24 Some Comments o n the Electronic Structure o f
Extended Interactions between Metal Ions Downloaded from pubs.acs.org by IOWA STATE UNIV on 01/04/19. For personal use only.
K r o g m a n n Salts and the Stability of Pt AARON
N.
BLOCH*
and
R.
BRUCE
†
2.3
WEISMAN
†
T h e Johns H o p k i n s U n i v e r s i t y , B a l t i m o r e , Md. 21218
I.
Introduction
S a l t s of the d i v a l e n t tetracyanoplatinateo r dioxaloplatinate i o n s typically d i s p l a y c r y s t a l s t r u c t u r e s in which the p l a n a r comp l e x anions a r e stacked t o form l i n e a r c h a i n s , separated by comp a r a t i v e l y wide channels c o n t a i n i n g counterions and water molec u l e s (1). From s o l u t i o n s o f the complex which have been partially o x i d i z e d , c r y s t a l s can be grown having s i m i l a r s t r u c t u r e s but cons i d e r a b l y reduced metal-metal d i s t a n c e s (1) and a formal platinum valence (1) c l o s e t o 2.3+. Nominally, these a r e "mixed-valence" compounds, but t h e term is probably m i s l e a d i n g inasmuch as X-ray (1), i n f r a r e d (2,3), and p h o t o e l e c t r o n (4) s p e c t r o s c o p i c s t u d i e s show the o x i d a t i o n s t a t e s o f all the metal atoms t o be e q u a l . Rather, t h e r e is ample evidence (1,5) f o r t h e formation o f a well-defined quasi-one-dimensional band s t r u c t u r e , i n c l u d i n g a partially filled conduction band o f a p p r e c i a b l e width. Hence, w h i l e their d i v a l e n t parent compounds a r e electrical i n s u l a t o r s (1), the partially o x i d i z e d "Krogmann salts" d i s p l a y l a r g e electrical (5,6) and o p t i c a l (7) c o n d u c t i v i t i e s along the c h a i n a x i s , and r e c e n t l y have e x c i t e d widespread i n t e r e s t as prototypes for the study o f one-dimensional conductors. From this p o i n t o f view, our understanding o f the p h y s i c s o f these m a t e r i a l s is by now w e l l developed (5,8-10). T h e i r theoretical chemistry, however, has r e c e i v e d l e s s a t t e n t i o n , and s e v e r a l fundamental questions remain outstanding, (a) Why do these unique s t r u c t u r e s occur in o n l y two chemical forms (1), the f i l l e d - b a n d (Pt2+) i n s u l a t o r s and a s e r i e s o f conductors whose conduction-band occupations fall in a narrow range near f i v e - s i x t h s filling (Pt 2.3+)? (b) Why do the i n t e r m e t a l l i c spacings (1) v a r y among the former group o f compounds over t h e enormous range 3.09-3.60Å, w h i l e those in t h e latter group a r e much s h o r t e r and r e s t r i c t e d t o the range * A l f r e d P. Sloan Foundation F e l l o w Present address: Department o f Chemistry, U n i v e r s i t y o f Chicago, Chicago, I l l i n o i s 60637
356
24.
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AND
WEISMAN
Krogmann
Salts
357
2.88-2.98A f a r the cyanides and 2.80-2.85A f o r the o x a l a t e s ? (c) F i n a l l y , why do cyanide and o x a l a t e , alone among common l i g a n d s t o platinum, form concourais o f t h i s c l a s s ? The f i n a l d i s p o s i t i o n o f such q u e s t i o n s must o f course await d e t a i l e d c a l c u l a t i o n s o f t h e e l e c t r o n i c s t r u c t u r e o f the m a t e r i a l s . Pending these, however, enough experimental i n f o r m a t i o n i s a v a i l a b l e t o guide a p r e l i i n i n a r y i n q u i r y i n t o the b a s i c p r i n c i p l e s involved. Such a c o n t r i b u t i o n has a l r e a d y been made by Krogmann (1), who proposed a p l a u s i b l e answer t o (a) and (b) based on simp l e one-dimensional band-structure arguments. I n t h i s a r t i c l e we c o n s i d e r t h e s e arguments i n more d e t a i l . We f i n d , s u r p r i s i n g l y , t h a t w h i l e they probably do answer q u e s t i o n (b), they do not r e s o l v e (a). We suggest i n s t e a d t h a t the f r a c t i o n a l v a l e n c e i s a c o v a l e n t molecular e f f e c t , and represents the optimum v a l u e f o r s t a b i l i t y o f the complex a n i o n i t s e l f . A t e n t a t i v e response t o (c) follows d i r e c t l y . The paper i s d i v i d e d i n t o seven p a r t s . I n S e c t i o n I I our approach i s formulated w i t h i n the framework o f c u r r e n t e m p i r i c a l evidence. We conclude t h a t t h e arguments o f Krogmann (1) a r e t o be c a s t i n terms o f the c o n t r i b u t i o n o f a s i n g l e f i v e - s i x t h s - f i l l e d one-dimensional conduction band t o the i n t e r n a l energy o f the c r y s t a l . As an i l l u s t r a t i o n , t h i s c a l c u l a t i o n i s performed i n S e c t i o n I I I u s i n g a simple t i g h t - b i n d i n g model. We f i n d t h a t t h e bands t r u c t u r e energy gained from o x i d a t i o n o f the Krogmann-salt s t r u c t u r e t o P t 2.3+ i s much t o o s m a l l t o p r o v i d e a r e a l i s t i c answer t o q u e s t i o n (a). S e c t i o n IV i n q u i r e s whether t h i s c o n c l u s i o n i s a l t e r e d s i g n i f i c a n t l y by improving upon the simple t i g h t - b i n d i n g model. Appealing once more t o e m p i r i c a l evidence, we f i n d t h a t n e i t h e r t h e t i g h t - b i n d i n g l i m i t nor the f r e e - e l e c t r o n model r e c e n t l y proposed by Z e l l e r (10) i s f u l l y c o n s i s t e n t w i t h experiment. A simple intermediate treatment c o r r e c t s t h i s d e f i c i e n c y , but s t i l l does not account f o r the s t