Vibrational relaxation of molecules on alkali halide surfaces

Journal of Electron Spectroscopy and Related Phenomena, 54155 (1990) 39-63 Elsevier Science Publishers B.V., Amsterdam

Vibrational

Relaxation

of Molecules

Huan-Cheng

Changa and George

Department 47405

of

Chemistry,

Halide

Surfaces

E. Ewing

Indiana

'Present Address: Department Cambridge, MA 02138

on Alkali

University,

of Chemistry,

Bloomington,

Harvard

IN

University,

Abstract We have mapped all the relaxation channels from vibrationThe relaxation rates of these ally excited CO on NaCl(100). channels are: dephasing at k@ = 10" s-l, radiative at k,, = 11 s-l, transfer to phonons at kphn= 2x10' 5-l and vibrationally induced desorption at kvid5 10m4 5-l. Theoretical models to account for all these rates are explored. Our understanding of the system CO on NaCl(100) allows us to make predictions of relaxation channels for other molecules on alkali halide surfaces.

1.

AN INTRODUCTION

TO THE PROBLEM

This year, time-domain measurements of the vibrational relaxation of small molecules on single crystal metal [1,2], semiconductor [3] and insulator [4] surfaces have been reported These studies have been preceded by a for the first time. variety of experimental and theoretical explorations of the vibrational dynamics of molecules bound to surfaces reviewed elsewhere [5-81. Understanding problems of vibrational energy flow is important for developing mechanisms of many time-depenchemical reactions, dent processes that occur at surfaces: photochemistry, photodesorption, adsorption dynamics, etc. In this paper we shall review our recent studies [4,9-131 of vibrational relaxation of molecules on alkali halide surWe shall begin faces using CO on NaCl(100) as a model system. with an analysis of possible vibrational flow channels. Suppose A-B is physisorbed to S, the surface of an alkali Let us then excite A-B and consider the halide crystal.

036%2048/90/$03.50

0 1990 -

Elsevier Science Publishers B.V.

40 channels

of the vibrational

A-B*...S

-

A-B * ...S -

A-B

A-B

* *

. ..S

-

. ..S

-

km k red

[A-B***S]

A-B---S

relaxation:

*

+ hv

kp,n A-Bm..S * bd

A-B + S + AE

In eq. (l), the phase of the vibration initially localized in A-B* (the asterisk represents this excitation) is interrupted by motions against the surface bond (indicated by the dots). An experimental consequence of this relaxation is a broadening of the vibrational band profile as the temperature of the system is raised. Radiation from A-B* in eq. (2) proceeds with rate krd. In eq. (3), the vibrational excitation in A-B* is transferred to the underlying substrate and phonon excitation Finally if the vibrational energy of A-B* exceeds the results. surface bond strength, desorption is possible and A-B, now This vibrationally relaxed, flies away with kinetic energy AE. process is called vibrationally induced desorption as shown in eq. (4). Processes (2) to (4) resulting in loss of population of the vibrational excited state of A-B* are associated with time T,. Dephasing, which still maintains excitation in the vibrating chemical bond in A-B, is characterized by time T,. We shall next direct attention to the system CO*=*NaCl(lOO) in some detail and show how all the rate constants in eqs. (l)(4) have been obtained. Finally, we shall return to the more general system and comment on possible vibrational flow patterns of other molecules and other alkali halides.

2. THE SYSTEM 2.1

CO~~~NaCl(100)

Spectroscopy and bonding Spectroscopy and bonding of CO on NaCl(100) was first explored by Gevirzman, Kozirovski and Folman [14] on crystallites generated by subliming fragments of the salt. This was followed nearly two decades later by Richardson and Ewing [15, 163 and Heidberg, Stahmer, Stein and Weiss 1171 who obtained

