Halides Containing Multicentred Metal-Metal Bonds D.

D . L . K E P E R T

University of Western Australia, Nedlands, Western Australia

a n d K . V R I E Z E

Koninklijke Shell-Lahoratorium, Amsterdam (Shell Research N.V.), The Netherlands 1. Introduction . . . . . . . . . . . . . . . . . . . . 1 2. F a c t o r s Influencing Metal-Metal B o n d F o r m a t i o n . . . . . . . . 4

3. Compounds B a s e d o n t h e (MeXia)^^ Core 10 A . Introduction . . . . . . . . . 10

B . Monomeric Complexes . . . . . . . . . . . . . . . . 12 C. B i n a r y H a l i d e s . . . . . . . . . . . . . . . . . . 15 D . Magnetism, Spectra a n d B o n d i n g . , . . . . . . . . . . 16 4. Compounds B a s e d o n t h e (MeX8)*+ Core . . . . . . . . . . . . 26 A . Introduction . . . . . . . 26 B . Monomeric Complexes . . . . . . . . . . . . . 28

C. B i n a r y H a l i d e s 31 D . Spectra, Magnetism a n d B o n d i n g . . . . . . . . . . . . 32

5. Compounds B a s e d o n t h e (Re3X3)e+ Core . . . . . . . . . . 3 4 A. I n t r o d u c t i o n . . . . . . . . . . . . . . . . . . 34 B . Monomeric Complexes . . . . . . . . . . . . . . . . 36

C. B i n a r y HaHdes 39 D . Spectra, Magnetism a n d B o n d i n g . . . . . . . . . . . . 40

6. Other Compounds Containing Multi-centred M e t a l - M e t a l B o n d i n g . . . . 4 4 A . Introduction . . . . . . . . . . . . . . . . . . 44 B . H a l o g e n Bridges . . . . . . . . . . . . . . . . 45

C. O x y g e n Bridges 47 D . N o Bridging A t o m s . . . . . . . . . . . . . . . . 51

References . . . . . . . . . . . . . . . . . . . . 51

1 . Introduction

T h e lower halides of n i o b i u m , t a n t a l u m , m o l y b d e n u m , t u n g s t e n a n d r h e n i u m are b a s e d on cores containing clusters of m e t a l a t o m s t i g h t l y b o n d e d together, a n d t h e y exhibit a n u m b e r of p r o n o u n c e d chemical similarities. T h e c h e m i s t r y of t h e s e a n d closely r e l a t e d c o m p o u n d s will be discussed in t h i s review.

These lower halides are fairly readily p r o d u c e d b y r e d u c t i o n or 1

F I G . 1. T h e (MeXia)^"*" core. T h e m e t a l a t o m s in t h e octahedral cluster are s h o w n a s s h a d e d circles,while t h e bridging halogen a t o m s a b o v e t h e octahedral edges are u n s h a d e d .

F I G . 2. T h e (MeXg)*^ core. T h e m e t a l a t o m s in t h e octahedral cluster are s h o w n a s shaded circles, while t h e bridging halogen a t o m s a b o v e t h e octahedral faces are u n s h a d e d .

t h e r m a l disproportionation of t h e higher halides, a n d it h a s been k n o w n for a long t i m e t h a t t h e y are soluble in a q u e o u s acids from which well defined crystalline acids, a n d o t h e r derivatives, can be o b t a i n e d . H o w e v e r , t h e y are oxidized in alkaline solutions w i t h t h e evolution of h y d r o g e n . T h e n a t u r e of t h e s e c o m p o u n d s a w a i t e d t h e d e t e r m i n a t i o n of t h e s t r u c t u r e s of some of t h e derivatives of these acids, a n d t h e e v e n m o r e recent s t r u c t u r a l d e t e r m i n a t i o n s carried o u t on t h e halides t h e m ­ selves. All c o m p o u n d s were found t o be b a s e d on central cores com­

prising a central cluster of m e t a l a t o m s , w i t h bridging halogen a t o m s . T h e n i o b i u m a n d t a n t a l u m c o m p o u n d s are based on cores of t h e t y p e (McXig)^"^, consisting of a n o c t a h e d r a l cluster of m e t a l a t o m s w i t h a halogen a t o m a b o v e each o c t a h e d r a l edge (Fig. 1). T h e m o l y b d e n u m

