 ± 4.87
ArF D2 S3	234.0	16.8 ± 5.3
KrF P	248.4	1.73 ± 0.13	0.580 ± 0.071
ArF H2 S3	254.8	1.15 ± 0.22
Nd:YAG 4ν	265.9	0.48 ± 0.15
KrF D2 S1	268.3	0.418 ± 0.150	0.173 ± 0.120
KrF H2 S1	277.0	0.191 ± 0.027	0.0719 ± 0.0791
ArF H2 S4	285.0	0.071 ± 0.147
KrF D2 S2	291.8	0.438 ± 0.130	0.118 ± 0.123
KrF H2 S2	313.0	5.85 ± 0.47	4.72 ± 0.53
KrF D2 S3	319.6	5.10 ± 1.03	3.41 ± 0.78
KrF D2 S4	353.4	0.539 ± 0.227	0.449 ± 0.444
Nd:YAG 3ν	354.6	0.57 ± 0.20
KrF H2 S3	359.8	0.414 ± 0.064	0.165 ± 0.067
KrF D2 S5	395.2	0.512 ± 0.926
KrF H2 S4	423.0	−0.0130 ± 0.0565	0.0180 ± 0.0961

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Table 5 Photolysis cross-sections for NaO

Raman line^a	λ/nm	σ(λ) at 300 K/10^−18 cm^2	σ(λ) at 200K/10^−18 cm^2
a See Table 3.
ArF P	193.4	5.01 ± 2.32
KrF H2 A2	205.9	−0.42 ± 2.46
KrF D2 A2	216.3	14.9 ± 4.2	5.15 ± 3.14
KrF H2 A1	225.2	11.0 ± 2.7
KrF D2 A1	231.2	11.7 ± 2.2	3.53 ± 0.75
KrF P	248.4	2.06 ± 0.16	0.937 ± 0.157
Nd:YAG 4ν	265.9	1.8 ± 0.28
KrF D2 S1	268.3	1.60 ± 0.26	0.246 ± 0.178
KrF H2 S1	277.0	0.463 ± 0.049
KrF D2 S2	291.8	1.02 ± 0.29	0.955 ± 0.532
KrF H2 S2	313.0	12.5 ± 2.6
KrF D2 S3	319.6	10.7 ± 1.5	7.03 ± 1.28
KrF D2 S4	353.4	2.76 ± 0.67	1.19 ± 0.60
Nd:YAG 3ν	354.6	2.8 ± 0.72
KrF H2 S3	359.8	1.74 ± 0.92
KrF D2 S5	395.2	2.44 ± 1.36	1.55 ± 1.52
KrF H2 S4	423.0	0.522 ± 1.03

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Table 6 Photolysis cross-sections for NaO₂

Raman line^a	λ/nm	σ(λ) at 300 K/10^−18 cm^2	σ(λ) at 200K/10^−18 cm^2
a See Table 3.
ArF P	193.4	3.83 ± 0.85	1.88 ± 0.51
KrF H2 A2	205.9	1.46 ± 1.84	−1.17 ± 2.08
ArF H2 S1	210.3	5.42 ± 1.25	2.65 ± 0.76
KrF D2 A2	216.3	5.11 ± 2.08	1.92 ± 1.22
KrF H2 A1	225.2	2.35 ± 0.95	5.08 ± 0.93
ArF H2 S2+KrF D2 A1	230.8	9.35 ± 1.35	2.84 ± 0.49
KrF P	248.4	4.14 ± 0.88	2.86 ± 0.17
ArF H2 S3	254.8	5.50 ± 1.34	2.22 ± 0.58
KrF D2 S1	268.3	4.58 ± 0.73	2.18 ± 0.24
KrF H2 S1	277.0	1.81 ± 0.42	1.63 ± 0.19
ArF H2 S4	285.0	0.734 ± 0.330	0.355 ± 0.189
KrF D2 S2	291.8	1.68 ± 0.33	0.683 ± 0.103
KrF H2 S2	313.0	1.27 ± 0.41	0.955 ± 0.142
KrF D2 S3	319.6	0.121 ± 0.113	0.252 ± 0.096
KrF D2 S4	353.4	0.162 ± 0.165	0.283 ± 0.169
YAG 3ν	354.6	0.35 ± 0.22
KrF H2 S3	359.8	0.610 ± 0.251	0.419 ± 0.103
KrF D2 S5	395.2	1.08 ± 0.94	1.16 ± 0.85
KrF H2 S4	423.0	0.428 ± 0.309	0.211 ± 0.105

