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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 .
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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
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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).
In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
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
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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
In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
energy
7.
C A R N A L L A N D FIELDS
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
In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
92
LANTHANIDE
ACTINIDE
CHEMISTRY
Ce°'
l l l l
4.5
I
I
p3+
3.0
r
1.5 0
I
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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).)
In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
λ
is the
7.
C A R N A L L A N D FIELDS
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
In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
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
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cm."
1
|oj7 II 7 9 ° |3 H % Il 5 15 F "*3 5 7 3 197 137 19 9 5
I7
u
<
—30000
are n o t p r e s e n t l y feasible because of the difficulty i n m a k i n g e n e r g y
3 I 17 7 5
%
13 3
15 II
5
9 15
13
7
3 159
II
III II ! I l I I I llll >
I
ια. or ο Φ ω
<
oc
<
T J
^.52 9IO *0 4
3 8
52 7
64
il m II min
Pu+3
- *
2(
6 5 0 4
ιι
M i l l
3
I
I A m
o
j
2J-
15 9
17
3
Lii 28
Figure 6.
26
3 7
II
A i
24
22
Absorption
ι
Υι
L
ι
l
A
- '
•
I
+
li-J* I
3
ι
1
1 L
5
Cm
, t
20
, . t 18
I 16
, I 14
cm"
1
12
X
I0
10
s
6
. 1 . 1
4
2
0
3
spectra of U , Np \ Tu \ acid solution s+
8
+ 3
s
Am , s+
and Cm
s+
In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
in dilute
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7.
C A R N A L L A N D FIELDS
Absorption
97
Spectra
ζ Figure
7.
Variation the
of F with atomic 4£ and 5f series 2
number
Ζ in
l e v e l assignments. I n t u r n i n g to s i m i l a r a t t e m p t e d fitting p r o c e d u r e s w i t h the a c t i n i d e elements one is i m m e d i a t e l y i m p r e s s e d b y the p o o r c o r r e l a tions o b t a i n e d . T e n t a t i v e values of τ
λ
for the l i g h t t r i v a l e n t actinides are
g i v e n i n T a b l e I V . T o a c e r t a i n extent the large errors i n the parameters m a y b e t r a c e d to p o o r c o r r e l a t i o n b e t w e e n and
levels o b s e r v e d
i n crystals
those f o u n d i n s o l u t i o n , b u t a m o r e d e t a i l e d e x a m i n a t i o n of
p r o b l e m reveals that, for e x a m p l e , i n P u
3 +
the
( F i g u r e 6 ) t h e m a t r i x elements
n e e d e d to a c c o u n t for the l a r g e d o u b l e b a n d c e n t e r e d near 17500 c m . "
1
are too s m a l l . T h e reason for these p o o r fits i n the l i g h t actinides is n o t o b v i o u s since the assumptions m a d e i n d e r i v i n g t h e t h e o r e t i c a l expression for o s c i l l a t o r strength s h o u l d a p p l y to b o t h the l a n t h a n i d e s a n d actinides. O n e p o s s i b l e e x p l a n a t i o n m a y arise f r o m the fact that e x c i t e d c o n f i g u r a tions i n the actinides seem to o c c u r at l o w e r energies
than their lan
t h a n i d e counterparts. It is, therefore, p a r t i c u l a r l y significant that b e g i n n i n g w i t h A m the fits to e x p e r i m e n t a l i n t e n s i t y d a t a a p p e a r to i m p r o v e .
3 +
The
In Lanthanide/Actinide Chemistry; Fields, P., et al.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.
-Cm
3 +
large
98
LANTHANIDE/ACTINIDE
deviations i n τ
and τ
2
in C m
4
CHEMISTRY
reflect the fact t h a t t h e y are p o o r l y
3 +
d e t e r m i n e d — m o s t of the b a n d intensities o b s e r v e d are a c c o u n t e d f o r b y r . 6
B a s e d o n a set of eigenvectors d e r i v e d f r o m the e x t r a p o l a t e d values
of F
2
a n d ζ for C f , the c o m p a r i s o n b e t w e e n c a l c u l a t e d a n d o b s e r v e d 3 +
o s c i l l a t o r strengths for the first seven o b s e r v e d b a n d s is satisfactory. A n i m p r o v e d e n e r g y l e v e l fit to C f
3 +
w o u l d be expected
i n t e n s i t y c o r r e l a t i o n . A p p a r e n t l y , the agreement
to i m p r o v e t h e
between
theory
and
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e x p e r i m e n t i m p r o v e s as the actinides b e c o m e m o r e r a r e e a r t h - l i k e — t h a t is, as a t o m i c n u m b e r increases a n d 3 +
b e c o m e s the most stable v a l e n c e
state. U
Np
+ 3
+ 3
Pu Am Cm* + 3
+ 3
Bk
3
+ 3
Cf
Es* F m
+ 3
3
cm"'
+ 3
ο ACTINIDES Δ LANTHANIDES
cm 2800 - 1
2600 2400 £nf 2 2 0 0 2000 1800 1600 1400 1200 1000 800 6
0
Figure
0
Pr
+ 3
Nd Pm Srrf
8.
+3
+3
3
Eu
G
