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Energy distribution between spin-orbit states in NO scattered from organized amphiphilic monolayers
Volume 152, number 2,3
CHEMICAL PHYSICS LETTERS
11November 1988
ENERGY DISTRIBIJTION BETWEEN SPIN-ORBIT STATES IN NO SCATTERED FROM ORGANIZED AMPHIPHILIC MONOLAYERS Sidney R. COHEN, Ron NAAMAN Department
oflsotope
Research,
Weizmann Institute of Science, Rehovot 76100, Israel
and G.G. BALINT-KURT1 ’ Department
of ChemicalPhysics, Weizmann Institute of&fence,
Rehovot 76100, Israel
Keceived 2 1May 1988; in final form 15 September 1988
Kesults are presented on the energy distribution between the two spin-orbit states of NO scattered from an organic monolayer exposing a perfluorinated chain. The results were found to be similar to those obtained with inorganic and metallic surfaces. A model based on a qualitative picture of the electronic structure of NO and its interaction with a surface is presented and found to explain the general trends in all the data obtained.
1. Introduction The scattering of a molecular beam from organized amphiphilic monolayer surfaces was reported recently. In these studies both translational [ 1 ] and rotational [2] energy transfer were probed. Two different amphiphiles were used, one exposing an unsubstituted aliphatic chain (OTS), and the second exposing a perfluorinated tail (PFAE). The results obtained from these organic surfaces were similar to those found with inorganic metal or non-metal surfaces. In order to test further these similarities, the spin state population in NO scattered from organic monolayers has been investigated. In this Letter we present results obtained from a PFAE surface, compare them to work done on other surfaces and present a qualitative model that explains both our results as well as results obtained for NO scattered from inorganic surfaces. The investigation of rotational accommodation of NO on organic surfaces represents the most extensive body of experimental and theoretical studies to ’ Permanent address: School of Chemistry, University of Bristol, Bristol BS8 lTS, UK.
date; nevertheless, several experiments have addressed the issue of the distribution of the population between the two spin-orbit states [ 3-81 for such systems. The ground electronic state of NO is a H state due to the lone ptt electron. The two spin-orbit states (& l/2,3/2 or F,, F2 respectively) arise from the coupling of orbital and spin angular momentum of the A electron. The energy of the splitting is only about 120 cm-‘. Final spin-orbit populations for NO scattered from Ag( 1 1 1 ), graphite, and Ge ( 111 )/oxidized Ge surfaces have been recorded in the past, but very little discussion exists to explain the results [3-6 1. In some of these works, the rotational population distributions in the two spin-orbit states appear to be equal. In addition, the population ratio of the two spin-orbit states is that expected from a spinorbit temperature which is equal to the rotational temperature. This implied coupling between rotational and electronic energies appears to hold both for the low-J, linear region of the Boltzmann plots, and for the high-J “rainbow” [ $61. However, careful investigation of this feature for incident NO energy of 860 meV shows that the upper spin-orbit state is enhanced for the high-J rainbow [ 81. In a study at much lower incident energies, a dependence of
0 009-26 14/88 /$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
269
Volume 152,number 2,3
CHEMICALPHYSICSLETTERS
[Q=3/2]/[I;E=1/2] on incident energy has been noted [ 31. The form of this dependence was as follows: for incident energies between 15 and 200 meV, there is a gcncral increase in the [ Fz] / [F, ] ratio, excepting a minimum at 50 meV. Secondly, the average rotational energy of the F, state is higher than that of the F, state. Finally, the populations in the two states are influenced only minimally by the surface temperature. These results are only partially consistent with the NO/Ag( 111) scattering studies done at higher incident energies [4,5]. Close-coupled scattering calculations have been used in an attempt to model the variations in population of the [F,]/ [F, ] ratios [ 91. This work recognizes that scattering can take place on two potentials due to different possible orientations of the pn: orbital. Oscillations in the [Fz] / [F, ] ratios as a function of J were predicted. These have not yet been experimentally observed. An advantage of examining scattering from organic monolayers is that one has the capability of modifying particular features of the surface while leaving others unchanged. The amphiphilic surfaces generate an NO potential which is expected to be only slightly - or not at all - anisotropic, in contrast to those proposed for Ag( 111). The surface-induced spin-orbit coupling is expected to be much smaller for an organic surface than for metal surfaces.
