Pressure induced shifts in HCl/HF and HF/HCI systems

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1 Pressure induced shifts in HCl/HF and HF/HCI systems C. Boulet, A. Rosenberg To cite this version: C. Boulet, A. Rosenberg. Pressure induced shifts in HCl/HF and HF/HCI systems. Journal de Physique, 1981, 42 (2), pp < /jphys: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1981 HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 A As In J. Physique 42 (1981) FÉVRIER 1981, 203 Classification Physics Abstracts 33.20E 33.20F Pressure induced shifts in HCI/HF and HF/HCI systems C. Boulet Laboratoire d Infrarouge (*), Campus d Orsay, Bât. 350, Orsay Cedex, France and A. Rosenberg RCAASTRO, P.O. Box 800, Princeton, NewJersey 08540, U.S.A. (Reçu le 6 mai 1980, révisé le 2 septembre, accepté le 29 septembre 1980) 2014 Résumé. la suite d une précédente étude théorique consacrée aux déplacements des raies de vibrationrotation des molécules diatomiques perturbées par des gaz polaires, de nouveaux résultats expérimentaux ont été obtenus et sont présentés dans cet article. Ils concernent les déplacements des raies des bandes 01 et 02 de HCl perturbé par HF ainsi que des raies de la bande 02 de HF perturbé par HCl. Dans cet article, sont également confrontés à l expérience de nouveaux résultats théoriques, obtenus à partir d un formalisme proposé récemment par Robert et Bonamy, et qui améliore la théorie d Anderson. Un bon accord théorieexpérience est obtenu, grâce à la prise en compte dans le calcul des sections efficaces des effets de noncommutation du potentiel intermoléculaire Abstract. a sequel to a previous theoretical study of pressure induced lineshifts in the spectra of diatomic molecules pressurized by polar gases, some new experimental results became recently available and are reported in this paper. They concern the shifts in the HF(02) band due to HCl, and the HCl(01) and HCl(02) bands due to HF, for which predictions have been previously published. In the present paper, theoretical calculations have been again performed for these systems, starting from a formalism developed by Robert and Bonamy, which improves the Anderson theory. By taking into account, as shown previously, the non commutative character of the intermolecular potential, in the calculation of the differential crosssection, a good quantitative agreement with experiments has been obtained for all the considered cases. 1. Introduction. a previous paper [1] Boulet, Robert and Galatry have analysed the mechanisms which are responsible for the pressure induced lineshifts for diatomic molecules perturbed by polar gases. In reference [1], all the available literature data were rather well reproduced by the calculations. Then we have proposed as a possible extension of this study, new experiments conceming the vibrational dependence of the shifts of HCI perturbed by HF. Let us recall the main feature of our predictions. The shifts in the (02) Rbranch of HCI are expected to oscillate with rotational quantum number. At the sàme time, in the (01) Rbranch, the oscillation should be clearly attenuated. A paper by Guelachvili and Smith [2] has appeared recently, in which they have demonstrated experimentally the oscillating behaviour of the (02) HCI lineshifts due to perturbation by HF. But the gas pressure used was not high enough to get very accurate (*) Associé au C.N.R.S. measurements of the shifts. Moreover, no experimental results were obtained for the (01) band. In this paper we report the experimental results and the theoretical calculations of pressure induced shifts in the fundamental and the first overtone bands of HCI induced by HF, and in the fundamental band of HF induced by HCI. The oscillatory pattern of the shifts were observed in the HCI/HF system but were absent in the HF/HCl system. The measurements reported here were taken more than ten years ago in the infrared laboratory of the Weizmann Institute in Rehovoth, Israel. However the results were not published at that time due to the lack of an adequate theory that could interpretate the shifts oscillation quantitatively. The lines P(8) to R(6) and P(7) to R(8) in the 10 and 20 band of HCI respectively and P(5) to R(6) in the 20 band of HF were studied. The P(5) line in the 20 band of HCl could not be studied due to the interference of water vapour lines, In the HCI bands the lineshifts of both isotopes, H35C1 and H37CL were measured. Article published online by EDP Sciences and available at

