Intensity calculations of the VUV and UV photoabsorption and photoionisation of CF3Cl

Chemical Physics Letters 377 (2003) 189–196 www.elsevier.com/locate/cplett

Intensity calculations of the VUV and UV photoabsorption and photoionisation of CF3Cl A.M. Velasco, E. Mayor, I. Mart
ın

*

Departamento de Qu
ımica F
ısica, Facultad de Ciencias, Universidad de Valladolid, E47005 Valladolid, Spain Received 11 June 2003; in final form 3 July 2003 Published online: 24 July 2003

Abstract Absorption oscillator strengths and photoionisation cross-sections for CF3 Cl from its ground state are reported. The molecular-adapted Quantum Defect Orbital (MQDO) method has been employed in the calculations. Partial differential oscillator strengths for the different Rydberg series that constitute the ionisation channels of CF3 Cl, as well as the photoionisation cross-sections, from its ground state are reported. The calculated cross-sections conform fairly well with experimental and theoretical values found in the literature. Ó 2003 Published by Elsevier B.V.

1. Introduction The family of chlorofluoromethane (CFC) molecules exhibits a number of combined properties, which are useful in practical and industrial applications, particularly in high-energy systems with fast molecular energy transfer or efficient surface chemical attack. The ability of the CFCÕs to release ground-state and electronically excited fluorine atoms, fluorine ions and carbene radicals upon electron/ion impacts, in addition to their very low boiling points (a consequence of the weak intermolecular interactions in the ground state), make them particularly interesting. The production of highly reactive fragments and ions yields efficient plasmas to initiate chemical attack on low reactive *

Corresponding author. Fax: +34983423013. E-mail address: [email protected] (I. Mart
ın).

0009-2614/$ - see front matter Ó 2003 Published by Elsevier B.V. doi:10.1016/S0009-2614(03)01132-1

surfaces and quickly propagating gas reactions [1]. Semiconductor etching and the terrestrial ionosphere are well-known systems where fluoromethanes play an important role [2,3]. However, the chemical inertness of these compounds, which makes them so attractive for lab-based technology, is lost as they diffuse into the stratosphere, where they undergo solar UV photodissociation. The free Cl atoms liberated in this process are of major significance in the catalytic depletion of stratospheric ozone [4]. The consequences of ozone depletion on global bio-geo-chemical cycles, via increased UV-B radiation at the EarthÕs surface, have been of great general concern over the last years [5]. The UV and vacuum–UV photochemistry of the CFCÕs has consequently aroused much interest. An understanding of the photoabsorption dynamics of these molecules can provide useful information for atmospheric modellers.

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Whilst the UV photodissociation of many of the CFCÕs has been extensively studied, less work has been reported on the occurring vacuum–UV photodissociation processes. Yet, despite the fact that only a very small amount of the freons will avoid UV photodissociation in the stratosphere, some will diffuse higher up into the ionosphere where more vacuum–UV radiation (especially Lyman-a at 121.6 nm) is present, and it is important to know the fate of freon molecules under these conditions. In this context, knowledge of absolute photoabsorption oscillator strength data, for the single carbon freons, even at energies falling in the continuum, as well as of the variation in intensity of photoelectron bands as a function of photon energy, provides important information to further our understanding of the dynamics of the photoionisation process [5–7]. In this Letter we report theoretical absorption oscillator strengths in both the discrete and continuous regions of the spectrum for a number of Rydberg series that serve as partial ionization channels for CF3 Cl. A molecular-adapted version of the Quantum Defect Orbital (MQDO) method, which has proven to yield correct intensities for Rydberg transitions in a large variety of molecular species [8–12] as well as accurate photoionisation cross-sections of several molecules [13,14], has been adopted in the present calculations. The correctness of our procedure has been assessed with the help of experimental data available in the literature, and by the criterion of continuity of the differential oscillator strength across the ionisation threshold, for all the Rydberg series considered. One of the main goals of the present study was to assess the performance of the MQDO method in describing the spectrum of CF3 Cl before we could undertake the calculation of its photolysis rate constants as well as the photoabsorption parameters of other CFCÕs that are also relevant to atmospheric studies.