F I G . 3. T h e (Re3X3)6+ core. T h e m e t a l a t o m s in t h e triangular cluster are s h o w n as s h a d e d circles, while t h e bridging halogen a t o m s in t h e plane are u n s h a d e d .

suggesting s t r o n g m e t a l - m e t a l b o n d i n g . T h e bridging halogen a t o m s of t h e core are relatively non-labile. Useful trivial n a m e s for t h e s e cores are, for e x a m p l e , c h l o r o m o l y b d e n u m i n s t e a d of t h e m o r e s y s t e m a t i c octa-/x3-chlorohexamolybdenum(II) for t h e (MoeCls)^^ core, a n d chloro- n i o b i u m - i n s t e a d of dodeca-/x2-chlorohexaniobium (2-33) for t h e

(NbeCli2)^+ core.

T h e individual m e t a l a t o m s of t h e cluster can readily a d d a d d i t i o n a l d o n o r g r o u p s , including halide ions, forming, for e x a m p l e , t h e anionic complexes [(Nb6Cli2)Cl6]4-, [(Mo6Cl8)Cl6]2- a n d [(Re3Cl3)C]9]3-. T h e s y s t e m a t i c n a m e s for t h e salts would b e , for e x a m p l e , p o t a s s i u m h e x a - chloro-octa-jLt3-chlorohexamolybdate(II). A wide v a r i e t y of o t h e r ligands can o c c u p y t h e s e positions resulting in a fairly complex c h e m i s t r y . F o r e x a m p l e , reaction w i t h n e u t r a l u n i d e n t a t e ligands in suitable solvents p r e c i p i t a t e t h e non-electrolytes [(Nb6Cli2)Cl2(ligand)4], [(Mo6Cl8)Cl4(ligand)2] a n d [(Re3Cl3)Cl6(ligand)3] respectively. I n t h i s review, t h e central core containing t h e m e t a l a t o m s a n d t h e non-labile bridging halogen a t o m s will be s u r r o u n d e d b y p a r e n t h e s e s , a n d t h e o u t e r ligands b y s q u a r e b r a c k e t s as h a s been used a b o v e . I n t h e case of t h e o c t a h e d r a l m e t a l clusters, t h e o u t e r ligands are directed a w a y from t h e c e n t r e of t h e o c t a h e d r o n , a n d m a y for convenience b e called ''centrifugal" ligands. I n t h e case of (Re3Cl3)^+, each r h e n i u m a t o m can further coordinate t h r e e ligands, a n d only t h e one in t h e p l a n e of t h e r h e n i u m a t o m s will b e t e r m e d t h e centrifugal ligand. This distinction b e t w e e n halogen a t o m s inside a n d outside t h e core is preferred t o

" b r i d g i n g " a n d ' ' n o n b r i d g i n g " , as t h e b i n a r y halides a r e polymeric w i t h bridging centrifugal halogen a t o m s . T h e s y s t e m a t i c n a m i n g of t h e b i n a r y halides is m o r e difficult, a n d will n o t b e a t t e m p t e d .

a n d t u n g s t e n c o m p o u n d s a r e also b a s e d on o c t a h e d r a l clusters of m e t a l a t o m s , b u t in t h i s case t h e bridging halogen a t o m s lie a b o v e e a c h octa­

h e d r a l face, a n d t h e formula m a y b e w r i t t e n ( M 6 X 8 ) ^ + (Fig. 2). T h e r h e n i u m c o m p o u n d s h a v e (RegXg)^^ cores, consisting of a t r i a n g u l a r cluster of r h e n i u m a t o m s w i t h a halogen a t o m outside e a c h edge (Fig. 3). T h e m e t a l - m e t a l distances are shorter t h a n in t h e m e t a l s .

