13
H y p e r s e n s i t i v e T r a n s i t i o n s in
ƒ-Electron
Systems
B. R. JUDD
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Physics Department, The Johns Hopkins University, Baltimore, M D 21218
The sensitivity of the o p t i c a l a b s o r p t i o n s p e c t r a of rare-earth i o n s to t h e i r environment w a s d i s c u s s e d as long ago as 1930 by S e l w o o d (1). It w a s not u n t i l the s p e c t r a l l i n e s c o u l d be i n t e r preted as t r a n s i t i o n s between w e l l - d e f i n e d s t a t e s of the r a r e - e a r t h i o n s that the k e y feature of the phenomenon c o u l d be e s t a b l i s h e d : the i n t e n s i t i e s of a few l i n e s are e x c e p t i o n a l l y sensitive, and for t h e s e so-called h y p e r s e n s i t i v e l i n e s the s e l e c t i o n r u l e s on J, the t o t a l a n g u l a r momentum of the f e l e c t r o n s of the r a r e - e a r t h ion, are the same as those for quadrupole r a d i a t i o n . That is, the change i n J c a n be at most 2 . The effect w a s f i r s t n o t i c e d w h e n the a b s o r p t i o n spectra of aqueous s o l u t i o n s of r a r e - e a r t h n i t r a t e s and c h l o r i d e s , as found by H o o g s c h a g e n (2), were c o m p a r e d . For e x a m p l e , the onl y t r a n s i t i o n of Er3 + e x h i b i t i n g an i n t e n s i t y d i f f e r ence i s I -->2H . A g a i n , the l a r g e s t i n t e n s i t y change 4
15/2
11/2
4
for s o l u t i o n s o f N d3 + o c c u r s for I - G (3). A couple of y e a r s l a t e r , s e v e r a l more transitions for r a r e - e a r t h i o n s were noted (4). H y p e r s e n s i t i v i t y is not c o n f i n e d to r a r e - e a r t h i o n s . P a p p a l a r d o , Carnall, and F i e l d s (5) have i d e n t i f i e d two h y p e r s e n s i t i v e t r a n s i t i o n s i n Aml„ that c o r r e s p o n d to a change of two u n i t s i n J . It i s e v i d e n t that m e r e l e v a n t features of the 4f s h e l l carry o v e r to the 5f s h e l l , and so it i s c o n v e n i e n t to c o n s i d e r both the r a r e earth and the a c t i n i d e i o n s at the same t i m e . 9/2
1.
->4
5/2
Ions at S i t e s of N o n - V a n i s h i n g E l e c t r i c F i e l d
The natural r e a c t i o n to the e x p e r i m e n t a l r e s u l t s i s to c o n c l u d e that the h y p e r s e n s i t i v e t r a n s i t i o n s are e l e c t r i c q u a d r u p o l e . S u c h t r a n s i t i o n s i n v o l v e no change i n p a r i t y and are thus a l l o w e d w i t h i n c o n f i g u r a t i o n s of the type f . The s e n s i t i v i t y to environment c o u l d c o n c e i v a b l y depend on the v a r i a b i l i t y (due to c o v a l e n c y ) of 0-8412-0568-X/80/47-131-267$05.00/0 © and 1980 American Society In Lanthanide Actinide ChemistryChemical and Spectroscopy; Edelstein, N.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