a b i l i t y o f the f i v e - s i x t h s - f i l l e d band. We t h e r e f o r e suggest i n S e c t i o n V t h a t t h e e f f e c t must r e s i d e i n the c o v a l e n t i n t e r n a l energy o f the ccmplex anion, and b r i e f l y d i s c u s s the chemical p h y s i c s o f a system i n which t h e v a l e n c e can be t r e a t e d a s a continuous v a r i a t i o n a l parameter. We note t h a t t h e most s t a b l e o x i d a t i o n s t a t e o f a molecule need not be an i n t e g e r , and t h a t i n p r a c t i c e i t can be a t t a i n e d o n l y i n unique m o l e c u l a r c r y s t a l s t r u c t u r e s , such as those o f the Krogmann s a l t s , i n which the e f f e c t i v e t o t a l charge o f the molecule i s not quantized. The exi s t e n c e o f two s t a b l e o x i d a t i o n s t a t e s w i t h the same g e n e r a l c r y s t a l s t r u c t u r e has e l e c t r o c h e m i c a l i m p l i c a t i o n s as w e l l , and S e c t i o n VI p r e s e n t s a p r e l i m i n a r y experimental account o f the electrochemic a l o x i d a t i o n o f a s i n g l e c r y s t a l o f K2Pt(CN)4*2H20 t o a s o l i d state galvanic c e l l . I n S e c t i o n V I I we summarize our c o n c l u s i o n s . II.
General Remarks
Wë s h a l l f i n d i t u s e f u l a t the o u t s e t t o review b r i e f l y t h e s a l i e n t p h y s i c s o f the m a t e r i a l s . The Krogmann s a l t s represent a
358
EXTENDED INTERACTIONS BETWEEN M E T A L IONS
p a r t i c u l a r l y i n t e r e s t i n g c l a s s o f model systems i n which t h e r o l e s of i n s t a b i l i t i e s (11), f l u c t u a t i o n s (9), and d i s o r d e r (8,12) i n the p h y s i c s o f the one-dimensional e l e c t r o n gas can be s t u d i e d d i r e c t l y . The m e t a l l i c s t a t e i n one dimension i s i n h e r e n t l y u n s t a b l e (11), and the b e a u t i f u l experiments o f Z e l l e r and c o workers (10) have shown t h a t t h e p l a t i n u m c h a i n s do undergo a P e i e r l s d i s t o r t i o n (11) w i t h d e c r e a s i n g temperature. The phase t r a n s i t i o n i s , however, incomplete (13), probably owing t o t h e i n t r i n s i c s t r u c t u r a l d i s o r d e r (1) o f the systems. The s t a t i c potent i a l f l u c t u a t i o n s a s s o c i a t e d w i t h random occupantion o f the count e r i o n and water s i t e s tend t o suppress the t r a n s i t i o n , r e d u c i n g the m e a n - f i e l d t r a n s i t i o n temperature and p l a c i n g weakly l o c a l i z e d e l e c t r o n i c s t a t e s i n the P e i e r l s energy gap (12,14). Indeed, we have argued elsewhere (8,12,15) t h a t c e r t a i n f e a t u r e s o f the e l e c t r o n t r a n s p o r t and low-frequency d i e l e c t r i c response cannot be understood i n terms o f the P e i e r l s d i s t o r t i o n a l o n e , but a r i s e from a f i n i t e d e n s i t y o f l o c a l i z e d s t a t e s a t the Fermi l e v e l . For the p r e s e n t d i s c u s s i o n o f chemical s t a b i l i t y , however, the d i s o r d e r i s o f scant importance. The p o t e n t i a l f l u c t u a t i o n s r e q u i r e d t o e x p l a i n t h e observed t r a n s p o r t phenomena (8,12,15) a r e i n t h i s case but a s m a l l f r a c t i o n o f t h e unperturbed bandwidth (14), and t h e œnfigurational entropy a s s o c i a t e d w i t h the p a r t i a l l y occupied i n t e r c h a i n s i t e s make a c o n t r i b u t i o n o f but o r d e r kT t o the t o t a l f r e e energy p e r molecule (16). The e l e c t r o n i c entropy o f t h e p a r t i a l l y f i l l e d conduction band i s a n a l l e r s t i l l (16). We conclude t h a t the s t a b i l i t y o f P t 2.3+ r e s i d e s i n the i n t e r n a l energy o f the c r y s t a l , and t h a t t h i s i s n e g l i g i b l y d i f f e r e n t from t h a t o f a h y p o t h e t i c a l analogous ordered system. We w r i t e t h i s energy s c h e m a t i c a l l y a s : U
=
U
C
+
U
B
+
U
R
+
U
M
( 1 )
where U i s t h e t o t a l c o v a l e n t b i n d i n g energy o f the complex anion, 1% t h e band-structure s t a b i l i z a t i o n o f the c h a i n s , U R t h e r e p u l s i v e energy between adjacent p l a n a r complexes on a c h a i n , and % t h e remainder o f the Madelung energy o f the c r y s t a l . Admittedly, these d i s t i n c t i o n s a r e t o some e x t e n t a r b i t r a r y — t h e f i r s t and second terms, f o r example, a r e never f u l l y s e p a r a b l e — b u t we s h a l l f i n d them t o be o f conceptual v a l u e . Now, we can immediately d i s m i s s on e m p i r i c a l grounds t h e p o s s i b i l i t y t h a t the number o f conduction e l e c t r o n s p e r molecule, Z, and i n t e r m e t a l l i c spacing, R, i n t h e P t 2.3+ Krogmann s a l t s a r e determined p r i m a r i l y by Among the dozens o f compounds i n t h e c l a s s , s t r u c t u r a l and chemical d i f f e r e n c e s which presumably l e a d t o s u b s t a n t i a l d i f f e r e n c e s i n Madelung energy produce o n l y minor d i f f e r e n c e s i n Ζ and R (1). From those o f a t y p i c a l example such a s K2Pt(CN)4Bro.3*3H20, these parameters change but l i t t l e when CI i s s u b s t i t u t e d f o r Br; when halogen i s excluded a l t o g e t h e r i n f a v o r o f a d e f i c i e n c y o f c a t i o n s ; when o x a l a t e i s s u b s t i t u t e d f o r cyanide; when any a l k a l i o r a l k a l i n e e a r t h metal i s s u b s t i t u t e d f o r K; when c
24.