2. Experimental The experimental apparatus and procedures have been described in detail elsewhere [2]. Briefly, a pulsed (nominal 50 ps width) molecular beam of NO seeded in argon, helium, or hydrogen strikes the surface of the sample at an incident angle of 30”. The scattered NO is detected in the same chamber using resonance-enhanced two-photon ionization. Tunable UV radiation is obtained by mixing the frequency-doubled output of a Nd : YAG-pumped dye laser with residual 1064 nm light. The ion signal is collected and amplified by a microchannel plate. As mentioned in the earlier work, the incident beam has significant population in only the lowest two rotational states, and the population ratio between the FI/FZ states is 1000 : 1. Recent work has shown that fluctuations in laser 270
I1 November
1988
intensity can cause the signal to vary in a fashion that does not allow a priori normalization to a simple function of the laser fluence [ lo]. Monitoring of the constancy of the average laser output thoughout the scan with a Laser Precision RjP 735 energy meter, together with sufficient signal averaging (40-50 laser pulses per grating step) were therefore used. The effectiveness of this approach was measured on a roomtemperature effusive beam of NO created by choking the source chamber pumping and sampling the effusive thermal beam thus created several hundred microseconds after conclusion of the valve pulse. The rotational population in both the F, and F2 states fits to a rotational temperature of 275 & 1.5”. The derived electronic temperature is 3 10 f 20”. NO at incident energies between 220 and 460 meV was scattered from PFAE ( lH, IH,2H,2H-perfluorododecyl- 1O-carboxy- 1-decanoate) which is entirely fluorinated over the outer ten carbons of the chain. Characteristics of this monolayer have been described previously [ 1,2]. The scattering was measured at the surface normal, at a distance of 2 cm from the surface.
3. Results To analyze quantitatively the data, it was necessary to devise a consistent method for comparing the total populations in the two electronic levels. The method used must take into account that differences in population are expected between the unresolved I doublet levels [8,9] and that lines arising from the various rotational branches have different behavior [ 10,111. A further complication is that in some cases the rotational plane of the scattered NO may be oriented, thus leading to enhancement of certain branches for detection by the polarized laser light [ 12-141. All of these effects can be dependent upon both the incident energy and the final J state. The ideal treatment of the data would be to compare intensities from specific Q, I, and J states at varying incident energy while monitoring the effect of polarization. This complete approach has not been performed in this work nor in other experiments which investigated NO scattering, although some researchers separately investigated spin-orbit lambda doubling, and polarization at a single incident energy for
Volume 152, number 2,3
CHEMICAL
scattering from Ag( 111) [ 81. Since we are concerned here with electronic excitation only, the analysis has been performed in a fashion which allows both qualitative and quantitative presentation of the results. For qualitative visual inspection, Boltzmann plots showing the rotational energy distributions in the two electronic states are shown in the following section. This presentation shows the general features of the scattering. It would be possible from such a plot to derive the [ F7] / [F, ] averaged values for the different energies, as was done in the past [ 31. This procedure, however would not properly treat the differences arising from intermediate state alignment, lambda doubling levels, or variations of [ F2 ] / [F, ] ratio with J. The approach in the present work was simply to compare the populations of several individual J states from the F, and Fz levels. The choice of the rotational branch for the lines compared thus fixes the complicating contributions outlined above. In fig. 1 the Boltzmann plots for NO scattered from PFAE at three different incident energies are shown. One observes a monotonic inCrt%Se in rOtatiOna energy with incident energy. This strong dependence of rotational energy on incident energy has been discussed previously [ 2 1. Quantitative analysis of this data has been made using the line-for-line procedure described above. In table 1, the results of this comparison are reported. Overall consistency of this method was measured in repetitive experiments (thus including both experimental and analysis uncertainties) and the reported uncertainties represent
I 0
200
400
600 800 1000 1200 Roiatlonal Energy (cm-‘)
1400
1600
Fig. I. Boltzmann plot for NO scattered from PFAE. Upper plot is for NO incident energy of 460 meV. Middle plot is for NO incident energy of 340 meV. Lower plot is for NO incident energy of 160 meV. n Jz=
I /2,0
R=3/2.
