ACCESS OF EXCITED STATES TO THE CONTINUUM

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ACCESS OF EXCITED STATES TO THE

CONTINUUM

C. Jørgensen

To cite this version:

JOURNAL D E PHYSIQUE

Colloque C7, supplkment au nOIO, Tome 46, octobre 1985

page C7-409

ACCESS OF E X C I T E D STATES TO T H E CONTINUUM

Section de

Ch?:mie.

Universite' de GenBve.

30

Quai Ansermet.

CH 1211

Geneva

4 ,

SwitzerZand

RQsum6 - La d e s e x c i t a t i o n n o n - r a d i a t i v e d e s niveaux J de l a n t h a n i d e s t r i - v a l e n t ~ en m a t i e r e condensee e s t d i s c u t e e en r e l a t i o n avec un fond c o n t i n u

(au-dessus 2 eV) t r o u v 6 dans d e s mol6cules s i m p l e s e t dans l ' e a u l i q u i d e . A b s t r a c t - The n o n - r a d i a t i v e r e l a x a t i o n o f e x c i t e d J - l e v e l s of t r i v a l e n t

l a n t h a n i d e s i n condensed m a t t e r i s d i s c u s s e d , w i t h emphasis on a weak continuous background above 2 eV found i n simple molecules and i n l i q u i d water.

Even t h e g r o u n d s t a t e of a gaseous atom ( i f c o n f i n e d i n a l a r g e volume) i s immedi- a t e l y followed by a t r a n s l a t i o n a l continuum.This i s a l s o t r u e f o r a l l gaseous molecules,having a d d i t i o n a l Born-Oppenheimer f a c t o r s of r o t a t i o n and v i b r a t i o n . The e l e c t r o n i c t r a n s i t i o n s between d i s c r e t e l e v e l s E2 and E can only b e s t u d i e d ,

1 .

because t h e r a t e of t r a n s f o r m a t i o n of E t o continuum s t a t e s 1s s u f f i c i e n t l y small. I n condensed m a t t e r ( e s p e c i a l l y above 280 K) luminescence i s t h e e x c e p t i o n r a t h e r t h a n t h e rule.Schuurmans and van D i j k [ l ] analyzed t h e competing mechanisms of non- r a d i a t i v e decay with s p e c i a l emphasis on t r i v a l e n t 1anthanides.The Born-Oppenheimer f a c t o r i z a t i o n i s such a good approximation because e l e c t r o n s have a rest-mass 0.00055 amu,small compared t o c o n v e n t i o n a l n u c l e i [ 2 ] around A amu.Chemistry, spectroscopy and n e a r l y a l l d a i l y - l i f e experience i s governed by t h i s f a c t of a d e f i n i t e s m a l l ( b u t p o s i t i v e ) rest-mass of i n d i s c e r n i b l e e l e c t r o n s .

However,condensed m a t t e r compensates a t j u s t one p o i n t t h e p r a c t i c a l d i f f i c u l t y of o b t a i n i n g 1uminescence.The l i n e s p e c t r a of monatomic e n t i t i e s ( w i t h one n u c l e u s ) obey extremely severe s e l e c t i o n r u l e s f o r e l e c t r i c d i p o l a r t r a n s i t i o n s , a n d many m e t a s t a b l e s t a t e s E would l i v e f o r d a y s , i f it was n o t f o r t h e exceedingly weak e f f e c t s [ 3 ] of imper&ect c o n s e r v a t i o n of p a r i t y (having important consequences f o r

- r a d i o a c t i v i t y ) .Condensed m a t t e r i s f a r more p e r m i s s i v e , t h e a b s o r p t i o n bands of c o l r e d t r a n i t i o n group m a t e r i a l s t y p i c a l l y having o s c i l l a t o r s t r e n g t h s P between lo-' and lo-' being due e.g. t o t r a n s i t i o n s among non-bonding and anti-bonding d - l i k e o r b i t a l s [ 4 , 5 ] , i n t h e u r a n y l i o n t o e l e c t r o n t r a n s f e r bandsL61 from t h e h i g h e s t f i l l e d molecular o r b i t a l s t o t h e empty 5f s h e l l non-bonding o r b i t a l s r 7 1 , o r between t h e J - l e v e l s [ 8 ] of a p a r t l y f i l l e d 4f s h e l l . T h e concomitant r a d i a t i v e l i f e - t i m e s u s u a l l y f a l l i n t h e m i l l i s e c o n d r a n g e . I f t h e r a t e of n o n - r a d i a t i v e de- e x c i t a t i o n i s x times l a r g e r , t h e quantum y i e l d of luminescence i s l / ( l + x ) and i s