3 Lineshifts The Lineshifts Lineshifts 204 From a theoretical point of view, since the publication of reference [1], further improvements have been introduced in the calculation of linewidth and shift. For instance, D. Robert and J. Bonamy [3] have developed a formalism in which a more realistic representation of the trajectory is used for close collisions together with a non perturbative exponential form of the differential crosssection which avoids the use of any cutoff procedure. In this paper, we will apply this improved formalism to the calculation of the shifts in the HCI/HF and HF/HCI systems in order to verify our previous predictions. 2. Experimental. pressure shifts in the mixtures HCI/HF and HF/HCI were measured with the. Rehovoth 5m EbertFastie spectrometer equipped with a special facility that enabled scanning very slowly a small portion of the spectrum ( 0.5 cm1) without turning the grating [4]. The technique of employing this scanning unit to measure the small lineshifts ( cm1) has been described elsewhere [5]. It consists mainly of comparing the relative position of the centre of a given line on two succesive recordings, one using a cell with a small amount of the absorbing gas, and the other using a cell containing the same amount of the abs rbing gas with the addition of a large amount of a foreign gas. A special stainless steel gas handling sys m [6] and four stainless absorption cells equippe with sapphire windows, were used for this exp riment. All the measurements were made at room temperature. Pressure shifts of lines in the 10 band of HCI were studied using about 1 cm Hg pressure of HCI in cells of 5, 8 and 15 cm length, and an added, pressure of 4060 cm Hg of HF in the last two cells. The shorter Fig. 2. in the HCI 0. 1 band perturbed by HF. e : H35Cl observed shifts. 0 : H37Cl observed shifts. A : calculated shifts without velocity averaging (v v) and using the ATC trajectory = model. x : calculated shifts without velocity averaging and ùsing the BBR trajectory model. Fig. 1. in the HF 02 band perturbed by HCI. 0 : observed shifts. A : calculated shifts without velocity averaging (v V), and using the ATC trajectory model. = x : calculated shifts without velocity averaging, and using the BBR trajectory model. Fig. 3. in the HCl 02 band perturbed by HF. 0 : H35C1 observed shifts. 0 : H3 7 CI observed shifts. x : calculated shifts without velocity averaging (v v) and using the BBR trajectory = model. A : calculated shifts with velocity averaging and using the BBR trajectory model.

4 In The 205 of the two çells with the low pressure of HF was used to measure the low J lines of the Rbranch. The shifts of these lines were the most difficult ones to measure due to the strong absorption and the large width of thçse transitions. In the 20 bend of HCI 15 and 30 cm length cells were used, with 5 cm Hg pressure of HCI. The longer of the two cells was pressurized with HF up to a total pressure of 50 cm Hg. The partial pressure of HCl was taken into account in calculating the shifts. These two cells were also used for measuring the shifts in the 20 band of HF, with 1 cm Hg pressure of HF in the short cell and the same amount of HF with HCI up to a total pressure of 50 cm Hg in the long cell. The shift of each of the individual lines was measured 10 times for the two overtone bands of HCI and HF and 20 times for the fundamental band of HCI. The mean experimental error of the HCI lineshifts in both bands was less than ) 1 cm atm: 1 and in the HF band was less than ) cm1 atm: 1. A second series of measurements was carried out after an interval and the results were within of about three months these errors. The expérimental results are shown in figures Theory. impact theory of pressure broadening [ gives lôrentzian line shapes for non ôverlapping ines. For cases in which the impact and classical path approximations hold, the halfwidth Yf; and the shift ôfi of the considered line i f are related to collision processes by : where nb is the density of perturbing particles, PV2j2 is the Boltzmann distribution of the internal levels of the perturber and f (v) is the Maxwellian relative velocity distribution. The quantity S(b, v, (2)) called the collision efficiency function is given by [3, 810] with : where C( j f j;1, mf m; M) is a ClebschGordan coefficient [11]. Moreover, the Liouville S matrix is defined through : Ha and Hb are respectively the hamiltonian of the active molecule and of the perturber and V(t) the radiatorperturber interaction. In order for the theory to be numerically applied, three problems must be now solved : i) The collision efficiency function must be calculated up to an infinité order in V(t) for strong collisions, i.e. low b values. But it must be recalled that only the first and second order contributions to S(b, v, (2)) can be easily calculated for diatomdiatom collisions. ii) A convenient trajectory model is required where it is necessary to actually calculate the efficiency function for close collisions, corresponding to impact parameters b around the LennardJones diameter (1. iii) Sufficiently realistic representations of the angle dependent intermolecular potential and of the vibrational dependence of the isotropic one must be available. 3.1 CALCULATION OF THE COLLISION EFFICIENCY the Anderson Tsao Curnutte theory FUNCTION. (ATC) the S(b, v, (2)) function is approximated by its second order expansion in the interaction potential. This approximation is only valid for distant collisions. For stronger collisions, i.e. for small values of the impact parameter, it is necessary to use some cutoff procedure in order to obtain a reasonable behaviour of the efficiency function. But in most cases the calculations are rather sensitive to the cutoff used, then it is quite clear that this method of calculation is questionable [8]. Murphy and Boggs [9] have improved the ATC theory by including some,of the higher order terms through an exponential form of the efficiency function, but they have neglected elastic effects. It