2. Method of calculation The MQDO technique, formulated to deal with molecular Rydberg transitions has been described in detail elsewhere [8]. A brief summary of this

method follows. The MQDO radial wavefunctions are the analytical solutions of a one-electron Schr€ odinger equation that contains a model potential of the form, V ðrÞa ¼

ðc  da Þð2l þ c  da þ 1Þ 1  ; 2r2 r

ð1Þ

where a represents the set of quantum numbers that define a given molecular state. Solutions of this equation are related to Kummer functions. The parameter da is the quantum defect and c is an integer chosen to ensure the normalization of the orbitals and their correct nodal pattern. The number of radial nodes is equal to n  l  c  1. In order to account for the non-spherical symmetry of the molecular core, the angular part of the orbitals has been formulated as a symmetry-adapted linear combination of spherical harmonics, so that the MQDO orbitals form bases of the appropriate irreducible representations of the moleculeÕs point group. The quantum defect, da , is related to the energy eigenvalue of the corresponding state through the following equation, Ea ¼ T 

1 2ð na  da Þ

2

;

ð2Þ

where T is the ionization energy. Both T and Ea are expressed here in Hartrees. The absorption oscillator strength for a transition between two bound states a and b may be expressed as 2 2 f ða ! bÞ ¼ N ðEb  Ea ÞQfa ! bgjRab j : 3

ð3Þ

The photoionisation cross-section for transitions between a bound a and a continuous state b is expressed, in units of megabarns (1 Mb ¼ 1018 cm2 ) as follows " # Znet 1 2 Qfa ! bgjRab j2 : r ¼ N 2:6891 þk 2 2k ðn  dÞ ð4Þ In Eqs. (3) and (4), N is the number of equivalent electrons in the MO where the transition originates, and Qfa ! bg referred to as angular factors, result from the integration of the angular

A.M. Velasco et al. / Chemical Physics Letters 377 (2003) 189–196 Table 1 Values of non-zero angular factors Qfa ! bg of CF3 Cl, for C3v symmetry and for ‘ ¼ 0; 1; 2 QfnpeðX1 A1 Þ ! nsa1 ð1 E1 Þg ¼ 1=3 QfnpeðX1 A1 Þ ! ndeð1 A1 ; 1 A2 ; 1 E1 Þg ¼ 3=5 QfnpeðX1 A1 Þ ! nda1 ð1 E1 Þg ¼ 1=15

part of the transition integral, of which Rab is the radial contribution, Rab ¼ hRa ðrÞjrjRb ðrÞi:

ð5Þ

The present calculations for both bound–bound and bound–continuum transitions have all been considered to take place through the electric dipole (E1) mechanism. The radial transition moments (5) within this model result in closed-form analytical expressions, which offers, in our view, an important computational advantage. The detailed algebraic expressions for the radial transition moments are given in [15], as originally formulated for photoionization in atomic systems, and in [9] as generalized for bound–bound transitions in molecules, where the angular functions are also described. The values of Qfa ! bg for the C3v symmetry group, to which the Rydberg states of CF3 Cl belong, are collected in Table 1.

3. Results and analysis The electronic configuration of the ground state of CF3 Cl may be written as follows [16,17], Inner shells: (Cl 1s)2 (F 1s)6 (C 1s)2 (Cl 2s)2 (Cl 2p)6 . 2 4 2 2 4 2 Valence shells: ð1a1 Þ ð1eÞ ð2a1 Þ ð3a1 Þ ð2eÞ ð4a1 Þ 4 4 2 2 4 1 ð3eÞ ð4eÞ ð1a2 Þ ð5a1 Þ ð5eÞ : A1 . The HOMO (5e) essentially contains the lonepair electrons from the chlorine atom [16]. The ionization energy (IP) of the outer valence orbital 5e adopted in the present calculations was measured by high resolution HeI and HeII photoelectron spectroscopy (PES) by Cvitas et al. [16] The energy data chosen for our calculations on the electronic Rydberg states have been the experimental values measured by Au et al. [18] and King and McConkey [19]. For higher Rydberg states the energy has been extrapolated through the quan-

