Catalyst Characterization Science - American Chemical Society

34 Vibrational Analysis of Adsorbed Molecules H. Ibach and J. E. Müller

Downloaded by UNIV LAVAL on July 3, 2014 | http://pubs.acs.org Publication Date: October 16, 1985 | doi: 10.1021/bk-1985-0288.ch034

Institut für Grenzflächenforschung und Vakuumphysik and Institut für Festkörperphysik, Kernforschungsanlage Jülich, D-5170 Jülich, Federal Republic of Germany

The principles of v i b r a t i o n analysis are outlined. The v i b r a t i o n spectrum of a surface species serves as a fingerprint r i c h enough i n d e t a i l s to reveal the essentials of the structure and bonding of the species containing up to about 20 atoms. The analysis usually involves a comparison to spectra of free molecules or model compounds. Mode assignment i s performed through the use of isotopes. Selection rules can be used to determine the point group of a surface species. Surface decomposition reactions are easily studied using the technique of v i b r a t i o n analysis. Recently, r e l i a b l e calculations of the electronic structure of adsorbed species have become available. Calculated equilibrium geometries and frequencies provide an important connection between theory and experiment. Results of such calculations for H2O andNH3are presented and compared to experimental data. Our understanding of the chemistry of molecules adsorbed on metals has greatly improved i n recent years. Much of our present knowledge i s owed to the advent of r e l i a b l e tools to study the v i b r a t i o n spectrum of adsorbed species (1,2). Though v i b r a t i o n spectroscopy i s not an exact method and the methodology does not follow a p a r t i c u l a r routine pattern, i t yields important qualitative information on the structure, the adsorption sites and reaction paths of surface species, as we s h a l l see. The purpose of this paper i s to summarize the important principles i n the analysis of v i b r a t i o n spectra from surfaces and to demonstrate the type of information which i s obtained. Regarding the experimental technique we s h a l l refer to electron energy loss spectroscopy (ELS) only i n this paper. The reason i s that t h i s method provides for the largest amount of information on the entire v i b r a t i o n spectrum. It i s suited for adsorption studies on single c r y s t a l surfaces as well as on real surfaces, as long as they are stable i n vacuum. Other techniques, i n particular infrared r e f l e c t i o n absorption spectroscopy have a higher resolution i n a l i mited spectral range. They frequently serve as a source of a d d i t i onal information on the d e t a i l s of the structure. 0097-6156/85/0288-0392$06.00/0 © 1985 American Chemical Society In Catalyst Characterization Science; Deviney, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

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On s i n g l e c r y s t a l s u r f a c e s v i b r a t i o n a l modes a r e i n p r i n c i p l e w a v e l i k e e x c i t a t i o n s w i t h the wave v e c t o r p a r a l l e l t o the s u r f a c e . For most m o l e c u l e s d i s p e r s i o n e f f e c t s are s m a l l , however, and s h a l l be d i s r e g a r d e d i n t h i s paper which i s more o r i e n t e d towards the chem i c a l a s p e c t s . However, d i s p e r s i o n o f adsorbate modes has been measured r e c e n t l y ( 3 ) . The second p a r t o f the paper i s devoted t o some a s p e c t s o f the c u r r e n t s t a t u s o f the t h e o r y o f c h e m i s o r p t i o n . There, i n p a r t i c u l a r , the a d s o r p t i o n o f water and ammonia w i l l be s t u d i e d and d i s c u s s e d . Through the t h e o r y a q u a l i t a t i v e understanding o f the bonding o f these m o l e c u l e s t o s u r f a c e s i s a c h i e v e d which i s i n agreement w i t h the e x p e r i m e n t a l o b s e r v a t i o n s .