41

the polarized infrared spectra of CO on the (100) face of single crystal NaCl. Their results confirmed the theoretical considerations [17] that CO is bound perpendicular to the (100) face. The bonding is believed to be dominated by electrostatic interactions which indicate that the C end is down and over the Na+ ion [18]. Thermodynamic studies of CO on NaCl(100) single crystal through isotherm measurements are found consistent with Langmuir adsorption [19]. A later statistical mechanics analysis revealed an adsorption bond strength of D0 = 16 kJ mol-' with a surface bond stretching mode of cr = 100 cm“, frustrated rotation of cc, v" = 140 cm-', and frustrated translation of yIx,yIv= 30 cm ?T [20]. This analysis neglected the small attractive van der Waals bonding among CO molecules within the monolayer estimated to be 1 kJ mol-' [21]. Since the heat of adsorption of monolayer CO on NaCl(100) of AH = -14 kJ mol-' at 55 K [19] is considerably larger than that the heat of sublimation of the Q-CO solid phase of -9 kJ mol-' [22] it is easy to prepare the monolayer free of multilayer adsorption. The 55 K isotherm for CO on NaCl(lOO), a composite from several experiments, is shown in figure 1. Notice that the scale becomes logarithmic for pressures beyond lo-? mbar and coverages beyond e=l. The circles are from infrared (IR) photometry measurements [9,23] and the squares are from X-ray photoelectron spectroscopic (XPS) studies [19]. For pressures below lo-* mbar the solid curve is the theoretical Langmuir isotherm [24]. The solid curve near 1 mbar represents the onset of a-CO condensation [22]. We have developed techniques for preparing the monolayer free of multilayer at temperatures from 60 K to 4 K. Multilayer samples from e=5 to -lo3 at temperatures between 30 K and 4 K can also be prepared [13,25]. The UHV chamber and optical arrangement for our spectroscopic measurements, described in detail elsewhere [15,16,25], are shown in figure 2. Two air-cleaved NaCl crystals, with their (100) faces exposed, are mounted at a near Brewster's The total base angle to incoming polarized IR radiation. pressure of the evacuated system was 8~10-'~ mbar and was The spectrum of the monomainly due to Hz and inert gases. The absorbance shown here layer is shown on figure 3 at 22 K. No absorption by the monolayer is obseruses Ep polarization. ved using E, polarization since CO is bound perpendicular to By controlling the flow of CO a multilayer can the surface.

42

also be produced whose spectrum is shown on figure 3. This data is from the work of Chang, Richardson and Ewing [25]. The first layer CO absorption band is only slightly affected by the The multilayer is shown to be presence of the multilayer. identical to a-CO, the low temperature crystalline phase of a The structure of monomacroscopic sample of carbon monoxide. layer and multilayer CO consistent with this spectroscopy is represented in figure 4.

‘O.’

0

l.O-

e

== I

:

OB-

0.6-

P(mbar)

Figure 1. Isotherm for CO on NaCl(100) at 55 K. The squares are from thermodynamic measurements [19] and the circles from photometry [9,23] of the submonolayer and monolayer. The curve for the region 0 I 1 is the theoretical Langmuir isotherm. The vertical line is from vapor pressure measurements of a-CO [22]. Note change to logarithmic scale beyond lo-' mbar and 9=1.

The infrared spectra of monolayer CO on NaCl(100) (no multilayer is present) at several temperatures [12] is provided in figure 5. The integrated absorbance, $ = sbwd log I,,/1dc = 0.018 f 0.002 cm-' for '2C160is invariant over this temperature range and allows a determination of the integrated cross section of Gz along the molecular axis [9]. In experiments to

43

be described later, we shall sometimes find it to our advantage to use other isotopes of CO. The optical constants of these isotopes vary slightly, consistent with known reduced mass dependent changes [26]. We shall soon use Gz to obtain kr,. The bandwidth at 30 K decreases with temperature to a full width at half height (FWHH) of t,,, = 0.09 cm-' at 10 K. It remains at this limiting value as the temperature is lowered to 4 K. To our knowledge this is the narrowest infrared vibrational bandwidth for any surface bound molecule. If this bandwidth were associated with homogeneous broadening it would

SP

1

cm

4

10 cm I

Figure 2. The UHV chamber and optical schematic. The lower portion of the figure shows the chamber. Transfer optics carry radiation from the Fourier Transform Infrared (FTIR) interferometer through two optical ports, a polarizer (P), and onto an InSb detector. These ports, are also used for the laser induced desorption experiment. The upper port is used for laser access in the laser induced fluorescence measurements. The fourth port goes to a guadrupole mass spectrometer (QMS). The upper portion of the figure shows an enlarged view of the salt crystals (cross-hatched) and their relationships to Ep polarized light. Four surfaces are available for adsorption.