The preparation of compounds of these metals in the same oxidation states but from sources other than the halides (which in turn are pre­

pared at elevated temperatures) do not contain clusters of metal atoms, although they m a y contain metal-metal bonds. F o r example, reduction of p e r r h e n a t e in t h e presence of neutral ligands leads to ReClg.S E t g P h P , ReCl3(Et2PhP) (PhgP CH2 CH2 PPhg), [ReCl2(Ph2P CHg CH2 PPh2)2]Cl (Chatt and Rowe, 1962) and [ReX2(o-CeH4(AsMe2)2)2]X where X is CI, Br or I (Curtis et al,, 1958). However, under other conditions the anions Re2Cl8^~ and Re2Br8^" can be obtained as salts with a variety of inorganic and organic cations (Cotton et al., 1965).

The structure shows extremely short rhenium-rhenium distances of 2-24 Â (Cotton and Harris, 1965), which are even shorter than in the (RcgCla)^"^ complexes discussed in this review, and is thought to involve the first quadruple bond between a n y two atoms (Cotton, 1965).

Related compounds containing the Tc2Cl8^~ anion have also been iso­

lated (Eakins et al, 1963) (Cotton and B r a t t o n , 1965), Similarly the formally (i^-Mo(0Ac)2 prepared from molybdenum hexacarbonyl con­

tains two molybdenum atoms only 2-11 Â apart, with four bridging b i d e n t a t e acetate groups (Stephenson et al., 1964; L a w t o n and Mason, 1965). However, a large number of compounds of Mo(II) w i t h o u t m e t a l - metal bonds can be obtained from t h e carbonyl or by reduction of aque­

ous solutions of M o ( I I I ) , for example [MoBr2(CO)3(o-C6H4(AsMe2)2)]

and [MoBr2(o-C6H4(AsMe2)2)2] respectively (Nigam et al., 1960; Lewis et al, 1962, 1963).

2. Factors Influencing Metal-Metal Bond Formation

A number of compounds will be quoted in this section as having metal-metal bonds, but without quoting the original literature refer­

ences. F o r full details of those metal-metal bonded compounds without clusters of metal atoms, the reader is referred to a more general review of metal-metal bonds (Kepert et al, 1967).

T h e distribution of metal-metal bonding throughout the periodic system can be discussed from two points of view: from thermodynamic considerations, or from the size of the bonding orbitals and the extent of metal orbital-metal orbital overlap.

T h e thermodynamics of the systems will be considered first. A n illustrative approach is to calculate the thermodynamic stability of the hypothetical ''ionic dihalides" and "ionic trihalides" of the groups I V , V, V I and V I I transition metals through the simple Born-Haber cycle ( K e p e r t et al, 1967; Vrieze, 1964). F o r example the heat of f o r m a t i o n of the hypothetical "ionic WClg" is equal to the sum of the atomization energy and the first and second ionization potentials of tungsten, the

dissociation energy a n d twice t h e n e g a t i v e of t h e electron affinity of chlorine, a n d t h e n e g a t i v e v a l u e of t h e ionic lattice energy, assuming t h a t it would be isomorphous w i t h CrClg. T h e result shows t h a t t h e h e a t of formation would be +dS kcal mole-^ a t 298°K, t h e positive value indicating t h a t it would be u n s t a b l e w i t h respect t o t h e elements.

I n t h e case of t h e h y p o t h e t i c a l "ionic MoClg", a l t h o u g h t h e h e a t of f o r m a t i o n w o u l d b e n e g a t i v e (—7 kcal mole-^) a n d i t w o u l d b e stable w i t h respect t o t h e elements, calculations show t h a t it would be u n ­ stable t o disproportionation, each mole of "ionic MoClg" liberating 30 kcal on formation of t h e p e n t a h a l i d e a n d t h e m e t a l . T h e experi­

m e n t a l h e a t of formation of M0CI2 is —44 kcal mole-^ a n d it is stable w i t h respect t o d i s p r o p o r t i o n a t i o n .

Similar calculations show t h a t t h e h y p o t h e t i c a l " i o n i c " dihalides

"ZrCla", "HfClg", "NbCla", "TaCl^" a n d "ReClg", as well as t h e h y p o ­ thetical " i o n i c " trihalides "HfCl3", "NbCla", "TaClg", "WCI3" a n d

"ReCla" would b e u n s t a b l e w i t h respect t o t h e elements a n d / o r t o disproportionation. T h e h y p o t h e t i c a l " i o n i c " trihalides "ZrCl3",

"M0CI3" a n d "TcClg" would be e x p e c t e d t o b e t h e r m o d y n a m i c a l l y stable, b u t of course t h i s does n o t rule o u t t h e possibility of gaining e x t r a stability t h r o u g h t h e formation of m e t a l - m e t a l b o n d s .