P r i n c i p l e s o f the V i b r a t i o n a l A n a l y s i s The V i b r a t i o n Spectrum as a F i n g e r P r i n t . The methodology o f v i b r a t i o n a l a n a l y s i s comprises a v a r i e t y of d i f f e r e n t a s p e c t s . I n some cases a w e l l e s t a b l i s h e d path o f l o g i c a l r o u t i n e i s f o l l o w e d . I n o t h e r cases the a n a l y s i s works on a n a l o g i e s to a l a r g e group o f known compounds and t h e i r v i b r a t i o n spectrum. We s h a l l d i s c u s s the l a t t e r aspect f i r s t . F i n g e r p r i n t i n g works w i t h the n o t i o n t h a t , b y and l a r g e , the v i b r a t i o n a l mode i s a s s o c i a t e d w i t h a p a r t i c u l a r bond w i t h i n a m o l e c u l e , be i t i n gas phase o r adsorbed on the s u r f a c e . T h i s i s , o f c o u r s e , a v e r y approximate concept o n l y , a s i n p r i n c i p l e the v i b r a t i o n a l mode i s a p r o p e r t y o f the e n t i r e system and not a p r o p e r t y o f a n i n d i v i d u a l bond. Y e t , the comparison o f v i b r a t i o n a l s p e c t r a o f a l a r g e number o f molecules as w e l l as dynamical c a l c u l a t i o n s shows t h a t , t o a l a r g e r o r l e s s e r degree, the concept o f a v i b r a t i o n a l mode c h a r a c t e r i z i n g a bond can be used. T y p i c a l examples are the hydrogen s t r e t c h i n g v i b r a t i o n s . Hydrogen has a s i g n i f i c a n t l y s m a l l e r mass than the atom w h i c h i t bonds t o ( c a r b o n , s i l i c o n , oxygen) · Consequently i t s v i b r a t i o n a l modes a r e r a t h e r l o c a l i z e d t o the hydrogen bond and t h e i r f r e q u e n c i e s a r e l i t t l e a f f e c t e d by the r e s t o f the m o l e c u l e . The f r e q u e n c i e s a r e s e n s i t i v e , however, t o the o r b i t a l s t r u c t u r e o f the atom which hydrogen bonds t o . Thus one c a n d i s t i n g u i s h between sp, sp and sp h y b r i d i z e d carbon atoms. T h i s p r o v i d e s a sound b a s i s f o r d i s c r i m i n a t i n g s a t u r a t e d and u n s a t u r a t e d h y d r o c a r b o n s even on s u r f a c e s . V i b r a t i o n a l a n a l y s i s o f a l a r g e number o f m o l e c u l e s i n s u r f a c e compounds has a l s o shown t h a t the c a r bon-carbon s t r e t c h i n g v i b r a t i o n i s c h a r a c t e r i s t i c o f the bond and s i n g l e , double and t r i p l e bonds can be d i s t i n g u i s h e d . When a m o l e c u l e i s adsorbed on a s u r f a c e and a v i b r a t i o n a l anal y s i s i s attempted one u s u a l l y t r i e s t o r a t i o n a l i z e the v i b r a t i o n spectrum i n analogy t o the w e l l documented v i b r a t i o n s p e c t r a o f f r e e m o l e c u l e s . T h i s renders a f i r s t guess. F r e q u e n t l y , a l s o , the answer i s p r o v i d e d as t o whether the molecule decomposes upon a d s o r p t i o n o r not. The s i m p l e s t case t h e r e i s the a d s o r p t i o n o f d i a t o m i c m o l e c u l e s where the absence o r presence o f the c h a r a c t e r i s t i c s t r e t c h i n g v i b r a t i o n d e c i d e s upon the q u e s t i o n o f d i s s o c i a t i o n . For l a r g e r molec u l e s and a more d e t a i l e d a n a l y s i s o f the v i b r a t i o n spectrum, t h e comparison t o the s p e c t r a o f f r e e m o l e c u l e may not s u f f i c e . Here the comparison t o o r g a n o m e t a l l i c compounds of known s t r u c t u r e and v i b r a t i o n spectrum can be most h e l p f u l . A good example i s p r o v i d e d w i t h the a n a l y s i s o f the s p e c i e s formed from e t h y l e n e adsorbed on P t ( l l l )

In Catalyst Characterization Science; Deviney, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1985.

