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Polarized x-Ray Absorption Spectroscopy J A M E S Ε. HAHN and K E I T H O. H O D G S O N Stanford University, Department of Chemistry, Stanford, CA 94305
The applications of polarized x-ray absorption spectroscopy (PXAS) for structure determination in inorganic and bioinorganic systems are discussed. PXAS studies of oriented samples add angular detail to the information obtained from x-ray absorption edges and from EXAFS. In some cases, PXAS can be used to determine molecular orientation. In other cases, PXAS can be used to infer the details of electronic structure or of chemical bonding. Some of the potential future applications of PXAS are discussed. During the l a s t decade there has been a dramatic i n c r e a s e i n the use of x-ray absorption spectroscopy (XAS) f o r determining and understanding chemical s t r u c t u r e s . T h i s i n c r e a s e i s i n l a r g e part a t t r i b u t a b l e to the a v a i l a b i l i t y of synchrotron r a d i a t i o n from high-energy e l e c t r o n storage r i n g s (1^.2^3)· The high i n t e n s i t y of synchrotron r a d i a t i o n l i g h t sources allows r a p i d c o l l e c t i o n of high q u a l i t y XAS data. XAS d a t a c o m p r i s e s b o t h a b s o r p t i o n edge s t r u c t u r e and extended x-ray absorption fine s t r u c t u r e (EXAFS). The a p p l i c a t i o n of XAS to systems of chemical i n t e r e s t has been w e l l reviewed (4,_5)· B r i e f l y , the s t r u c t u r e superimposed on the x-ray absorption edge r e s u l t s from the e x c i t a t i o n of c o r e - e l e c t r o n s i n t o h i g h - l y i n g vacant o r b i t a l s (6,_7) and i n t o continuum s t a t e s (£,9). The shape and i n t e n s i t y of the edge s t r u c t u r e can f r e q u e n t l y be used to determine i n f o r m a t i o n about the symmetry of the absorbing site. For example, the ls+3d transition i n first-row transition metals i s dipole forbidden in a centrosymmetric environment. In a non-centrosymmetric e n v i r o n m e n t t h e a d m i x t u r e o f 3d and 4p o r b i t a l s c a n g i v e i n t e n s i t y to t h i s t r a n s i t i o n . T h i s has been observed, f o r example, i n a study of the i r o n - s u l f u r p r o t e i n rubredoxin, where the i r o n i s t e t r a h e d r a l l y coordinated t o four s u l f u r atoms ( 6 ) . 0097-6156/83/0211-0431$06.00/0 © 1983 American Chemical Society
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INORGANIC CHEMISTRY: TOWARD THE 21 ST CENTURY
The EXAFS, which occurs at higher energies above the edge, i s due t o the i n t e r f e r e n c e between the o u t g o i n g and the b a c k s c a t t e r e d p h o t o e l e c t r o n waves (10-14 ). EXAFS p r o v i d e s information about the l o c a l s t r u c t u r e of the x-ray absorbing atom. T y p i c a l l y , nearest neighbor bond lengths and c o o r d i n a t i o n numbers can be determined to ±0.02 Â (1%) and one atom i n four (25%) ( 4 ) . The accuracy of these determinations i s somewhat worse f o r o u t e r - s h e l l atoms, f o r disordered systems, or f o r systems with asymmetric d i s t r i b u t i o n s of atoms w i t h i n a s h e l l U5,JL6). Angular information i s notably absent from the l i s t of s t r u c t u r a l parameters normally obtained from XAS. One approach to o b t a i n i n g angular d e t a i l i s to make use of m u l t i p l e s c a t t e r i n g e f f e c t s (17). Unfortunately, t h i s technique i s only u s e f u l f o r outer s h e l l s (non-nearest neighbor atoms) where there are atoms i n t e r v e n i n g between the a b s o r b e r and the s c a t t e r e r . This technique s u f f e r s from complications i f the s h e l l s of i n t e r e s t overlap i n distance with other s h e l l s of atoms. An a l t e r n a t e method f o r o b t a i n i n g angular information i s to make use of the plane p o l a r i z e d nature of synchrotron r a d i a t i o n . I t has long been known that XAS should e x h i b i t a p o l a r i z a t i o n dependence f o r a n i s o t r o p i c samples (18) ; however i t i s only r e c e n t l y that attempts have been made to e x p l o i t t h i s e f f e c t . E a r l y attempts to observe a n i s o t r o p i c XAS s u f f e r e d from the low i n t e n s i t y and i n c o m p l e t e p o l a r i z a t i o n o f c o n v e n t i o n a l x - r a y sources. This work has been reviewed by A z a r o f f (19). In t h i s chapter, we b r i e f l y d i s c u s s the t h e o r e t i c a l background of p o l a r i z e d x-ray absorption spectroscopy (PXAS). Many of the recent a p p l i c a t i o n s of synchrotron r a d i a t i o n to p o l a r i z e d absorption edge s t r u c t u r e and to EXAFS are discussed, with p a r t i c u l a r emphasis being given to the study of d i s c r e t e molecu l a r systems. We present here some i n d i c a t i o n of the p o t e n t i a l a p p l i c a t i o n s of PXAS to systems of chemical and biological interest. Theory The g e n e r a l e x p r e s s i o n crosssection σ i s σ = Σ Ki|