5 The 206 must be recalled that in some cases like HCIAr analysed by Smith, Giraud and Cooper [8], this is not a good approximation. More recently, Robert and Bonamy [3] have generalized this method by taking into account the elastic contributions. In this approach that we, will use in the following, the matrix element is calculated through the linked cluster theorem, limiting the expansion to the second order diagrams. The method of reference [3] then gives the result that the efficiency function S(b, v, (2)) can be written in terms of the psual interruption functions Sl(b, v, (2)) and S2(b, v, (2)) of the ATC theory [lu,12] In this expression, all the symbols have their usual meaning. Note only that the subscript ND indicates those of the contributions to the S2 middle function which correspond to inelastic virtual transitions of the perturber. Note also that if the vibrationrotation coupling is disregarded, the pure vibrational dephasing is rigorously taken into account up to the infinite order through the SlSO(b, v, (2)) contribution. At last it must be recalled that, due to the noncommutative character of V in the interaction representation, the S2 ôu er functions are complex quantities [1]. The analytical expressions of all these functions may be found in references [1, 12]. Finally from equations (1), (5), it comes for yf; and l5fi : From these equations, it appears that such an approach avoids the use of any questionable cutoff for small b values, due to the partial resummation of the V(t) even order contributions through the linked cluster theorem KINEMATICAL MODEL. For distant collisions, b > Q, it is well known that the influence of the isotropic interaction on the classical trajectories can be neglected, resulting in the usual straight line trajectory described with constant velocity v (ATC model). But when b decreases [b Q], such a trajectory description is no longer valid and some calculations using this model for every b values have had only a limited success. Starting from a model proposed by Tipping and Herman [13], Bonamy, Bonamy and Robert have elaborated a model which includes both the influence of the force Fiso derived from the isotropic potential on the motion near the distance of closest approach ri together with the influence of Viso on the energy conservation. In this BBR model the true trajectory is replaced by an equivalent straight path around rc described with a velocity v c given by [14] : of the trajectory description on the shift calculation for the considered gas mixtures INTERMOLECULAR POTENTIAL. first the anisotropic part of the potential, we have taken into account all the electrostatic contributions up to one. It will be Concerning and including the octopoleoctopole shown later that for strongly polar and resonant mixtures this approximation correctly describes the potential for practically all the values of the impact parameter which necessitate an actual and rather precise calculation of the efficiency function. The equations defining the vibrational dephasing calculated through a limited expansion of Viso in terms of the reduced vibrational coordinates are given explicitly in references [14, 15]. Finally, we point out that they are no adjustable parameters in the present calculation. All the molecular constants, which are given in reference [1], have been obtained from independent sources. for a 612 Lennard Jones isotropic potential. In the present work, we will compare the results obtained with this two models in order to study the influence 4. Results and discussion. calculated shifts and the experimental data have been plotted on figures 13 as a function of the m quantum number

6 From 207 (m = j; in the Pbranch and j; + 1 in the Rbranch). In general, the agreement between our predictions and experiment is good. In particular, the calculation reproduces well the general trends of the experimental results, like for instance the strong asymmetry in the Pbranches with respect to the Rbranches (cf. Fig. 1). It also reproduces the aperiodic behaviour of the shifts for HF perturbed by HCI (cf. Fig. 1) in contrast with the oscillating behaviour of the shifts for HCI perturbed by HF (cf. Figs. 2, 3). Let us remark that in the Rbranch of the 01 band of HCl pressurized by HF, the oscillations are clearly attenuated at low m values, which is not true in the 02 band. The theory exhibits exactly the same behaviour. An interpretation of all the shifting mechanisms has been given in a previous work from a slightly different formalism, using a cutoff procedure for calculating the low b efficiency function [1]. In reference [1] the