44

0.30-

0.20-

O.lO-

J 0.00 . 2160

multilayer

L

monolayer

h

I 2140

I

I 2120

I

I 2100

I 2080

7 (cm-‘)

Figure 3. Infrared absorption of monolayer and multilayer CO on NaCl(100) at 22 K. The spectra taken with Ep polarization Natural abundance isoare displaced vertically for clarity. Adapted from ref. [25]. topic CO was used for these spectra.

correspond to a Heisenberg lifetime, (2~c~,,z)-',of 60 ps. However, we have given reasons why we believe this broadening is determined by heterogeneities of the NaCl(100) surface [21]. Moreover we shall soon show that the three relaxation channels associated with T,, are incompatible with a 60 ps lifetime. The bandwidth contributions above 10 K however we believe are associated with T,, the dephasing time. We shall now explore, in turn, measurements of k*, krad, k phn and kvid' Dephasing rate: kw As shown in figure 5 both the position of the infrared absorption and the bandwidth of CO on NaCl(100) change with temperature. A quantitative analysis shows that the changes in both frequency and bandwidth follow the same exponential dependence on temperature [lo]. Fitting this change to a Boltzmann factor reveals an energy gap of 40 cm-'. This behavior is 2.2

45 consistent with a dephasing mechanism as shown first for organic liquids [27] and then adsorbed molecules [28-311. For our system it is argued that thermal fluctuations leading to the excitation and de-excitation of a level at 40 cm-' at higher temperatures interrupt the phase of the vibrating CO molecule to produce the observed broadening. Our previous statistical mechanics analysis allows us to associate this excitation with the frustrated translational motion of CO on NaCl(100) estimated to be near 30 cm-' [20]. If we ignore the coupling of vibrational motions among the CO molecules within the monolayer we arrive at a dephasing rate of kW = 10" s-'

[lOI *

d-CO

MONOLAYER-CO

NaCl

Na+ ClFigure 4. The structure of monolayer Adapted from reference [25].

and multilayer

0 C CO.

This analysis is surely inadequate since vibrational motions of CO molecules within the monolayer are coupled [31]. Indeed the vibration is best treated by an exction model [21]. Never-the-less, band broadening by about 0.2 cm-', as we observe in the highest temperature spectra of figure 5, is consistent with a Heisenberg relaxation rate of =lO" s-l. This completes our discussion of T, for now, however the analysis needs more study. 2.3

Radiative rate: kr, If there were neither

photodesorption

nor relaxation

into

the substrate, population loss of excited vibrational levels by radiation alone would contribute to T,. Fluorescence decay would then follow the rate kr,. However, as we shall soon see the fluorescence decay is largely determined by kphn. We can however obtain k,, without time-domain measurements by using From the intethe optical cross section of CO on NaCl(100). grated absorbance measurement, we have obtained Gz = 9.8x10“' cm molecule-' for the 13C160isotope. Using

where c is the speed of light and c = 2107.40 cm“ we found (The radiative rate and cross sections of k;i = 11 s-' [ll]. the other isotopes differ slightly [9]). This rate is about one-third that of the isolated gas phase molecule [32]. However, as shown elsewhere the polarizability of the molecules within the monolayer and the electric fields at the surface of the salt are responsible for most of this reduction in the radiative rate [9,33]. 2.4

Relaxation by phonons: kphn We can use the fluorescence decay rate, k,, as a clock to evaluate the rate constraints kphn and kvid from the relationship

kdas= krad+ kphn+ which

kvid

sums all the population

rate losses of eqs.

(2) to

(4).

As we shall soon show, the photodesorption rate is exceedingly small and can be neglected in the above equation. It would annear that we already have kr, and it remains only to measure kd% to find kph,,. However we need to look more closely at the nature of the fluorescence experiment. Anticipating efficient relaxation from excited CO to the substrate, we began our fluorescence measurements from a multilayer 1131. In order to match the multilayer absorbance with the output of a line-tuned CO gas laser, we prepared adsorbed SaITtpleS from 8=5 to 390 layers of the '3C180isotope. The PS2(12) line at v" = 2042.81 cm-' of the laser source excites the region of the high frequency doublet of the r3C'80multilayer. (This absorption is analogous to the region near 2141 cm-' of the multilayer 12C160isotopic sample in figure 3.) The

47

laser operating in the Q-switch mode at 50 Hz delivered 300 fi per pulse into the exciting line. The excitation was focused through the upper port of the UHV chamber of figure 2 onto the adsorbed sample on the upper surface of the right hand salt crystal. Fluorescence from this region was focused by transfer optics (not shown in figure 2) onto the entrance slits of a monochromator and after dispersion caught by a liquid nitrogen cooled InSb detector. The fluorescence, monitored in the first overtone region (Au = -2) and signal averaged for 6=390, is shown in figure 6. The excitation is distributed from levels v=8 to u=30. A similar distribution was found for 6=40. Recalling that laser excitation is principally only to the u=l level, how do the upper vibrational levels become populated?

