Lanthanide and Actinide Absorption Spectra in Solution - Advances in

7

Downloaded by STANFORD UNIV GREEN LIBR on September 24, 2012 | http://pubs.acs.org Publication Date: June 1, 1967 | doi: 10.1021/ba-1967-0071.ch007

Lanthanide and Actinide Absorption Spectra in Solution W. T. CARNALL and P. R. FIELDS Chemistry Division, Argonne National Laboratory, Argonne, Ill. We have calculated sets of theoretical energy levels for the trivalent actinides and lanthanides and correlated these levels with transitions observed in the solution absorption spectra of these elements. Using the eigenvectors resulting from this energy level calculation, we have computed the theoretical matrix elements required to account for the observed band intensities in the two series of elements. The extent to which the theoretical calculations can be correlated with experimental results has been discussed, and some applications for the intensity relationships are pointed out. >nphe s o l u t i o n a b s o r p t i o n spectra of the t r i v a l e n t l a n t h a n i d e s a n d a c t i nides are c o m p r i s e d of d i s t i n c t i v e s h a r p , r a t h e r w e a k a b s o r p t i o n b a n d s w h i c h h a v e b e e n o b s e r v e d p r i m a r i l y i n the v i s i b l e - n e a r u.v. r e g i o n of the spectrum.

M o s t of these b a n d s arise f r o m transitions w i t h i n the /^-elec-

t r o n configuration. H o w e v e r , the extent to w h i c h b o t h t h e i r energies a n d intensities c a n be c o r r e l a t e d w i t h t h e o r e t i c a l l y c a l c u l a t e d energies intensities has b e e n e x p l o r e d o n l y r e c e n t l y (2, 14).

and

I n this p a p e r w e w i l l

e m p h a s i z e the t h e o r e t i c a l treatment of e x p e r i m e n t a l results i n t w o r e l a t e d stages.

F i r s t , the energies of the transitions o b s e r v e d i n d i l u t e a c i d s o l u -

t i o n are r e l a t e d to c a l c u l a t e d energy levels.

T h e eigenvectors

derived

f r o m the energy l e v e l c a l c u l a t i o n s are t h e n u s e d as a basis to c a l c u l a t e b a n d intensities. M o s t p u b l i s h e d w o r k o n the energy levels i n the t r i v a l e n t l a n t h a n i d e s a n d actinides has b e e n c a r r i e d out i n c r y s t a l l i n e m e d i a , w h e r e the i d e n t i t y of a l e v e l i n terms of a g i v e n c o u p l i n g scheme c a n be e s t a b l i s h e d (8, 19).

experimentally

I n a t t e m p t i n g s i m i l a r correlations i n aqueous s o l u -

t i o n , one m u s t r e l y h e a v i l y o n the l e v e l identifications e s t a b l i s h e d i n crystals. W h e r e c r y s t a l d a t a is not a v a i l a b l e , e x t r a p o l a t i o n of parameters 86 In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

7.

C A R N A L L A N D FIELDS

Absorption

87

Spectra

f r o m n e i g h b o r i n g elements is r e q u i r e d to m a k e l e v e l assignments. O n e objective of this s t u d y is to correlate the e n e r g y levels a n d intensities of a l l t h e t r i v a l e n t l a n t h a n i d e s a n d actinides i n a single solvent m e d i u m . F o r t h e i n t e n s i t y s t u d y , r e l a t i o n s h i p s d e v e l o p e d i n aqueous solutions c a n t h e n serve as a basis f o r c o m p a r i n g the results i n m a n y other m e d i a i n w h i c h s t r o n g complexes are f o r m e d .


Experimental T h e s p e c t r a l measurements w e r e m a d e i n f u s e d s i l i c a cells w h o s e p a t h lengths v a r i e d f r o m 1.0 to 5.0 c m . a n d w e r e o b s e r v e d u s i n g a h i g h r e s o l u t i o n p r i s m - g r a t i n g r e c o r d i n g spectrophotometer. T h e u s e f u l spec t r a l r a n g e of t h e i n s t r u m e n t w a s 0.18-2.6 μ. T h e l a n t h a n i d e s u s e d w e r e o b t a i n e d c o m m e r c i a l l y as oxides w i t h a stated p u r i t y of > 9 9 . 9 % ; h o w ever, e a c h b a t c h of o x i d e w a s c h e c k e d s p e c t r o g r a p h i c a l l y b e f o r e use. T h e s e oxides w e r e d i s s o l v e d i n either D C 1 0 o r H C 1 0 f o r t h e a b s o r p t i o n s p e c t r a measurements ( 3 ) . Solutions of t h e actinides w e r e p r e p a r e d f r o m h i g h l y p u r i f i e d stock solutions b y t e c h n i q u e s p r e v i o u s l y discussed (4). 4