11 November
PHYSICS LETTERS Table 1 Population ratios F,/F, with PFAE. Uncertainty E,
Q(25.5)
230 290 340 460
0.63 0.83 0.76 0.84
=)
(0.06) (0.07) (0.07) (0.06)
1988
for NO scattered from surface covered indicated in parentheses P(29.5)
b,
0.58 (0.15) 0.48 (0.04) 0.63 (0.05) 0.72 (0.06)
R( 16.5) c) 0.67 (0.1) 0.68 (0.04) 0.80 [ 0.15) 0.94 (0.16)
a) (QZz+R,,)/(Q,,+Pz,), lO%Rcharacterinnumerator, P character in denominator. b, (PLz+ QIz) /P, ,, 29% Q character in numerator. cl R22/(Rll +Qz,), 44% Q character in denominator.
10%
the 95% confidence limits obtained. In fact, no surprising information is obtained from this treatment, and the monotonic increase in the F, population with increasing incident energy (allowing for experimental uncertainty) conforms with the qualitative bchavior seen in the Boltzmann plots.
4. Discussion The results regarding the spin-orbit state population obtained from scattering of NO from all types of surfaces can be summarized as follows: ( 1) The ratio [ Fz ] / [F, ] increases with increasing collision energy for all surfaces studied. (2) The population ratio approaches unity, with sufficiently high collision energy, for all surfaces. Although several theoretical treatments for the spin-orbit redistribution of molecules scattered from surfaces exist [ 9,151, they are dependent upon potentials which are not always well known. Since the observations stated above seems to be a general feature observed in all the scattering experiments on NO, for very different surface types, a qualitative model may provide some new insight on this matter. The model presented below is based on ideas which have been used in the scattering theory of collision partners possessing both spin and electronic angular momentum [ 16,171, and in the theory of photodissociation processes [ 18-201. In the model we consider the main electronic effect on the dynamics of the collision to arise from the orientation of the outer n: antibonding electron of the NO either parallel or perpendicular to the surface. This same model has been explored quantitatively by Smedley et al. [9] 271
CHEMICAL
Volume 152, number 2,3
PHYSICS LETTERS
in discussing the scattering of NO from Ag surfaces. Here we present the model from a more heuristic viewpoint, emphasizing the way in which it might explain the general trends observed in the scattering of NO from a wide variety of surfaces. We first define the two possible x antibonding molecular orbitals of NO corresponding respectively to - 1 and + 1 units of electronic angular momentum about the NO molecular axis: R- = (n,-iK.V)/fi,
(la)
n+ = - (7tX+in,)/&.
(lb)
n, and R, are orbitals from the surface-molecule basis, with n, representing parallel orientation of the outer x antibonding NO electron with respect to the surface, and n,, the perpendicular orient&ion. The Hamiltonian for the system is composed of an “electronic” and a spin-orbit part: A=&
+A,,
*
(3) where ?t denotes an orbital with j3 spin. The scattering problem must be treated in terms of these spinorbit states, as they correctly describe the system at large separations [ 201. We assume that the spin-orbit part of the Hamiltonian does not depend on R. Itis therefore always diagonal in the ~7 basis. At smaller R the main electronic term dominates the Hamiltonian. fiC, is assumed to be diagonal in the “surface-molecule” basis I K, ) , 1iit, >, 1n!, ) , I RI,)
1201. Its matrix elements
are
(~,I~~,I~,>=~~=(~.,Iti,,Iic,), (rr,,I~~,I~“)=~“=(~“I~~i,,I~n,), 272
(4)
1988
where V, is the potential for the approach of NO to the surface with its antibonding R electron parallel to the surface, and V, corresponds to this electron being perpendicular to the surface. The equalities (4 ) hold because the electron spin has no cffcct on the surface-NO potential. The matrix elements of the spin-orbit Hamiltonian in the spin-orbit coupled basis are
(5)
txT”l~~i,,IxT”>=txrlir,,IxP>=tl/z.