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Table 7 Photolysis cross-sections for NaO₃

Raman line^a	λ/nm	σ(λ) at 300 K/10^−18 cm^2
a See Table. 3
KrF D2 A2	216.3	13.1 ± 5.8
KrF D2 A1	231.2	2.28 ± 0.71
KrF D2 P	248.4	1.19 ± 0.18
KrF D2 S1	268.3	0.949 ± 0.174
KrF D2 S2	291.8	1.45 ± 0.25
KrF D2 S3	319.6	3.45 ± 0.59
KrF D2 S4	353.4	0.556 ± 0.211
KrF D2 S5	395.2	0.717 ± 0.565

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Ab initio quantum calculations

The experimental measurements were complemented by a series of ab initio quantum calculations using the Gaussian 98 suite of programs.¹⁵ The ground-state geometries of NaHCO₃ , NaOH, NaO and NaO₂ and NaO₃ were first optimised using Hartree–Fock (HF) theory with the large flexible 6-311+G(2d,p) basis set, which has both polarization and diffuse functions added to the atoms.¹⁶ These molecules all have highly ionic ground states with large dipole moments (6.9, 6.6, 8.6, 8.3 and 7.4 D, respectively). We have published the details of their geometries and vibrational frequencies elsewhere.^4,17,18 Calculations on the vertical electronic excited state energies and transition oscillator strengths were performed using configuration interaction-singles (CIS) theory.^15,16

In order to investigate the photolysis products of NaHCO₃ , calculations were performed on the HCO₃ radical using hybrid density functional/Hartree–Fock B3LYP theory with the 6-311+G(2d,p) basis set. Fig. 3 illustrates the optimised geometry of this species, as well as the saddle-point geometry for dissociation to OH+CO₂ . Finally, calculations were carried out on the ground and excited states of the NaOH–H₂O and NaHCO₃–H₂O complexes, to examine the effect of water clustering on photolysis. The H₂O binding energies were determined using the very accurate complete basis set (CBS-Q) theory,¹⁹ and the calculations on the excited states of the clusters were determined at the CIS/6-311+g(2d,p) level. The ground state geometries of these clusters are also illustrated in Fig. 3.

Fig. 3 Molecular geometries predicted by ab initio quantum theory at the B3LYP/6-311+G(2d,p) level: (a) HCO₃ (planar); (b) the HCO₃ → OH+CO₂ saddle point (H–O–C–O[bottom left] dihedral angle = 68°); (c) the NaOH–H₂O cluster (H[top right]–O–Na–O dihedral angle = 144°); (d) the NaHCO₃–H₂O cluster (planar).

Discussion

Inspection of Tables 3–6 shows that the cross-sections measured in the flow reactor and the fast flow tube agree very well, even though the Na compounds were prepared somewhat differently in each type of system. Fig. 4 illustrates the photolysis cross-section spectra of NaHCO₃ , NaOH, NaO₂ and NaO. Note that the maximum cross-section for NaHCO₃ is a factor of 10 smaller than the maxima in the spectra of the other compounds, and it only begins to absorb quite far into the ultra-violet. Shown on the figure and also listed in Table 2 are the thermodynamic limits to photolysis, calculated from the respective bond energies D₀(Na–X). The sources of these bond energies are given in the footnotes to Table 2. For NaHCO₃ , NaOH and NaO, the thermodynamic limit is close to the onset of photolysis in each case, implying that the relevant excited states have rather flat potential energy curves i.e. they are essentially covalent and at best weakly bound. This is supported by the CIS quantum calculations, which show that the Mulliken electron population on the Na atom, which is greater than +0.9 in the ground state, is less than +0.1 in these excited states. These calculations indicate that transitions to these covalent states should lead to prompt dissociation to Na atoms.

Fig. 4 Photolysis cross-section spectra of NaHCO₃ , NaOH, NaO₂ and NaO at 200 K (thin line) and 300 K (heavy line). The solid lines drawn through the experimental points are to guide the eye. Error-bars correspond to 1σ uncertainties. The positions and oscillator strengths of the vertical transitions predicted by CIS theory are plotted on the top abscissa of each panel. Note that the excited state energies have been shifted with respect to the ground state (see text).