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the average v a l u e of r for an f e l e c t r o n , w h i c h p l a y s a k e y role i n the q u a d r u p o l a r i n t e n s i t i e s . U n f o r t u n a t e l y , an a c t u a l c a l c u l a t i o n s h o w s that t h i s m e c h a n i s m f a l l s short of e x p e r i m e n t by r o u g h l y f i v e orders of m a g n i t u d e (4). It i s n o w w e l l e s t a b l i s h e d t h a t a l m o s t a l l t r a n s i t i o n s w i t h i n the f s h e l l are e l e c t r i c d i p o l e i n n a t u r e . The b r e a k d o w n of the Laporte parity rule i s brought about by n o n - c e n t r o - s y m m e t r i c terms i n the c r y s t a l - f i e l d H a m i l t o n i a n V , w h i c h h a v e the e f f e c t of m i x i n g d a n d g s t a t e s into the f s h e l l . T r a n s i t i o n s w h i c h are n o m i n a l l y f to f t a k e p l a c e b e c a u s e of the p e r m i t t e d t r a n s i t i o n s f - * d a n d f - » g . A n e a r l y a t t e m p t (6) t o e x p l a i n t h e h y p e r s e n s i t i v i t y u s e d the f a c t that for r a r e - e a r t h or a c t i n i d e i o n s at s i t e symmetries of the types
c , c s
1 #
c , c 2
2 v
, c , c , c , c , c , c 3
3 v
4
4 v
6
6 v
t h e r e are t e r m s i n V that c o r r e s p o n d to t h e s p h e r i c a l harmc^nics Y., . W e c a n n o w u s e Y., to connect an i n i t i a l state of f to a lm lm v i r t u a l state of f ^ * d , f ^ * d * , or f^ * g ; and the e l e c t r i c - d i p o l e o p e r a t o r , i t s e l f a h a r m o n i c of rank 1 , c o m p l e t e s the l i n k a g e to the f i n a l state of f . S i n c e the c r y s t a l s p l i t t i n g s of the terms of the e x c i t e d c o n f i g u r a t i o n s are s m a l l c o m p a r e d to the e n e r g i e s of e x c i t a t i o n , we c a n contract the two h a r m o n i c s , w i t h the r e s u l t that w e get an operator w h o s e transformation properties (when a s c a l a r i s s u b t r a c t e d out) a r e i d e n t i c a l to t h o s e of Y . S u c h a n o p e r a t o r w o u l d y i e l d s e l e c t i o n r u l e s o n J i d e n t i c a l to t h o s e for q u a d r u p o l e r a d i a t i o n . A n y structural change that produces any of the site symmetries l i s t e d above w o u l d provide a source for an enhanced transitions probability. +
?
P l a u s i b l e though this mechanism i s , it came under c r i t i c i s m (7) b e c a u s e , i n t e r a l i a , i t c o u l d n o t a c c o u n t f o r t h e i n t e n s e h y p e r s e n s i t i v e t r a n s i t i o n s o f t h e g a s e o u s r a r e - e a r t h t r i h a l i d e s (8). H o w e v e r , there i s recent e v i d e n c e that the h a l i d e s are not p l a n a r (9, 10), a s h a d b e e n p r e v i o u s l y s u p p o s e d . If t h i s i s i n f a c t t h e c a s e , the i m p o r t a n c e of the m e c h a n i s m b a s e d o n Y^ terms i n V remains undecided. It s h o u l d b e p o i n t e d o u t t h a t t h e d e r i v a t i v e s o f t h e Y , t e r m s do not a l l v a n i s h at the o r i g i n . There a p p e a r s to be an e l e c t r i c f i e l d a c t i n g o n the n u c l e u s of the r a r e - e a r t h or a c t i n i d e i o n - a n i m p o s s i b i l i t y if the i o n i s i n e q u i l i b r i u m . The r e s o l u t i o n of t h i s p a r a d o x l i e s i n the a d m i x t u r e s of d a n d g s t a t e s into the f s h e l l . The r e d i s t r i b u t i o n of e l e c t r o n i c charge of the r a r e - e a r t h or a c t i n i d e i o n produces a s e c o n d e l e c t r i c f i e l d at the n u c l e u s that e x a c t l y c a n c e l s the f i r s t .
In Lanthanide and Actinide Chemistry and Spectroscopy; Edelstein, N.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
13.
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2 .