4

Energy Level Calculations T h e t o t a l e n e r g y of a system consisting of a p o i n t n u c l e u s w i t h a n infinite mass, s u r r o u n d e d b y Ν electrons

can be represented

b y the

Hamiltonian (19),

where p

o

represents t h e k i n e t i c energy of a l l t h e electrons a n d t h e i r

c o u l o m b i n t e r a c t i o n w i t h the n u c l e u s ; p between

p a i r s of electrons, a n d p

s o

e

involves the coulomb interaction

takes i n t o account

the magnetic

interactions of t h e electrons, of w h i c h t h e c o u p l i n g of s p i n a n d o r b i t a l a n g u l a r m o m e n t a is t h e most i m p o r t a n t effect f o r /-electrons. U s i n g a c e n t r a l field a p p r o x i m a t i o n i n w h i c h i t is a s s u m e d t h a t e a c h e l e c t r o n moves i n d e p e n d e n t l y i n a n average s p h e r i c a l l y s y m m e t r i c p o t e n t i a l , i t is possible to solve f o r t h e energies of t h e different configurations. C a l c u l a t i o n s of this t y p e s h o w that t h e /^-configuration is the lowest e n e r g y c o n f i g u r a t i o n f o r the t r i v a l e n t l a n t h a n i d e s a n d a c t i n i d e s . Since i t can be demonstrated that the term p

o

does n o t affect t h e

e n e r g y l e v e l structure w i t h i n a g i v e n c o n f i g u r a t i o n a n d since t h e a b s o r p t i o n s p e c t r a of t h e t r i v a l e n t l a n t h a n i d e s a n d actinides i n v o l v e transitions b e t w e e n states w i t h i n t h e /^-configuration, i t is n o t necessary to c o n c e r n ourselves w i t h p

a n y f u r t h e r . A s u b s t a n t i a l s i m p l i f i c a t i o n is also possible

o

i n f o r m u l a t i n g p . I n c l u d i n g t h e effect of electrons i n c l o s e d shells i n e

the c a l c u l a t i o n m e r e l y shifts t h e e n e r g y of a c o n f i g u r a t i o n ; t h u s , f o r o u r purposes

i t is o n l y necessary

to consider

t h e electrostatic i n t e r a c t i o n

b e t w e e n electrons i n t h e i n c o m p l e t e 4/ or 5 / s h e l l .

In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

88

LANTHANIDE/ACTINIDE

CHEMISTRY

T h e s o l u t i o n of the r e m a i n i n g terms i n the H a m i l t o n i a n , p

e

and $ l

s o

c a n b e w r i t t e n as E = E -\6 e

where

£

so

Y]fF

=

e

E

k

(k even)

k= 0


and T h e electrostatic e n e r g y is expressed as a s u m of r a d i a l integrals F , f c

a n d coefficients Similarly A

so

f

w h i c h represent the a n g u l a r p a r t of the i n t e r a c t i o n .

represents the a n g u l a r p a r t of the s p i n - o r b i t i n t e r a c t i o n a n d

£ / is a r a d i a l i n t e g r a l , r e f e r r e d to as the s p i n o r b i t c o u p l i n g constant.

The

Λ

a n g u l a r parts of

both

p e r t u r b a t i o n energies

can be

evaluated

using

R a c a h ' s tensor o p e r a t o r f o r m a l i s m , a n d a s s u m i n g the R u s s e l l - S a u n d e r s ( S L J ) c o u p l i n g scheme. T h e r a d i a l d e p e n d e n c e is difficult to c a l c u l a t e t h e o r e t i c a l l y , a n d i n p r a c t i c e these functions are t r e a t e d as parameters to b e e v a l u a t e d f r o m e x p e r i m e n t a l d a t a . T h e r e are, therefore, three elec trostatic parameters, F , F , a n d F 2

