This argumentation is however still controversially discussed.(79)
In any case, it is well known from other fields of chemistry, that energy transfer as well as electron transfer are strongly orientation dependent. For example, F¨orster energy transfer favors specific relative directions of each molecule’s transition dipole (80) and electron transfer in the gas–phase is explained in terms of the relative orientation of donor and acceptor orbitals(81).
2.6 Rotational excitation in gas–surface collisions
The incidence molecular orientation was also found to have a strong impact on the rotational excitation in gas–surface collsions. This topic created a lot of interest in the 1980s and early 1990s and was referred to as rotational rainbow scattering. I would like to explain this on the example of the scattering NO (v = 0) from Ag(111). This and other examples can be found in a review article from A. W. Kleyn.(82)
Figure 2.15 shows early results from Kleyn et al. for the rotational state distributions when NO scatters from Ag(111). (83) The rotational excitation was found not to result from equilibration with the surface temperature and actually non–thermal; the excita-tion increases with the incidence translaexcita-tional energy. This was explained by a direct scattering process in which incidence translational energy in converted to rotational energy of surface scattered molecules. An interesting feature of the rotational state distributions was that they appeared to have two components: one component at low rotational energy (originally labelled asthermal) and one component with a maximum at high rotational energy which was called rotational rainbow. Already in this early work it was suspected, that the rotational structure could only be explained by an interaction potential between the NO molecule and the surface that strongly depends on the orientation angle.(83)
The orientation dependence of the rotational excitation was later confirmed in exper-iments using oriented NO molecular beams. Fig. 2.16 shows results for the scattering of NO from Ag(111) from Geuzebroek et al. for the highest incidence translational energy of 0.34 eV where orientation could be achieved with the hexapole orientation technique. The data proves, that the highJ component of the rotational state distri-butions results predominantly from collisions in which the O–atom in pointing towards the surface, whereas N–atom first collisions produce population in lower rotational
2. Theory and previous results
Figure 2.15: Boltzmann plot of the rotational state distributions of NO scat-tering from Ag(111) – Rotational–state distributions for NO scattered from Ag(111) as a function of internal energy (bottom scale) or rotational quantum numberJ (top scale).
TheJ–scale shown applies to the Ω = 1/2 spin–orbit state. From top to bottom: Etransi
= 1.0 eV, θi = 15◦; Etransi = 0.75 eV, θi = 15◦; Etransi = 0.32 eV, θi = 15◦; Etransi = 0.32 eV, θi = 40◦. The energies given as En–labels are the components normal to the surface. Molecules were detected at specular angle. Reprinted (abstract/excerpt/figure) with permission from (83). Copyright 1981 by the American Physical Society.
2.6 Rotational excitation in gas–surface collisions
states.(84) The rotational rainbow scattering was also discussed in several theoretical
Figure 2.16: Rotational state distributions for oriented NO scattering from Ag(111) – The top panels show the scattering of a molecular beam with enhanced N–
atom first orientation and the bottom panels for enhanced O–atom first approach. The molecules impinge the surface at an incidence scattering angle of -45◦ at a translational energy of 0.34 eV. The data is given for scattering angles of 35◦ (towards the surface normal, a), 53◦ (b), and 70◦ (towards the surface, c). The strongest high J rotational rainbow is observed for O–atom first collsions for molecules scattered towards the surface (bottom right panel). Reprinted with permission from (84). Copyright (1991) American Chemical Society.
studies (see (82, 85, 86, 87) and references therein). All of these studies reduced the problem to the elastic scattering of a rigid rotator from a flat surface (no surface corru-gation and no surface motion) and two dimensional (orientation angle θand molecule surface distancez) model potentials were developed. These were refined by comparing the results of classical or quantum mechanical trajectory calculations to the experimen-tal rotational state distributions.
One of the most recent model potentials was suggested by Tenneret al.(87, 88) in 1990.