for a dipole-coupled
e-r l f > l
2
absorption
(D
where represent the i n i t i a l and f i n a l s t a t e wavefunc t i o n s , ê i s a u n i t vector p o i n t i n g i n the d i r e c t i o n of the p o l a r i z a t i o n , r=(x,y,z) i s a u n i t vector p o i n t i n g i n the d i r e c t i o n of the x, y or ζ axes, and the sum i s taken over a l l o r i e n t a t i o n s (20). The EXAFS, χ, i s p r o p o r t i o n a l to absorption c r o s s - s e c t i o n . Equation 1 can be s i m p l i f i e d to χ = Σ Ki|
r |f>|2
2
C O
s e
(2)
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HAHN AND
HODGSON
Polarized
x-Ray Absorption
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Spectroscopy
where θ i s the angle between ê and r . The matrix element can be evaluated to give the f a m i l i a r i s o t r o p i c EXAFS expression (c.f. references 10-14). In the s i n g l e - e l e c t r o n approximation, t h i s matrix element i s o n l y s i g n i f i c a n t i f r p o i n t s i n the d i r e c t i o n of the unoccupied s t a t e of i n t e r e s t (edge s t r u c t u r e ) or the b a c k s c a t t e r e r of i n t e r e s t (EXAFS). Thus, we can i d e n t i f y θ i n Equation 2 w i t h the angle between e and an unoccupied o r b i t a l (edge s t r u c t u r e ) or an absorber-backscatterer vector (EXAFS). T h i s i s i l l u s t r a t e d f o r EXAFS i n Figure 1. For a r i g o r o u s development of the theory of PXAS, the reader i s r e f e r r e d t o , f o r example, reference 20. For c r y s t a l l i n e samples of cubic or higher symmetry, f o r p o l y c r y s t a l l i n e samples, or f o r amorphous m a t e r i a l s (e.g. for most XAS experiments), symmetry r e q u i r e s that the observed XAS be s p h e r i c a l l y symmetric (20,21). In these cases the angular dependence i n Equation 2 must be averaged over a l l o r i e n t a t i o n s , g i v i n g a f a c t o r of 1/3. 9
Edges Although there are notable exceptions, most a p p l i c a t i o n s of edge s t r u c t u r e f o r determination of molecular geometry have concentrated on an e m p i r i c a l c o r r e l a t i o n of absorber s i t e sym metry and chemical environment with edge s t r u c t u r e . This i s a r e s u l t of the d i f f i c u l t y i n q u a n t i t a t i v e l y i n t e r p r e t i n g much of the edge s t r u c t u r e . When the i n c i d e n t photon has an energy just barely above the absorption threshold, the resulting photoelectron can undergo numerous m u l t i p l e s c a t t e r i n g events, g r e a t l y complicating the t h e o r e t i c a l a n a l y s i s (22). Thus, while t r a n s i t i o n s to bound s t a t e s are reasonably w e l l understood, a complete t h e o r e t i c a l t r e a t m e n t o f the edge s t r u c t u r e i s difficult. Oriented samples allow the p o s s i b i l i t y of g r e a t l y s i m p l i f y i n g the i n t e r p r e t a t i o n of the edge s t r u c t u r e . The information obtained from p o l a r i z e d edge s t u d i e s i s i n many ways analogous to the information obtained from p o l a r i z e d o p t i c a l spectroscopy. S i n c e edge s t r u c t u r e i n c l u d e s t r a n s i t i o n s i n t o h i g h - l y i n g molecular o r b i t a l s ( f o r d i s c r e t e molecular systems) or h i g h - l y i n g bands ( f o r extended s o l i d - s t a t e s t r u c t u r e s ) , the p o l a r i z a t i o n dependence o f t h e s e t r a n s i t i o n s can, i n p r i n c i p l e , p r o v i d e i n f o r m a t i o n about the symmetry p r o p e r t i e s of s p e c i f i c o r b i t a l s or bands. The observed symmetry i s a product of the symmetries of the i n i t i a l s t a t e , the f i n a l s t a t e , and the operator c o u p l i n g these s t a t e s . Κ and L ( I ) absorption edges thus have an important s i m p l i f i c a t i o n over o p t i c a l spectroscopy s i n c e the i n i t i a l s t a t e (Is or 2s) i s s p h e r i c a l l y symmetric and does not i n f l u e n c e the observed orientational dependence of the transition. U n f o r t u n a t e l y , the i d e n t i f i c a t i o n of x - r a y a b s o r p t i o n edge t r a n s i t i o n s i s not always unambiguous, e s p e c i a l l y f o r t r a n s i t i o n s i n t o s t a t e s that are near the continuum.