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the water content i s changed; o r when the gross c r y s t a l s t r u c t u r e i t s e l f changes from t e t r a g o n a l t o t r i c l i n i c , m o n œ l i n i c , o r o r t h o hcmbic ( 1 ) . I t i s as though t h e i n t e r c h a i n s p e c i e s had been l e f t t o a d j u s t themselves t o dimensions and chemical composition which a r e e s s e n t i a l l y f i x e d by s t r o n g i n t r a c h a i n f o r c e s . Toward an e l u c i d a t i o n o f these f o r c e s , Krogmann ( 1 ) has suggested i n e f f e c t t h a t the s t a b i l i t y o f t h e o x i d a t i o n s t a t e Pt 2.3+ ( Z = 1 . 7 ) a r i s e s frcm an o p t i m i z a t i o n o f the band-structure term 1%. Such an e f f e c t would represent a rough one-dimensional analog o f the well-known Hume-Rothery r u l e s ( 1 7 ) f o r the composit i o n of alloys. We s h a l l c a s t these arguments i n a simple mathematical form. As a preamble, we observe t h a t i n c a l c u l a t i n g 1% we a r e d e a l i n g w i t h a s i n g l e conduction band, not degerate w i t h any other band a t t h e Fermi l e v e l . T h i s we a f f i r m by u s i n g the P e i e r l s d i s t o r t i o n as a probe o f band occupancy. The d i s t o r t i o n r e f l e c t s the underl y i n g divergence o f the one-diinensional e l e c t r o n i c response f u n c t i o n s a t wavenumber q=2kp, where kp i s the Fermi wavenumber ( 1 8 ) . Where the conduction e l e c t r o n s a r e shared by two one-dimensional bands which o v e r l a p i n energy a t the Fermi l e v e l , the Fermi "surf a c e " c o n s i s t s i n g e n e r a l o f two d i s t i n c t v a l u e s o f k ; o n l y when such degeneracy i s absent does kp assume the s i n g l e v a l u e TCZ/2R. Now, i t i s found (13) experimentally t h a t w i t h the s m a l l v a r i a t i o n s i n Ζ which do occur among the d i f f e r e n t Krogmann s a l t s ( i n f e r r e d from t h e i r s t o i c h i c m e t r i e s ), the p e r i o d o f the d i s t o r t i o n a l s o v a r i e s , and always corresponds p r e c i s e l y t o a reduced wavenumber o f πΖ/R. We conclude t h a t o n l y one hand i n t h e system i s p a r t i a l l y occupied. F
III.
Band-Structure Energy ϋ" i n the T i g h t - B i n d i n g Model ρ
F o r s i m p l i c i t y o f i l l u s t r a t i o n , we t r e a t t h i s band i n i t i a l l y i n t h e o n e - e l e c t r o n t i g h t - b i n d i n g l i m i t ( 1 9 ) , and d e f e r t o the next s e c t i o n a d i s c u s s i o n o f the adequacy o f t h i s approximation and the r o l e s o f h y b r i d i z a t i o n and the P e i e r l s d i s t o r t i o n . L e t E° be the energy o f the r e l e v a n t molecular o r b i t a l |i>, centered on s i t e i o f the c h a i n , i n the presence o f the Madelung f i e l d but the absence of any i n t e r a c t i o n between adjacent molecules on t h e c h a i n . When t h e s t a t e |i> i s perturbed by the l a t t i c e p o t e n t i a l o f the c h a i n , l jïi j ' 9Y t ^ o n e - e l e c t r o n conduction-band s t a t e o f waveSumœr k i s : H
=
v
t
h
e
e n e r
o
f
= E° - α - 2(3 cos kR
(2)
Here - a i s t h e band s h i f t , and-β the c h a r g e - t r a n s f e r i n t e g r a l . As u s u a l , o v e r l a p i n t e g r a l s S o f the form have been ignored. C l e a r l y , E° c o n t a i n s l o c a l c o n t r i b u t i o n s t o OQ and U M - T O e v a l u a t e % , we i n t e g r a t e the q u a n t i t y E - E ° over a l l occupied s t a t e s |k> o f the band: k
EXTENDED INTERACTIONS BETWEEN M E T A L IONS
360
U
= - Ζα -
B
ψ
sin
φ
(3)