4

6

a n d one s p i n - o r b i t p a r a m e t e r , £ , to n /

b e d e t e r m i n e d b y a fit to o b s e r v e d e n e r g y levels f o r w h i c h assignments h a v e b e e n m a d e i n a n a p p r o p r i a t e c o u p l i n g scheme ( i n this case S L J ). Since the s p i n - o r b i t i n t e r a c t i o n is large for the l a n t h a n i d e s a n d e s p e c i a l l y l a r g e for the a c t i n i d e s , the S L J basis states are m i x e d , a n d the c a l c u l a t i o n s are a c t u a l l y c a r r i e d out i n i n t e r m e d i a t e c o u p l i n g . T o i l l u s t r a t e the effect of the v a r i o u s p e r t u r b a t i o n s , consider as a t y p i c a l e x a m p l e , P r . A s s h o w n i n F i g u r e 1, c o n s i d e r a t i o n of the electro 3 +

static i n t e r a c t i o n of t w o 4/-electrons degenerate e n e r g y levels.

( P r ) gives rise to a set of 3 +

seven

T h e s e are f u r t h e r s p l i t b y i n c l u s i o n of s p i n -

o r b i t i n t e r a c t i o n , to 13 levels w h i c h are c a l l e d

field-free

levels since t h e y

represent the s p e c t r u m of P r * as o b s e r v e d i n P r * v a p o r w h e r e there are 3

n o l i g a n d s a b o u t the P r

3 +

3

ions. I n fact, these levels are also

degenerate.

A d d i t i o n a l s p l i t t i n g does o c c u r w h e n the i o n is i n c o r p o r a t e d i n either a s o l i d or l i q u i d m a t r i x . T h i s l i g a n d field s p l i t t i n g is s m a l l c o m p a r e d w i t h the other effects c o n s i d e r e d , a n d the i n d i v i d u a l levels are n o r m a l l y not r e s o l v e d i n s o l u t i o n spectra. F o r o u r purposes i t is sufficient to i d e n t i f y the center of g r a v i t y of a g i v e n a b s o r p t i o n b a n d w i t h the a p p r o p r i a t e field-free

level.

Since at this p o i n t w e h a v e no m e t h o d of e x p e r i m e n t a l l y i d e n t i f y i n g a g i v e n a b s o r p t i o n b a n d i n s o l u t i o n i n terms of its d e s c r i p t i o n i n the S L J c o u p l i n g s c h e m e , w e r e l y o n the s i m i l a r i t y i n b a n d e n e r g y w i t h that e s t a b l i s h e d for P r

3 +

i n v a r i o u s c r y s t a l matrices.

F i g u r e 2 shows the ex

p e r i m e n t a l l y d e t e r m i n e d positions of the center of g r a v i t y of the levels of P r * i n L a C l 3

3

(17), L a F

3

( 5 ) a n d the levels f o u n d i n P r

3 +

vapor (7,18).


7.

CARNALL

A N D FIELDS

Absorption

89

Spectra

F o r i s o l a t e d b a n d s there is n o q u e s t i o n o f t h e p r o p e r assignment, b u t as c a n b e seen, e v e n w h e n t h e b a n d s are n o t i s o l a t e d i t m a y b e reasonable to m a k e assignments to t h e s o l u t i o n spectra. spectra i n L a F

3

I n t h e case o f P r , t h e 3 +

resembles q u i t e closely that f o u n d i n s o l u t i o n .

A s t h e n u m b e r o f /-electrons increases, t h e process o f a s s i g n i n g levels b e c o m e s m o r e c o m p l i c a t e d . I t is n o t often t h a t t h e p u b l i s h e d results f o r


l a n t h a n i d e spectra i n c r y s t a l m e d i a c o m p a r e as f a v o r a b l y as those f o r

ENERGY Energy cm" χ I0" 50 1

45 0.4

LEVELS

OF P r

+ 3

(4f ) 2

3

,—ο

' S - '

25 f-

μ

20 h-

0.5μ

"Ρ — •ι 30000 c m . " . 1

T h e same t y p e of a p p r o a c h i n terms of

fitting

energy levels to the

a b s o r p t i o n b a n d s o b s e r v e d i n the t r i v a l e n t a c t i n i d e elements has a l r e a d y been reported (4).

H e r e the p r o b l e m s w e r e s o m e w h a t m o r e f o r m i d a b l e

because of the p a u c i t y of c r y s t a l data a n d the m u c h greater d e n s i t y of levels o b s e r v e d

i n the s p e c t r a l r e g i o n o v e r w h i c h s o l u t i o n a b s o r p t i o n

spectra c o u l d be o b t a i n e d .