This potential refines a model potential originally developed by Voges and Schninke (VS potential)(85) with the addition of a second term for a deeper attractive well depth and is thus called VSW potential. This potential reproduces experimental results for the orientation dependent scattering of NO from Ag(111) reasonably well. Fig. 2.17 shows
2. Theory and previous results
Figure 2.17: Theoretical explanation of the orientation dependent rotational excitation – (left): Contour representation of a model potential energy surface for the NO/Ag(111) interaction. The potential has an attractive well of 0.2 eV and is strongly asymmetric with respect to the orientation angle (here labelled asγand calledθelsewhere in thesis). (right) Classical molecular dynamics simulations on the PES show that the scattered rotational energy (hereErot) of the initially non–rotating molecule is also strongly orientation dependent. The calculation was done on an initially stationary surface cube of mass 240. The scattered energy Es is also slightly orientation dependent, but always close to the Baule limit of approximately 0.1 eV. The remaining energy (Es−Er) is in the final translationEf. The orientation angle is defined as in the left panel. Reprinted from Publication (88)Classical trajectory study of the interaction of oriented NO and Ag(111), 242/1–3, Tenneret al., 376 – 385, Copyright (1991), with permission from Elsevier.
2.6 Rotational excitation in gas–surface collisions
a contour plot of the VSW potential as function of the orientation angle and the energy transfer predicted by the model. The potential has an attractive well of 0.2 eV and is strongly asymmetric (more repulsion for an O–first than for an N–first orientation).
According to molecular dynamics simulations on that potential, the highest rotational energy is obtained for an orientation angle of approximately 50◦ on a scale where 0◦ corresponds to an O–atom first end–on collision and 180◦ to an N–atom first end–on collision. End–on collisions never lead to rotational excitation for anyV(z, θ) potential, as no torque is exerted to the molcule.
An open question is how the rotational state distributions evolve, in case molecular collisions lead to a change of the vibrational state. Rettner et al.(89) measured very similar rotational state distributions in v = 0 and v = 1 in vibrational excitation ex-periments for NO v = 0 scattering from Ag(111), which lead to the conclusion that
“rotational and vibrational excitation mechanisms are decoupled and that rotational rainbows are formed in an identical way for bothv= 0 andv= 1.”(82) As opposed to this, Wodtke et al. found that NO (v = 2) scattering from Au(111) lead to less rota-tional excitation in the vibrarota-tionally inelastic channels (v = 2 → 1) and (v = 2 → 3) compared to the vibrationally elastic channel (v = 2 → 2). This was referred to as Rotational cooling associated with vibrational relaxation and was attributed to either an effect of the molecular orientation or the surface corrugation.(90)
2. Theory and previous results
3
Experimental
3.1 Vacuum chamber with molecular beam
Figure 3.1 shows a schematic of the surface scattering apparatus used in my Thesis. A pulsed molecular beam of rotationally cold (rotational temperature≈5 K) nitric oxide (NO) is generated in a supersonic jet expansion into vacuum through a piezoelectric valve (1 mm diameter nozzle, 10 Hz repetition rate, 3 atm stagnation pressure, approx-imate opening time 170µs).
The velocity of the molecular beam is controlled by seeding NO in different carrier gases. The beam velocities vf were determined experimentally, but can be approxi-mately estimated with the equation (91)
vf = r2
¯
mc¯pT0, (3.1)
where ¯mis the average mass of the molecules expended, ¯cpis their average heat capacity at constant pressure andT0 is the nozzle temperature, which was room temperature in this work. 3 cm downstream from the nozzle, the beam passes a 2 mm electro-formed skimmer (Ni Model 2, Beam dynamics Inc.) and enters the differential chamber. This chamber is used for preparing the NO molecules in excited vibrational states. This is done via vibrational overtone pumping to v = 3 with pulsed infrared laser radiation (the laser system is described in section 3.3.1) or with several UV-Vis laser pulses with the Pump-Dump-Sweep technique (see section 5). In order to control the optical preparation, the chamber is equipped with a photo-multiplier tube detector (PMT, Hamamatsu, R7154).
3. Experimental
Figure 3.1: Experimental setup– The molecular beam originates at the nozzle on the left side of the figure. Molecules are optically pumped to excited vibrational states in the differential chamber next to the photomultiplier tube (PMT). A high voltage electrode in the surface chamber allows for the orientation of NO molecules prior to their collision with the Au(111) surface. Ar-Ion gun, Auger spectrometer and residual gas analyser (RGA) are attached to the machine to ensure the cleanliness of the Au(111) surface. The pressures in the chambers when the molecular beam is running are given as labels. The positions, where pump laser(s) for the vibrational excitation of the NO molecules and the UV REMPI laser for probing scattered state distribtuions cross the molecular beam are shown as blue arrows in the enlargement of the surface chamber (right panel). Defining the nozzle to be at positionx= 0 (withxbeing along the axis of the molecular beam), the skimmer is at x= 3 cm, the pump lasers cross atx= 12 cm and the surface atx= 32 cm.