We note t h a t both α and β a r e f u n c t i o n s o f R and Z, and t h a t the p r i n c i p a l dependence o f β on these parameters i s s u r e l y expo n e n t i a l . Taking t h e r a d i a l screening constant f o r t h e wavefunction I i> t o have roughly the S l a t e r form (20), we w r i t e t h i s dependence a s
β - 3 exp [ - ( y - n Z ) R ]
(4)
o
where βο, μ, and η « μ a r e constants. I n c o n t r a s t , the v a r i a t i o n o f t h e s m a l l (19) energy α w i t h each o f t h e parameters R and Ζ i s a t most a paver-law dependence, comparable w i t h those o f t y p i c a l c o n t r i b u t i o n s t o the Madelung energy U . T h i s o b s e r v a t i o n has s p e c i a l s i g n i f i c a n c e f o r t h e f i l l e d band case Z=2, where U according t o Equation 3 i s simply -2a. Under these circumstances, we expect R t o be determined l a r g e l y by % r a t h e r than U . We thereby account f o r t h e wide v a r i a t i o n i n R among the d i v a l e n t parent cxmpounds (1), i n p a r t i a l answer t o q u e s t i o n (b). With p a r t i a l o x i d a t i o n o f these m a t e r i a l s t o form Krogmann s a l t s , t h e s t r o n g l y R- and Z - dépendait second term i n Equation 3 e n t e r s U , and the s i t u a t i o n i s a l t e r e d d r a s t i c a l l y . On t h e b a s i s o f o u r d i s c u s s i o n i n t h e preceding s e c t i o n , i t i s n o t unreasonable t o regard t h e i n t e r c h a i n channels a s a "charge s i n k " , capable o f accormodating a s many counterions a s are necessary t o balance any Ζ i n t h e range o f i n t e r e s t . To t h e extent t h a t t h i s i s t r u e , t h e c h a i n s c o n s t i t u t e a c h e m i c a l l y unique system i n which the number o f bonding e l e c t r o n s may be regarded a s a v a r i a t i o n a l parameter. I f , as suggested by Krogmann (1), Ζ i s determined by U , then f o r g i v e n R the observed Ζ must correspond t o a minimum i n 1%: M
B
B
B
B
R
s i n -γ)
(5)
When Equations 4 and 5 a r e combined, a t r a n s c e n d e n t a l equa t i o n i s obtained r e l a t i n g R and Z. A t y p i c a l s o l u t i o n i s shown i n F i g u r e 1. Here we have simply determined μ and η a c c o r d i n g t o S l a t e r ' s r u l e s (20), and adjusted t h e r ^ t i o βς/α s o as t o reproduce the experimental v a l u e Z=1.7 f o r R=2.88A. More e l a b o r a t e f i t t i n g procedures a r e c e r t a i n l y a v a i l a b l e , but we have found no p h y s i c a l l y reasonable c h o i c e o f parameters which s u b s t a n t i a l l y a l t e r s Figure 1 o r our f i n a l conclusions. Under t h e c o n d i t i o n imposed by Equation 5, we a r e now i n a p o s i t i o n t o c a l c u l a t e U from Equations 3 and 4. The r e s u l t i s B
π Λν - V ~ a
7 + ù
sin(ïïZ/2) (π/2)cos (πΖ/2) + (3£ηβ/9Ζ) sin(πΖ/2)
l 0 j
Equation 6 i s p l o t t e d i n F i g u r e 2, which represents t h e v a r i a t i o n o f U w i t h R under t h e c o n s t r a i n t t h a t each R, Ζ i s s e l f c o n s i s t e n t l y t o be r e a d j u s t e d so a s t o minimize U . Q u a l i t a t i v e l y , the c a l c u l a t i o n i s c o n s i s t e n t w i t h t h e B
B
BLOCH
AND
WEiSMAN
Krogmann
Salts
Figure 1. Variation of conduction-band occupation, Z, with lattice constant, R, for a one-dimensional tight-binding system under the constraint of Equation 5
EXTENDED
INTERACTIONS
BETWEEN
METAL
R(A)
,2.0 I
I
I.I
2.6 2.7 I
I
12
2.85
2.8 i
1.3
1.4
l
2.88
29
l
1.5
1.6
ι
1.7
1.8
1.9
2.0
Ζ
Figure 2. Variation of band-structure stabilization U with R and Ζ for a one-dimensional tight-binding system under the constraint of Equation 5. At the experimental values Ζ — 1.7 and R = 2.88 A , U (Z)-Ui*(2) is much too small to account for the stability of Pt 2.3+. B
B
IONS
24.
