ELECTRONIC STRUCTURE AND ELECTRIC FIELD GRADIENT TENSOR IN POTASSIUM FERRICYANIDE

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ELECTRONIC STRUCTURE AND ELECTRIC FIELD GRADIENT TENSOR IN POTASSIUM

FERRICYANIDE

R. Reschke, A. Trautwein, F. Harris, S. Date

To cite this version:

R. Reschke, A. Trautwein, F. Harris, S. Date. ELECTRONIC STRUCTURE AND ELECTRIC FIELD GRADIENT TENSOR IN POTASSIUM FERRICYANIDE. Journal de Physique Colloques, 1979, 40 (C2), pp.C2-280-C2-282. �10.1051/jphyscol:1979299�. �jpa-00218690�

JOURNAL DE PHYSIQUE Colloque C2, supplément au n° 3, Tome 40, mars 1979, page C2-280

ELECTRONIC STRUCTURE AND ELECTRIC FIELD GRADIENT TENSOR IN POTASSIUM FERRICYANIDE

R. Reschke , A. Trautwein , F.E. Harris and S.K. Date

Angewandte Physik, Universitat des Saarlandes, 6600 Saarbriieken, W-Germany Department of Physios, University of Utah, Salt Lake City, Utah 84112, U.S.A.

Tata Institute of Fundamental Research, Bombay 400005, India

Résumé.- Des techniques de calcul LCAO-MO et de tenseur d'intensité ont été utilisées ont été utili- sées pour étudier la structure électronique et le gradient de champ électrique dans le ferrocyanure de potassium. On trouve qu'il est nécessaire d'inclure les effets dus à l'existence de deux sites de fer non équivalents et des effets de polytypisme pour rendre compte des effets expérimentaux.

Abstract.- LCAO-MO and intensity tensor techniques have been employed to study the electronic struc- ture and electric field gradient tensor in potassium ferricyanide. It is found necessary to include the effects of non-equivalence of the two iron sites and polytypism for the agreement with the expe- rimental results.

1. Introduction.- The structural, electronic and ma- gnetic behaviour of potassium ferricyanide, K Fe(CN) has been the subject of rather intensive experimen-

tal and theoretical investigations, due to the fact that the ferricyanide complex is considered as a typical example for covalent bonding and strong in- teraction between the ferric ion and the ligand field. From X-ray structural investigations /1,2/, the unit cell of K3Fe(CN)6 has been described as monoclinic, orthorhombic or pseudoorthorhombic. This

controversy concerning the crystal structure arises from the occurance of polytypism due to the diffe- rent stacking periodicities of the basic monoclinic cell. However, each unit cell contains two crystal- lographically different iron sites, Fe and Fe , both surrounded by a distorted octahedron of six CN~

groups. The electronic structure for the ferricyanide complex has been also studied extensively using the ligand field theory formalism /3,5/, taking into account its low symmetry components, and spin-orbit coupling. However, these components are considered not to be affected by polytypism. The nuclear qua- drupole interaction, magnetic susceptibility and their temperature dependence has been calculated with various models. These calculations with a tempe- rature invarient ligand field do not explain the experimental results obtained from Mossbauer and magnetic susceptibility measurements with powder samples in the temperature range 4.2 - 300 K.

Single crystal Mossbauer measurements in the parama- gnetic region have also been carried out. The depen- dence of the area ratio of the two quadrupole part- ners on the direction of the Y-rays relative to the crystal structure has been studied accurately /4/

but without taking into account the non-equivalence of the two iron sites and polytypism. These results are inconsistent with the expectation from the crys- tal structure that the principal axes of the EFG tensor at the two F e3 + sites lie in the directions of elongation of the cyanide octahedra.

In view of the uncertainties about the struc- tural, electronic and magnetic properties of K3Fe(CN)6, we have looked again at the ferricyanide

complex in two ways; (i) the experimental single crystal Mossbauer results are analysed using Zimmer- mann's intensity tensor method /6/, and (ii) molecu-

lar orbital calculations are performed based on K8Fe(CN)5 + clusters using Fe (3d, 4s, 4p) C and N (2s, 2p) and K (4s) atomic orbitals. In both cases, the non-equivalence of the two iron sites and the polytypism in potassium ferricyanide are considered.

2. Re-analysis of single crystal Mossbauer data.- Recently, Zimmermann Id/ has proposed a method to evaluate an EFG tensor from the intensity analysis.