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(4) and P d ( l l l ) (5_) a t room temperature. While i t became c l e a r v e r y q u i c k l y t h a t the s p e c i e s on the s u r f a c e c o u l d not be a c e t y l e n e as was assumed i n the o l d e r l i t e r a t u r e , the p r e c i s e n a t u r e of the spec i e s was debated f o r a w h i l e . The f i n a l answer came when the model compound C C l ^ i ^ i C C O g , named t r i c o b a l t - e t h y l i d e n e - n o n a c a r b o n y l , was prepared and the v i b r a t i o n spectrum was s t u d i e d ( 6 ) . F i g u r e 1 shows t h a t the v i b r a t i o n spectrum of the s u r f a c e s p e c i e s c o r r e l a t e s v e r y w e l l w i t h the spectrum of the model compound. This c o r r e l a t i o n a l s o i n c l u d e s the symmetry assignment of the modes f o r which we s h a l l d e s c r i b e the methodology s h o r t l y . Isotopes. As we have seen, the f r e q u e n c y of modes c o n t a i n s important i n f o r m a t i o n on the nature of the bonding. While the i n f o r m a t i o n i s q u a l i t a t i v e i t s t i l l serves f o r an educated f i r s t guess on the s t r u c t u r e of the m o l e c u l e . For the i d e n t i f i c a t i o n of the s p e c i e s i n F i g u r e 1, e.g., the assignment of modes r e v e a l s the 1130 cm mode as the C-C s t r e t c h i n g v i b r a t i o n . This frequency i s w i t h i n the t y p i c a l range of C-C s i n g l e bond s t r e t c h i n g f r e q u e n c i e s , however, f a l l s below the range of the t y p i c a l C-C double bond f r e q u e n c i e s (1500-1800 cm )· Thus from the assignment i t i s c l e a r t h a t the s p e c i e s has the bonding c h a r a c t e r i s t i c s of a s a t u r a t e d hydrocarbon. The q u e s t i o n i s , of c o u r s e , how the c o r r e c t assignment i s a c h i e v e d . Here s t u d i e s o f i s o t o p e s are i n d i s p e n s a b l e . Upon t o t a l or p a r t i a l d e u t e r a t i o n one n o t i c e s the CH v i b r a t i o n s t o s h i f t downwards by a f a c t o r of ~ 1.35 w h i l e the C-C v i b r a t i o n changes v e r y l i t t l e . In a few cases , where a s t r o n g c o u p l i n g between the C-C s t r e t c h i n g v i b r a t i o n and the CH s t r e t c h i n g v i b r a t i o n s of the same symmetry e x i s t s , l a r g e r s h i f t s of the "CC" v i b r a t i o n can o c c u r . Such s h i f t s a r e , however, not complet e l y a r b i t r a r y . The f r e q u e n c i e s o f modes w i t h i n the same r e p r e s e n t a t i o n of the p o i n t group of the s u r f a c e s p e c i e s f o l l o w the T e l l e r R e d l i c h r u l e when atoms are d i s p l a c e d by i s o t o p e s . The T e l l e r - R e d l i c h r u l e a l s o serves a u s e f u l purpose to check whether a proposed symmetry and the assignment of the mode a c c o r d i n g to the proposed symmetry i s c o r r e c t . An example i s p r o v i d e d w i t h the modes of C2H2 and C D on Fe(110) (7_). There i t was shown by the T e l l e r - R e d l i c h a n a l y s i s t h a t the o n l y symmetry of the s p e c i e s c o n s i s t e n t w i t h the s p e c t r a i s C^, t h a t i s , the s t r u c t u r e i s such t h a t no element o f symmetry e x i s t s . While t h i s i s somewhat d i s a p p o i n t i n g t o the t h e o r i s t as i t c o m p l i c a t e s the t h e o r e t i c a l a n a l y s i s of the bonding, the low symmetry f i n d s a n a t u r a l e x p l a n a t i o n i n the s t r u c t u r e of the lowest unoccupied o r b i t a l of a c e t y l e n e . 2

2

S u r f a c e P o i n t Groups and S e l e c t i o n R u l e s . The most important p o i n t groups of s u r f a c e s p e c i e s are C j , C , C , C , C 3 , C/ . Except f o r C , examples a r e known f o r each of the p o i n t groups. The a n a l y s i s of the p o i n t group of the s u r f a c e s p e c i e s makes use of the f a c t t h a t the s p e c t r o s c o p y i m p l i e s p a r t i c u l a r s e l e c t i o n r u l e s . Here a g a i n the advantage of ELS over o t h e r v i b r a t i o n s p e c t r o s c o p i e s f o r s t r u c t u r e a n a l y s i s becomes o b v i o u s . ELS has the unique c a p a b i l i t y t o employ d i f f e r e n t s c a t t e r i n g mechanisms merely by o b s e r v i n g under d i f f e r e n t s c a t t e r i n g c o n d i t i o n s . When s p e c t r a are observed i n the d i r e c t i o n s of s p e c u l a r r e f l e c t i o n ((OO)-beam) d i p o l e s c a t t e r i n g i s employed w h i c h means t h a t o n l y the t o t a l l y symmetric v i b r a t i o n s are e x c i t e d . Impact s c a t t e r i n g i s used when the spectrum i s observed o f f the speg

