The Scattering of Hg(6"P,) by CO, N2 and CO, BY JOHN COSTELLO, MALCOLM A. D. FLUENDY AND KENNETH P. LAWLEY* Department of Chemistry, University of Edinburgh, West Mains Road, Edinburgh EH9 3JJ Received 3rd May, 1976 The differential scattering pattern of a thermal beam of Hg(63Pz) from CO, Nz and CO, has been nxasured from 10" to 160" (CM). Pronounced and regular oscillations are observed over the \thole angular range in each system. However, the envelope is not that of purely elastic scattering, the x4I3 sin xZ(x) plot showing an almost monotonic decrease over the whole angular range. The spacing of the oscillations indicates a deflection function with an unusually broad bowl, interfering branches being 3 A apart. Two models are put forward; both include partial adsorption of the wave front and the operation of two potentials.Detailed fitting of one model shows that a highly attractive long range potential (well depth z 10 kT) is needed, but although the interference structure is well reproduced, the necessary range of the optical potential is not consistent wit.h known quenching cross sections. A second model is given in outline and involves an avoided crossing around 8 8, producing a rapid steepening of the potential gradient at that point. Quenching begins at impact parameters -7 thus indicating a very large quenching cross section unless a rather sharply peaked adscrption function is postulated with a width of only -1 8, to give the known values of oqU. The scattering of many ground electronic state species has now been thoroughly explored over a wide energy range by crossed beam techniques.The scattering of low lying excited electronic species remains largely unexplored and is, in a sense, complementary to ground state scattering in the 10-100 eV range in that there elec- tronic excitation is frequently observed in the products. By starting with an excited state (of necessity a metastable one for beam work), curve crossings and diabatic state mixing become accessible at thermal kinetic energies, and may be expected to lead to marked inelastic scattering. So far, excited state phenomena have largely besn studied through kinetic spectroscopic observation of quenching or collision induced fluorescence l s 2 though the more energetic metastable species (those of the ir:ert gases) have been used in elastic3 and Penning ionization studie~.~ Only relative quenching cross sections for Hg(3P2+1) have been measured in a beam e~periment.~ Hs(~~P,) is an attractive candidate for beam studies in that the nearest electronic state (the 3P1) is only 0.57 eV away and provides a route for quenching.The J = 2 state is not sufficiently energetic (5.4 eV above the ground state) to ionize most small molecules. The following studies of the thermal elastic scattering (or, rather, scattering without change of electronic state) of Hg* by CO, N2 and C02 were undertaken to see if more light could be cast on the known quenching processes in these systems by examining the perturbation of the elastic scattering differential cross section. EXPERIMENTAL The crossed beam apparatus has been described before.6 Hg+(3P2 with less than 15% of the 3P0 state') is generated by electron bombardment (at 10 eV) of an effusive beam of Hg and crosses a thermal effusive beam of the target gas.The angular resolution is 0.5" LAB.292 THE SCATTERING OF H S ( ~ ~ P ~ ) BY CO, N2 AND C 0 2 The detector, a fresh K surface, responds to the 3Pz state, to the 3P0 state with probably lower efficiency but not to the ground state. The 3P1 state decays in flight between scattering centre and detector (transit time 5 x s) and so is not detected. Typical main bemi signals were lo5 C.P.S. and counting techniques were used. The CM scattering patterns, averaged over the stated number of scans, are reproduced as the lowest curve in fig. 1,2 and 3. The factor x4l3 sin x multiplying the scattered intensity conveniently places all the observations within the compass of a linear scale and renders the envelope of scattering from an R6 potential horizontal.The location of the major maxima and minima is reproduced in independent sets of four or five scans, though the peak-to-valley amplitude ratio varies. The envelope is unchanged by selecting different scans for averag- ing. The sudden fall-off in intensity at less than 16" is due to imperfect unfolding of the main beam coupled with the attenuating effect of the x4/3 sin x term at small angles. In the case of CO, closer examination of the data shows a barely visible high frequency structure in the 16-20' CM region with a period N" 1.25'. INTERPRETATION AND FITTING The three scattering patterns are broadly similar (CO and N2 being very similar) in the following respects: (i) the envelope is basically monotonically decreasing across the whole angular range, though in each case there is a maximum around 90-100" (arrowed as xz) and there is a pronounced perturbation of the envelope at 20' in the case of CO and N2 and at 380" for C 0 2 , labelled as xl, (ii) oscillatory structure with an only slowly increasing period extends across the whole angular range, but the amplitude is not regular and is clearly perturbed by another frequency.The envelope must be compared with that expected from