d i f f i c u l t t o d e t e c t i f x i s above 1000.However,time-resolved emission s p e c t r a may h e l p a l o t , i n p a r t by showing growth of t h e c o n c e n t r a t i o n of E2 by f e e d i n g it

from h i g h e r s t a t e s E3,

...

and i n p a r t because t h e luminescence of E2 i s n e a r l y a s i n t e n s e ( f o r a very s h o r t t i m e ) a s it would be from a long-lived l e v e l .

It i s very r a r e t h a t an a b s o r p t i o n band ( n o t superposed on o t h e r , s t r o n g e r t r a n s i - t i o n s ) cannot b e d e t e c t e d a t i t s p r e d i c t e d p o s i t i o n , t h o u g h such l a c k of p e r c e p t i b l e i n t e n s i t y happens when 3 changes by 7,8,9,

...

u n i t s i n 1anthanides.Thi.s behavior can be describedL8-111 by t h e Judd-Ofelt theory,where P (of a b s o r p t i o n o r emission) i s p r o p o r t i o n a l t o Q 2 u 2 + R 4 u 4 +Q6u6 i n v o l v i n g t h r e e ( h i g h l y overdetermined) parameters f o r a given m a t e r i a l (varying a l s o w i t h t h e l a n t h a n i d e ) and t h r e e

t

m a t r i x elements U d e r i v e d from t h e 3 - l e v e l e n e r g i e s and 4fq wave-functions i n i n t e r m e d i a t e coupf i n g

.

I n genuine monatomic e n t i t i e s ,U2 would d e s c r i b e v e r y weak

JOURNAL

DE

PHYSIQUE

e l e c t r i c quadrupolar t r a n s i t i o n s , a n d U 4 and U6 t h e sub-microscopically s m a l l proba- b i l i t i e s . f o r 16- and 64-polar t r a n s i t i o n s - T h e huge a r e a s p e c i f i c e f f e c t of

t systems c o n t a i n i n g s e v e r a l n u c l e i .

An e x c i t e d J - l e v e l E may t r a n s f e r energy t o t h e surroundings i n many d i f f e r e n t 2

ways.Adjacenlld- o r f-group s y s t e s may have l e v e l s

_Y

<

E a s seen by energy t r a n s f e r i n v o l v i n g 4f e r b i u m ( I I 1 ) and 3d manganese(I1) [12,13l~cross-relaxation may occur between two ( i d e n t i c a l o r d i f f e r i n g ) l a n t h a n i d e s , ( E -E ) b e i n g s l i g h t l y above ( o r

2 1

i d e n t i c a l t o ) (E' -E' ) of t h e o t h e r system winding up i n t h e s t a t e E' ( t h i s i s a 0

major mechanism $ o r quenching of luminescence a t h i g h e r c o n c e n t r a t i o n ? b u t t h e most f r e q u e n t n o n - r a d i a t i v e d e - e x c i t a t i o n l l , 8 , 1 4 1 i n v o l v e s t h e t r a n s f o r m a t i o n of t h e energy ( E -E ) (E may a l s o be t h e groundstat-e) t o a number of phonons %W which a r e

2 1 1

u s u a l l y t a k e n t o be t h e h i g h e s t v i b r a t i o n a l normal mode of a polyatomic molecule o r complex i o n , o r t h h i g h e s t frequency i n t h e c r y s t a l . E m p i r i c a l l y , i t was found t h a t t h e r a t e

w

( i n s-') of multi-phonon d e - e x c i t a t i o

_-?

i s Bexp (- K (

d ~ )

) where C((having t h e dimension of a r e c i p r o c a l energy) i s ( a f i ~ ) , t h e small c o n s t a n t a = 0.4 f o r H20 and D 0 aqua i o n s , a n d varying i n c r y s t a l s from 0.25 i n LaC13 t o 0 . 5 i n Y203 ;