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AND
WEISMAN
Krogmann
363
Salts
d e s c r i p t i o n o f f e r e d by Krogmann (1). F o r l a r g e R, we have Z=2 and ϋβ/α independent o f R. With decreasing R, the bandwidth 4β i s increased, u n t i l the h i g h e s t - l y i n g s t a t e s i n the band become a n t i bonding w i t h r e s p e c t t o E ° . The band-structure energy 1% now f a v o r s p a r t i a l o x i d a t i o n o f the chains, and the parameters Ζ and R a r e coupled according t o F i g u r e 1. With p r o g r e s s i v e o x i d a t i o n and shrinkage o f the l a t t i c e , energy 1% i s gained a s shewn i n F i g u r e 2. U l t i m a t e l y , however, the compression and hence the o x i d a t i o n must o f course be l i m i t e d by the r e p u l s i v e term U R i n Equation 1, which r i s e s r a p i d l y f o r R s m a l l and decreasing. The r e s u l t i s a minimum i n the sum U + U a t seme s h o r t R and f i x e d o x i d a t i o n s t a t e 1
,10,
366
EXTENDED INTERACTIONS BETWEEN METAL IONS
S u b s t i t u t i n g (9) i n t o (10) and assuming 3 » a S , we f i n d t h a t f o r Z=1.7 the t h e r m o e l e c t r i c power i s p o s i t i v e f o r s m a l l S, and c r o s s e s z e r o near S=0.37. From the v e r y s n a i l p o s i t i v e v a l u e s observed, we estimate S~0.35. Then u s i n g Equations 7 and 9 and the observed plasma frequency (7,24,29) o f 15,800 cm" , we have 3-aS~0.32 eV. The bandwidth 1
W - i S f c f U 2.5 eV 1-4S
(11)
Z
i s t h e n comparable w i t h Ru)p. The o b s e r v a t i o n o f a w e l l - d e f i n e d plasmon a b s o r p t i o n (24,29) suggests t h a t the t r u e v a l u e o f W i s somewhat s m a l l e r s t i l l , but t h e o v e r a l l agreement w i t h experiment i s good enough t o demonstrate t h a t a minimal improvement upon t h e s i m p l e s t t i g h t - b i n d i n g approximation, such as Equation 8, i s a reasonably a c c u r a t e r e p r e s e n t a t i o n o f the conduction band i n t h e Krogmann s a l t s . I n accounting f o r t h e s t a b i l i t y o f P t 2.3+, however, the im proved d e s c r i p t i o n f a r e s no b e t t e r than the o l d . Indeed, the bands t r u c t u r e term U now tends t o d r i v e P t 2.3+ l e s s s t a b l e than P t 2+. I n t e g r a t i n g Equation 8 (31), r e c a l l i n g t h a t S s c a l e s roughly as 3, and proceeding as i n the p r e v i o u s s e c t i o n , we f i n d t h a t w i t h t h e same v a l u e s o f μ and η, ϋβ f o r Z=1.7 i s p o s i t i v e w i t h r e s p e c t t o Z=2 by about 0.1 eV. T h i s r e s u l t i s not s u b s t a n t i a l l y a l t e r e d f o r any p h y s i c a l l y reasonable c h o i c e s o f μ and η. Improving the a c c u r acy o f our r e p r e s e n t a t i o n o f the conduction band has simply r e a f f i r m e d our c o n c l u s i o n t h a t the s t a b i l i t y o f P t 2.3+ i s not a s s o c i a t e d w i t h the k i n e t i c energy o f the conduction e l e c t r o n s . B
V.
The Covalent Energy
U
c
I n the p r e c e d i n g s e c t i o n s we have argued t h a t t h e v a r i a t i o n s i n 1 % H % H J i n Equation 1 a r e t o o s n a i l , and p o s s i b l y o f the wrong s i g n , t o be r e s p o n s i b l e f o r the p e c u l i a r s t a b i l i t y o f P t 2.3+. The remaining term i s the c o v a l e n t b i n d i n g energy UQ o f the complex c y a n o p l a t i n a t e i o n i t s e l f , and we now suggest t h a t t h i s term accounts f o r the observed e f f e c t . I t i s w e l l known t h a t i n square-planar complexes o f d^ t r a n s i t i o n metals the occupied molecular o r b i t a l s uppermost i n energy a r e weakly antibonding. The complex i s n e v e r t h e l e s s s t a b l e because the r e p u l s i v e c o n t r i b u t i o n from these o r b i t a l s t o U i s more than compensated by the a t t r a c t i v e c o n t r i b u t i o n from o t h e r o r b i t a l s , p r i n c i p a l l y the s t r o n g l y σ-bonding a^g, b^g, and e (23,32). Let us c o n s i d e r the o x i d a t i o n o f such a complex under OTrffitlons where, as i n t h e Krogmann s a l t s t r u c t u r e , the (time-averaged) occupation Ζ o f a h i g h - l y i n g o r b i t a l may be regarded as a continuous r a t h e r than a d i s c r e t e v a r i a b l e . S i n c e the removal o f an i n f i n i t e s i m a l amount o f charge from the d complex lowers the occupation o f an antibonding o r b i t a l , i t c e r t a i n l y tends t o s t a b i l i z e the complex. With p r o g r e s s i v e R
c
u
8
24.