It is based on the fact that main components of EFG tensor can be directly represented by an intensity tensor, I . Its principal components have following three properties :

(i) The asymmetry parameter of the EFG is given by ri - (I -I )/I .

XX yy zz

(ii) The maximum absolute value of I , i.e. I , pp zz has the same sign as V

zz

(iii) The test factor "IA"» defined in the same way Supported by Deutsche Forschungsgemeinschaft.

++

Supported by National Science Foundation.

+++

Supported by Alexander v. Humboldt Stiftung.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979299

a s t h e s q u a r e of t h e quadrupole s p l i t t i n g , i s cons- I t may be r e c a l l e d t h a t from t h e a n a l y s i s of t a n r and u n i t y , i . e . I A = 16 1: (1+3n2) = 1. e a r l i e r ESR experiments a covalency f a c t o r of 0.875 These p r o p e r t i e s show t h a t t h e t r a c e l e s s i n t e n s i t y has been found a s one of t h e s o l u t i o n s i n f i t t i n g t e n s o r and t h e EFG t e n s o r a r e p r o p o r t i o n a l . Our r e - t h e d a t a . A l i m i t e d c o n f i g u r a t i o n i n t e r a c t i o n (CI) a n a l y s i s of t h e a v a i l a b l e d a t a on i n t e n s i t y r a t i o s

from t h e s i n g l e c r y s t a l measurements (modified t o zero-absorber t h i c k n e s s ) c l e a r l y show t h r e e i n t e r e s - t i n g r e s u l t s ; ( i ) i t i s p o s s i b l e t o t a k e i n t o ac- counts t h e e f f e c t s of two non-equivalent i r o n s i t e s and polytypism ( i i ) t h e o r i e n t a t i o n of

v:-c

d e r i v e d by Oosterhuis and Lang / 4 / , i s one p o s s i b l e s o l u t i o n o u t of a manifold of o t h e r s o l u t i o n s , and ( i i i ) t h e o r i e n t a t i o n of V components of t h e lo-

z z

c a l EFG t e n s o r s i s p e r p e n d i c u l a r t o t h e q u a s i t e t r a - gonal a x i s . It must be p o i n t e d o u t t h a t i t i s i n c o n t r a s t t o what u s u a l l y i s found i n i o n i c compounds, namely t h a t t h e d i r e c t i o n of t h e V component i s

Z Z

p a r a l l e l t o t h e a x i s along which t h e l a r g e s t d i s t o r - t i o n i s observed.

3. Semi-empirical LCAO-MO c a l c u l a t i o n s . - We have performed semi-empirical molecular o r b i t a l c a l c u l a - t i o n s / 7 / f o r each of t h e two i r o n s i t e s i n t h e f e r - r i c y a n i d e complex, based on K8Fe(CN)'+ c l u s t e r s , u s i n g Fe (3d, 4 s , 4p) C and N (Zs, 2p) and K ( 4 s ) atomic o r b i t a l s . The f e r r i c y a n i d e complex i s repre- s e n t e d by d i f f e r e n t c l u s t e r geometries, known a t 95 and 300 K, f o r t h e two i r o n s i t e s . F r o m the l i n e a r combination of t h e b a s i s s e t of 65 atomic o r b i t a l s , NOS a r e c o n s t r u c t e d , which a r e occupied by 65 e l e c -

t r o n s w i t h a t o t a l s p i n =

.

a r e h i g h e s t i n energy ( @ 3 1 , @ 3 2 , c $ ~ ~ ; see i n F i g . l a ) a r e of mainly i r o n c h a r a c t e r w i t h a covalency f a c t o r of about 0.8.

c a l c u l a t i o n i s t h e n performed on t h r e e configurations Y , , Y , and Y 3 ( a s d e f i n e d i n Fig. l a ) r e s u l t i n g i n t h r e e C I s t a t e s Y:', _and Y$', which remained n e a r l y pure, b u t t h e i r energy sequence i s i n t e r c h a n -

ged :