A l t h o u g h t o o m u c h reliance should n o t be placed on t h e s e detailed figures, these B o r n - H a b e r cycle calculations do p o i n t t o t h e m o r e i m p o r t a n t energy factors, for e x a m p l e , a l t h o u g h t h e ionization p o ­ tentials a r e large, t h e y a r e u n i m p o r t a n t , as t h e y will be t h e s a m e w h e t h e r or n o t t h e halide formed h a s m e t a l - m e t a l b o n d s . T h e m a i n factor which causes these h y p o t h e t i c a l halides t o be u n s t a b l e is t h e high a t o m i z a t i o n energy of t h e second a n d t h i r d row t r a n s i t i o n m e t a l s . T h e lattice energy is of lesser i m p o r t a n c e , a l t h o u g h t h e high lattice energy of t h e fluorides suggests t h a t for c o m p o u n d s which are b a s e d on one of t h e n o r m a l fluoride s t r u c t u r e s , m e t a l - m e t a l b o n d s will n o t form because of t h e rigidity of t h e lattice, a l t h o u g h m e t a l - m e t a l b o n d s c o m m o n l y cause distortion of lattices containing m o r e polarizable anions. This a r g u m e n t does n o t of course a p p l y t o t h e m u l t i c e n t r e d m e t a l - m e t a l b o n d e d cluster n o t b a s e d on close p a c k e d anion s t r u c t u r e s which is t h e m a i n t h e m e of this review, as shown b y NbFg.s which h a s o c t a h e d r a l clusters of niobium a t o m s .

Since these calculations show t h a t t h e a t o m i z a t i o n energy is t h e m o s t i m p o r t a n t factor in t h e destabilization of t h e " i o n i c " halides m e n t i o n e d a b o v e , a n d since t h e s e halides h a v e all b e e n found t o c o n t a i n m e t a l - m e t a l b o n d s , it is worthwhile t o look i n t o t h i s q u a n t i t y , t h e a t o m i z a t i o n energy, in m o r e detail.

A n interesting theoretical a p p r o a c h t o t h e cohesive energies of

t r a n s i t i o n m e t a l s h a s been given b y Griffith (1956). T h e a s s u m p t i o n s in his t h e o r y are t h a t t h e valence electrons in t h e gaseous a t o m s a r e coupled as far as possible w i t h parallel ones, while in t h e m e t a l t h e electrons are coupled as far as possible antiparallel t o electrons from o t h e r m e t a l a t o m s . T h e essential features of his t h e o r y are t h a t in order t o form a m e t a l in which all t h e electrons are coupled antiparallel, it is necessary t o b r e a k d o w n t h e parallel i n t r a - a t o m i c spin couplings.

Neglecting a small crystal field contribution, Griffith derives a formula s t a t i n g t h a t t h e a t o m i z a t i o n energy ΔΗ is t h e s u m of t w o c o m p o n e n t s :

-ΔΗ = p + Ρ

I n t h i s formula Ρ is positive a n d r e p r e s e n t s t h e energy required t o bring t h e a t o m s i n t o a n o n - s t a t i o n a r y s t a t e M, in w h i c h t h e i n t r a - a t o m i c spin couplings are uncoupled. This q u a n t i t y could be calculated for t h e first t r a n s i t i o n m e t a l series. T h e q u a n t i t y p, which is n e g a t i v e , is t h e h e a t of formation of t h e m e t a l from t h e m e t a l a t o m s in s t a t e M.

ρ w a s calculated as t h e s u m oi ΔΗ a n d Ρ a n d varies s m o o t h l y along t h e first t r a n s i t i o n m e t a l series w i t h m a x i m a a t v a n a d i u m a n d m a n g a n e s e a n d w i t h a small d i p a t c h r o m i u m . T h e q u a n t i t y ρ per u n p a i r e d valence electron varies b e t w e e n 30 a n d 40 kcal a n d is a m o r e funda­

m e n t a l q u a n t i t y t h a n t h e a t o m i z a t i o n energy per valence electron.