0.12

s 5

0

0.08

B II

a

2156

2155

2154

Y(cm-l) Figure 5. Infrared absorption of monolayer CO on NaCl(100) at various temperatures. The CO has been depleted in 13C and is principally 12C160.Adapted from ref. [12].

Since the multilayer sample we are exciting is essentially the o-CO solid phase, we can draw from the analysis of this system by Legay-Sommaire and Legay [34]. Up-pumping to higher u levels occurs by vibrational pooling which begins with

48

CO(lJ=l)+ CO(u=l) = CO(v=2) + CO(u=O) + AE

(7)

Vibrational anharmonicity makes the reaction of eq. (7) exothermic. The energy defect, AE = 24 cm-' for 13C180,iS taken up by phonon excitation of the a-CO lattice. Similar energy pooling of v=2 to v=3 and higher levels continues until population to the v=30 level is achieved.

1

r

14+12

I

3800

I

3600

I

I

3400

I

3200

I

3000

I

2800

Y(cm-')

Figure 6. Dispersed overtone fluorescence of a CO multilayer on NaCl(100). The sample at 22 K consists of 823390layers and fluorescence is from the r3C'80isotope. The assignment of one transition is shown. Adapted from ref. [13].

The decay of the excited multilayer occurs by a complicated cascade mechanism. For thick samples of a-CO the principle relaxation channel is radiation to lower v levels. As the multilayer becomes thinner, decay by excitation of the phonons of the substrate becomes increasingly important. Fluorescence from samples with layers 0 = 120, B = 30 and 0 = 5, from our previous work [13], is shown in figure 7. Here the monochromator used to obtain the data for figure 6 was replaced by a filter and overtone emission from all excited

49

levels was monitored. For the thickest sample a double exponential decay is apparent. The fast decay we have interpreted as being due to relaxation from the multilayer to the monolayer. The longer time decay is associated with relaxation from the monolayer to the substrate. Deconvolution of rate constants from the decay curves of samples with varying number of layers leads to an estimate of ktin. This rate constant is of course a composite of relaxation to the substrate phonons from a variety of high v levels.

8

16

Time (ms)

Figure 7. Decay of overtone fluorescence of CO multilayers on The sample is at 22 K and fluorescence from '%'a0 NaCl(100). was captured at all frequencies shown in figure 6. The intensity has been scaled by the indicated factors for the Adapted from ref. [13]. lower coverages.

The more direct measurement of fluorescence from monolayer CO on NaCl(100) has just been achieved [4] and leads to a more reliable measurement of kphn. A single layer of r3C160free of multilayer was prepared and cooled to 22 K. The absorption profile matched the P,_,,(9)line of our exciting CO laser. Again first overtone fluorescence was monitored and because of

50

An average of low light levels no monochromator was used. 50,000 decay curves revealed a fluorescence rate of k, = 2.3 f 0.2 x 102 s-1. Based on the demonstrated up-pumping in multilayer fluorescence of figure 6 we expect high u levels to be Indeed use of filters in populated in the monolayer as well. the fluorescence measurements suggest excitation to about the u=15 level. From other studies of spontaneous emission of excited CO levels it is known that the rate increases by a factor of 10 from u=l to u=15 [34]. We therefore scale our measured radiation rate, k:z = 11 s-', by the geometric mean of this factor, 1O1/2, to obtain an effective radiative rate of k = 30 s-1. Taking k, = kpd + kphn, by neglecting the kiz term in eq. (6), we therefore uncover kphn = 2 x 102 s-1 as an effective phonon relaxation rate for levels 1~~515. The value of k*,, just determined is in reasonable agreement with the classical model developed by Chance, Prock, and Silbey (CPS) [35]. Here an oscillating point dipole located at a distance R from a surface transmits its radiation at rate k. The ability of the substrate, the receiver, to accept thdis radiation depends on the value of its complex dielectric constant. The dielectric constant at the frequency of the radiation, c, is defined by 2(c) = (n + in)2 where n is the This index of refraction and IC the extinction coefficient. simple model allows easy calculation of the relaxation to phonons through 3ntck,, kphn =

16~~ c31@(;) + 112 R3

’

(‘3)

As before we take the effective radiative rate for 1~~15 to be k = 30 s-1. The geometric mean of the '3C'60fundamental f&uency in the range u=l to u=15 is v" = 1930 cm-' [26]. We take R = 3.3 x lo-* cm to be the distance between the CO center of mass and the center of an Na+ ion at the surface [9]. From the bulk optical properties of NaCl we obtain n = 1.52 and IC = 1.8 x 1O-9 [36]. The result of the calculation is kp,, = 1.8 x 102 s-1 which is in remarkable, indeed fortuitous, agreement with the measured value of 2 x lo2 s-l. 2.5