Experimental data a n d calculated


energy

7.


Absorption

91

Spectra

levels are s h o w n i n F i g u r e 6. T h e f o u r parameters d e r i v e d f r o m t h e d a t a are also s h o w n i n T a b l e I . T h e values o f F

2

f o r t h e t r i v a l e n t l a n t h a n i d e s a n d actinides are

plotted vs. Ζ (atomic n u m b e r )

i n F i g u r e 7, a n d those of ζ a r e s h o w n

g r a p h i c a l l y i n F i g u r e 8. V a l u e s o f F a n d £ 2

5 /

f o r actinides a b o v e c u r i u m

w e r e e x t r a p o l a t e d f r o m t h e l i g h t h a l f of t h e series a s s u m i n g a l i n e a r r e l a t i o n s h i p f o r t h e parameters

( 9 ) . T h e s e parameters, i n t u r n ,

were

u s e d t o c a l c u l a t e the e x p e c t e d energy levels f o r B k , C f , E s , a n d F m . Downloaded by STANFORD UNIV GREEN LIBR on September 24, 2012 | http://pubs.acs.org Publication Date: June 1, 1967 | doi: 10.1021/ba-1967-0071.ch007

3 +

3 +

3 +

3 +

T h e s e , together w i t h the a b s o r p t i o n s p e c t r u m o f C f , w h i c h was r e c e n t l y 3 +

m e a s u r e d j o i n t l y w i t h scientists f r o m t h e L a w r e n c e R a d i a t i o n L a b o r a tories ( 6 ), are s h o w n i n F i g u r e 9. Sets of eigenvectors w h i c h describe e a c h o f the states i n i n t e r m e d i a t e c o u p l i n g , are o b t a i n e d f r o m t h e c a l c u l a t i o n s of t h e e n e r g y levels. eigenvectors

are a n essential element

These

i n establishing the correlation

b e t w e e n e x p e r i m e n t a l b a n d intensities a n d those c a l c u l a t e d f r o m theory. Table I. Parameters Used to Calculate Energy Levels Observed in the Solution Absorption Spectra of the Trivalent Actinides and Lanthanides No. of {-electrons

Nd Pm Sm Eu Gd Tb Dy Ho Er Tm U Np Pu Am Cm Bk Cf Es Fm

3 + 3 + 3 +

3 + 3 +

3 + 3 +

3 +

3 + 3 +

3 +

3 +

3 + 3 + 3 +

3 +

3 + 3 + 3 +

2 3 4 5 6 7 8 9 10 11 12 3 4 5 6 7 8 9 10 11

F

Ej 304.7 333.6 351.0 371.8 470.6 488.4 486.7 420.0 415.0 433.2 447.6 196 225 240 419 370 299 318 338 358

50.82 48.06 47.70 54.02 70.91 46.28 69.17 58.00 68.80 67.10 67.12 27.9 32.0 34.1 55.6 21.0 42.5 45.2 48.1 50.9

ζ

6

714.5 874.1 1030 1171 1297 1454 1681 1900 2163 2393 2652 1666 2070 2292 2190 2918 3263 3580 3900 4220

5.106 5.450 5.300 6.027 4.953 6.219 5.859 6.346 7.270 7.360 7.336 3.16 3.62 3.86 1.98 4.90 4.81 5.12 5.44 5.76

Calculation of Intensities A n y t h e o r e t i c a l t r e a t m e n t of t h e intensities o f t h e i n t r a transitions o b s e r v e d

f-electron

i n t r i v a l e n t l a n t h a n i d e a n d a c t i n i d e spectra m u s t

b e g i n w i t h a c o n s i d e r a t i o n of t h e p o s s i b l e m e c h a n i s m s i n v o l v e d , a n d a n u m b e r of authors h a v e e x a m i n e d this p r o b l e m i n d e t a i l ( I , 2, 19). T h e


92

LANTHANIDE

ACTINIDE

CHEMISTRY

Ce°'

l l l l

4.5

I

I

p3+

3.0

r

1.5 0

I


6.0

I

I

Nd 3+ ο ω

< cr < _j

ο 2

0 4

^ ι ι ι ii ' ι i ii' Ίι' ι «'*V

ιΊ^

ί

Ίι V ^ ' ^

I

I

0

Pm

2.0

...

0 2.0

III I III I II I I III llll

1

0 1.0 0.5

Ο

Figure

À l

II l l l l

JL

hi

28

3.

