J. Phys. Chem. 1993,97, 2063-2071
2063
Molecular Beam Studies of Weak Interactions of Open-Shell Atoms: The Ground and Lowest Excited States of Rare-Gas Chlorides Vincenzo Aquilanti,' David Cappelletti, Vincent Lorent,' Emilio Luzzatti,$ and Fernando Pirani Dipartimento di Chimica dell'Universitb. I-061 00, Perugia. Italy Received: August 14, 1992; In Final Form: October 22, 1992
A source for the production of a thermal energy beam of C1 atoms has been characterized by a Stern-Gerlach magnetic analysis of the involved atomic sublevels. These open-shell atoms are here found in their electronic ground state 2 Pand ~ this analysis allows us also to vary the weights of their magnetic sublevels in a controlled way during scattering experiments. The atomic beam of C1 atoms is produced in a microwave discharge source in pure Cl2 and, after velocity and magnetic selection, is used for absolute total cross-section measurements in collisions with the rare-gas atoms He, Ne, Ar, Kr,and Xe. The data are obtained in the beam velocity range 0.4-2.3 km/s and under different populations of magnetic sublevels of C1 atoms. The analysis of the data, using an adiabatic decoupling scheme to derive the interaction in terms of a spherical and an anisotropic component, permits an accurate characterization of the ground and lower lying excited states of the weakly bound complexes between C1and rare gases. Nonadiabatic coupling matrix elements and other general features of these interactions are also presented.
1. Introduction
The weak bond in the complexes involving open-shell atoms and closed-shellparticles may be stronger than purevan der Waals interaction because the peculiar electronic structure of the openshell atom itself induces an anisotropy of interaction. This electronic anisotropy plays a fundamental role in determining strength, range, and shape of the intermolecular forces and leads to the description of the whole interaction in terms of a manifold of potential energy surfaces.' The characterization of the structure and the dynamicsof these weakly bound systems is motivated for several reasons. For the rare-gas oxides and halides, which are responsible for excimer laser action in the UV region, the electronically excited and in general the stronglybound states are better known than the weakly bound ground states, in spite of the fact that the features of the latter also affect the structure of the emission band~.2-~In addition, the study of the low-lying states of these molecular complexes is very interesting also for understanding the peculiar nature of the involved bonds,' the transport properties of openshell atoms in nonreactive baths,I0,l1the dynamics of photodissociation in clusters,I2 and the selective role of long-range forces in chemical reactivity.'3J4 Recent advances in the quantum mechanicaltreatment of openshell atom collisionsls-'7 allow the use of measurements of scattering cross sections as fundamental data for the characterizationof the involved interactions.'*~I9Considerable experimental progress in this direction is achieved by coupling molecular beam techniques and state selection of the sublevels of the open-shell atom in the beam;t0.21in particular, for ground-state atoms such asGa(ZP),O(3P),and F(zP),it has been proven that the magnetic analysis is the technique of choice for probing their interaction with rare gases and simple molecules.22-j2 In our scattering experimentswe use a Stern-Gerlach magnetic selector in the Rabi configuration:33J4 the inhomogeneous magnetic field induces a different deflectionon the paramagnetic particles of the beam depending on their magnetic moments. This technique is of interest (i) to characterize the electronic states and the relative magnetic sublevel weights in the produced
' Present address: Laboratoire de Physique des Lasers, UniversitC ParisNord, 93430 Villetaneuse, France. I On leave from lstituto di Metodologic Avanzate lnorganiche del Consiglio Nazionale delle Ricerche, 00016 Monterotondo (Rome), Italy.