T h e q u a n t i t y Ρ was n o t calculated for t h e second a n d t h i r d t r a n s i t i o n m e t a l series, b u t it a p p e a r s t o decrease on m o v i n g d o w n t h e columns of t h e periodic s y s t e m , t h a t is, t h e i n t r a - a t o m i c spin couplings are b r o k e n m o r e easily. This decrease is i n d i c a t e d b y t h e absence of residual u n ­ p a i r e d spins in t h e second a n d t h i r d row t r a n s i t i o n m e t a l s , a n d in t h e m u c h g r e a t e r t e n d e n c y of their c o m p o u n d s t o form m e t a l - m e t a l b o n d s , b o t h in t h e lower a n d in t h e higher oxidation s t a t e s .

C h r o m i u m a n d m a n g a n e s e are therefore r a t h e r averse t o forming m e t a l - m e t a l b o n d s , n o t because of t h e r a t h e r low a t o m i z a t i o n energy, b u t because t h e factor Ρ is v e r y large for t h e s e elements.

A l t h o u g h t h e a b o v e a r g u m e n t is a v e r y q u a l i t a t i v e one a n d neglects factors such as spin-orbit coupling which becomes m o r e i m p o r t a n t in t h e heavier elements, a n d also t h e influence of ligands a n d anion packing, it affords some insight i n t o t h e f u n d a m e n t a l difference in b e h a v i o u r b e t w e e n t h e c o m p o u n d s of t h e first r o w t r a n s i t i o n m e t a l series on t h e one h a n d a n d t h e c o m p o u n d s of t h e second a n d t h i r d row t r a n s i t i o n m e t a l series o n t h e o t h e r h a n d .

Some a t t e m p t s h a v e been m a d e t o e s t i m a t e t h e m e t a l - m e t a l b o n d energies in c o m p o u n d s . Schafer a n d Schnering (1964), for e x a m p l e , h a v e t a k e n t h e a t o m i z a t i o n energy, which is a less f u n d a m e n t a l q u a n t i t y t h a n t h e q u a n t i t y ^ , as a m e a s u r e of t h e b o n d energy in t h e

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F I G . 4. H e a t s of formation ΔΗ of v a n a d i u m , n i o b i u m a n d t a n t a l u m chlorides a n d oxides as a function of stoichiometry.

metallic s t a t e . T h e y considered t h a t t o form chlorides containing m u l t i - centred clusters of m e t a l a t o m s , t h e m e t a l - m e t a l b o n d energy m u s t b e g r e a t e r t h a n t h e m e t a l - c h l o r i n e b o n d energy (which is a b o u t 80-90 kcal mole-^ for a n y t r a n s i t i o n m e t a l chloride), t h a t is, t h e y m u s t be restricted t o t h e second a n d t h i r d rows of t h e t r a n s i t i o n m e t a l s , from zirconium t o a b o u t p a l l a d i u m a n d from hafnium t o a b o u t gold respectively.

H o w e v e r , A r i y a a n d K h e r n b u r g (1964) h a v e found t h a t t h e b o n d i n g energy per electron in t h e metallic s t a t e is c o n s t a n t for a large n u m b e r of m e t a l s . T h e y observed t h a t for a n u m b e r of m e t a l s t h e h e a t s of formation of t h e oxides are p r o p o r t i o n a l t o t h e degree of oxidation, as shown b y t h e s t r a i g h t line o b t a i n e d for t h e n i o b i u m oxides in F i g . 4. I t was concluded t h a t t h e g r a d u a l o x i d a t i o n of t h e m e t a l results in t h e g r a d u a l r e p l a c e m e n t of m e t a l - m e t a l b o n d s b y m e t a l - o x y g e n b o n d s . Similar s t r a i g h t line plots were o b t a i n e d , for e x a m p l e , w i t h t i t a n i u m a n d t u n g s t e n oxides. H o w e v e r , o t h e r m e t a l s such as v a n a d i u m show a d i s c o n t i n u i t y (Fig. 4) indicating t h a t a t a certain degree of o x i d a t i o n all t h e m e t a l - m e t a l b o n d s are b r o k e n a n d n o further energy is available