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c u l a r d i r e c t i o n . Then, a l l even modes w i t h r e s p e c t t o the s c a t t e r i n g plane c o n t r i b u t e to the spectrum p r o v i d e d the s c a t t e r i n g plane i s a l i g n e d a l o n g a plane o f symmetry. In a g e n e r a l o r i e n t a t i o n o f the s c a t t e r i n g p l a n e , a l l modes a r e e x c i t e d . These s e l e c t i o n r u l e s a l l o w the d e t e r m i n a t i o n of the p o i n t group of the s u r f a c e s p e c i e s i n most cases. A famous, y e t s i m p l e example i s CO. CO tends t o adsorb i n h i g h l y symmetric p o s i t i o n s on low index s u r f a c e s , so t h a t the p o i n t groups are C , C^ and C^ . The t o t a l l y symmetric v i b r a t i o n s then are the CO s t r e t c h i n g and the h i n d e r e d t r a n s l a t i o n of the m o l e c u l e v e r t i c a l to the s u r f a c e (metal-carbon stretch)· C o n s e q u e n t l y , t h e s e two modes are seen i n d i p o l e s c a t t e r i n g . Another example i s p r o v i d e d w i t h ammonia F e ( l l O ) ( F i g u r e 2 ) , when the coverage i s low ( 8 ) . Again, o n l y the t o t a l l y symmetric v i b r a t i o n s appear, under the p o i n t group C g . I n t e r e s t i n g l y here, the p o i n t group C^ i s i n c o n s i s t e n t w i t h the symmetry of the s u b s t r a t e s u r f a c e atoms (C )» The d i r e c t product o f C χ c o n t a i n s o n l y the i r r e d u c i b l e r e p r e s e n t a t i o n o f C . I f the r e l e v a n t p o i n t group of ammonia would be C , however, many more modes would appear. One must, t h e r e f o r e , conclude t h a t the b r e a k i n g of the m o l e c u l a r symetry through the s u r f a c e i s n e g l i g i b l e . T h i s i s b e s t r a t i o n a l i z e d when the NHo-molecule i s adsorbed w i t h the n i t r o gen atom bonded head on a s u r f a c e atom ( i n s t e a d of b r i d g i n g c o n f i g u r a t i o n s ) s i n c e then the symmetry o f the adsorbed ammonia i n c l u d i n g the n e a r e s t neighbor s u r f a c e atom i s 0^ · We s h a l l see l a t e r i n t h e t h e o r e t i c a l s e c t i o n t h a t the proposed s t r u c t u r e i s i n accordance w i t h t o t a l energy c a l c u l a t i o n s . 2y



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C o n t r o l l e d Reactions. V i b r a t i o n a l a n a l y s i s of surface chemical r e a c t i o n s , decomposition r e a c t i o n s i n p a r t i c u l a r , i s a l s o f e a s i b l e . A number of d e c o m p o s i t i o n r e a c t i o n s have been s t u d i e d a l r e a d y . The s i m p l e s t of these i n v o l v e the d i s s o c i a t i o n of d i a t o m i c m o l e c u l e s such as CO, 0 , H , and NO. Y e t , a l s o the d e c o m p o s i t i o n of more com p l e x o r g a n i c m o l e c u l e s , w h i c h proceed v i a s e v e r a l s t e p s w i t h metas t a b l e i n t e r m e d i a t e compounds, has been i n v e s t i g a t e d . T y p i c a l l y such an experiment i s performed w i t h the molecule adsorbed a t low tempe r a t u r e s . The temperature i s then r a i s e d up t o a p a r t i c u l a r v a l u e f o r a p a r t i c u l a r t i m e . S p e c t r a are recorded a t t h a t temperature or w i t h the sample c o o l e d down a g a i n . The e t h y l i d e n e s p e c i e s from F i g u r e 1 r e p r e s e n t s such an i n t e r m e d i a t e . We have seen t h a t the a n a l y s i s of t h a t s p e c i e s was f i n a l l y confirmed through comparison t o an appro p r i a t e o r g a n o m e t a l l i c compound. T h i s , however, was the l a s t s t e p un d e r t a k e n i n o r d e r to c o n f i r m an a l r e a d y e x i s t i n g p r o p o s i t i o n . To a r r i v e a t a r e a s o n a b l e c o n j e c t u r e about the n a t u r e of an u n i d e n t i f i e d o b j e c t on the s u r f a c e , the method of p r e p a r a t i o n p r o v i d e s e q u a l l y v a l u a b l e h i n t s . For the example d i s c u s s e d here,e.g., i t was i m p o r t a n t t o l e a r n t h a t the s p e c i e s c o u l d be grown from adsorbed e t h y l e n e , but a l s o from coadsorbed a c e t y l e n e and hydrogen. The s p e c i e s , t h e r e f o r e , had to have more than two hydrogen atoms, y e t no more than f o u r . An o t h e r example where the " h i s t o r y " was important i s the methoxy s p e c i e s formed from the d e c o m p o s i t i o n of methanol on many m e t a l s u r f a c e s . There, t h e s i m i l a r i t y o f the spectrum of methoxy t o m e t h a n o l , except f o r the removal of the OH s t r e t c h i n g v i b r a t i o n from the spec trum upon warming the sample t o h i g h e r temperature, was the i m p o r t a n t clue (9> 2