atomic beam and (ii) to vary in a controlled way, at each beam velocity, the magnetic sublevel weights and then to perform scattering experiments under those conditions. For the proper use of this technique it is necessary to know the behavior of the open-shell atom as a function of magnetic field strength, in particular the specific decouplings of the atomic angular momenta, which produce variations in the effective magneticmoments. In thecase of halogen atoms, having a nuclear angular momentum I different from zero, the coupling of I with the total electronic angular momentum J must be taken into account. In a recent paper" we applied the magnetic selection technique to analyze halogen atom beams in the electronicground *PJstate, where J is the quantum number associated to the total electronic angular momentum, and we exploited the possibility to obtain selected beams essentially composed by atoms in the upper fine structure level J = l / 2 . We are applying this selection method to measure total cross section for scattering of chlorine atoms by rare gases and simple molecules. In this paper we report experimental results for the C1(2PJ)He, -Ne, Ar, and -Kr systems and their analysis in terms of the three involved adiabatic potential energy curves. These potentials have been obtained from total cross-section data, which, being governed by collisions occurring respectively with large and intermediate impact parameters, provide direct information on the interaction at large and intermediate interatomic distances. For the Cl(2PJ)-He, -Ne, Ar, and -Kr systems the results reported here represent the first reliable characterization of the involved interactions at long range and in the well depth region. For the C1(2PJ)-Xe system we have recently published3z experimental results of the same type: their analysis, performed also taking into account of other scatteringj5and spectroscopicproperties36 that are available for this system, has allowed an accurate characterization of the interactions in a wider distance range. Therefore the results discussed here, together with those recently published on the C1(2PJ)-Xe system,)2give a comprehensive view of the interactions for the whole series of the rare-gas chlorides. Section 2 outlines those experimental details that are specific ofthis workand resumes thegeneral basisof the magneticselection technique. Section 3 summarizes the theoretical background for the analysis of present scattering experiments. The results and their analysis are reported in section 4, while a discussion and the conclusions follow in sections 5 and 6,respectively.
QO22-3654/93/2Q97-2Q63s04.QQ/Q0 1993 American Chemical Society
2064
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 magnetic selector velocity selector
I
mass filter
scattering chamber
Figure 1. Schematicview oftheapparatususedin thepresent experiments. The magnet length and the distance of the detector from the exit of the magnet are 12 cm and 50 cm, respectively, while the ratio ( a B / a z ) / B between the field gradient to the field itself, which essentially depends on the features of the polar expansion^,)^ has been estimated to be 4 cm-I.
Aquilanti et al. It is alsoimportant tonote that for theproper useof the magnetic analysis it is fundamental to know, as discussed in section 2.2, the behavior of the atom in the magnetic field. 2.2. Coupling Schemes for Magnetic Moments of Atomic Sublevels. A paramagnetic open-shellparticle traveling inside a magnet with an inhomogeneous field B, whose direction z is orthogonal to that of the initial motion of the particle, undergoes a deflection along z,at a given distance from the magnet, which depends on the field gradient a B / a z , on the length of the magnet, and on mass, velocity, and effective (Le., along the field gradient direction) magnetic moment of the parti~le.~' In a definite angular momentum coupling case, for which the atomic "good" quantum number in the magnet and its projection along the z direction are for definiteness labeled K and MK, respectively, IK M K )properly describes the atomic state in the field. The effective magnetic moment is given by