BLOCH
AND
WEiSMAN
Krogmann
Salts
367
o x i d a t i o n , however, the nany-electron wavefunction i s r e a d j u s t e d and the e f f e c t i v e one-electron e n e r g y - l e v e l scheme renormalized s o as t o accommodate the change i n elœtron-elecrtron i n t e r a c t i o n and screening o f the c o r e p o t e n t i a l . I n p a r t i c u l a r , the h i g h - l y i n g o r b i t a l s must drop i n energy, r e f l e c t i n g the i n c r e a s i n g d i f f i c u l t y o f f u r t h e r o x i d a t i o n ; e v e n t u a l l y the h i g h e s t occupied o r b i t a l becomes bonding, and the o x i d i z e d s p e c i e s d i s p l a y s s u b s t a n t i a l electron a f f i n i t y . I n the case o f square-planar platinum complexes, t h i s has apparently happened by the time one f u l l e l e c t r o n i s removed. Hence P t 3+ i s unstable, and four-coordinated P t 4+ does not occur i n the square-planar geometry. Viewed from t h i s p e r s p e c t i v e , t h e u s u a l P t 2+ i n the f r e e complex does not represent a t r u e minimum i n Ut a s a f u n c t i o n o f Z, a s the presence o f f i l l e d antibonding o r b i t a l s a t t e s t s . Rather, P t 2+ i s the b e s t ccmprcmise which can be a t t a i n e d under the c o n s t r a i n t t h a t Ζ be an i n t e g e r . When t h i s c o n s t r a i n t i s l i f t e d , the r e a l minimum occurs a t t h a t f r a c t i o n a l o x i d a t i o n s t a t e f o r which the energy o f the p a r t i a l l y occupied o r b i t a l passes through zero. C l e a r l y , t h i s occurs somewhere between P t 2+ and P t 3+, and we suggest t h a t i n the c y a n o p l a t i n a t e i o n i t o c c u r s c l o s e t o P t 2.3+. I t i s h a r d l y necessary t o emphasize t h a t t o t e s t t h i s conjec t u r e r e q u i r e s more d e t a i l e d c l a c u l a t i o n s than have been presented here. Nevertheless, we a r e impressed a t t h i s p r e l i m i n a r y stage by i t s p l a u s i b i l i t y and by the l a c k o f a reasonable a l t e r n a t i v e , u n l i k e the weak (or non-existent) minimum i n U B + U R , the minimum i n UQ o c c u r s a t a s h a r p l y d e f i n e d value o f Z, and presumably r e p r e sents a s u b s t a n t i a l g a i n i n the b i n d i n g energy o f the complex. The e x i s t e n c e o f such a minimum a t a f r a c t i o n a l valence i s not o f course unique t o c y a n o p l a t i n a t e , but probably o c c u r s f o r any mole c u l e whose ground s t a t e i n c l u d e s f i l l e d antibonding o r b i t a l s . The r e a l i z a t i o n o f the minimum i n p r a c t i c e , however, r e q u i r e s a unique s t r u c t u r e , such a s t h a t o f the Krogmann s a l t s , i n which c o v a l e n t , m e t a l l i c , and i o n i c bonding c o e x i s t . VI. Electrochemical Oxidation o f C r y s t a l l i n e K Pt(CN), t o a S o l i d State Galvanic C e l l 2
Before concluding, we d i g r e s s t o remark t h a t the e x i s t e n c e o f two s t a b l e o x i d a t i o n s t a t e s i n the same general c r y s t a l s t r u c t u r e has i n t e r e s t i n g p r a c t i c a l r a m i f i c a t i o n s . I n p a r t i c u l a r , t h e m a t e r i a l s are known t o e x h i b i t i o n i c c o n d u c t i v i t y . I t has been shown by Gcmm and U n d e r h i l l (33), and independently by others (28,34), t h a t s u f f i c i e n t l y strong e l e c t r i c f i e l d s reduce the Krogmann s a l t K2Pt(CN)4Bro.3*2.3H20 t o a compound o f d i v a l e n t platinum. We have found t h a t , c o n t r a r y t o an a s s e r t i o n by Gcmm and u n d e r h i l l (33), the r e v e r s e r e a c t i o n can a l s o be induced: hydrated s i n g l e c r y s t a l s o f KjPt(CN)4 are e a s i l y and r e v e r s i b l y o x i d i z e d by a p p l i c a t i o n o f modest e l e c t r i c f i e l d s along the needle a x i s , u s i n g mercury o r s i l v e r - p a s t e e l e c t r o d e s . A f t e r the f i e l d i s r a i s e d
368
EXTENDED INTERACTIONS BETWEEN M E T A L IONS
above a t h r e s h o l d o f c a . 100 V/cm, t h e r e s i s t a n c e f a l l s a b r u p t l y by two o r d e r s o f magnitude, and a dark, rapper-colored area forms a t t h e anode and spreads toward t h e cathode, where vigorous e v o l u t i o n o f hydrogen gas i s observed. When t h e p o l a r i t y i s r e v e r s e d the r e a c t i o n i s r e v e r s e d a l s o , and t h e sharp boundary between t h e two phases recedes u n t i l t h e o r i g i n a l white c r y s t a l i s recovered. A t constant temperature, humidity, and a p p l i e d v o l t a g e , t h e c u r r e n t does n o t d i m i n i s h a s t h e r e a c t i o n proceeds t o completion. The (hydrated) product c r y s t a l d i s p l a y s t h e coppery l u s t u r e and d i c h r o i s m c h a r a c t e r i s t i c o f Krogmann s a l t s (1), and has shrunk t o about 90% o f i t s former l e n g t h ; t h i s corresponds t o the t y p i c a l d i f f e r e n c e i n t h e l a t t i c e spacing R between Krogmann s a l t s and t h e i r d i v a l e n t parent ocmpounds (1). By monitoring t h e i n f r a r e d t r a n s m i s s i o n spectrum o f the c r y s t a l a s t h e r e a c t i o n proceeds, we c o n f i r m t h a t t h e product i s a Krogmann s a l t , and t h a t P t 2+ and P t 2.3+ a r e the o n l y o x i d a t i o n s t a t e s present i n measurable q u a n t i t y . We have accumulated e v i dence t h a t t h e r e a c t i o n proceeds v i a a p r o t o n - t r a n s f e r - a n d r e d u c t i o n mechanism s i m i l a r t o t h a t suggested by Lecrone and P e r l s t e i n (35) f o r the e l e c t r o c h e m i c a l r e d u c t i o n o f mixed-valence o x a l o p l a t i n a t e systems, and we a s s i g n t o the product t h e p r e v i o u s l y unreported formula. K2Pt (CN) 4 (OH) ·ηΗ2θ, where x~0.3. I f t h e a p p l i e d f i e l d i s removed b e f o r e the r e a c t i o n i s com p l e t e , a p o t e n t i a l d i f f e r e n c e e x i s t s between t h e o x i d i z e d and unoxidized s e c t i o n s , and t h e p a r t i a l l y converted c r y s t a l a c t s as a galvanic c e l l . The Krogmann-salt r e g i o n i s t h e anode. Because o f the h i g h i n t e r n a l r e s i s t a n c e a s s o c i a t e d w i t h t h e K2Pt (CN) 4 s e c t i o n , t h i s m i n i a t u r e s o l i d - s t a t e b a t t e r y f u n c t i o n s as a c u r r e n t r a t h e r than a v o l t a g e source. As i n t h e i n i t i a l o x i d a t i o n , t h e c u r r e n t i s q u i t e s e n s i t i v e t o water vapor i n t h e surrounding atmosphere, and i s i n f a c t a measure o f r e l a t i v e humidity. Near 100% humidity and 22°C, we f i n d t y p i c a l c u r r e n t d e n s i t i e s o f c a . 5 ma/cm and an o p e n - c i r c u i t p o t e n t i a l o f 1.35 V. χ
2
VII.