Vibrationally induced desorption rate: kvid The last relaxation channel to explore is the one leading to photodesorption. For the experimental measurement of this

51 process, we choose a cw rather than a pulsed laser source [ll]. This avoids possible complications from non-linear effects that can accompany the high peak powers of a pulsed laser [37,38]. The principle exciting line of the laser source was P_,(9) which falls within the absorption profile of the 13C160monolayer at 22 K as shown in figure 8. The focusing optics for the laser beam directed it along the same path as the interrogating FTIR radiation shown in figure 2 while a beam block (not shown) protected the InSb detector. An area of 0.1 cm* was bathed by the laser or the FTIR radiation interrogating the monolayer before and after excitation. Use of geometric factors dictated by the optics and the cross section of the monolayer at the laser frequency together with the source power of 10 mW yielded a pumping rate from the u=O to the u=l level of kp = 10 s-l. The low power of the laser and relaxation to the substrate, at rate kphn, prevented saturation of the u-1 level. Thus neither stimulated emission from the 1131 level nor The experiment up-pumping to higher levels is important. involved measuring the integrated absorbance change of the monolayer before excitation by the laser and after excitation The absorbance change for a time of t = 2 x lo4 s (6 hr.). an upper was negligible as shown in figure 8. Never-the-less limit was given to this change by the error in the absorbance measurement. With ?$, the integrated absorbance before excitation, and AX,, the error limit on the absorbance change, the fraction of molecules removed during the 6 hr of excitation is given by Y = A$$ -< 0.06. Analysis of the coupled equations of excitation of the ~=l level and its depopulation by the variety of channels we have considered [ll] reveals Y = kVi,, kpt/(kp + kr, + kphn)

Using values of the rates already determined, we uncover JCid I 10-4 s“. This rate implies a considerably less efficient desorption than found by Heidberg et al. [17,39] in pulsed laser excitation of CO on NaCl crystallites. Why is this vibrationally induced desorption rate so We can answer this question by reviewing some simple small? propensity rules we have developed [12,40,41]. We write ‘vid

-’ =

where

k

vid

=

1o13 exp[-r(An, + An, + Ant + An,,) I

1013 s“ gives the magnitude

of the translational

(10) colli-

52 sion frequency (= v",c)of the adsorbed molecule (e.g. CO) against the substrate (e.g. NaCl(100)). The argument of the exponent gives the total change in quantum numbers during the relaxation process. This equation states that the lifetime of the excited state, through this relaxation channel, depends exponentially on the total quantum change for the process. While values of kvid resulting from the rate expression of eq. (10) are quantitatively unreliable, the qualitative predictions provide understanding to both experimental results and involved theoretical calculations.

0.00 2110

I

2109

I

2108

I

2107

I

2106

21i 15

P (cm-‘)

Figure 8. Vibrationally induced desorption of monolayer CO on NaCl(100). The absorption band of the rsC'60isotope before and after 6 hr of laser excitation is shown. The sample was maintained at 22 K. Adapted from ref. [ll].

The individual quantum number changes in the exponential of eq. (10) are An"=IAvI for the change in vibrational state of the vibrationally excited molecule during the relaxation process. For the relaxation of eq. (4), i.e. CO(v=l)~~~NaC1(100), where CO(u=l) desorbs to give CO(u=0) we have An" = 1. The change in rotational state is given by An,. If An, = 0, the product of desorption leaves the surface rotationally cold. The number of phonons within the substrate that are excited by

53

the desorption process is roughly given by AnP. Usually the biggest contribution to the total quantum number change is given by the translational quantum number change, An, = (2mAE) ‘12/2afr

.