2. Experimental Technique and Magnetic Analysis 2.1. The Apparatus. The experimental apparatus used to measure the total collision cross section as a function of the beam velocity is the same previously employed in similar scattering studies with other open-shell atoms23,24,27-30 and to analyze the halogen beams by magnetic ~election.~'A schematic view is reported in Figure 1 and only the experimental details that are specific to this work are here outlined. Briefly the chlorine atoms are produced in a 2450-MHz microwave discharge source and, after collimation,the produced beam undergoes a mechanical velocity selection to within 5% (fwhm), crosses the scattering chamber, and finally is detected by a quadrupole mass filter. As indicative of typical conditions, in the case of discharge in pure C12, at a pressure of -2.6 Torr (nozzle diameter -1 mm), we have estimated a dissociation percentageof C12 molecules of about 80%and the produced atomic beam exhibits a broad velocity distribution (only slightly supersonic), which allows measurement of the total scattering cross section in a sufficiently wide energy range (0.4-2.3 km/s). Specifically for the present experiments, we have measured the attenuation of a velocity-selected 3sClbeam when it crosses the scattering chamber filled with the target gas. The latter is in the pressure range l t 2 - l t 3 Torr and cooled at liquid air temperature, to decrease the blurring of quantum glory undulations by thermal motion of the target gas. As previously,23J4J7-30J2 the absolute values of the total cross sections have been obtained by an internal calibration based on the direct measurement of the gas flow in the scattering chamber and on the absolute values of the He-Ar total cross sections reported in ref 37. The dimension of the slits defining the beam size and the length of the beam path assure us that in this procedure no correction, due to poor angular resolution, is necessary to obtain the value of the true cross section. As outlined above an important step in these experiments is thecharacterization and the controlof the population of the atomic sublevels in the open-shell atomic beam, carried out here according to the method discussed previously3' through the use of the magnetic analysis. The Stern-Gerlach magnetic selector is inserted along the beam path, between the scattering chamber and the detector. The applied inhomogeneous magnetic field has a nonzero gradient in the direction orthogonalto the beam velocity, and this allows a selective and controlled deflection of the atomic sublevels according to their magnetic moments. Scatteringmeasurements have been performed at zero magnetic field and at well-defined values of B/u2, where B is the applied magnetic field intensity and u the selected velocity of the beam. The B/u2 parameter is proportional to the ratio between the interaction energy with the applied magnetic field (see below) and the kinetic energy of the beam particles. As previously discussed3Iand remarked in section 2.3, experimentsat increasing B/u2 values favor, in the case of halogen atoms, the conditions for probing the interaction of the J = state.
where po = 9.27 X I t 2 * J/G is the Bohr magneton and gK is the Landb g-factor relative to the quantum number K. For atoms such as the halogens, which have the total electronic angular momentum quantum number J and the nuclear spin quantum number Z both different from zero, it is not possible, at a given applied magnetic field, to assess a priori the exact coupling of the angular momenta and therefore directly to define the effective magnetic moments. Two different limiting cases are of interest: in the first coupling scheme, when B approaches zero, the quantum number F (defined as F = J + I) is the good one; the second scheme is the opposite case where B is so large to decouple J from I (Back-Goudsmit effect). In this limit the nuclear spin contribution can be neglected and the effective magnetic moments are exclusively due to J. As the magnetic field increases from zero, a progressive Back-Goudsmit effect is induced, up to the limiting field value necessary for a total decoupling. Therefore J is the atomic good quantum number when the magnetic field intensity is in the range where AF,F+~and AJ,J+Iare the hyperfine and fine intervals, respectively. When d, which represents the energy of the interaction of the atom with the magnetic field, is of the order of magnitude of AJ,J+I, the RussellSaunders coupling of spin and orbital electronic angular momentum to give J is broken and the Paschen-Back effect is observed. The magnetic field intensities of the present experiments (B C 10 kG) are too low to produce the Paschen-Back effect ( B > lo4kG in the typical case of chlorine atoms). However, it is fundamental to take into account the possibility of the Back-Goudsmit effect for the definition of the effective magnetic moment p, which in general, for a particle with a potential energy E in an external magnetic field B,is given by33 p
= - -aE
aB
It is therefore necessary to study the variation of the atomic energy levels as a function of the magnetic field (Zeeman effect). Detailed studies in this direction were performed in the past on chlorine atom,384' giving hyperfine constants, Landb g-factors, and electricquadrupoleinteraction.Recently3'we havecomputed the Zeeman energy levels and the relative effective magnetic moments for the two fine structure levels J = ]/2 and J = 3/2 of chlorine atom and we concluded that, at the magnetic field intensities used in the present experiments (1-10 kG),J is the good quantum number to evaluate the p values for the ground J = 3 / 2 state, through eq 1; the excited J = ' / 2 state is instead characterized by a partial decoupling between J and I, therefore the effective magnetic moments are obtained, at each field value, through eq 2 (an explicit equation to calculate p is reported in