HCIHF system for which no data were available, was analysed in order to suggest some new experiments. From the present work, it is quite clear that the observed shifts verify those predicted by the theory (cf. Ref. [1], figure 14 and the present results). Nevertheless, it must be recalled that the present formalism avoids the use of any questionable cutoff procedure in contrast with the previous calculation. From a more quantitative point of view, some additional remarks must be made. i) First, the calculated shifts are rather insensitive to the trajectory model used, except perhaps at high m values (cf. Fig. 1). This feature can be explained from equation (5) which gives the b dependence of the efficiency function S(b, v, (2)) in terms of the ATC interruption functions S1(b, v, (2)) and S2(b, v, (2)). Starting from a high b value, where S(b, v, (2)) 1 1, let b decreases. Let us recall that, for not too high m values, the strong long range dipolar interaction is near resonant, at least for the most populated perturber levels. Therefore the interruption function will reach values higher than some units before any problem arises concerning either the trajectory model or the electrostatic expansion of the anisotropic potential (typically b higher than Q, [b = 2 or 3 Q]). But it results from equation (5) that when In other words, the low m shifts are essentially sensitive to sufficiently distant collisions in which the ATC trajectory model and the multipolar approximation of the angle dependent potential are both physically meaningfull. At high m values, the BBR trajectory model appears to give better results than the ATC one (cf. Fig. 1) but it must be kept in mind that the problem remains to take into account for theses lines, the influence of both the long and short range forces on the broadening and shifting processes. ii) The theoretical shifts are strongly dependent on averaging or not the partial crosssections over the relative velocity. For instance, the amplitude of the shift oscillation is considerably reduced (cf. Fig. 3) when the velocity averaging is performed, giving a better agreement with experiment. This feature must also be connected with the relative long range character of the efficient collisions, which are more sensitive to any variation of the initial relative velocity than for instance the short range collisions. iii) Finally, it must be said that any improvement of the quantitative agreement between calculated and observed vibrationrotation lineshifts depends on a better knowledge of the vibrational dependence of the isotropic potential. Part of the discrepancy between theory and experiment is almost certainly caused by the fact that the numerical values of the potential derivatives in terms of the vibrational coordinates are poorly known, even at the f rst order [15]. Moreover nothing can be said, conceming the eventual influence, especially in harmonic bands, of the second order terms, which has been presently neglected, since the requisite molecular constants are not available. 5. Conclusion. this work, which has confirmed and completed the previous one [1] it appears that the formalism of Robert and Bonamy [3] is basically correct in the description of the shifts of vibrationrotation lines of diatomic molecules perturbed by polar ones. This fact is due to the sufficient partial resummation of the even V(t) contributions through an exponential of the second order interruption function S2(b, v, (2)) in the calculation of which the crucial non commutative character of the potential has been taken into account, according to a previous analysis [1]. Finally, a more quantitative agreement between calculated and experimental shifts probably depends on a more realistic description of the short range anisotropic potential together with a better knowledge of the vibrational dependence of the isotropic one.

7 208 References [1] BOULET, C., ROBERT, D. and GALATRY, L., J. Chem. Phys. 65 (1976) [2] GUELACHVILI, G. and SMITH, M. A. H., J. Quant. Spectrosc. Radiat. Transfer 20 (1978) 35. [3] ROBERT, D. and BONAMY, J., J. Physique 40 (1979) 923. [4] JAFFE, J. H., Adv. Spectrosc. 2 (1961) 263. [5] KIMEL, S., HIRSHFELD, M. A. and JAFFE, J. H., J. Chem. Phys. 31 (1959) 81. [6] JAFFE, J. H., ROSENBERG, A., HIRSHFELD, M. A. and GAI LER, N. M., J. Chem. Phys. 43 (1965) [7] RABITZ, H., Ann. Rev. Phys. Chem. 25 (1974) 155. [8] SMITH, E. W., GIRAUD, M. and COOPER, J., J. Chem. Phys. 65 (1976) [9] MURPHY, J. S. and BOGGS, J. E., J. Chem. Phys. 47 (1967) 691. MEHROTRA, S. C. and BOGGS, J. E., J. Chem. Phys. 58 (1977) [10] TSAO, C. J. and CURNUTTE, B., J. Quant. Spectrosc. Radiat. Transfer 2 (1962) 41. [11] ROSE, M. E., Elementary Theory of Angular Momentum (John Wiley & Sons Inc., New York) [12] ROBERT, D., GIRAUD, M. and GALATRY, L., J. Chem. Phys. 51 ( 1969) [13] TIPPING, R. H. and HERMAN, R. M., J. Quant. Spectrosc. Radiat. Transfer 10 (1970) 881. [14] BONAMY, J., BONAMY, L. and ROBERT, D., J. Chem. Phys. 67 (1977) [15] BOULET, C. and ROBERT, D., Chem. Phys. Lett. 60 (1978) 162.