2

and

d

E i s t h e energy d i f f e r e n c e from t h e e x c i t e d l e v e l considered t o t h e c l o s e s t lower-lying l e v e l . However ,good r e a s o n s e x i s t [ 1

I

f o r s u b t r a c t i n g t w i c e %w :

W = B*exp(- O<( d ~ - 2 h b l ) ) w i t h B* given by

(1) l o g B* = loglOB - 0 . 8 6 ~ ? 1 0 = loglOB

-

(0.86/a)

10

Most m a t e r i a l s have loglOB* between 7 and 8 , b u t it i s 6.2 f o r t h e Y3Al5OI2 g a r n e t

and o n l y 5.8 f o r aqua ions.B* and Wdo n o t depend on t h e l a n t h a n i d e chosen.Eight J - l e v e l s of holmium(II1) i n f t u o r i d e g l a s s e s [ l l , l 4 1 show d e t e c t a b l e f l u o r e s c e n c e , t h o s e with

A

E above 1900 cm-

.

One might imagine t h a t we now can e x p l a i n away any i n s t a n c e of weak o r i m p e r c e p t i b l e

luminescence.However,the s i t u a t i o n may be even more comp1icated.Vibrations of a molecule w i t h N n u c l e i ( a t l e a s t 3) t a k e p l a c e on (3N-5)-dimensional p o t e n t i a l s u r f a c e s i n t h e Born-Oppenheimer approximation.Though t o t a l l y symmetric s t r e t c h i n g a t t r a c t s most a t t e n t i o n when d e s c r i b i n g t h e quenching by e l e c t r o n t r a n s f e r s t a t e s [ l 5 ] and i n )1u of e q . ( l ) , t h e o t h e r normal modes may be important too.Photochemical r e a c t i o n s a r e a n o t h e r n o n - r a d i a t i v e p r o c e s s (though much more f r e q u e n t i n o r g a n i c molecules t h a n i n i n o r g a n i c compounds) on t h e (3N-5)-dimensional hypersurface.The main purpose of t h i s n o t e i s t o draw a t t e n t i o n t o o t h e r k i n d s of n o n - r a d i a t i v e competition with luminescence.

I n t e x t b o o k s , t h e s i m i l a r i t y o f ( r e l a t i v e o r a b s o l u t e ) minima on t h e p o t e n t i a l s u r f a c e s w i t h harmonic o s c i l l a t o r p a r a b o l o i d s i s given a s r e a s o n f o r t h e much weaker i n t e n s i t y of o v e r t o n e s (corresponding t o a m u l t i p l e of a s t r e t c h i n g frequency o r t o a combination of s e v e r a l normal modes) compared t o t h e fundamental a b s o r p t i o n l i n e . N e v e r t h e l e s s , t h e o v e r t o n e s can b e measured and show an i n t e r e s t i n g s t r u c t u r e i n H 0 vapor[l6-181 and o t h e r gaseous molecules[l8,19].One of t h e enigma

_-1'

IC e f f e c t s i s

tht

simple molecules such a s CHq may show l i n e widths below 0.01

2~

whereas l a r g e r , g a s e o u s molecules t e n d t o show l i n e widths of t h e o r d e r 100 cm [18l.The width i s a non-monotonic f u n c t i o n of t h e o v e r t o n e number n i n C H [20].Another

6 6

c u r i o u s e f f e c t i n t h e benzene molecule i s t h e "Channel t h r e e phenomenon" t h a t t h e luminescence-guantum y i e l d d e c r e a s e s s h a r p l y when t h e e x c i t i n g photons have more t h a n 3000 cm h i g h e r energy t h a n t h e o r i g i n o f t h e f i r s t e x c i t e d s i n g l e t stateL211.

I t i s , o f c o u r s e , f r e q u e n t t o observe a sudden smearing o u t of v i b r a t i o n a l s t a t e s of a gaseous molecule above a c e r t a i n energy allowing non-Franck-Condon d i s s o c i a t i o n i n two fragments.This s p e c t r o s c o p i c e f f e c t of " p r e - d i s s o c i a t i o n " i s r a t h e r analogous t o a u t o - i o n i z i n g q u a s i - s t a t i o n a r y s t a t e s s i t u a t e d above t h e f i r s t i o n i z a t i o n energy of a monatomic species,which a r e more o r l e s s broadened according t o t h e Heisenberg u n c e r t a i n t y r e l a t i o n f o r r a p i d o r l e s s r a p i d ionization.Though v i b r a t i o n a l Franck- Condon broadening i s one source of width of i n n e r - s h e l l p h o t o - e l e c t r o n s i g n a l s (e.9.

m a n i f e s t a t i o n s of a underground movement suddenly opening t r a p s under ( o t h e r w i s e q u i t e c o n v e n t i o n a l ) e x c i t e d s t a t e s .