Weak Interactions of Open-Shell Atoms ref 33, see also ref 3 1). The different behavior has been ascribed to the higher hyperfine constants of the J = state with respect to those of the J = 3 / 2 ground states3' 2.3. Distribution of Magnetic Sublevels in the Transmitted Beam. For a characterization of the beam of chlorine atoms we have measured its transmittance across the Stern-Gerlach magnetic selector, as a function of the magnetic field strength. The obtained value of this property is determined by the statistical weights of the atomic sublevels present in the beam and by the comparison between the dimension of the detector slit and the deflection of the considered substates; the latter depends, for the same type of particles and at a given velocity, on the value of the effective magnetic moments and on the applied magnetic field ~trength.~' Therefore the analysis of the beam transmittance must take into account the values of the magnetic moment calculated under the appropriate decoupling schemes of angular momenta; this directly gives the relative weights PKM, of the magnetic sublevels IK MK)a t zero applied field. The results so obtained for a chlorine atom beam, produced under a variety of discharge source conditions, are reported in ref 3 1. A similar procedure allows us to determine how the relative weights WKM,, in the transmitted beam and a t each field value, In particular the vary with respect to those at zero field, PKM,. WKMnvalues of the substates with lower magnetic moments increase in the selected beam and therefore this result is very interesting for scattering applications. To this aim it is important to note that during collisional studies the proper quantization axis points in the direction of the electric field along the intermolecular axis: at large distances this direction coincides with that of the beam velocity. Since the magnetic field direction is orthogonal to that of the atomic beam (see Figure l), a rotation by 7r/2 of the reference axis, using the appropriate Wigner rotation matrix elements, gives the desired weights W,,, in the collision frame (see, e.g., ref 31). For scattering applications the useful weights are WJ,,, described in terms of J and M J (or rather the modulus of the latter): in fact, during the collision, the electric field acting along the intermolecular axis, even at large distances, is strong enough to decouple J from I. Moreover, only the M J components along the beam direction are important for scattering studies, since at large internuclear distances the molecular quantum number 52, which describes the absolute value of the projection of J along the intermolecular axis, coincides with lmd.27-32 To exploit this approach, it is appropriate to consider the following cautionary remarks: (i) The scattering zone and the magnetic selection region must have the same magnetic quantization axis in order to avoid the so-called Majorana flops, Le., the spontaneous transitions between the components of the atomic sublevels, induced by rapid variations in the direction of the magnetic field.20.33In our experiments this is achieved by using a weak homogenous magnetic field produced by two bars of permeable material connected a t the magnetic expansions. The external magnetic field satisfies the above requirement, being a weak extension of the relatively strong field present inside the magnetic selector: it reaches a value between 10 and 50 G in the scattering chamber. This requirement is particularly stringent when the atomic state, as, e.&, Cl(2P3,2), exhibits several magnetic sublevels. (ii) The evolution of atoms through the crossing points of the Zeeman levels (see ref 31) has to be adiobotic, when they travel from the low magnetic field outside the magnet to the high field inside it. This condition limits this approach to low velocity beams and is fulfilled in the thermal energy range of our experiments. (iii) For atoms having I # 0 and whose magnetic selection falls in the Back-Goudsmit regime, the degree of polarization is reduced by possible recoupling of J and I in the region between the magnetic selector and the scattering chamber. This problem,
The Journal of Physical Chemistry, Vol. 97, No. 10, 1993 2065
TABLE I: Distribution of Sublevel Weights WJ,,,,in the Transmitted CI Beam at the Used Bly2 Values B Ju2 a 0 21 45 a
w3/2.3/2
0.355
0.15 0.03
B in IO2 G and u in km
W3p.I 1 2 0.355 0.25 0.04
w1/2.1/2
0.29 0.60 0.93
SKI.