(11)

Essentially eq. (11) counts the number of nodes of the plane wave describing the relaxed molecule of mass m near the surface as it leaves with kinetic energy AE. A Morse function is used to model the physisorbed bond and is characterized by a range parameter a. For CO on NaCl(lOO), the energy gap is the difference between the vibrational energy of CO, z = 2107 cm-', and that needed to break the surface bond AE = v"-D = 800 cm-'. The mass of CO is 29 amu. The range parametei is unfortunately difficult to estimate and a typical value is a = 2 x 10' cm-' For a generous uncertainty we assume a range from 1.5 x [411* lo8 to 3.0 x 10' cm-' which gives An, = 6 to 12. With An" = 1 and Anr = 0, An = 0 we arrive at kvid = 10m5 to lo3 s-'. This estimate, whill exceedingly approximate, does encompass the experimental rate of kVi$10m4 s-l we have determined. Returning to the question: why is kvid so small for CO(~=l)~~~NaC1(100)? The answer is because the change in total quantum numbers for the process is so large. Others by theoretical considerations have not found kvid to be small for this system. Ben Ephram et al. [42] suggest an important role for rotations in the photodesorption process. However this rotation-assisted channel is likely closed in the monolayer of coupled CO. Their estimate of kvid differs 15 orders of magnitude from our measurement. Muckerman et al. [43], who we believe use an unrealistic value of a, calculate \id to be of the order of 1012 s-'. Gortel et al. [44] address the importance of AnP in their discussion of phonon-assisted desorption. Their estimate for kvid, assuming similar values of the a parameter, is essentially in agreement with our result.

3. 3.1

SYSTEMS

A-B*.*S

Spectroscopy and bonding Infrared spectroscopy of other small molecules on For CO, 145,461, C2% 1471 NaCl(100) has also been explored. and CH,, [48] on NaCl(lOO), the positions of the spectroscopic

54 features coincides with their gas phase values to within about 1%. However, unlike the single absorption observed for CO on NaCl(100) multiple features are found in these other systems. These splittings are a result of interactions of the adsorbed molecules with the substrate or with their neighbors in the While photochemistry following W excitamonolayer [45-481. tion of molecules or LiF(lOO) has been explored [37,49] we know of no vibrational spectroscopy on this single crystal subHowever the infrared spectroscopy of a variety of strate. small molecules on NaCl, LiF, CsI and other alkali halide crystallites produced by sublimation has been reported [50-531. Again the spectroscopic features are near their gas phase values indicating only subtle perturbations by the alkali halide substrate. The integrated cross section, 0, for both CO and CO, on The NaCl(100) are comparable to their gas phase values [9,45]. differences observed are largely accounted for by polarizaThe dramatic bility effects within the monolayer [9,33,45,54]. increase in 0 (or LX") found for CO adsorbed to metals [28-301 is not observed for the NaCl substrate. However for the case of Hz on alkali halide crystallites weak infrared absorption is found as expected from the dipole induced by the electric field emanated from ions of the substrate [50]. Thermodynamic measurements [14,18-20,46,50] as well as theoretical analysis [14,18] are consistent with physisorbed The bonding for small molecules on alkali halide substrates. dominant attractive contributions to bonding are of electrostatic and dispersive origin. Interactions among molecules within the adsorbate layer is small relative to the surface bond energy in CO on NaCl(100) as we have noted [21]. However for CO, [45,46], C,H, [47] and CH, [48] on NaCl(lOO), the adsorbates attract each other so that islands form in the submonolayer. This is evident both from the spectroscopy [45-481 and the form of the adsorption isotherms [46-481 which deviate significantly from the Langmuir behavior of CO on NaCl(100) we have seen in figure 1. We now need to consider how these differences in the spectroscopy and bonding of A-B on S will effect the energy flow patterns. 3.2

Dephasing rate, k* To the best of our knowledge, the dephasing rate for CO on NaCl(100) is the only molecule explored so far on a well-

55

defined alkali halide surface. However the theoretical developments of Persson et al. [28-301 imply comparable results for other A-R on S systems. We reach this conclusion because the rather mild interactions leading to molecular adsorption to alkali halide crystallites [50-531 results in only small changes in the spectroscopic constants from their gas phase values. Thus while adsorbed CO on metals can give rise to temperature dependent changes in vibrational frequency and bandwidth of -10 cm-' [28-301 leading to dephasing rates of 10'2 s-1, comparable changes for molecules on alkali halide are anticipated to be an order of magnitude less. 3.3

Radiative rate, k,, The radiative rate is simply tied to the integrated cross section. For the case where the transition dipole is perpendicular to the surface, eq. (5) gives this rate. Based on the experience with CO and CO* on NaCl(100) in which a is comparable to its gas phase values [9,45] and the subtle changes in other spectroscopic constants for other molecules on alkali halides [50-531, we anticipate radiative rates for adsorbed molecules to be comparable to their gas phase values. Thus values of krd -1 to lo3 s-' are predicted to be typical. 3.4