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CATALYST C H A R A C T E R I Z A T I O N S C I E N C E

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399

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F i g u r e 5.

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MULLER


401

v e r y enharmonic energy v a r i a t i o n . The mode has a v e r y l a r g e z e r o p o i n t m o t i o n , which t o g e t h e r w i t h the l a r g e dynamic d i p o l e g i v e s r i s e t o a s t r o n g EELS s i g n a l ( 1 4 ) . The d y n a m i c a l d i p o l e i s a p p r o x i mately g i v e n by άμ/άα^ = 2μ s i n a , where μ - 0.7 a.u. (1 a.u. - 2 . 5 Debye) i s the permanent d i p o l e of H 0 and the f a c t o r 2 ( i n our c a l c u l a t i o n o n l y 1.4) i s the enhancement due to the image. I t has been observed t h a t w i t h the f o r m a t i o n H 0 l a y e r s t h i s mode s t i f f e n s and becomes even s t r o n g e r ( 1 5 ) . For ΝΗβ the o r i e n t a t i o n a l energy i s q u i t e l a r g e . However, s i n c e i n the ground s t a t e the permanent d i p o l e i s p e r p e n d i c u l a r to the s u r f a c e , the d y n a m i c a l d i p o l e f o r t h i s mode i s z e r o , so t h a t the mode i s EELS-inactive. I n t e r n a l Bend ( F i g u r e s 4c and 5 b ) . The i n t e r n a l modes a r e used to i d e n t i f y the adsorbed s p e c i e s , and a comparison w i t h the i s o l a t e d m o l e c u l e v a l u e s i n d i c a t e s t o what e x t e n t the m o l e c u l e i s a f f e c t e d by the s u r f a c e . I n the " s c i s s o r s mode" of H 0, the p r o t o n s move p a r a l l e l t o the s u r f a c e and the o s c i l l a t i o n frequency i s almost u n a f f e c t e d . For NH3, on the o t h e r hand, the so c a l l e d " u m b r e l l a mode" i s d r a s t i c a l l y s t i f f e n e d by the s u r f a c e because the p r o t o n s move a g a i n s t the s u r f a c e and s u f f e r a s t r o n g Coulomb r e p u l s i o n . Here a g a i n the d y n a m i c a l d i p o l e moment i s dμ/dα^ « 2 μ^. s i n d a ^ . For NH3, where μ - 0.53 a.u., the enhancement of the dynamic d i p o l e by the s u r f a c e i s com pensated by the s m a l l e r o s c i l l a t i o n a m p l i t u d e . I n t e r n a l S t r e t c h ( F i g u r e s 4d and 5 c ) . I n s p i t e o f an enhance ment of the m a t r i x elements by the s u r f a c e , t h i s mode shows a r a t h e r s m a l l i n t e n s i t y and e s s e n t i a l l y no change i n f r e q u e n c y . The o c c u r rence o f a l a r g e peak s h i f t e d t o lower f r e q u e n c i e s must be i n t e r p r e t e d i n terms of hydrogen bonded networks ( 1 5 ) . Μ