which could be avoided by the use of magnetic fields strong enough to decouple J and I along the whole beam path between scattering chamber and magnetic selector, is not serious for halogen atom beams, as. e.g., needed for scattering applications. In fact one of the main purposes of this analysis is to study the scattering of halogen atom beams at high B/u2 values, mainly probing the interaction of the J = ' 1 2 state, which shows the lower magnetic moment values and correlates during the collision (see below) with only a single adiabatic potential energy curve. However, a correct evaluation of the magnetic sublevel weights in the transmitted beams must take into account possible angular momenta recouplings in the intermediate region: in the present study this problem concerns in particular only the sublevels of the J = '/, state. For example, the M J= * l / 2 magnetic sublevels of Cl(2P3/2)are found, by proper reference axis rotation, to give different contributions to the Imj = 3 / 2 and Imd = components at each value of the external field. These contributions are 0.366 and 0.634 a t zero field, 0.383 and 0.617 a t a magnetic field of -20 G (as typical in the scattering chamber), and 0.750 and 0.250 a t high magnetic field (>1 kG). The WJ,, values obtained from this analysis at the B/u2values relevant for the present scattering applications are reported in Table I. 3. Theoretical Description of the Scattering of Rare Gases
2PAtoms by
The theory needed to interpret the experimental scattering results and to obtain information on the involved interaction potentials has been gi~enl5-I~ and reviewed elsewhere.' At the low collision energy conditions of these experiments, the interaction between a 2P atom such as C1 and a IS rare-gas atom is described by three effective adiabatic potential energy curves V J ~ ( R Here ) . R is the distance between the particles and 52 is the absolute value of the projection of the total electronic angular momentum J along the R axis. At large interatomic distance 52 tends to the atomic sublevel projection lmj and the adiabatic potential energy curve correlates with the atomic state IJ mJ). It is convenient' to express the potentials VJ, in terms of the coefficients Vo(R) and V2(R) of the Legendre expansion of the electrostatic interaction and of the spin-orbit constant A as follows: 1
'3/2.3/2
= ' 0 - Jv2
(3)
1 1 1 9 2 vl/2+l,2 = v, + -v2 + -A + -(--v; + A, - J v 2 ~ ) '( 5i )2 10 2 2 25 where in the case of the ground-state chlorine atom A is equal to 882.4 cm-I = 109.4 meV, the fine structure splitting between the J = 3 1 2 and J = ' 1 2 components. The Vo(R) and V2(R) coefficients represent respectively the spherical and anisotropic components of the electrostatic interaction and are related to the more familiar Vz(R) and Vn(R) terms byI6.17.4244
2066 The Journal of Physical Chemistry, Vol. 97, No.10, 1993
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, A the ground V3/2,1/2 becomes a 22state and the VI/Z,~/Z correlates with a 211 state, while the V3/2,3/2 is always a 211 state at all R values. At long range, when IV,l A, and the system is in the molecular Hund’s case (a); the two interactions are very similar when the system is in the diatomic Hund’s case (e), at intermediate and large distances, where IV2l < A an important consquence is that the total cross sections measured at B/u2 = 45, with a beam containing essentially C1(2P1/2)atoms, give direct information on the well features of the Vo potential also for largely anisotropic systems such as Cl-Kr and Cl-Xe. In Table 111 some features of the Kr-rare gas potentials are
Aquilanti et al.
2070 The Journal of Physical Chemistry, Vo1. 97, No. 10, 1993
3.0
4.0
5.0
6.0
R , A Figure 9. Electrostatic interaction V z ( R )(see text) for the C1-He, -Ne, -Ar, -Kr, and -Xe systems.
TABLE I V Maxima in Nonadiabatic Coupling Elements. ,, Distances R,, and Values P CI-He
CI-Ne
CI-Ar
CI-Kr
CI-Xe
1.91 0.53
2.45 0.54
2.92
3.22
0.54
0.54
3.49 0.61
R,,,,A P,,,, A-1
also reported, for comparison with the present ones, since the Kr atom has a polarizability value (2.49 A3) near to that of chlorine (2.18 As) and should give similar van der Waals interaction^.