Summary and Conclusions
We summarize o u r c o n c l u s i o n s a s f o l l o w s . The p a r t i a l l y o x i d i z e d Krogmann s a l t s a r e c h a r a c t e r i z e d by a s i n g l e f i v e - s i x t h s f i l l e d conduction band which i s adequately d e s c r i b e d n e i t h e r by the n e a r l y - f r e e - e l e c t r o n model n o r by c o n v e n t i o n a l t i g h t - b i n d i n g theory. Instead, a reasonable intermediate r e p r e s e n t a t i o n , c o n s i s t e n t w i t h experiment, i s obtained by extending t h e t i g h t - b i n d i n g formalism t o i n c l u d e t h e e f f e c t s o f o r b i t a l o v e r l a p between neighboring molecules. The e l e c t r o n i c k i n e t i c energy o f such a band cannot account f o r t h e s t a b i l i t y o f t h e f i v e - s i x t h s f i l l e d bard (Pt 2.3+). Rather, we suggest t h a t t h e appearance o f t h i s phase i s a molecu l a r e f f e c t , r e p r e s e n t i n g the mijiimization o f t h e c o v a l e n t b i n d i n g energy o f t h e complex anion w i t h r e s p e c t t o t h e band occupation Z. Such an e f f e c t can o n l y occur, o f course, i n an unusual c r y s t a l
24.
BLOCH
AND
Krogmann
WEiSMAN
Salts
369
s t r u c t u r e i n which t h e o x i d a t i o n s t a t e o f the canplex i s continuously adjustable. Once Ζ i s f i x e d i n t h i s manner, the i n t e r m e t a l l i c spacing R i s c l o s e l y c o n t r o l l e d by the band energy U as suggested by Krogmann (1) and d e p i c t e d i n F i g u r e 1. I n c o n t r a s t , R i n the P t 2+ parent compounds i s determined by the Madelung energy and hence v a r i e s w i d e l y frcm ccmpound t o compound. Thus we answer questions (a) and (b) posed i n the I n t r o d u c t i o n . In response t o ( c ) , we suppose t h a t o n l y i n the o x a l o - and cyancrp l a t i n a t e complexes i s the balance between σ-bonding and π-"backbonding" such t h a t t h e 5 a i g ( d z ) o r b i t a l l i e s h i g h enough i n energy t o form a band which can be o x i d i z e d t o Z=1.7. F o r example, t h i s band must not i n t e r s e c t any o f the f l a t bands d e r i v e d frcm the o t h e r h i g h - l y i n g occupied o r b i t a l s (23) above the Z=1.7 Fermi l e v e l . I f these c o n c l u s i o n s a r e c o r r e c t , i t appears l i k e l y t h a t t h e p a r t i a l l y o x i d i z e d Krogmann s a l t s a r e c h e m i c a l l y unique systems i n which, by a c c i d e n t , a s e t o f r a t h e r e x a c t i n g e n e r g e t i c and s t r u c t u r a l c r i t e r i a a r e simultaneously s a t i s f i e d . I f t h i s i s so, then the s y n t h e t i c search f o r analogs i s l i k e l y t o be f r u s t r a t i n g . F i n a l l y , we remark t h a t these c o n s i d e r a t i o n s probably do not apply t o most o f the o r g a n i c TCNQ s a l t s (12,27,36), whose s t r u c t u r a l and p h y s i c a l p r o p e r t i e s a r e i n some r e s p e c t s s i m i l a r t o those o f the Krogmann s a l t s . Here packing c o n s i d e r a t i o n s seem t o p r e c l u d e any adjustment o f the c o u n t e r i o n p o p u l a t i o n so as t o minimize U , and the s m a l l v a l u e o f W s e v e r e l y l i m i t s the i n f l u e n c e o f ϋρ. A p a r t i a l exception i s the newly developed c l a s s o f o r g a n i c semimetals such as TTF-TCNQ (36), i n which t h e conduction e l e c t r o n s a r e d i s t r i b u t e d between two d i f f e r e n t s p e c i e s o f conducting c h a i n s . I n these, the b e s t o r g a n i c conductors known, t h e r e i s r e a l promise o f a d j u s t i n g Z, and hence the e l e c t r i c a l p r o p e r t i e s , through chemical c o n t r o l o f U (36). B
2
c
c
Literature Cited 1. Krogmann, Κ., Angew. Chem. I n t e r n a t . Ed., (1969), 8, 35, and references therein. 2. Evstaf'eva, Ο. Ν., Russ. Jour. Inorg. Chem., (1966), 11, 711. 3. Rousseau, D. L., B u t l e r , Μ. Α., Guggenheim, H. J . , Weisman, R. B. and Bloch, Α. Ν., Phys. Rev. B, 10 ( i n p r e s s ) . 4. B u t l e r , Μ. Α., Wertheim, Κ., Rousseau, D. L., and Hüfner, S., Chem. Phys. L e t t . , (1972), 13, 473. 5. Z e l l e r , H. R., Adv. S o l . S t . Phys. X I I I , (1973), and r e f e r e n c e s therein. 6. Minot, M. J . and P e r l s t e i n , J. H., Phys. Rev. L e t t . , (1971), 26, 371. 7. Bernasconi, J . , Brüesch, P., Kuse, D., and Z e l l e r , H. R., Brown-Boveri Res. Report KLR-73-05 (Brown-Boveri Res. Center, Baden, S w i t z e r l a n d , 1973). 8. B l o c h , Α. Ν., Weisman, R. B., and Varma, C. M., Phys. Rev. L e t t . , (1972), 28, 753.