191

tum defect formula given in Eq. (2), as the quantum defects along an unperturbed Rydberg series, characterised by a given angular momentum and a particular irreducible representation of the molecular symmetry group, display a very nearly constant value. In this form, we have been able to predict intensities for transitions that have not been observed experimentally. For the continuum orbitals we have used the same quantum defect as that of the bound states with the same symmetry. All quantum defects are collected in Table 2. In Table 3 we show the absorption oscillator strengths for the 3pe ðX1 A1 Þ ! nsa1 ð1 E1 Þ, 3pe (X1 A1 Þ ! nda1 ð1 E1 Þ and 3pe (X1 A1 Þ ! ndeð1 A1 ; 1 A2 ; 1 E1 Þ electron transitions, together with the experimental values found in the literature [18–21]. The reason for the multiple symmetry notation concerning the nde Rydberg series is the lack of an unambiguous assignment for this series. The present results conform fairly well with the most recent measurements, performed with a high-resolution dipole (e,e) technique, by Au et al. [18]. A general good agreement of the present calculations with the comparative data is apparent, and more so if we take into account their estimated uncertainties, also written in Table 3. It should be noted that the higher magnitude of the oscillator strengths reported by King and McConkey [19] may in part be attributed to the fact that their measurements, with a zero angle electron energyloss technique, were normalised to those of Gilbert et al. [22] and Jochims et al. [23]. The data reported Table 2 Energy levels and quantum defects of bound and continuum ‘ ¼ 0; 1; 2 states of CF3 Cl State

E (eV)

d

4sa1 ð1 E1 Þ 5sa1 ð1 E1 Þ, 3da1 ð1 E1 Þ

9.69a 11.60a

1sa1 ð1 E1 Þ, 1da1 ð1 E1 Þ

Continuum

4deð1 A1 ; 1 A2 ; 1 E1 Þ 1deð1 A1 ; 1 A2 ; 1 E1 Þ

12.10b Continuum IP ¼ 13:08c

2.00 1.97(s), )0.03(d) 2.0(s), )0.03(d) 0.27 0.27

a

Au et al. [18]. King and McConkey [19]. c Cvitas et al. [16]. b

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Table 3 Oscillator strengths for the 3pe ðX1 A1 ! nsa1 ð1 E1 Þ, 3pe ðX1 A1 ! nda1 ð1 E1 Þ, and 3pe ðX1 A1 ! nde ð1 A1 ; 1 A2 ; 1 E1 Þ transitions of CF3 Cl MQDOa

Expt.b

Expt.c

Expt.d

Expt.e

3pe ðX1 A1 Þ–4sa1 ð1 E1 Þ 3pe ðX1 A1 Þ–5sa1 ð1 E1 Þ 3pe ðX1 A1 Þ–6sa1 ð1 E1 Þ 3pe ðX1 A1 Þ–7sa1 ð1 E1 Þ 3pe ðX1 A1 Þ–8sa1 ð1 E1 Þ 3pe ðX1 A1 Þ–9sa1 ð1 E1 Þ 3pe ðX1 A1 Þ–10sa1 ð1 E1 Þ

0.1191 0.0225 0.0087 0.0043 0.0109 0.0067 0.0044

0.1625  0.032

0.1516  0.015

0.220  0.088

0.1503

3pe ðX1 A1 Þ–3da1 ð1 E1 Þ 3pe ðX1 A1 Þ–4da1 ð1 E1 Þ 3pe ðX1 A1 Þ–5da1 ð1 E1 Þ 3pe ðX1 A1 Þ–6da1 ð1 E1 Þ 3pe ðX1 A1 Þ–7da1 ð1 E1 Þ 3pe ðX1 A1 Þ–8da1 ð1 E1 Þ 3pe ðX1 A1 Þ–9da1 ð1 E1 Þ 3pe ðX1 A1 Þ–10da1 ð1 E1 Þ

0.0120 0.0060 0.0033 0.0019 0.0012 0.0008 0.0005 0.0004

3pe ðX1 A1 Þ–4de* 3pe ðX1 A1 Þ–5de* 3pe ðX1 A1 Þ–6de* 3pe ðX1 A1 Þ–7de* 3pe ðX1 A1 Þ–8de* 3pe ðX1 A1 Þ–9de* 3pe ðX1 A1 Þ–10de*

0.1031 0.0508 0.0285 0.0176 0.0116 0.0080 0.0058

a

MQDO, this work. Au et al. [18]. c Suto and Lee [20]. d King and McConkey [19]. e Doucet et al. [21]. b

by Jochims et al. [23] are systematically higher than all the existing values up to date. The accuracy of the earliest values, by Doucet et al. [21] is difficult to establish, since both the extinction coefficient and the bandwidth have been determined graphically. In Figs. 1–3 we have plotted the MQDO oscillator strength spectral density, df/dE, in the continuum and the related oscillator strengths, f, in the discrete spectral region vs. photon energy in the same graph for the 3pe ðX1 A1 Þ ! nsa1 ð1 E1 Þ, 3pe ðX1 A1 Þ ! nda1 ð1 E1 Þ and 3pe ðX1 A1 Þ ! nde ð1 A1 ; 1 A2 ; 1 E1 Þ Rydberg series. We have followed a procedure originally developed by Fano and Cooper [24] and previously employed in some of our calculations on molecular systems [13,14]. The data that pertain in the continuum are also collected in Table 4. No comparative values of either