I n condensed m a t t e r , b o t h d i s s o c i a t i o n and pronounced d i l a t a t i o n of i n t e r n u c l e a r d i s t a n c e s (and o f e l e c t r o n i c clouds i n Rydberg s t a t e s ) a r e impeded by t h e crowded neighbor atoms.However,quasi-continuum behavior s t a r t s a t lower e n e r g i e s because of impaired Born-Oppenheimer f a c t o r i z a t i o n . W i t h r a r e e x c e p t i o n s of almost s p h e r i c a l molecules ( o r polyatomic i o n s ) a t n o t t o o low t e m p e r a t u r e , r o t a t i o n i s n o t f e a s i b l e i n condensed matter,and i s r e p l a c e d by l i b r a t i o n s ( f r u s t r a t e d r o t a t i o n s o v e r a small a n g l e ) combined with o t h e r n u c l e a r displacements having small f o c e c o n s t a n t s - T h e

_-5

corresponding e x c i t a t i o n s t y p i c a l l y occur between 10 and 100 cm .Almost by d e f i n i - t i o n , s u c h e x c i t a t i o n s do n o t form an e q u i d i s t a n t s e r i e s of energy l e v e l s ( l i k e a harmonic o s c i l l a t o r ) b u t a r e l i k e l y t o e n t e z many overtone combinations,and t o c o n t r i b u t e t o a moderate line-width i n a b s o r p t i o n spectra.Because of t h e almost p a r a l l e l p o t e n t i a l s u r f a c e s of d i f f e r i n g 4fq s t a t e s , c o - e x c i t a t i o n of v i b r a t i o n s i s

unconspicuous i n l a n t h a n i d e compounds,though it ha; been observed i n complexes of b i d e n t a t e n i t r a e [251 and i n t h e r a t h e r e x c e p t i o n a l hexahalide complexes 1261 a l s o

₅

known 1271 of 5f uranium(1V) .Recently ,Car0 1281 p o i n t e d o u t t h a t t h e l a r g e v a r i a b i - l i t y of width of sub-level a b s o r p t i o n bands (measured a t l i q u i d helium) s u g g e s t s resonances w i t h t h e m u l t i t u d e of v i b r a t i o n a l s t a t e s , e s p e c i a l l y i n complexes of o r g a n i c l i g a n d s (bound by oxygen and/or n i t r o g e n atoms t o t h e l a n t h a n i d e ) . Bohren[29] performed very c a r e f u l measurements of a b s o r p t i o n of l i g h t between 400 and 580 nm i n pure water,and demonstrat d t h a t a shallow minimum of o p t i c a l d e n s i t y

-4

o = l . 17.10 /cm a t 430 nm ( D i s I .33~lO-'/cm a t 400 nm) i s n o t caused by l i g h t being s c a t t e r e d n o r y absorbing i m p u r i t i e s (whereas t h e u s u a l mihum r e p o r t e d c l o s e t o

_-9

.

550 n m and 10 /cm 1s determined by such e f f e c t s ) . T h e f i r s t f o u r overtone b a n d s ( n = 2 t o 5) i n l i q u i d water were e s t a b l i s h e d b e f o r e 1934 (cf.Landolt-Bornstein Tables I / Z , s e c t i o n 141476 and 1 / 3 , s e c t i o n 142033) and though t h e v a r i o u s D(=55

E)

show a few enigmatic d i s c r e p a n c i e s , t h e y seem roughly p r o p o r t h a 1 t o f o r n s t a r t i n g

-4 with 3.This trend1291 c o n t i n u e s f o r t h e s h o u l d e r s a t 520 and 460 nm having DNlO and 10- above t h e s t r o n g e r background:

The take-over by t h e almost i n v a r i a n t continuum up t o 25000 cm-I reminds about t h e s t o c h a s t i c i r r e u l a r motions r e p l a c i n g t h e l o c a l modes of v i b a t i o n i n gaseous H20 above 30000 c ~ - ' [I61 and which may a l r e a d y s t a r t a t 20000 cm-5 i n t h e l i q u i d [ I71

.