q1

i n t o account s p i n - o r b i t coupling among t h e s e t h r e e C I s t a t e s by a f i r s t - o r d e r p e r t u r b a t i o n t r e a t m e n t , r e s u l t i n g i n a energy l e v e l diagram shown i n f i g u r e I ( b ) . I n o r d e r t o c a l c u l a t e t h e temperature depen- dence of quadrupole i n t e r a c t i o n , we temperature ave- rage t h e EFG t e n s o r s f o r t h e two i r o n s i t e s a c c o r d i n g t o Boltzmann s t a t i s t i c s . This i s a p p l i c a b l e i n t h e c a s e of K3Fe(CN)G, s i n c e we a r e i n t h e f a s t r e l a x a t i o n l i m i t due t o s t r o n g s p i n - l a t t i c e i n t e r a c - t i o n . From a d e t a i l e d a n a l y s i s , we f i n d f o r t h e two i r o n s i t e s t h a t t h e i r e n e r g i e s A1 and A, and t h e i r c a l c u l a t e d G s s b a u e r parameters, V,,, 17 and AE a r e

Q

s l i g h t l y d i f f e r e n t . The o r i e n t a t i o n of V Z z (Fe,) and V Z z (Fe,) w i t h r e s p e c t t o t h e a ' b c axes system d w i a -

t e t o some e x t e n t compared t o t h e o r i e n t a t i o n o b t a i - ned from t h e i n t e n s i t y t e n s o r a n a l y s i s .

F i g u r e 2 ( a ) shows t h e temperature dependence of AEQ c a l c u l a t e d on t h e b a s i s of t h e s t r u c t u r a l d a t a o b t a i n e d a t 95 K and 300 K. From t h e c u r v e s , i t i s obvious t h a t t h e experimental AE (T) v a l u e s

Q

i n t h e temperature range T < 130 K can only be f i t t e d w i t h temperature dependent s t r u c t u r a l d a t a i . e . w i t h temperature dependent l i g a n d f i e l d parameters A , and A,. F i g u r e 2(b) shows t h e temperature dependence of A, and A 2 n e c e s s a r y f o r f i t t i n g t h e experimental AE (T) v a r i a t i o n . These r e s u l t s a r e i n q u a l i t a t i v e

Q

agreement w i t h t h e temperature dependent l i g a n d f i e l d model used i n a e a r l i e r s t u d y 181.

4. Conclusions.

-

- - -

doubly occup~ed MO's

9,

Fig. l a : LCAO MOs 4. ( i = 31, 32, 33) i n K,Fe(CN), c a l c u l a t e d w i t h t h e c l u s t e r geometry o b t a i n e d a t 95 K. The c o o r d i n i t e system used i n t h e YO c a l c u l a t i o n s i s t h e f o l l o w i n g :

z i s p a r a l l e l t o t h e a x i s which connects t h e two CN- groups having maximum Fe-C d i s t a n c e and y i s p a r a l l e l c-axis.

C2-282 JOURNAL DE PHYSIQUE LCAO-MO method have e s t a b l i s h e d t h e e l e c t r o n i c

s t r u c t u r e o f t h e f e r r i c y a n i d e complex, which i s i n r e a s o n a b l y good agreement w i t h t h e p u b l i s h e d work.

Fig. Ib : Many e l e c t r o n CI s t a t e s 'if1 ( i = 1 , 2 , 3 ) t o g e t h e r w i t h t h e i r e n e r g y s e p a r a t i o n s A, and A 2 i n K,Fe(CN),.

F u r t h e r d e t a i l s of o u r s t u d y , i n c l u d i n g t h e compu- t a t i o n of e l e c t r o n d e n s i t y a t t h e i r o n n u c l e u s , ma- g n e t i c s u s c e p t i b i l i t y and gyromagnetic t e n s o r s and t h e i r comparison w i t h e x p e r i m e n t a l r e s u l t s w i l l be p u b l i s h e d e l s e w h e r e .

F i g . 2 : a) Temperature dependence o f q u a d r u p o l e s p l i t t i n g , AE (T), o f K,Fe(CN), which i s a 1: 1 a v e r a g e from Q e l and Fe, s i t e s . Curve a i s c a l c u l a t e d w i t h t h e 300 K c l u s t e r geometry; c u r v e b c o r r e s p o n d s

t o t h e 95 K c l u s t e r geometry, however, assuming tem- p e r a t u r e dependent e n e r g y s e p a r a t i o n s AI and A2 a s

shown i n f i g u r e 2b.

b) Temperature dependence o f e n e r g y s e p a r a - t i o n s A, and A, o f K,Fe(CN), f o r Fe, and Fe, s i t e . Curves 2 and 3 c o r r e s p o n d t o A l and A, of Fe,;

c u r v e s I and 3 c o r r e s p o n d t o F e z .

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