From eqs. ( 3), (4) and (5) we can construct the total Hamiltonian matrix (H) in the spin-orbit basis (i.e. H,,= (xy lfllx,“> ):
H= v+ +c3/2 0
(2)
Asymptotically at large R (large distances from the surface), the electronic Hamiltonian which describes the interaction of the NO with the surface, is zero. At these large distances we consider the eigenfunctions of the system to be the spin-orbit basis functions given below:
I1 November
-
i
0
v-
0
0
-v-
0
-v_
V++6,2
0
V+
+c1/2
0
-
v0
’
v+ +%I2I (6)
whereV+=f(C/,+P’,,) and V_=f(P’-V,,). The proposed model includes no spin-dependent interactions between the NO molecule and the surface. If there is a difference between the V, and V,, potentials (i.e. if the NO interacts differently with the surface when its antibonding x electron is oriented parallel or perpendicular to the surface), as there almost inevitably will be, then V_ in eq. (6) will be non-zero. The consequence of this is that xs” and xSp are coupled and x$” and x7 are also coupled, but there is no coupling between the two pairs. A transition between xp and XSp(or betweenx:p and xr”) corresponds to a change of spin-orbit state. The central experimental observation is that there is always a large, and very similar, probability of changing the spin-orbit state of NO when it collides with a surface, no matter whether the surface is organic (present work) or metallic [ 41. This experimental finding has motivated, and is in full agreement with, our model. The model shows that the explanation of the experimental findings does not necessitate the use of any spin-dependent interactions between the NO molecule and the surface. Another important experimental observation is that the probability of spin-orbit changing transi-
Volume 152, number 2,3
CHEMICAL PHYSICS LETTERS
tions grows with increasing collision energy. This has been discussed for NO+Ag( 111) scattering in the work of Kubiak et al. [ 41. In the present study involving NO scattering from an organic monolayer, it may be seen from the results reported in table 1. The NO molecules incident on the surface may be considered to be cntircly in their F, state. Under single-collision conditions, the final populations in the F, state is therefore a direct measure of the spin-orbit transition probability. From the table we see clearly that this probability increases with increasing energy. This general behaviour, observed in NO collisions with both metallic [4] and organic (present work) surfaces is again explained in a very natural manner by our model. As the collision energy is increased the NO molecule penetrates progressively closer to the surface (governed by the diagonal potential matrix elements V,). The probability of changing spin-orbit states is governed by the magnitude of V (the coupling potential) at the point of closest approach of NO to the surface. Thus the observation that the probability of changing spin-orbit state increases with increasing collision energy implies that the potential V_ increases (in magnitude) as we approach closer to the surface. To summarise, we have suggested a physical mechanism for the mixing of spin-orbit states in NO surface collisions, in which the details of the potentials involved, although relevant, do not change the gross features of the predictions. The model also implies that collisions of NO with any surface will lead to an efficient mixing of the spin-orbit states irrespective of whether there are any spin-dependent interactions.
Acknowledgement We thank Professor M. Shapiro for many valuable discussions and M.N.R. Ashfold for some helpful
I1 November 1988
suggestions. GGBK thanks the Chemical Physics Department of the Weizmann Institute of Science for support and hospitality during his visit. This work is partially supported by the US-Israel Binational Science Foundation.