Relaxation by phonons, kphn The success of the CPS model [35] to account for the relaxation of CO* l**NaCl(lOO) by phonons is encouraging. Let us therefore consider this model for other molecules on NaCl and other alkali halides as well. We first combine eqs. (5) and (8) to obtain 14

kphn=

nnGz 2x2 ;I&(;) + 11' R3

-

(12)

In order to present a somewhat quantitative view of the phonon relaxation rate we shall first consider NaCl using values of n and IC from Palik's review [36]. We also take Gz = l~lO_'~cm molecule-', the value of CO [9], as typical. Integrated cross sections for allowed infrared transitions of other molecules can be an order of magnitude larger or smaller [55]. We also retain the separation R = 3.3 A as before. The theoretical phonon relaxation rate for molecules on NaCl is presented in figure 9. The circle lists the experimental value for

56 (The calcuCO(u)~~*NaCl(lOO) with l&&15 we have uncovered. lated value on the solid curve is about three times smaller For molesince Qz used is appropriate to the O-r1 transition.) cules with vibrational frequencies above 2000 cm-' relaxation by phonons is comparable to typical radiative rates of k,, 10 s-1. Below 2000 cm-' molecular relaxation to surface phonons becomes increasingly efficient and reaches its highest rate near the absorption maximum of NaCl at 265 cm-' [36]. Relaxation of molecules on LiF is also predicted on figure 9. Values of e(6) are again taken from Palik [36] but iz and R are

1

j

I

I

I

4000

3000

2000

1000

(j

i;(cm-l) Figure 9. Phonon relaxation rates of A-B**e=S. The curves are from the theoretical model of Chance, Prock and Silbey [35] using parameters given in the text. The vibrational frequency of A-R* is c and the substrate S is either NaCl or LiF. The circle is from experiments of CO***=NaCl(lOO) described in the text. fixed at their previous level. The calculated rates are usually higher than for NaCl because LiF has a higher value of n. (It absorbs light in the infrared region more efficiently.) The fluorescence we have observed for CO on NaCl(100) would be considerably quenched on LiF(lOO) and much more difficult to

57

observe. The curves generated on figure 9 are calculated for c(Y) values of the salts near 20°C [36]. Because optical properties are somewhat temperature dependent, some alteration in kphn is expected particularly at the lower frequencies for substrates at cryogenic temperatures. The order of magnitude predictions of figure 9 should however be valid. Molecular dynamics calculations for NO(u=l) on LiF(lOO) have been directed toward understanding nonradiative relaxation to the substrate following collisions of the excited molecule with the surface [56]. Inefficient relaxation for this molecule, with Z = 1900 cm-', is consistent with the result in figure 9. Experimental study of vibrationally excited CO, colliding with LiF(lOO) cannot uncover an unambiguous rate for [571. However in the region of the bending mode at 670 23 figure 9 suggests a rapid relaxation rate. More sophisticated treatments have also been developed lately. Nitzan and Tully [58] consider energy relaxation as a process of anharmonic coupling between an oscillator and a heat bath. Direct transfer of vibrational energy from the high frequency molecular mode to the low frequency phonon mode is assumed. When using stochastic classical trajectory simulations, rates in the range 1010-107 s-' are found for the multiphonon processes they consider. However, Benjamin and Reinhardt [59] very recently point out that multiphonon coupling cannot be the most efficient channel. Instead the energy is considered to flow rapidly from the molecular vibrational mode to the surface bond modes, whose excitations are then dissiNeverpated by the excitation or de-excitation of phonons. the-less presentations like those of figure 9 for all alkali halide substrates would seem to offer reasonable estimates of kphn for any A-B****S system. 3.5

Vibrationally induced desorption rate: kvid To our knowledge there has been no clear experimental demonstration of direct vibrationally induced desorption. Several experiments, reported by Heidberg et al., are however consistent with thermal desorption of C%F [603, and Desorption of pyridine on KCl(100) has C& 1611 from NaCl. been measured by Chuang et al. 1621. Time-of-flight mass spectra demonstrate that photodesorption has taken place but the results are consistent with surface heating with rate In all these systems constant kphn followed by desorption.

58 a single vibrational excitation of the adsorbate is insufficient to break the surface bond so multiphonon absorption is required for desorption. Up-pumping from the first excited level to higher vibrational levels through intermolecular energy transfer is necessary for the desorption process that photo[443. We have seen for CO(~=l)~~~NaC1(100) desorption is energetically possible but qid is exceedingly slow.