purely elastic scattering. For a potential with an R" attractive branch a horizontal (s = 6) or slowly rising (s < 6) envelope with increasing x is found.The absence of a well defined rainbow (the features at x2 do not fall away quickly enough on the dark side to be typical rain- bows) may either mean orbiting, the superposition of scattering from several rather different potentials with an overlapping rainbow structure or extensive adsorption of the incident wave front beginning at impact parameters somewhat greater than the rainbow value. The fact that interference structure is visible at all makes it unlikely that several rather different potentials are operating, for then the supernumerary spacing would be confused by the multiplicity of interfering branches. Although orbiting cannot be ruled out, it would upset the regularity of the supernumerary spacing by introducing further interfering branches (albeit of small amplitude).The same considerations apply to rainbow angles greater than 180'. The near regularity of the interference structure across such a wide angular range (especially noticeable in the case of N2) is unusual because supernumerary rainbow spacing (or inter-branch interference in general when both branches correspond to deflections in the same sense) usually decrease markedly with falling angle of observa- tion as the two branches diverge in impact parameter. The present structure seem to indicate a dominant deflection function with nearly parallel sides, i.e., that the rainbow angle is very large. The fact that the period of oscillation of o(x) nevertheless slowly increases with angle indicates that we are not observing interference structure arising between the positive and negative branches of a deflection function.Putting the remaining experimental observations and the above deductions together, we arrive at the simplest model (I) for a trial fitting: (i) The scattering is predominantly from a single deep potential that gives rise to a rainbow ZlSO",JOHN COSTELLO, ET A L . 293 (ii) The doniinant potential must lead to a deflection function in which the separa- tion of the two attractive branches is ~3 8, at small angles (from Ax = 2z/kAb). (iii) Scattering from a second, shallower potential is needed to account for the maxima in the envelopes of the CO and N2 date around x2 and the change of gradient of the COz scattering in this region. These rainbow positions serve to fix the well depths of the shallow potentials.(iv) Adsorption sets in early on both surfaces and is responsible for the falling envelope of 001). (v) The very high frequency structure with poorly resolved periodicity of -1.25' is interpreted as glory oscillations (interference between the positive and negative branches of the deflection function around x = 0') and serves to assign the impact parameter bo for the inner zero of the deflection function at 5.3 in all cases. In fact, there is not too much latitude in this value if a sensible length parameter (position of the inner zero, a) is to be obtained for the potential especially when very highly attractive potentials are operating. With two potentials the possibility of mutual interference arises. Two different fits were obtained, with and without inter-state interference.Such structure, being predominantly between the outer attractive branches of two deflection functions, is inevitably of much lower angular frequency than that originating across a single deflection function unless the two deflection functions are considerably displaced from each other-in this case by -3 A. In the present model the dominant source of interference structure is between the two negative branches of the deep deflection function ; inter-state interference produces only a small change in the scattering pattern, but agreement with experiment is marginally improved. In order to fit the scattering pattern, a flexible deflection function divided into 7 sections was employed. In each section a simple functional form was adopted subject only to the constraint of a smooth join to the neighbouring sections.In order to complete the partial wave summation, the deflection function was smoothly joined to a tail resulting from the following C(6) values; Hg*/CO, 0.83 x J m6; Hg*/N2 0.77 x J m6. It was found in all three systems that an R" potential could not be used for impact parameters less than -10 A since it gave too slowly varying a deflection function for x > 15", but C6) is not well determined by the present experiments. The best fits are shown as the upper curves in fig. 1,2 and 3, the associated deflec- tion functions in fig. 4, 5 and 6. The potentials derived by Firsov inversion of these deflection functions are plotted in fig. 7, 8 and 9. J m6 and Hg*/C02, 1.12 x DISCUSSION The overall fits are good.Both the dominant angular structure and the envelope are well reproduced, with only isolated features such as the dips in Zk) at x1 un- accounted for. However, this agreement is achieved only with the aid of a pair of unusually long range potentials and an equally long range adsorption function. In fig. 7 the Hg*/CO potential is contrasted with a Lennard-Jones potential with the same well depth and R, value. The much greater width of the potential bowl is apparent. The range of the outer branch of V(R) comes directly from the range of the outer branch of x(1) and this, in turn, comes inescapably from adding the glory lo value to the width AZ across the bowl dictated by the dominant interference structure. Thus, at x = 40" a A1 value of 90-100 is required, giving an impact parameter for this deflection of -7 A. The adsorption function P(b) has to be similarly long range, rising to 0.9 at 9-10 A,294 THE SCATTERING OF Hg(63P2) BY CO, N2 AND C02 10 FIG.1.