Fig. 1. MQDO oscillator strength spectral density for bound and continuum spectral regions of the 3pe ðX1 A1 Þ ! nsa1 ð1 E1 Þ (n ¼ 4–10, 1) Rydberg series in CF3 Cl.

experimental or theoretical character have been found in the literature. In the figures, the oscillator strengths of the discrete transitions are included in the form of a histogram. The continuous region of the spectrum

A.M. Velasco et al. / Chemical Physics Letters 377 (2003) 189–196

Fig. 2. MQDO oscillator strength spectral density for bound and continuum spectral regions of the 3pe ðX1 A1 Þ ! nda1 ð1 E1 Þ (n ¼ 3–10, 1) Rydberg series in CF3 Cl.

193

Inspection of Figs. 1–3 reveals a complete consistency between the calculated photoionisation cross-sections and oscillator strengths. In all the Rydberg series, the extrapolation of the f value in the discrete spectrum leads to the same point at the ionisation threshold as does the extrapolation of the oscillator-strength spectral density form the opposite direction (that of decreasing energy). In the absence of comparative data, these features exhibited by the present MQDO results make us feel confident in their, at least qualitative, reliability. Fig. 4 shows the MQDO oscillator strength density for the absorption from the ground state of CF3 Cl in a range of 14–100 eV of photon energy. The total cross-section for the photoionisation from a state i in a molecule, to which the above property is proportional (Eq. (6)), may be expressed as a sum of partial cross-sections which correspond to all compatible absorption processes i ! j, X ri ðhmÞ ¼ ri!j ðhmÞ: ð7Þ j

Fig. 3. MQDO oscillator strength spectral density for bound and continuum spectral regions of the 3pe ðX1 A1 Þ ! ndeð1 A1 ; 1 A2 ; 1 E1 Þ (n ¼ 4–10, 1) Rydberg series in CF3 Cl.

is included in terms of the spectral density of the oscillator strength, which is related to the photoionisation cross-section through the expression: rðEÞ ¼ 1:098 1016

df cm2 eV: dE

ð6Þ

The tops of the blocks in the histogram constructed in this way form a staircase, which constitutes an extrapolation of the continuum spectrum below the ionisation limit. In other words, the staircase and the continuum oscillator strength should join smoothly across the threshold if the data are correct, as the discrete part of the spectrum for any spectral series can be considered as an appendage of the continuum [24]. It is apparent that the present results depicted in Figs. 1–3 comply with this requirement, and, thus, the crosssection at the photoionisation threshold, which could not be directly calculated given that n ¼ 1, may be interpolated from the graphs.

Making use of this expression, we have determined the total cross-section for the three possible ionisation channels from the ground state of CF3 Cl, 3pe ðX1 A1 Þ, 3pe ðX1 A1 Þ ! nsa1 ð1 E1 Þ, 3pe ðX1 A1 Þ ! nda1 ð1 E1 Þ and 3pe ðX1 A1 Þ ! ndeð1 A1 ; 1 A2 ; 1 E1 Þ. The corresponding differential oscillator strengths are collected in Table 4. In Fig. 4, the experimentally measured crosssections by Novak et al. [25], Cooper et al. [26], Zhang et al. [27] and Bozek et al. [28], as well as those obtained in a theoretical calculation with the continuum MS Xa method by Bozek et al. [28], have also been included. Novak et al. [25] and Bozek et al. [28] converted measurements of the moleculeÕs photoelectron branching ratios into absolute photoionisation cross-sections by normalising them to experimental [29,30] cross-sections in a given photon energy range. The main disadvantage of the above approach is the scarcity of the available data in the 10–100 eV photon energy range, even for simple molecules. In addition to this drawback, there may be contributions to the total photoionisation cross-section from double ionisation, shakeup and Auger transitions

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Table 4 Differential oscillator strengths, df/dE, for different Rydberg channels arising from the excitation of the 3pe ðX1 A1 Þ ground state of CF3 Cl, in eV1 E (eV)