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INTERACTIONS
BETWEEN
METAL
IONS
9. Lee, P. Α., R i c e , T. M., and Anderson, P. W., Phys. Rev. L e t t . , (1973), 31, 462. 10. Z e l l e r , H. R., this volume, and r e f e r e n c e s t h e r e i n . 11. P e i e r l s , R. Ε . , "Quantum Theory o f Solids", pp. 108 ff, Clarendon P r e s s , Oxford, 1955. 12. B l o c h , Α . Ν., in Masuda, K. and Silver, Μ., ed., "Energy and Charge T r a n s f e r in Organic Semiconductors", p . 159, Plenum P r e s s , New York, 1974, and r e f e r e n c e s t h e r e i n . 13. Z e l l e r , H. R., p r i v a t e communication. 14. Sen, P. and Varma, C. Μ., Bull. Am. Phys. Soc., (1974), 19, 49. 15. B l o c h , A. N. and Varma, C. M., J. P h y s i c s C., (1973), 6, 1849. 16. Weisman, R. B., unpublished work. 17. See,forexample, Heine, V. and Weaire, D., Sol. S t . Phys., (1970) 24, 250. 18. See,forexample, R i c e , M. J. and S t r a s s l e r , S., S o l . St. Comm., (1973), 13, 697. 19. See,forexample, Friedel, J. in Ziman, J. M., ed., "The P h y s i c s o f Metals I : Electrons", pp. 340 ff, Cambridge U n i v e r s i t y P r e s s , Cambridge, 1969. 20. See,forexample, E y r i n g , H., Walter, J., K i m b a l l , G. E . , "Quantum Chemistry", pp. 162-3, Wiley, New York, 1944. 21. Lee, P. Α., R i c e , T. M., and Anderson, P. W., S o l . S t . Comm., (1974), 14, 703. 22. Piepho, S. Β., Schatz, P. Ν., and McCaffery, A. J., J. Am. Chem. Soc., (1969), 91, 5994. 23. I n t e r r a n t e , L. V. and Messmer, R. P., this volume. 24. W i l l i a m s , P. F., B u t l e r , Μ . Α., Rousseau, D. L., and B l o c h , A. N., Phys. Rev. B, (1974), 10, 1109. 25. W i l l i a m s , P. F. and B l o c h , A. N., Phys. Rev. B, (1974), 10, 1097. 26. McKenzie, J. W., Wu, C., and Bube, R. Η., A p p l . Phys. L e t t . , (1972), 21, 1. 27. Schegolev, I . F., P h y s i c a S t a t . Solidi, (1972), A12, 9, and references therein. 28. Minot, M. J., (Ph.D. T h e s i s , The Johns Hopkins University, 1973). The experiments o f References 26 and 28 show t h a t t h e s m a l l n e g a t i v e thermopower r e p o r t e d by Kuse and Z e l l e r [ S o l . S t . Comm., (1972), 11, 355] is probably t h e result o f u s i n g partially dehy drated c r y s t a l s . 29. Wagner, H., G e s e r i c h , H. P., B a l t z , R. V., and Krogmann, Κ., S o l . S t . Comm., (1973), 13, 659. 30. See,forexample, Daudel, R., LeFebvre, R., and Moser, C., "Quantum Chemistry: Methods and Applications", pp. 67 ff, I n t e r s c i e n c e , New York, 1959. 31. Gradshteyn, I . and R y z h i k , I . Μ., "Tables o f I n t e g r a l s , S e r i e s , and Products", p. 148, Academic P r e s s , New York, 1965. 32. See,forexample, Ballhausen, C. J, "Ligand Field Theory", McGraw-Hill, New York, 1962. 33. Gomm, P. S. and Underhill, Α. Ε . , Chem. Comm., 1971, 511; J . Chem. (Dalton), 1972, 34. 34. Würfel, P., Hausen, H. D., Krogmann, Κ., and Stampfl, R.,
24.
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AND
WEISMAN
Krogmann
Salts
371
Phys. S t a t . S o l . , A10, (1972), 537. 35. Lecrone, F. and P e r l s t e i n , Chem. Comm., 1972, 75. 36. Bloch, Α. Ν., Cowan, D. O., and Poehler, T. O., in Masuda, K. and S i l v e r , Μ., Ed., "Energy and Charge T r a n s f e r i n Organic Semi conductors", p. 167, Plenum P r e s s , New York, 1974, and r e f e r e n c e s therein. Acknowledgments We a r e g r a t e f u l t o the M v a n c e d Research P r o j e c t s Agency o f the Department o f Defense and t o the N a t i o n a l Science Foundation f o r p a r t i a l support o f t h i s r e s e a r c h .