-Observed angular scattering plot for Hg*/CO (lowest trace), velocity = 680 m s-l, number of scans = 9. Calculated curves (a) and (6) differ only in the upper state deflection function while (c) incorporates interference between upper and lower states (see fig. 4). A displacement of the upper state clearly has little effect on the calculated scattering pattern. centre of mass angle 0 0 FIG. 2.-Scattering in the Hg*/N2 system. Experimental, lowest trace velocity = 614 m s-l, number of scans = 4. (a) is calculated from the sum of scattering from a deep and shallow potential (see fig.3, (b) includes interference between them. so that the scattering down to -20" is affected. The behaviour of P(b) for b < bo is not really probed by the present experiments. The maximum adsorption cross section implied by the above adsorption function is ~3350 Hi2 and the minimum 270 Hi2 in the case of N2, where the two possible shapes of P(b) are sketched in fig. 5. Implied quenching cross sections are slightly larger in the other two systems. Other quenching and depolarization cross section measurements on Hg(3P2) are few and may be summarized by saying that with N2 as partner the total quenching cross section (ie., to all possible final states) is8~9*5 11-19 A2; with C 0 2 as partner the cross section for 3Pz + 3Pr is ~ 0 .4 A2 and with CO as partner the cross section for the J = 2 -+ 1 transition is similar to that with N2. The depolarization cross sections are all much larger8 (up to -600 A2) but they seem to be due to a long range angle dependent term in the potential, probably a quadrupole-quadrupole term not con- nected with electronic state quenching.JOHN COSTELLO, ET A L . r 295 0 FIG. 3.-Scattering in the Hg*/C02 system. Experimental, lowest trace velocity = 466 m s-', number of scans = 6. (a) Is calculated from the sum of scattering from a deep and shallow potential (see fig. 6), (b) includes interference between them. FIG. 4.-Deflection and adsorption functions for fig. 1 (Hg*/CO). The two functions * give rise to the plots (a) and (b) in fig.1, --- to plot (c), both taken in connection with the lower state -; b-scale in A. An observed quenching cross section of -20 A2 implies a maximum impact parameter for quenching rather less than 3 A. This range of attentuation function would, however, produce no detectable effect on the elastic scattering in the angular range of the present experiments unless the intermolecular potential were of rather short range. However, the interference structure points to an unusually long range potential. In interpreting an elastic scattering envelope, there is a direct relationship between V(R) and the adsorption function necessary for a fit. Classically, the differential cross section is proportional to IdX/dbl-lP(b) and without an independent knowledge of P(b) one cannot unambiguously separate the two terms. In the present case, if a296 THE SCATTERING OF Hg(63P2) B Y co, N, AND coz \ i r _ _ - - _ - u i -n L --- - .FIG. 5.-Deflection and adsorption functions for fig. 2 (Hg*/N,). The function - - gives rise to the best fit including interference, --- to the best fit without interference with the lower state -. Two possible continuations of P(b) are shown leading, respectively, to the maximum and minimum quenching cross sections compatible with the postulated deflection function. FIG. 6.-Deflection and adsorption functions for fig. 3 (Hg*/C02). The * * * function gives the best fit without interference with the lower state -, --- optimises the fit with interference. less steeply rising P(b) is required, a more steeply falling deflection function must be employed.In order to preserve the periodicity of the observed interference structure the inner negative branch of the deflection function must be softened as the outer branch is hardened. A rapidly varying potential at 8 A (close to the smallest angle of observation) suggests an avoided crossing in which the diabatic Hg(3P,) - AB(%) pair state is depressed by interaction with another close lying state. A rather sudden change in, gradient of the potential would produce a dip in ak) and tentatively we assign the perturbations at x1 in each of the systems to this cause.JOHN COSTELLO, ET AL. 297 FIG. 7.-Potentials for Hg*/CO. The two upper state potentials - - and --- are derived from the corresponding deflection functions in fig.4. Inset is the Lennard Jones function having the same E and R, values; R scale in A. FIG. 8.-Potentials for Hg*/N,. The upper state potentials . - - and --- are derived from the cor- responding deflection functions in fig. 6. t L- FIG. 9.