The CIS method, which models excited states as combinations of single substitutions out of the Hartree–Fock ground state, is an approximate treatment for excited states.¹⁶ In the present case it systematically over-predicts the vertical excitation energies from the ground state. In order to obtain sensible agreement with the positions of the observed absorption bands, the upper states of each molecule were shifted downwards by the same amount with respect to the ground state. These shifts are listed in Table 8 for the five molecules, and range from 0.6 to 2.7 eV. The (shifted) wavelength positions for transitions where the transition oscillator strength f is greater than 10⁻³ (and therefore significant), are marked on the top abscissa of each of the panels in Fig. 4 along with their f values. There is reasonable agreement with the measurements, implying that the relative energies of the covalent upper states are quite well predicted with respect to each other. However, the change from ionic to covalent character between the ground and the upper states is not well described by CIS theory, since the Hartree–Fock orbitals used to describe the excited states are biased to the ground-state configuration.¹⁶

Table 8 Energy corrections applied to CIS theory

Compound	Energy correction/eV
NaHCO3	2.72
NaOH	1.12
NaO2	0.94
NaO	0.56
NaO3	0.69

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Fig. 4 shows that some of the bands of NaO and NaO₂ exhibit marked positive temperature dependences. A smaller dependence may be present in the case of NaOH, whereas NaHCO₃ exhibits no apparent dependence. This is probably explained by vibrational excitation of the ground state molecule leading to better Franck–Condon overlap with its excited states. For example, CIS calculations show that the ground state of NaOH is linear, whereas the covalent excited states are bent: hence, excitation in the degenerate bending modes should increase σ(λ). Table 2 lists the lowest vibrational frequencies of NaHCO₃ , NaOH, NaO₂ and NaO, and the ratios of the Boltzmann population of v′′ = 1 at 300 K compared to 200 K. This ratio increases markedly from 1.3 for NaHCO₃ to 3.3 for NaO, in accord with the observed variation in temperature dependence shown in Fig. 4.

There is an interesting aspect to the spectrum of NaO in the near ultra-violet. Langhoff et al.²⁰ carried out multi-reference configuration-interaction calculations on the first three states of NaO. This showed that the C ²Π state should be accessible about 25 000 cm⁻¹ (≈400 nm) above the X ²Π ground state. Furthermore, because the equilibrium Na–O separation of the C state is about 1.5 Å larger than the X state, the theory predicted that NaO(C–X) absorption would be followed by emission to high vibrational levels of the X state, producing a band system from 500 to 2000 nm and peaking around 1000 nm. However, Pugh et al.²¹ failed to observe an LIF spectrum for NaO in the 390–430 nm region. Ellis has reported a similar finding.²²

The absence of fluorescence is now explained by the present study, which shows that absorption in this region leads to photolysis (Fig. 4). The implication is that NaO(C ²Π) is crossed by a higher-lying ²Π state, causing pre-dissociation to Na+O. Further theoretical work should be carried out on this system. It should also be noted that the reaction between Na and N₂O produces NaO in both the X(²Π) and A(²Σ⁺) states.^23,24 There is some evidence that NaO(A ²Σ⁺) is not quenched very efficiently, and has a radiative lifetime of more than 20 ms.²⁴ Hence, the cross-sections measured in this study may describe a mixture of the X and A states. These are separated by about 2050 cm⁺¹,^20,24 corresponding to ≈20 nm in the near-UV, which may explain the rather broad bands in the NaO spectrum (Fig. 4).

The results for NaO₂ are in excellent agreement with a previous study using a slow flow reactor.⁹ The only other work on the absorption spectrum of NaO₂ appears to be a matrix isolation study where Na atoms and O₂ were co-deposited in argon.²⁵ The resulting superoxide species gave rise to bands with maxima at 232, 250 and 272 nm, which correspond approximately with bands in the 200 K spectrum in Fig. 4.