t

Μ

2


2

2

Μ

Comparison Between Theory and

Experiment 9

In Table I we compare c a l c u l a t e d f r e q u e n c i e s and m a t r i x elements M ( i n p a r e n t h e s i s ) f o r H 0 and NHo on A l ( 1 0 0 ) w i t h e x p e r i m e n t a l v a l u e s f o r the NH -Fe(110) and H 0-Cu(100) systems, the data t a k e n from (8) and ( 1 4 ) . Only r e l a t i v e v a l u e s of M a r e presented because o f d i f f i c u l t i e s i n d e t e r m i n i n g the s u r f a c e coverage. Even though we a r e com p a r i n g d i f f e r e n t s y s t e m s j the good agreement found f o r the i n t e r n a l modes i s an i n d i c a t i o n t h a t these modes are r a t h e r independent o f the s u b s t r a t e and t h e r e f o r e can be used t o c h a r a c t e r i z e the adsorbed s p e c i e s . The h i n d e r e d modes, on the o t h e r hand are much more sub s t r a t e s p e c i f i c . For i n s t a n c e , NH3 binds more s t r o n g l y t o Fe than t o A l , and H 0 more weakly t o Cu than t o A l . Note t h a t the t i l t e d ground s t a t e geometry reduces the i n t e n s i t y of the i n t e r n a l H 0 modes by a f a c t o r cos α = 0.25, the i n t e r n a l s t r e t c h a p p a r e n t l y below the l i m i t of d e t e c t i o n . The h i n d e r e d r o t a t i o n , on the o t h e r hand, i s o n l y ob s e r v a b l e i n the t i l t e d geometry. As mentioned above, t h i s mode i s f o r b i d d e n by symmetry f o r NH3, but o b s e r v a b l e w i t h l a r g e i n t e n s i t y f o r H 0. F i n a l l y , the h i n d e r e d t r a n s l a t i o n e x h i b i t s a s m a l l but f i n i t e a m p l i t u d e b o t h f o r NH3 and H 0, i n d i c a t i n g charge t r a n s f e r , i n t h i s case from the m o l e c u l e to the m e t a l . 2

3

2

2

2

2

2


CATALYST C H A R A C T E R I Z A T I O N

402

SCIENCE

Table I. Comparison o f c a l c u l a t e d f r e q u e n c i e s and m a t r i x elements M ( i n p a r e n t h e s e s ) f o r H 0 and N H on A l ( 1 0 0 ) w i t h e x p e r i m e n t a l v a l u e s f o r t h e NH -Fe(1107 and H 0-Cu(100) s y s t e m s . 2

2

3

3

2

H 0-Cu

H 0-A1

NH -Fe

NH ~A1

(exp)

(theory)

(exp)

(theory)

Hindered translation

121 cm". (0,.60)

290 cm" (0.33)

1

Hindered rotation

230 cm" (26.0)

400 cm" (24.0)

1

Internal bend

1590 cm".. (2,• 7)

1480 cm" (2.7) 3640 cm" (0.7)


2

2

1

Internal stretch

3

3

429 cm" (0,• 09)

370 cm" (0,• 05)

1

1170 cm" (15.0)

1

1260 cm" (15.0)

1

1

3310 cm" (1..2)

1

3310 cm" (1..2)

1

1

1

Next we d i s c u s s t h e e f f e c t o f d e u t e r a t i o n on low frequency modes i n v o l v i n g the p r o t o n s . Because o f t h e anharmonic v a r i a t i o n o f t h e e n ergy as a f u n c t i o n o f t i l t a n g l e α ( F i g . 4b), t h e h i n d e r e d r o t a t i o n s o f H 0 and D 0 t u r n out t o be q u a l i t a t i v e l y d i f f e r e n t . The f i r s t v i b r a t i o n a l e x c i t e d s t a t e o f H 0 i s l e s s l o c a l i z e d than t h a t o f D 0 , because o f i t s l a r g e r e f f e c t i v e mass. The o s c i l l a t i o n frequency o f the mode decreases by a f a c t o r 1.19 and t h e m a t r i x elements by a f a c t o r 1.51 upon d e u t e r a t i o n . T h e r e f o r e , t h e harmonic a p p r o x i m a t i o n , which y i e l d s an i s o t o p i c f a c t o r 1.4 f o r both the frequency and t h e i n t e n s i t y , i s q u i t e i n a p p r o p r i a t e f o r t h i s mode. In Table I I we compare the c a l c u l a t e d frequency and m a t r i x e l e ment M ( i n p a r e n t h e s i s ) f o r t h e DoO-AKlOO) h i n d e r e d r o t a t i o n w i t h e x p e r i m e n t a l r e s u l t s f o r D 0-Cu(100) ( 1 4 ) . The e x p e r i m e n t a l i s o t o p i c f a c t o r i s 1.16 f o r t h e frequency and - 1.6 f o r t h e m a t r i x e l e m e n t s , i n good agreement w i t h our c a l c u l a t i o n . I n Ref. 14, u s i n g t h e h a r monic a p p r o x i m a t i o n , t h e anomalous i s o t o p i c f a c t o r f o r t h e f r e q u e n c y was i n t e r p r e t e d as due t o m i x i n g w i t h t h e h i n d e r e d t r a n s l a t i o n . How e v e r , as we have shown, t h e harmonic a p p r o x i m a t i o n i s i n a p p r o p r i a t e i n t h i s case. 2