-Potentials for Hg*/C02. The upper state potentials a a * and --- are derived from the corresponding deflection functions in fig. 7.298 THE SCATTERING OF Hg(63P2) BY CO, N, AND CO, Trying to accommodate the quenching data within the limits set by the scattering results, we construct model 11: (i) The small angle scattering < xl) is from a single potential identified with the shallow state of model I. (ii) This state is perturbed by a second state at a separation A, z 8-8.5 A. The crossing is sufficiently avoided for the motion to be almost adiabatic and most of the trajectories follow the lower surface.Nevertheless, sufficient amplitude ( -10%) is found in the upper state for the shallow rainbow at x2 to be observed, though with low amplitude. At some impact parameter less than b,, adsorption ensues on the lower surface and reaches 90% by the time the forward glory on the lower surface is reached. FIG. 10.-The type of deflection functions needed to minimise the opacity function. The upper state ~ ( 6 ) is taken unchanged from fig. 4. The lower state function is sufficiently steep to produce the observed envelope of a(x). Two possible extrapolations of P(b) are shown, the lower one leading to oSu - 30 A2. (iii) The steepness of the attractive branch of the lower surface is at least three times greater than in model I in order to permit a much reduced P(b) function at large b.The broad features of the deflection function and P(b) function indicated by this model are given in fig. 10. The softening of the inner attractive branch is apparent, though it must be remembered that phase shifts in the presence of an optical potential do contain a contribution from the imaginary part of the potential and it is by no means clear that the ordinary semi-classical analysis holds. The inner branch to the potential must thus be regarded as conjectural. Even with an almost vertical outer branch to x(b) adsorption must set in rapidly at b E b, (the rainbow value) and unless the P(b) function is restricted to a band of b values between 5 and 6 A the implied value of the quenching cross section is still E 150 A in each system. The configuration interaction responsible for the perturbation of the outer branch of the potential energy function is still a matter of conjecture.A steeply plunging ionic state (Hg+AB' seems the more likely charge distributionlO*ll in view of the high I.P. of the molecular partners) has been postulated in the quenching of Hg(",) by Na, but none of the present molecular partners has a positive electron afhnity13JOHN COSTELLO, ET AL. 299 and a crossing of the 3P2 state at "8 A hardly seems feasible. More likely as the source of the perturbation is the interaction of the Hg(3P) - AB(2) pair state with the state dissociating to Hg('S,) - AB(1*311,). All three molecular partners have excited states close to 6 eV in which the In, orbital is occupied and this level is nearly resonant with the Hg 3P2 level at 5.4 eV.Although the overlap of the relevant orbitals would be small at 8 A (neither the 6p nor In orbitals are grossly different from highest occupied orbitals in the ground electronic states) l3 the interaction energy need only be lowered by 4 x erg from the normal dispersion energy at this separation to give the observed potential. CONCLUSIONS The thermal scattering of HgFPJ from CO, N2 and C 0 2 exhibits a fairly simple interference structure that persists out to the largest angle of observation, nearly 180" (CM). Each system also shows evidence of quenching or an attenuation of the elastic scattering compared with that expected from a normal Rd potential which begins at quite small angles of scattering.The very fact that structure is observed at all points to the conclusion that either the three molecular states evolving from the separated species (0 = 0-, 1 and 2 in the linear configuration) have very similar potentials or that selective quenching on some branches simplifies the scattering pattern. The spacing of the interference oscillations leads almost inescapably to a deflection function and hence to a potential that is very broad compared with the Lennard-Jones form. The simplest detailed model that fits most of the scattering data is a two state one correlating with degenerate levels at infinite separation. Adsorption is needed on both surfaces from -10 A inwards. Suitably broad potentials give a good fit to the observed angular structure which is interpreted as supernumerary bows in a deep well.The model, however, leads to unacceptably large values of the quenching cross section (-300 A') and a second model is therefore proposed in which the outer branch of the deflection function is considerably steepened at separations "8-8.5 A to account for some of the fall-off of the elastic scattering with increasing angle. A second, shallow potential is still needed to account for some of the features of the scattering. Even with an outer branch of almost infinite gradient [vanishing contribu- tion to ak)], an adsorption function has to be applied to the inner attractive branch which now becomes the dominant one. Quenching cross sections "150 A2 would thus follow unless the adorption function was rather sharply peaked around 6 A. The Excitedstate in Chemical Physics, ed. J. W. McGowan, Adv. Chem. Phys. (Wiley, New York, 1975), vol. 28. M. Bourene, 0. 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