An absolute absorption spectrum for NaOH in the ultraviolet has been obtained by Rowland and Makide,²⁶ based on spectroscopic data when aqueous NaOH solutions were aspirated into flames between 900 and 2300 °C. Fig. 5 is a comparison of the flame absorption cross-section spectrum with the photolysis spectrum from the present study. There is generally good agreement in the absolute magnitudes of the cross-sections, particularly for the strong band around 235 nm and in the absence of absorption between 265 and 290 nm. The discrepancy beyond 310 nm could be caused by hot-band absorption by vibrationally-excited NaOH in the high temperature flames: indeed, Rowland and Makide²⁶ pointed out that the flame absorption spectrum continued beyond the thermodynamic limit set by the D₀(Na–OH) bond energy (see below). Another possibility is that the apparent structure in the flame spectrum beyond 320 nm is actually due to other absorbing species present in the flame that were not accounted for in the analysis. Finally, it should be noted that photolysis at 193 nm of NaOH produces Na(3 ²P) which then fluoresces at 589 nm. This is employed as a diagnostic for sodium in combustion systems, where NaOH is the dominant form at temperatures above 1500 °C.²⁷ The threshold for Na(²P) production is about 226 nm, which is close to the onset of the third absorption band in the NaOH spectrum in Fig. 4.

Fig. 5 The photolysis cross-section of NaOH at 300 K from the present study, compared with an absorption cross-section measured in flames (ref. 25).

Atmospheric implications

The photodissociation coefficients for these Na-containing species were computed from the relation:where Φ(λ) is the solar actinic flux in the upper mesosphere.²⁸ The integration was performed by using a smooth interpolation between the experimental results at discrete wavelengths (see Fig. 4). In the case of NaO₂ , where photolysis at wavelengths longer than 440 nm is thermodynamically possible, the CIS calculations indicate that there are no low-lying states (Fig. 4). Photolysis at wavelengths shorter than 190 nm will make only a minor contribution to J because the solar flux decreases very rapidly in the vacuum ultra-violet.²⁸ The calculated J values and the lifetimes of the molecules against photolysis are listed in Table 9. In a previous study of the photolysis of NaO₂ where σ(λ) was only measured at three wavelengths,⁹ the estimate of J(NaO₂) = (4.8 ± 2.8) s⁻¹ is about a factor of 2 larger than the result of the present study, although there is agreement within the quoted error.

Table 9 Photolysis J-values and 1/e-lifetimes at 90 km altitude

Compound	J(300 K)/ s^− 1	J(200 K)/ s^− 1	τ(300 K)/s	τ(200 K)/ s
NaHCO3	1.28 ± 0.47  ×  10^−4	1.27 ± 0.66  ×  10^−4	7800	7860
NaOH	0.0240 ± 0.0077	0.019 ± 0.005	42	54
NaO2	0.023 ± 0.013	0.019 ± 0.011	44	53
NaO	0.093 ± 0.038	0.055 ± 0.029	11	18
NaO3	0.026 ± 0.015		38	—

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Fig. 6 compares the calculated J values for the four important Na species with their most rapid chemical loss processes. These involve reaction of atomic H with NaHCO₃ and NaOH, atomic O reacting with NaO and NaO₂ . The conditions are midday in June at 40 °N (see the figure caption for further details). In the case of NaO and NaO₂ , photolysis is not competitive: atomic O is very abundant in the upper mesosphere, and these species react rapidly with O.^14,29 In contrast, photolysis of NaHCO₃ and NaOH dominates their removal during daytime: atomic H is 2–3 orders of magnitude less abundant than O, and the rates of the reactions of these species with H are quite slow.^3,4

Fig. 6 Height profiles of the first-order removal rates of (a) NaHCO₃ and NaOH by photolysis and reaction with atomic H, and (b) NaO₂ and NaO by photolysis and reaction with atomic O. The conditions are midday, June at 40°N. The profiles of O and H are taken from the thermosphere–ionosphere–mesosphere–electrodynamics general circulation model (TIME GCM, ref. 32).

In terms of understanding the chemistry of Na in the mesosphere, the photolysis of NaHCO₃ is clearly important since this species is believed to be the major gas-phase sodium reservoir below about 85 km.³ With a lifetime against photolysis of only about 2 h, a large diurnal cycle in atomic Na below 85 km would be predicted. Since this is not in fact observed,⁶ NaHCO₃ must be removed from the system, most likely through uptake on meteoric smoke particles.³⁰ We are currently examining this with a new diurnal Na model.