IIII

26

I

«

ι

II I II I

t . Ilk

I I

I

I

I

I III

I

I Sm

• 14°

I

I

I

I

I

22

Absorption

20

18

16

14

12

ιΟ

spectra of Ce , Pr , Nd , dilute acid solution 3+

3+

8

6

Pm ,

3+

4

Sm ,

3+

3+

I

3 +

l l l l

Eu

Note chonge in scale

24

3 +

3+

2

and Eu

3+

in

results s h o w that w h i l e there is some m a g n e t i c d i p o l e character i n a f e w transitions, o n l y a n i n d u c e d e l e c t r i c d i p o l e m e c h a n i s m c a n account for the intensities o b s e r v e d for most of the b a n d s . T h e d e s i g n a t i o n i n d u c e d or f o r c e d e l e c t r i c d i p o l e is u s e d to a c k n o w l e d g e the fact that true e l e c t r i c d i p o l e transitions r e q u i r e a p a r i t y c h a n g e a n d cannot o c c u r w i t h i n the same c o n f i g u r a t i o n because the i n i t i a l a n d parity.

final

states h a v e the

same

S i n c e the intensities of the i n t r a f - e l e c t r o n transitions are ex v

t r e m e l y w e a k c o m p a r e d w i t h true e l e c t r i c d i p o l e transitions, t h e y c a n b e a c c o u n t e d for b y a s s u m i n g that a s m a l l a m o u n t of the c h a r a c t e r of h i g h e r - l y i n g configurations of opposite p a r i t y are m i x e d into the /^-elec t r o n states. T h i s m i x i n g is a s s u m e d to b e a c c o m p l i s h e d via the o d d terms i n the p o t e n t i a l o w i n g to the l i g a n d field e x p e r i e n c e d b y the l a n t h a n i d e or a c t i n i d e i o n . It w i l l be n o t e d that the i n v e r s i o n operator cannot b e one of the s y m m e t r y elements i n s u c h a l i g a n d J u d d (14)

field.

has a p p l i e d the f o r c e d e l e c t r i c d i p o l e m e c h a n i s m to t r a n

sitions w i t h i n the f - e l e c t r o n c o n f i g u r a t i o n a n d was able to d e v e l o p v

expression for the oscillator strength of a g i v e n t r a n s i t i o n . of c o m p a r i n g results w e h a v e defined τ term used i n Judd's paper

λ

=

(2/ +

1) Τ

λ

an

( F o r purposes where Τ

(2,14).)


λ

is the

7.


Absorption

93

Spectra

T h i s expression c a n b e w r i t t e n : Ρ =

Μχ

σ

[

T 2

(M )2 + 2

T 4

=(f^||U 0

5

D

2

Yb

in

3+

2; M

4

for

d e t e r m i n e d the

T h e r e is one other t r a n s i t i o n w i t h i n the s p e c t r a l

2

r a n g e for w h i c h m e a n i n g f u l assignments s e e m e d p o s s i b l e a n d this w a s a Δ/ =

6 t r a n s i t i o n . S i m i l a r l y , the b a n d s o b s e r v e d i n G d

o n l y v a l u e s for τ

2

and τ

6

3 +

were such that

could be calculated.

I n the case of T b , o n l y one l e v e l ( D ) 3 +

indicated parameters for T b

5

3 +

4

c a n at present b e fit. T h e

i n T a b l e I I I are e x t r a p o l a t e d , b a s e d o n


96

LANTHANIDE/ACTINIDE

CHEMISTRY

those c a l c u l a t e d for other m e m b e r s i n the series. T h e values of τ

λ

for Y b

are also e x t r a p o l a t e d , since there is o n l y one / ^ - t r a n s i t i o n i n Y b .

3 +

The

3 +

i n d i c a t e d p a r a m e t e r s a l l o w a g o o d fit to the o b s e r v e d i n t e n s i t y . I t is c l e a r f r o m the present d a t a t h a t the t h e o r y does successfully a c c o u n t for the e x p e r i m e n t a l l y o b s e r v e d intensities of l a n t h a n i d e a b s o r p t i o n b a n d s u p to ^ 3 0 0 0 0 c m . " .

Intensity calculations beyond

1


cm."

1

|oj7 II 7 9 ° |3 H % Il 5 15 F "*3 5 7 3 197 137 19 9 5

I7

u

I

ια. or ο Φ ω

Lanthanide and Actinide Absorption Spectra in Solution - Advances in

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