^' This comparison, together with the above considerations,suggests that, for highly anisotropic systems, the nature of interaction in / ~ in the first excited V3/2,3/2 cannot be the ground V ~ / Z Jand regarded as that typical of van der Waals bonds. Additional insight is provided by the behavior of the nonadiabatic coupling matrix elements P(R), eq 8, reported in the lower panel of Figure 7. The P(R) functions show a maximum with a value of P,,, constant but shifted toward larger interatomic distances in going from Cl-He to Cl-Xe (see also Table IV). As discussed elsewhere (refs 27-30 and section 3), the maximum position marks the transition between an atomic angular momentum coupling scheme (Hund’s case (c) at long range, where lV2l< A and IJ 0 ) as good quantum numbers) and the molecular coupling scheme (Hund’s case (a) at short range, with IV2l> A and 111 a ) as good quantum numbers). The position of the P(R) maximum indicates that while the well depths for all the systems are confined in the Hund’s case (c), the one for the ground V3/2,,12 state of Cl-Xe has a more prominent molecular character, as typical of Hund‘s case (a). Finally, it has to be noted that the low value of the nonadiabatic coupling matrix elements P implicitly confirms the correctness of the adiabatic decoupling scheme (section 3) employed in the analysis: such a coupling is known to be of the order of Pz,in units of 1L2/2p,27and may be of interest for the calculation of inelastic cross sections involving fine structure and depolarization effects. 6. Conclusions
The present paper confirms the important role of the magnetic selection of atomic substates toobtain a detailed characterization of potential interactions in systems involving open-shell atoms. Since total cross-section data are here analyzed, this characterization concerns essentially the well region and the long-range attractive part of the involved interactions. The present C1(2PJ)-
rare-gas interaction potentials should also be reliable in the repulsive region not far from the well depth, which is governed by the a2 parameter (which defines the short-range stepness of the Vz(R)component) and by the BM parameter (which defines, in addition to the shape of the well depth, also the repulsive behavior of the Vo(R)interaction). Further information on the repulsive interaction at shorter ranges should come from a combined analysis with other experimental data such as diffuse emission spectra: some data are available for X e C P and KrCl.63 The present study demonstrates that the spherical component VO of the interaction is of the van der Waals type, whose well depth and location change in agreement with correlationformulas between potential parameters and polarizability of the interacting partners; on the other hand, the anisotropic VZcomponent,which embodies the Z-II splitting (see eq 6), is essentially due to configuration interaction between the lowest covalent states and the excited ionic states, which are more strongly bound. This configuration interaction contribution plays only a minor role in the Cl-He system, while in the Cl-Kr and Cl-Xe cases produces a significant modification in the three adiabatic interaction potentials V Jwith ~ respect to the isotropic component Vo. The main result of the present paper is therefore the acquisition of a full and completecharacterization of the adiabatic potential curves VJQand of the relative nonadiabatic coupling term, describing the low-lying states of rare-gas-chloride molecules. In future work we are planning touse these results inconnection with those obtained for other open-shell-closed-shell ~ y s t e m P - ~ ~ to obtain the anisotropic component VZdescribed with simple and general correlations, expressed in terms of fundamental physical properties of the interacting particles. For interactions involving fluorine atoms with several atoms and simple molecules an attempt to finding such a correlation in terms of ionization potentials of the involved atoms has shown to be a reasonable first step.65 Its extension requires further study, which will have to include also further systems under investigation, such as the interactions of chlorine atoms with hydrogen and methane molecules:66along these lines thecorrelations may yield reasonable estimates of the interaction features for those weakly bound pairs that are difficult to study experimentally and theoretically and for which, in addition to themainspherical interaction component VO,the electronic anisotropy, embedded in the V2 component, plays an important role.
Acknowledgment. Financial support from ENEA and the Italian Consiglio Nazionale delle Ricerche (under Progetti Bilaterali and Progetto Finalizzato Chimica Fine e Secondaria) is gratefully acknowledged. V.L.was supported by an EEC fellowship. References and Notes ( 1 ) Aquilanti, V.; Liuti, G.; Pirani, F.; Vecchiocattivi, F. J . Chem. Soc., Faraday Trans. 2 1989,85, 955. (2) Tellinghuisen. J.; Hays, A. K.; Hoffman, J. M.; Tisone, G. C. J . Chem. Phys. 1976, 65,4473. (3) Tellinghuisen, J.; Tellinghuisen, P. C.; Tisone, G. C.; Hoffman, J. M.; Hays, A. K. J . Chem. Phys. 1978, 68, 5177. (4) Tellinghuisen, P. C.; Tellinghuisen, J.; Coxon, J. A.; Velazco, J. E.; Seetser, D.W. J . Chem. Phys. 1978, 68, 5187. (5) Simmons, J . D.;Maki, A. G.; Hougen, J. T. J . Mol. Specfrosc.1979,
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