3pe ðX1 A1 Þ ! nsa1 ð1 E1 Þ

3pe ðX1 A1 Þ ! nda1 ð1 E1 Þ

3pe ðX1 A1 Þ ! ndeð1 A1 ; 1 A2 ; 1 E1 Þ

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 52 54 56 58 60

0.08225 0.07160 0.06288 0.05565 0.04960 0.04447 0.04009 0.03632 0.03305 0.03020 0.02770 0.02549 0.02354 0.03090 0.02023 0.01849 0.01756 0.01643 0.01539 0.01445 0.01359 0.01280 0.01207 0.01142 0.01081 0.01024 0.00972 0.00923 0.00878 0.00837 0.00798 0.00761 0.00727 0.00695 0.00666 0.00638 0.00611 0.00563 0.00520 0.00482 0.00448 0.00417

0.01743 0.01791 0.01792 0.01763 0.01717 0.01659 0.01595 0.01528 0.01462 0.01395 0.01332 0.01270 0.01210 0.02065 0.01100 0.01015 0.01001 0.00956 0.00913 0.00873 0.00835 0.00799 0.00765 0.00734 0.00704 0.00675 0.00648 0.00623 0.00599 0.00576 0.00554 0.00534 0.00514 0.00496 0.00478 0.00461 0.00445 0.00416 0.00389 0.00364 0.00342 0.00322

0.18994 0.18119 0.17105 0.16052 0.15013 0.14018 0.13080 0.12206 0.11396 0.10649 0.09961 0.09328 0.08746 0.08210 0.07717 0.07263 0.06845 0.06458 0.06101 0.05771 0.05464 0.05180 0.04916 0.04670 0.04441 0.04228 0.04028 0.03842 0.03667 0.03504 0.03350 0.03206 0.03070 0.02943 0.02822 0.02709 0.02602 0.02405 0.02228 0.02070 0.01927 0.01797

at high photon energies. Such contributions are not normally included in photoelectron branching ratios, and their neglect can lead to errors in the determination of absolute partial cross-sections with this method.

Bozek et al. [28] also performed theoretical calculations with a semi-quantitative model, the continuum MS Xa method [31] and remarked that although the main observed features in the crosssection profiles are often correctly reproduced by

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195

above 60 eV was not observed for the equivalent 5e chlorine lone-pair orbital of CF3 Cl. This is consistent with these authorsÕ assignment of this effect to interchannel coupling involving the I 4d shell, which is of course absent in chlorine. 4. Concluding remarks

Fig. 4. MQDO photoionisation cross-section of CF3 Cl from its ground state 3pe ðX1 A1 Þ.

the calculations, the predicted magnitudes and positions may only be approximate in nature. Consequently, these authors used the theoretical results only as a guide in their assignment and discussion of the cross-sections and branching rations. The MS-Xa calculations proved to be in generally good agreement with their experimental values. Zhang et al. [27] employed dipole (e,e) spectroscopy, to obtain absolute photoabsorption values by TRK sum rule normalization. Cooper et al. [26] used synchrotron radiation (SR) in the range 41–100 eV, and derived partial photoionisation cross-sections making use of total photoabsorption values [27]. Fig. 4 reveals a good agreement between the present results and the comparative data. The experimental photoionisation cross-sections exhibit a largely monotonic decrease with increasing photon energy instead of the oscillating behaviour reported to have been observed in the b spectra of this molecule [17,32] which our calculations also exhibit. Even the cross-section oscillation associated with the Cooper minimum for ionisation from chlorine lone-pair orbitals, which is a pronounced feature in beta spectra, is likely to be very small according to recent absolute photoionisation cross-section measurements for atomic chlorine [33]. It is significant that the relative enhancement of the 5e band in the photoelectron spectrum of CF3 I observed by Bancroft et al. [34] at photon energies

Absorption oscillator strengths and photoionisation cross-sections for transitions involving Rydberg states of CF3 Cl have been calculated with the MQDO method. Partial differential oscillator strengths for the different Rydberg series that constitute the ionisation channels of CF3 Cl from its ground state have been calculated up to a photon energy of 100 eV. These data are supplied, to our knowledge, for the first time. The MQDO cross-section results are in good agreement with the data available in the literature. The MQDO has proven, once more, to be a very useful tool to estimate transition intensities. Our next goal is the study of rate constants corresponding to the photodissociation of CF3 Cl in the ionosphere. Acknowledgements This work has been supported by the D.G.E.S. of the Spanish Ministry for Science and Technology within Project No. BQU2001-2935-C02, by European FEDER funds, and by the J.C.L. within Project No. VA117/2002. A.M.V. and E.M. also wish to acknowledge their respective research agreement and grant from the same institution and from the Spanish Ministry for Education, respectively.

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