The ove t o n e s ( n

_-'E

= 2 t o 5 ) i n t h e gaseous molecule[l8,301 have wave-numbers 400 t o 500 cm h i g h e r t h a n i n e q . ( 2 ) , c o n n e c t e d with t h e i n t r i c a t e hydrogen bonding i n t h e 1iquid.The n=5 provide t h e l i n e s surrounding t h e two yellow Fraunhofer l i n e s of sodlum i n t h e s o l a r spectrum.Also benzene1201 has a continuous background ab- s o r p t i o n e n e a t h t h e h i g h overtones-The f e a s i b i l i t y of o p t i c a l f i b e r s w i t h D f a r

_-%

.

below 10 /cm 1n t h e n e a r i n f r a - r e d shows t h e absence of such an ambient continuum, b u t it may p l a y a r 6 l e i n t h e f l u o r e s c e n t g l a s s e s with a r i c h spectrum of l i b r a t i o n . This phenomenon h a s an i n t r i g u i n g connection with t h e o b s e r v a t i o n by Marcantonatos

131-331 t h a t g a d o l i n i u m ( I I 1 ) perch o r a t e and c h l o r i d y s o l u t i o n s have a l i f e - t i m e i n H 0 of t h e f i r s t e x c i t e d l e v e l 'P a t 32100 cm of 6 m s , d i s t i n c t l y below t h e

2 7/2

r a t h e r p r e c i s e l y known r a d i a t i v e l i f e - t i m e 10 ms,whereas t h e observed l i f e - t i m e i n D 0 i s above 9 ms.This cannot be e x p l a i n d by t h e exponenr&a:-$aw of multi-phonon

2

r e l a x a t i o n eq.

(!I

g i v i n g W below 0.01 s-' i n H20 and

<<

10 m D O.However,the 2

W c l o s e t o 60 s may be connected w i t h t h e continuum above n=6 i n e q . L 2 ) . I t may be added t h a t n i t r a t e (having a weak

_-%

and with€-7 a t t h e p o s i t i o n of P

7/2) quenches t h e f l u o r e s c e n c e even a t 10 molar concentration,which must be explained by t h e m u l t i p l e c o l l i s i o n s i n s o l u t i o n d u r i n g a m i l i s e c o n d , s i n c e t h e complex

_-

+

formation c o n s t a n t of GdO

NO+^

i s w e l l below 10 M (though e x c i t e d s t a t e s of

2

C7-412

JOURNAL

DE

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We have to accept that no excited state of a system containing several nuclei is ensured against adjacent quasi-continuum states of the same symmetry type,even at lower energy-This brings about the atrocious possibility that luminescence before the electronic origin is not due to defect sites,to excitons or whatever apology the socially acceptable spectroscopist is accustomed to profess.The imperfection may rather be in the Born-Oppenheimer factorization,perceptibly leaking in the overtone swamp with indeterminate transition probabilities loosely predicted to be zero divided by zero.

Acknowledgements.

I am grateful to Professors Renata Reisfeld and Minas D.Marcantonatos for valuable discussions.The studies were supported by grant 2.152.083 from the Swiss National Science Foundation.

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7.Jdrgensen C.K. and Reisfeld R.,Structure and Bonding =(1982)121.

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9.Peacock R.D.,Structure and Bonding z(1975183.

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11.Reisfeld R.,Eyal M.,Greenberg E. and Jdrgensen C.K.,Chem.Phys.Lett.,in press. 12.Reisfeld R.,Greenberg E.,Jacoboni C.,DePape,R. and Jdrgensen C.K.,

J. Solid State Chem.Z(l984) 236.

13.Reisfeld R.,Kisilev,A. and Jdrgensen C.K.,Chem.Phys.Lett.E(1984)19.

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24.Jbrgensen C.K.,Structure and Bonding 3(1975)1 and g(1976)141. 25.Hellwege A.M. and Hellwege K.H.,Z.Physik =(1952)174.

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