Figure 10. Vibrationally The total quantum change, described in the text.

induced desorption rates of A-B*me=S. An,, for the desorption process is

* Is it in general true that, for A-B l**S, kvid will be slow? To answer this question we turn again to eq. (10) and on figure 10, kvid against the total quantum change, plot,

An1 = An, + An, + An, + An,,

(13)

for vibrationally induced desorption. We need only estimate An, to find kvid. As we saw before for CO(v=l)~~~NaCl(lOO) we obtained Ant =

59

6 to 12, depending on the value of the range parameter a used, and consequently, with An" = 1, An, = 7 to 13. The uncertainty in \id# spanning many orders of magnitude, is indeed unfortunate. It is a consequence of 30% variations in Aq (i.e. 9f3), a large exponential value. The large exponent is in turn due to the large values of the momentum, (2mAE)'/', of the departing CO(u=O) photodesorption fragment. We can anticipate faster kvidwhen (2mAE)1'2 is smaller. Consider H2(u=1) l=*NaCl with a estimated surface bond of Do=800 cm-' and c = 4160 cm-' so AE=3360 cm-' [50]. With a typical range parameter of a = 2x10" cm-' we arrive at Ant = 5 and with An = 1 we have An, = 6 or kvid - 10' se'. The high frequency ovf H, is more than compensated by its light mass to reduce its momentum below that of CO. The integrated cross section for H,***NaCl(lOO) is not known, but if we assume the value for CO***NaCl(lOO) figure 9 suggests kphn -10 5-l. Variation of a and Ant by 30% still provides kvid faster than induced desorption for kphn' Thus we predict vibrationally H2(u=1)***NaC1(100). For polyatomic molecules on alkali halide surfaces, possibility for the photodesorbed product to carry away vibrational or rotational energy can have the effect of lowering the value We consider CH, or its of AnT as we discuss elsewhere [40,41]. isotopes on NaCl(100) likely candidates for vibrationally inWork on this system is in progress. duced desorption. Let us return to the question: will kvid always be slow? We believe the answer to this question is no. What is required is a small value of (2mAE)"', the momentum of the desorbed This can be accomplished if the kinetic energy, AE, product. is reduced, and therefore An, reduced, by the uptake of energy By in vibrational, rotational or phonon degrees of freedom. appropriate energy partitioning, AnT can then be minimized. This occurs in vibrational predissociating of van der Waals clusters where fragments are formed after excitation at rates up to 10" s-1 [41].

4.

AFTERWORD

We are led to the conclusion that alkali halide surfaces are remarkably passive to vibrational activity of adsorbed The most effimolecules for frequencies above -2000 cm“. cient relaxation channel leading to depopulation of excited

60 vibrational levels is likely to be to phonons in the substrate. This has been demonstrated for CO*l~*NaCl(lOO) and the success of the CPS model to account for this result lends credence to the predictions of kphn in other A-B****S systems as well. However, for some systems, e.g. Hz*~~*NaCl(lOO), it is possible that vibrationally induced desorption may be the most efficient relaxation channel. The passivity of alkali halide substrates to vibrational population relaxation processes, where lifetimes can be as long as milliseconds, is in sharp contrast to metal or semiconductor substrates where vibrational lifetimes of adsorbed molecules is on the picosecond [2] or nanosecond timescale [3]. However for low frequencies, well below 1000 cm-', alkali halide phonons can take up adsorbate vibrational excitations on the nanosecond timescale. Of what possible relevance is the passivity of alkali halide substrates to vibrational excitation of adsorbed layers? We have suggested elsewhere that the energy pooling observed in * CO l==NaCl(lOO) can lead to population inversions of some vibrational levels [4]. It is then possible that a monolayer of CO can act as an optical amplifier or even produce laser action. In the interpretation of surface photochemical measurements on LiF(lOO) [37] we can anticipate that electronic states with high vibrational excitation will retain this excitation for long times. However, low vibrational excitations will be rapidly dissipated to the substrate. These relaxation pathways are likely to influence the direction of photoinduced surface chemistry. At one time it was thought that vibrational excitation of surface bound molecules could be a feasible way to selectively photodesorb molecules [40,44,63]. Different isotopes for example could be separated by this method which has been given the name "photochromatography" [63]. However it now appears that the substrate will remove vibrational excitation through phonon excitation. In most, but not all, cases kphn >> kvid and photodesorption will be an inefficient process. We believe that the study of vibrational dynamics on alkali halide surfaces has lead to a rich and interesting area that deserves further exploration.

5.

ACKNOWLEDGMENT We thank

the National

Science

Foundation

for financial

61

support

6. 1 2 3 4 5

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

of this work.

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