References S.R. Cohen, R. Naaman and J. Sagiv, Phys. Rev. Letters 58 (1987) 1208. I S.R. Cohen, R. Naaman and J. Sagiv, J. Chem Phys. 88 (1988) 2757. G.D. Kubiak, J.E. Hurst, H.G. Rennagel, G.M. McClelland and R.N. Zare, J. Chem. Phys. 79 ( 1983) 5163. A.C. Luntz, A.W. Kleyn and D.J. Auerbach, J. Chem. Phys. 76 (1982) 737. [ 51 A.W. Klcyn A.C. Luntzand D.J. Auerbach, Phys. Rev. Letters.47 (1981) 1169. [6] A. Miidl, H. Robota, J. Segner, W. Vielhaber, M.C. Lin and G. Ertl, J. Chcm. Phys. 83 (1985) 4800. [ 71 F. Frenkel, J. H%ger, W. Krieger, H. Walther, G. Ertl, J. Segner and W. Vielhaber, Chem. Phys. Letters 90 ( 1982) 225. [ 8 ] AC. Luntz, A.W. Kleyn and D.J. Auerbach, J. Chem. Phys. 76 (1982) 737. [9] J.E. Smedley, G.C. Corey and M.H. Alexander, J. Chem. Phys. 87 (1987) 3218. [ IO] D.C. Jacobs and R.N. Zare, J. Chem. Phys. 85 (1986) 5457; D.C. Jacobs, R.J. Madix and R.N. Zare, J. Chem. Phys. 85 (1986) 5469. [ I1 ] J.P. Booth, S.L. Bragg and G. Hancock, Chem. Phys. Let1ers 113 (1985) 509. [ 121 G.O. Sitz, A.C. Kummel and R.N. Zare, J. Vacuum Sci. Technol. A 5 (1987) 513. [ 131A.C. Luntz, A.W. Kleyn and D.J. Auerbach, Phys. Rev. B 25 (1982) 4273. [ 141 D.C. Jacobs, K.W. Kolasinski, R.J. Madix and R.N. Zare, J. Chem. Phys. 87 (1987) 5038. [ 151 M.H. Alexander, J. Chem. Phys. 80 (1984) 3485. [ 161 H. Kaplan and M. Shapiro, Astro. Phys. J. 229 ( 1979) L9 1. 171 M.ShapiroandH.Kaplan, J.Chem. Phys. 71 (1979) 2182. 181 R. Schinke, V. Engel, P. Andresen, D. Hlusler and G.G. Balint-Kurti, Phys. Rev. Letters 55 (1985) 1180. 191 G.G. Balint-Kurti, J. Chem. Phys. 84 (1986) 4443. [20] SC. Givertz and G.G. Balint-Kurti, J. Chem. Sot. Faraday Trans.1182 (1986) 1231.
273
CHEMICAL PHYSICS LETTERS
11November 1988
ENERGY DISTRIBIJTION BETWEEN SPIN-ORBIT STATES IN NO SCATTERED FROM ORGANIZED AMPHIPHILIC MONOLAYERS Sidney R. COHEN, Ron NAAMAN Department
oflsotope
Research,
Weizmann Institute of Science, Rehovot 76100, Israel
and G.G. BALINT-KURT1 ’ Department
of ChemicalPhysics, Weizmann Institute of&fence,
Rehovot 76100, Israel
Keceived 2 1May 1988; in final form 15 September 1988
Kesults are presented on the energy distribution between the two spin-orbit states of NO scattered from an organic monolayer exposing a perfluorinated chain. The results were found to be similar to those obtained with inorganic and metallic surfaces. A model based on a qualitative picture of the electronic structure of NO and its interaction with a surface is presented and found to explain the general trends in all the data obtained.
1. Introduction The scattering of a molecular beam from organized amphiphilic monolayer surfaces was reported recently. In these studies both translational [ 1 ] and rotational [2] energy transfer were probed. Two different amphiphiles were used, one exposing an unsubstituted aliphatic chain (OTS), and the second exposing a perfluorinated tail (PFAE). The results obtained from these organic surfaces were similar to those found with inorganic metal or non-metal surfaces. In order to test further these similarities, the spin state population in NO scattered from organic monolayers has been investigated. In this Letter we present results obtained from a PFAE surface, compare them to work done on other surfaces and present a qualitative model that explains both our results as well as results obtained for NO scattered from inorganic surfaces. The investigation of rotational accommodation of NO on organic surfaces represents the most extensive body of experimental and theoretical studies to ’ Permanent address: School of Chemistry, University of Bristol, Bristol BS8 lTS, UK.