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INORGANIC C H E M I S T R Y : TOWARD T H E 21 ST C E N T U R Y
Figure 1. Polarized XAS. The orientations of ê and k and the angle θ (see Equa tion 2) are shown for a typical PXAS experiment. For this orientation, there can be no Cu-S contribution to the EXAFS (& — 90°). The Cu-N contribution to the EXAFS will be 3cos e-times that observed for an isotropic sample. 2
29.
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HODGSON
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x-Ray Absorption
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Spectroscopy
E l e c t r o n i c S t r u c t u r e Determination* Cox and Beaumont have studied the p o l a r i z e d x-ray a b s o r p t i o n edge of a s i n g l e c r y s t a l of ZnF^ (23), i n which the Zn has t e t r a g o n a l ( D ^ ) s i t e symmetry. The observed a n i s o t r o p i c K-absorption edges were explained i n terms of a ls+4p and a ls-K4p ,4p ) t r a n s i t i o n . Templeton and Templeton rfave observed a n i s o t r o p i c edges f o r the "oxo" species [V=0] and [ U 0 ] (24,25). In the vanadium case, a very strong pre-edge t r a n s i t i o n was observed only when the e l e c t r i c vector of the p o l a r i z a t i o n was o r i e n t e d p a r a l l e l to the V=0 bond. From t h i s ρ type symmetry and from the strength of t h e f e a t u r e ( i n d i c a t i n g an a l l o w e d t r a n s i t i o n ) , i t was suggested that t h i s peak i s due to a t r a n s i t i o n i n t o a molecular o r b i t a l c o n t a i n i n g vanadium 3d 2 d 4s o r b i t a l s and a sigma o r b i t a l (having ρ symmetry) from the vanadyl oxygen. In the u r a n y l case, the L ( I ) (2s i n i t i a l s t a t e ) and the L ( I I I ) (2p i n i t i a l s t a t e ) edges were both s t u d i e d (25). Because of t h e i r d i f f e r e n t i n i t i a l - s t a t e symmetries, these two edges give mutually e x c l u s i v e d.ipole s e l e c t i o n r u l e s . In agreement with t h i s , the authors observed not only o r i e n t a t i o n a l dependence f o r both edges, but a l s o a d i f f e r e n t o r i e n t a t i o n a l dependence f o r the d i f f e r e n t edges. y
2
2
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2
a n
Z
O r i e n t a t i o n Determination. While p o l a r i z e d edge s t u d i e s , together with a known sample o r i e n t a t i o n , can provide information about the e l e c t r o n i c s t r u c t u r e of the absorber, one can a l s o use p o l a r i z e d edges to probe ordered systems of unknown o r i e n t a t i o n . T h i s s o r t of approach was used i n a study of B ^ adsorbed on graphite (26,27). In t h i s case, the o r i e n t a t i o n a l dependence of an edge t r a n s i t i o n was used t o c a l c u l a t e t h e d e g r e e of o r i e n t a t i o n a l p u r i t y of the graphite s u r f a c e . Another example of the p o t e n t i a l u t i l i t y of p o l a r i z e d edge spectra f o r s t r u c t u r e determination i s found f o r [ M o 0 ^ 2 Î " (28)· T h i s molecule has C £ symmetry and the C2 axes of a l l of the molecules i n the u n i t c e l l are c o l l i n e a r . Thus, when the c r y s t a l i s o r i e n t e d with the p o l a r i z a t i o n p a r a l l e l to the S-S i n t e r a t o m i c v e c t o r , the p o l a r i z a t i o n i s perpendicular to the Mo-O bonds and n e a r l y p a r a l l e l to the Mo-S bonds. S i m i l a r l y , the c r y s t a l can be o r i e n t e d with the p o l a r i z a t i o n perpendicular to the Mo-S bonds and n e a r l y p a r a l l e l to the Mo-O bonds. For both o r i e n t a t i o n s , e x c e l l e n t agreement was obtained with SCF-X α c a l c u l a t i o n s of the edge s t r u c t u r e (8). Moreover, e x c e l l e n t agreement was a l s o observed between the p o l a r i z e d edge s p e c t r a of [MoO £ 1 ~ * , corresponding "pure" i s o t r o p i c s p e c t r a of [MoO^] ~ and [MoS^] " ( e*g., w i t h the p o l a r i z a t i o n p a r a l l e l to the 0-0 v e c t o r , an [MoO^] spectrum was observed) (8). In general, i f a molecule contains l i g a n d s which i n d i v i d u a l l y g i v e very d i f f e r e n t edge s t r u c t u r e s , i t may be pos s i b l e to determine the o r i e n t a t i o n of these l i g a n d s u s i n g p o l a r i z e d absorption edges. As shown here, the i s o t r o p i c spectrum of a "pure" compound, c o n t a i n i n g only one of the l i g a n d s , can be used to determine the ligand-dependent edge s t r u c t u r e s . 2
v
2
2
2
a n