NaHCO₃ and NaOH have very large dipole moments (see above), so that they can form stable H₂O clusters and this may affect their rates of photolysis. CBS-Q calculations indicate that the binding energies of H₂O to NaHCO₃ and NaOH are 51.7 and 84.5 kJ mol⁻¹, respectively. As we have shown previously,⁷ even in the very dry mesosphere with H₂O mixing ratios of a few ppm, these (and higher) clusters will dominate once the temperature falls below about 170 K. This situation occurs during mid-summer, particularly at high latitudes. CIS calculations on the excited states of NaHCO₃·H₂O show that the vertical excitation energies of the first 5 excited states increase by 31–62 kJ mol⁻¹; for NaOH·H₂O, the increase is 65–113 kJ mol⁻¹. These energy ranges are consistent with the respective binding energies of the clusters. This is to be expected, because H₂O binds strongly to the ionic ground states of these molecules (Fig. 3), but is weakly bound to the covalent upper states.

To test the effect of cluster formation, we performed a simple experiment on NaOH photolysis in the slow flow reactor. A flow of H₂O was added to the central chamber at 200 K, where the equilibrium H₂O concentration of 5.3 × 10¹³ cm⁻³ was sufficient to convert the NaOH overwhelmingly to the H₂O cluster. The large peak in the photolysis cross-section spectrum of NaOH, σ(231.2 nm) = (18.2 ± 0.18) × 10⁻¹⁸ cm², was reduced to (−0.13 ± 0.15) × 10⁻¹⁸ cm², i.e. effectively zero. In contrast, σ(248.4 nm) changed from (1.73 ± 0.13) × 10⁻¹⁸ cm² to (0.361 ± 0.044) × 10⁻¹⁸ cm⁻². These changes would be accounted for if the NaOH spectrum was shifted to shorter wavelengths by the equivalent of 75 kJ mol⁻¹, which is consistent with the NaOH–H₂O binding energy. If the NaHCO₃ photolysis spectrum is also shifted to shorter wavelengths by the NaHCO₃–H₂O binding energy, as predicted by theory, then the lifetime against photolysis in the mesosphere would increase from 2.2 to 4.5 h.

In the case of NaHCO₃ , the CIS excited state calculations show that the vertical transitions with large oscillator strengths (f > 0.02) that contribute to the absorption band between 210 and 230 nm all lead to dissociation to Na and the HCO₃ radical (Fig. 3). It has been speculated that HCO₃ could be formed in the atmosphere from the reaction

However, the present calculations reveal two significant features on the potential energy surface of reaction (R7). First, the complex is weakly bound, ΔH₀°(7) = −14 ± 20 kJ mol⁻¹. Second, there is a significant barrier ΔE₀^# = 74 kJ mol⁻¹ for HCO₃ to dissociate to OH+CO₂ . Thus, reaction (R7) is likely to be extremely slow. On the other hand, HCO₃ will also not dissociate very rapidly. We have estimated the rate of thermal dissociation using Rice–Ramsberger–Kassel–Marcus (RRKM) theory³¹ with the data in Table 10. This indicates that at a pressure of 0.01 Torr (the pressure at 80 km in the atmosphere), the rate of dissociation of HCO₃ is 1.4 × 10⁸ exp(−8400/T) s⁻¹. Even allowing for the expected uncertainty¹⁶ of ±14 kJ mol⁻¹ in the calculated barrier height, HCO₃ should be thermally stable for at least several days at 80 km, and is likely to be destroyed much more rapidly by reaction with atomic O or H.

Table 10 Calculated molecular parameters at the B3LYP/6-311+G(2d,p) level of theory for the minimum and saddle point on the OH + CO₂ → HCO₃ surface

Species (see Fig. 3)	Dipole moment^a	Rotational constants^b	Vibrational frequencies^c	ΔH0^o^d
a In D ≈ 3.33564 × 10^−30 C m. b In GHz. c In cm^−1. d In kJ mol^−1, with respect to OH +CO2 (zero-point energies included).
HCO3	2.84	13.8, 11.3, 6.20	458, 514, 556, 760, 1031, 1149, 1278, 1565, 3757	−13.5
HO–CO2 saddle point	2.17	13.7, 9.19, 5.59	569(i), 330, 395, 572, 675, 901, 1235, 2104, 3728	60.7

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Acknowledgements

This work, and a research studentship for DES, were supported by the Natural Environment Research Council (grant GR3/11754).

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