date; nevertheless, several experiments have addressed the issue of the distribution of the population between the two spin-orbit states [ 3-81 for such systems. The ground electronic state of NO is a H state due to the lone ptt electron. The two spin-orbit states (& l/2,3/2 or F,, F2 respectively) arise from the coupling of orbital and spin angular momentum of the A electron. The energy of the splitting is only about 120 cm-‘. Final spin-orbit populations for NO scattered from Ag( 1 1 1 ), graphite, and Ge ( 111 )/oxidized Ge surfaces have been recorded in the past, but very little discussion exists to explain the results [3-6 1. In some of these works, the rotational population distributions in the two spin-orbit states appear to be equal. In addition, the population ratio of the two spin-orbit states is that expected from a spinorbit temperature which is equal to the rotational temperature. This implied coupling between rotational and electronic energies appears to hold both for the low-J, linear region of the Boltzmann plots, and for the high-J “rainbow” [ $61. However, careful investigation of this feature for incident NO energy of 860 meV shows that the upper spin-orbit state is enhanced for the high-J rainbow [ 81. In a study at much lower incident energies, a dependence of
0 009-26 14/88 /$ 03.50 0 Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
269
Volume 152,number 2,3
CHEMICALPHYSICSLETTERS
[Q=3/2]/[I;E=1/2] on incident energy has been noted [ 31. The form of this dependence was as follows: for incident energies between 15 and 200 meV, there is a gcncral increase in the [ Fz] / [F, ] ratio, excepting a minimum at 50 meV. Secondly, the average rotational energy of the F, state is higher than that of the F, state. Finally, the populations in the two states are influenced only minimally by the surface temperature. These results are only partially consistent with the NO/Ag( 111) scattering studies done at higher incident energies [4,5]. Close-coupled scattering calculations have been used in an attempt to model the variations in population of the [F,]/ [F, ] ratios [ 91. This work recognizes that scattering can take place on two potentials due to different possible orientations of the pn: orbital. Oscillations in the [Fz] / [F, ] ratios as a function of J were predicted. These have not yet been experimentally observed. An advantage of examining scattering from organic monolayers is that one has the capability of modifying particular features of the surface while leaving others unchanged. The amphiphilic surfaces generate an NO potential which is expected to be only slightly - or not at all - anisotropic, in contrast to those proposed for Ag( 111). The surface-induced spin-orbit coupling is expected to be much smaller for an organic surface than for metal surfaces.
2. Experimental The experimental apparatus and procedures have been described in detail elsewhere [2]. Briefly, a pulsed (nominal 50 ps width) molecular beam of NO seeded in argon, helium, or hydrogen strikes the surface of the sample at an incident angle of 30”. The scattered NO is detected in the same chamber using resonance-enhanced two-photon ionization. Tunable UV radiation is obtained by mixing the frequency-doubled output of a Nd : YAG-pumped dye laser with residual 1064 nm light. The ion signal is collected and amplified by a microchannel plate. As mentioned in the earlier work, the incident beam has significant population in only the lowest two rotational states, and the population ratio between the FI/FZ states is 1000 : 1. Recent work has shown that fluctuations in laser 270
I1 November
1988
intensity can cause the signal to vary in a fashion that does not allow a priori normalization to a simple function of the laser fluence [ lo]. Monitoring of the constancy of the average laser output thoughout the scan with a Laser Precision RjP 735 energy meter, together with sufficient signal averaging (40-50 laser pulses per grating step) were therefore used. The effectiveness of this approach was measured on a roomtemperature effusive beam of NO created by choking the source chamber pumping and sampling the effusive thermal beam thus created several hundred microseconds after conclusion of the valve pulse. The rotational population in both the F, and F2 states fits to a rotational temperature of 275 & 1.5”. The derived electronic temperature is 3 10 f 20”. NO at incident energies between 220 and 460 meV was scattered from PFAE ( lH, IH,2H,2H-perfluorododecyl- 1O-carboxy- 1-decanoate) which is entirely fluorinated over the outer ten carbons of the chain. Characteristics of this monolayer have been described previously [ 1,2]. The scattering was measured at the surface normal, at a distance of 2 cm from the surface.