2

2

2

2

T a b l e I I . Comparison o f c a l c u l a t e d f r e q u e n c y and m a t r i x element M (τη p a r e n t h e s e s ) f o r t h e D 0-A1(100) h i n d e r e d r o t a t i o n w i t h e x p e r i m e n t a l r e s u l t s f o r D^O-CudOO). 2

D 0-Cu

D 0-A1

(exp)

(theory)

2

Hindered

198 cm"

rotation

(16.0)

2

1

337 cm"

1

(15.9)


2

34.

IBACH A N D M U L L E R


403

In concluding, we point out an essential role of v i b r a t i o n a l spectra in theoretical studies. Total energy calculations y i e l d quantities of much interest, l i k e equilibrium geometries and binding energies, which are not accessible i n a direct experimental way. Only the v i brational quantities can be meaningfully compared with experiment and provide a way to assess the adequacy of these calculations.

Literature Cited 1.


2. 3. 4. 5. 6. 7. 8. 9.

10. 11. 12.

13. 14. 15.

For a general review see: Ibach H.; M i l l s , D.L. "Electron Energy Loss Spectroscopy and Surface Vibrations", Academic Press: New York, 1982. Brundle, C.R.; Morawitz, M.; Eds. "Vibrations at Surfaces" Elsevier: Amsterdam, 1983. Szeftel, J.M.; Lehwald, S.; Ibach, H.; Rahman, T.S.; Black, J.E.; M i l l s , D.L. Phys. Rev. Lett. (1983) 51, 268. Steininger, H.; Ibach, H.; Lehwald, S. Surf. S c i . (1982) 117, 685. Kesmodel, L.L.; Gates, J.A. Surf. S c i . (1981) 111, L747. and i n (2) p. 307. Shinner, P.; Howard, M.W.; Oxton, L.A.; Kettle, S.F.A.; Powell, D.B.; Sheppard, N. J . Chem. Faraday Trans. 2 (1981) 77, 397. Erley, W.; Baro, A.M.; Ibach, H. Surf. Sci. (1982) 120, 273. Erley, W.; Ibach, H. i n (2) p. 263 and Erley W., private communication. Sexton, B.A. Surf. S c i . (1979) 88, 299. Demuth, J.E.; Ibach, H. Chem. Phys. Lett. (1979) 60, 395. Sexton, B.A. Surf. S c i . (1981) 102, 271. See, for instance, Port, D.; Baerends, E.J. Surf. S c i . (1981) 109, 167. See, for instance, Herman, K.; Bagus, P.S.; Brundle C.R.; Menz e l , D. Phys. Rev. Β (1981) 24, 7025. See, for instance, Wimmer, E.; Freeman, A.J.; Hiskes J.R.; Karo, A.M. Phys. Rev. Β (1983) 28, 3074 and Feibelman P.J.; Hamann, D.R. Phys. Rev. Lett. (1984) 52, 61. Müller, J.E.; Jones, R.O.; Harris, J. J. Chem. Phys. (1983) 79, 1874. Andersson, S.; Nyberg, C.; Tengstål, C.G. Chem. Phys. Lett. (1984) 104, 305. T h i e l , P.Α.; Hoffmann, F.M.; Weinberg, W.H. J. Chem. Phys. (1981) 75, 5556.

R E C E I V E D March 28,

1985


Catalyst Characterization Science - American Chemical Society

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