JUDD
Hypersensitive
Inhomogeneous
Transitions
in {-Electron
Systems
269
Dielectric and Dynamic Coupling
An e a r l y survey of the p o s s i b l e sources for the h y p e r s e n s i t i v i t y c o n c l u d e d that the most l i k e l y c a n d i d a t e w a s a m e c h a n i s m based o n the inhomogeneities of the d i e l e c t r i c surrounding the r a r e - e a r t h o r a c t i n i d e i o n (4). It r u n s a s f o l l o w s . T h e r a d i a t i o n f i e l d induces s i n u s o i d a l l y fluctuating dipole moments i n the ligands surrounding the i o n . These induced dipoles necessarily radiate, and the emitted f i e l d s impinge o n the rare-earth or a c t i n ide i o n . Because of the proximity of source and receiver, the p l a n e - w a v e c o n d i t i o n no longer a p p l i e s ; the w a v e fronts are s u f f i c i e n t l y distorted to produce s u b s t a n t i a l quadrupole c o m p o n e n t s . It s h o u l d b e s t r e s s e d , h o w e v e r , t h a t t h e r a d i a t i o n f i e l d s e e n b y the c e n t r a l i o n i s a s u p e r p o s i t i o n o f the f i e l d s p r o d u c e d by a l l the l i g a n d s , a n d w i l l , i n g e n e r a l , be quite different from the q u a d r u pole f i e l d produced by a s i n g l e , d i s t a n t , s o u r c e . Although the quadrupole s e l e c t i o n rules hold for J , we cannot make comparable statements for the corresponding magnetic quantum numbers M until an a n a l y s i s of the crystal structure i s carried o u t . The o r i g i n a l estimate of the importance of the above m e c h a n ism f a l l s short of experiment by a factor of 30. A n apparently more s u c c e s s f u l m e c h a n i s m h a s been i n t r o d u c e d b y M a s o n , P e a c o c k , a n d S t e w a r t (1_1, 7) . I n t h e i r m o d e l , t h e f e l e c t r o n s o f the rare-earth or a c t i n i d e i o n produce a f i e l d that p o l a r i z e s the ligands. If t h e c o m p l e x o f c e n t r a l i o n p l u s l i g a n d s d o e s n o t p o s s e s s a center of i n v e r s i o n , the complex e x h i b i t s an electric d i p o l e moment that can interact d i r e c t l y with the e l e c t r i c vector of the r a d i a t i o n f i e l d . This m e c h a n i s m has been referred to as d y n a m i c c o u p l i n g ( 7 , J J J . A l t h o u g h i t seems to be different from the m e c h a n i s m b a s e d o n a n inhomogeneous d i e l e c t r i c , the t w o a r e , in f a c t , i d e n t i c a l (12). They are s i m p l y different v e r b a l i z a t i o n s of the same m a t h e m a t i c s . The good agreement that M a s o n , Peacock, and Stewart find with experiment i s simply a reflection of better p o l a r i z a t i o n data for the l i g a n d s a n d more accurate structural information, both of w h i c h substantially reduce the d i s c r e p a n t f a c t o r o f 30 m e n t i o n e d a b o v e . H o w e v e r , neither the inhomogeneous d i e l e c t r i c m e c h a n i s m nor i t s e q u i v a l e n t , the d y n a m i c - c o u p l i n g m e c h a n i s m , makes a l l o w ance for the p o l a r i z a b i l i t y of the outer s h e l l s of the rare-earth or a c t i n i d e i o n . For an external quadrupole f i e l d to penetrate to the f e l e c t r o n s , w e m u s t i n c l u d e a s c r e e n i n g f a c t o r ( 1 - o^); t h e s a m e f a c t o r m u s t be i n t r o d u c e d i f w e t a k e the p o i n t o f v i e w o f d y n a m i c coupling and ask what reduction the quadrupole field of the f electrons experiences as it penetrates out to the l i g a n d s . For a
In Lanthanide and Actinide Chemistry and Spectroscopy; Edelstein, N.; ACS Symposium Series; American Chemical Society: Washington, DC, 1980.
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f r e e r a r e - e a r t h i o n , 0" c a n b e a s l a r g e a s 0 . 7 Q _ 3 , L 4 ) . W h e n the s c r e e n i n g f a c t o r i s s q u a r e d to o b t a i n the r e d u c t i o n i n i n t e n s i t y , i t i s f o u n d that the h y p e r s e n s i t i v e t r a n s i t i o n i n t e n s i t i e s are r e d u c e d by a n order of m a g n i t u d e . A l t h o u g h t h i s h a s the e f f e c t of p u t t i n g i n d o u b t a l l t h e g o o d fits between theory and experiment found by Peacock and h i s c o l l a b o r a t o r s , it removes the somewhat embarrassing r e s u l t that h y p e r s e n s i t i v e l i n e s i n the r a r e - e a r t h t r i c h l o r i d e s , w h i c h the theory w o u l d o t h e r w i s e p r e d i c t to be i n t e n s e , a r e e x p e r i m e n t a l l y unexceptional. It c o u l d w e l l t u r n o u t t h a t f o r i o n s i n c o n t a c t w i t h l i g a n d s ,