3. Results To analyze quantitatively the data, it was necessary to devise a consistent method for comparing the total populations in the two electronic levels. The method used must take into account that differences in population are expected between the unresolved I doublet levels [8,9] and that lines arising from the various rotational branches have different behavior [ 10,111. A further complication is that in some cases the rotational plane of the scattered NO may be oriented, thus leading to enhancement of certain branches for detection by the polarized laser light [ 12-141. All of these effects can be dependent upon both the incident energy and the final J state. The ideal treatment of the data would be to compare intensities from specific Q, I, and J states at varying incident energy while monitoring the effect of polarization. This complete approach has not been performed in this work nor in other experiments which investigated NO scattering, although some researchers separately investigated spin-orbit lambda doubling, and polarization at a single incident energy for
Volume 152, number 2,3
CHEMICAL
scattering from Ag( 111) [ 81. Since we are concerned here with electronic excitation only, the analysis has been performed in a fashion which allows both qualitative and quantitative presentation of the results. For qualitative visual inspection, Boltzmann plots showing the rotational energy distributions in the two electronic states are shown in the following section. This presentation shows the general features of the scattering. It would be possible from such a plot to derive the [ F7] / [F, ] averaged values for the different energies, as was done in the past [ 31. This procedure, however would not properly treat the differences arising from intermediate state alignment, lambda doubling levels, or variations of [ F2 ] / [F, ] ratio with J. The approach in the present work was simply to compare the populations of several individual J states from the F, and Fz levels. The choice of the rotational branch for the lines compared thus fixes the complicating contributions outlined above. In fig. 1 the Boltzmann plots for NO scattered from PFAE at three different incident energies are shown. One observes a monotonic inCrt%Se in rOtatiOna energy with incident energy. This strong dependence of rotational energy on incident energy has been discussed previously [ 2 1. Quantitative analysis of this data has been made using the line-for-line procedure described above. In table 1, the results of this comparison are reported. Overall consistency of this method was measured in repetitive experiments (thus including both experimental and analysis uncertainties) and the reported uncertainties represent
I 0
200
400
600 800 1000 1200 Roiatlonal Energy (cm-‘)
1400
1600
Fig. I. Boltzmann plot for NO scattered from PFAE. Upper plot is for NO incident energy of 460 meV. Middle plot is for NO incident energy of 340 meV. Lower plot is for NO incident energy of 160 meV. n Jz=
I /2,0
R=3/2.
11 November
PHYSICS LETTERS Table 1 Population ratios F,/F, with PFAE. Uncertainty E,
Q(25.5)
230 290 340 460
0.63 0.83 0.76 0.84
=)
(0.06) (0.07) (0.07) (0.06)
1988
for NO scattered from surface covered indicated in parentheses P(29.5)
b,
0.58 (0.15) 0.48 (0.04) 0.63 (0.05) 0.72 (0.06)
R( 16.5) c) 0.67 (0.1) 0.68 (0.04) 0.80 [ 0.15) 0.94 (0.16)
a) (QZz+R,,)/(Q,,+Pz,), lO%Rcharacterinnumerator, P character in denominator. b, (PLz+ QIz) /P, ,, 29% Q character in numerator. cl R22/(Rll +Qz,), 44% Q character in denominator.
10%
the 95% confidence limits obtained. In fact, no surprising information is obtained from this treatment, and the monotonic increase in the F, population with increasing incident energy (allowing for experimental uncertainty) conforms with the qualitative bchavior seen in the Boltzmann plots.
4. Discussion The results regarding the spin-orbit state population obtained from scattering of NO from all types of surfaces can be summarized as follows: ( 1) The ratio [ Fz ] / [F, ] increases with increasing collision energy for all surfaces studied. (2) The population ratio approaches unity, with sufficiently high collision energy, for all surfaces. Although several theoretical treatments for the spin-orbit redistribution of molecules scattered from surfaces exist [ 9,151, they are dependent upon potentials which are not always well known. Since the observations stated above seems to be a general feature observed in all the scattering experiments on NO, for very different surface types, a qualitative model may provide some new insight on this matter. The model presented below is based on ideas which have been used in the scattering theory of collision partners possessing both spin and electronic angular momentum [ 16,171, and in the theory of photodissociation processes [ 18-201. In the model we consider the main electronic effect on the dynamics of the collision to arise from the orientation of the outer n: antibonding electron of the NO either parallel or perpendicular to the surface. This same model has been explored quantitatively by Smedley et al. [9] 271
CHEMICAL
Volume 152, number 2,3
PHYSICS LETTERS
in discussing the scattering of NO from Ag surfaces. Here we present the model from a more heuristic viewpoint, emphasizing the way in which it might explain the general trends observed in the scattering of NO from a wide variety of surfaces. We first define the two possible x antibonding molecular orbitals of NO corresponding respectively to - 1 and + 1 units of electronic angular momentum about the NO molecular axis: R- = (n,-iK.V)/fi,
(la)
n+ = - (7tX+in,)/&.
(lb)
n, and R, are orbitals from the surface-molecule basis, with n, representing parallel orientation of the outer x antibonding NO electron with respect to the surface, and n,, the perpendicular orient&ion. The Hamiltonian for the system is composed of an “electronic” and a spin-orbit part: A=&
+A,,
*
(3) where ?t denotes an orbital with j3 spin. The scattering problem must be treated in terms of these spinorbit states, as they correctly describe the system at large separations [ 201. We assume that the spin-orbit part of the Hamiltonian does not depend on R. Itis therefore always diagonal in the ~7 basis. At smaller R the main electronic term dominates the Hamiltonian. fiC, is assumed to be diagonal in the “surface-molecule” basis I K, ) , 1iit, >, 1n!, ) , I RI,)
1201. Its matrix elements
are
(~,I~~,I~,>=~~=(~.,Iti,,Iic,), (rr,,I~~,I~“)=~“=(~“I~~i,,I~n,), 272
(4)
1988
where V, is the potential for the approach of NO to the surface with its antibonding R electron parallel to the surface, and V, corresponds to this electron being perpendicular to the surface. The equalities (4 ) hold because the electron spin has no cffcct on the surface-NO potential. The matrix elements of the spin-orbit Hamiltonian in the spin-orbit coupled basis are
(5)
txT”l~~i,,IxT”>=txrlir,,IxP>=tl/z.
From eqs. ( 3), (4) and (5) we can construct the total Hamiltonian matrix (H) in the spin-orbit basis (i.e. H,,= (xy lfllx,“> ):
H= v+ +c3/2 0
(2)
Asymptotically at large R (large distances from the surface), the electronic Hamiltonian which describes the interaction of the NO with the surface, is zero. At these large distances we consider the eigenfunctions of the system to be the spin-orbit basis functions given below:
I1 November
-
i
0
v-
0
0
-v-
0
-v_
V++6,2
0
V+
+c1/2
0
-
v0
’
v+ +%I2I (6)
whereV+=f(C/,+P’,,) and V_=f(P’-V,,). The proposed model includes no spin-dependent interactions between the NO molecule and the surface. If there is a difference between the V, and V,, potentials (i.e. if the NO interacts differently with the surface when its antibonding x electron is oriented parallel or perpendicular to the surface), as there almost inevitably will be, then V_ in eq. (6) will be non-zero. The consequence of this is that xs” and xSp are coupled and x$” and x7 are also coupled, but there is no coupling between the two pairs. A transition between xp and XSp(or betweenx:p and xr”) corresponds to a change of spin-orbit state. The central experimental observation is that there is always a large, and very similar, probability of changing the spin-orbit state of NO when it collides with a surface, no matter whether the surface is organic (present work) or metallic [ 41. This experimental finding has motivated, and is in full agreement with, our model. The model shows that the explanation of the experimental findings does not necessitate the use of any spin-dependent interactions between the NO molecule and the surface. Another important experimental observation is that the probability of spin-orbit changing transi-
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CHEMICAL PHYSICS LETTERS
tions grows with increasing collision energy. This has been discussed for NO+Ag( 111) scattering in the work of Kubiak et al. [ 41. In the present study involving NO scattering from an organic monolayer, it may be seen from the results reported in table 1. The NO molecules incident on the surface may be considered to be cntircly in their F, state. Under single-collision conditions, the final populations in the F, state is therefore a direct measure of the spin-orbit transition probability. From the table we see clearly that this probability increases with increasing energy. This general behaviour, observed in NO collisions with both metallic [4] and organic (present work) surfaces is again explained in a very natural manner by our model. As the collision energy is increased the NO molecule penetrates progressively closer to the surface (governed by the diagonal potential matrix elements V,). The probability of changing spin-orbit states is governed by the magnitude of V (the coupling potential) at the point of closest approach of NO to the surface. Thus the observation that the probability of changing spin-orbit state increases with increasing collision energy implies that the potential V_ increases (in magnitude) as we approach closer to the surface. To summarise, we have suggested a physical mechanism for the mixing of spin-orbit states in NO surface collisions, in which the details of the potentials involved, although relevant, do not change the gross features of the predictions. The model also implies that collisions of NO with any surface will lead to an efficient mixing of the spin-orbit states irrespective of whether there are any spin-dependent interactions.
Acknowledgement We thank Professor M. Shapiro for many valuable discussions and M.N.R. Ashfold for some helpful
I1 November 1988
suggestions. GGBK thanks the Chemical Physics Department of the Weizmann Institute of Science for support and hospitality during his visit. This work is partially supported by the US-Israel Binational Science Foundation.
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