from t h i s source. T h e position of t h i s b r e a k w a s considered t o be t h e valency of t h e a t o m in t h e metallic s t a t e which w a s found t o agree w i t h e s t i m a t e s derived from t h e m a g n e t i c p r o p e r t i e s of alloys. If t h e n u m b e r of valency electrons w a s divided i n t o t h e a t o m i z a t i o n e n e r g y a c o n s t a n t figure of 30-40 kcal p e r b o n d i n g electron w a s o b t a i n e d . F o r e x a m p l e , c h r o m i u m w a s found t o h a v e t h r e e b o n d i n g electrons p e r a t o m , m o l y b ­ d e n u m t o h a v e four or five b o n d i n g electrons, a n d t u n g s t e n t o h a v e six b o n d i n g electrons.

T h e s a m e t r e n d s are shown if t h e h e a t s of f o r m a t i o n of t h e chlorides (Schafer a n d Schnering, 1964) are used i n s t e a d of t h e oxides. T h e p l o t for t h e v a n a d i u m chlorides shows a b r e a k in a b o u t t h e s a m e position a s for t h e v a n a d i u m oxides (Fig. 4). A linear p l o t is again o b t a i n e d for niobium (and t a n t a l u m ) despite t h e profound s t r u c t u r a l changes which a c c o m p a n y chlorination:

Stoichiometry Compound Structure N b - N b D i s t a n c e (A)

N b Metal B o d y centred cubic 2-86

NbCl2.33 NbeCli4 Nbg Octahedra 2-89 a n d 2-95

NbCla.67 Nb3Cl8 Nbg Triangles 9.7»

NbCl3.i3 Nb^.ssCle D e f e c t NbgClg ύ ί Ό

NbCl^ (NbCl4)oo N b - N b Pairs 2-94

NbClg Nb^Clio N o N b - N b B o n d s —

I t is concluded t h a t t h e m e t a l - m e t a l b o n d energy is insensitive t o small changes in i n t e r n u c l e a r s e p a r a t i o n .

A l t h o u g h t h e conclusions of A r i y a a n d K h e r n b u r g a b o u t t h e v a l e n c y m a y b e a b i t t o o optimistic, it can be observed from t h e s e t h e r m o d y ­ n a m i c plots t h a t t h e first row t r a n s i t i o n m e t a l s are r e l u c t a n t t o u n c o u p l e t h e i n t r a - a t o m i c spin couplings. These w o r k e r s d r e w t h e interesting conclusion t h a t t h e m e t a l - m e t a l b o n d energy p e r electron seems t o b e a b o u t t h e s a m e for t h e m e t a l a t o m s of t h e s y s t e m s i n v e s t i g a t e d , t h a t is, t h e s a m e for all t h r e e t r a n s i t i o n m e t a l rows. I t would therefore seem worthwhile t o calculate t h e ρ v a l u e s for t h e second a n d t h i r d r o w t r a n ­ sition m e t a l s , where possible, in order t o see if t h e y would b e t h e s a m e as t h e respective jp values of t h e first t r a n s i t i o n m e t a l s in t h e s a m e column.

H a v i n g n o w discussed t h e t h e r m o d y n a m i c s which h a v e given us a r o u g h idea of t h e essential energy factors which are favourable for m e t a l - m e t a l b o n d formation, i t is enlightening t o discuss t h i s subject from t h e a t o m i c p o i n t of view.

Several a u t h o r s h a v e tried t o use semi-empirical e q u a t i o n s r e g a r d i n g t h e size of orbitals involved in t h e m e t a l - m e t a l b o n d i n g . F o r e x a m p l e ,

Sheldon (1964b) calculates t h e r a d i u s of t h e b o n d i n g electron b y using Slater's rules, a n d finds t h a t m e t a l - m e t a l b o n d i n g occurs if t h e m e t a l - m e t a l d i s t a n c e is less t h a n 0-4 Â g r e a t e r t h a n twice t h e o r b i t a l r a d i u s . G o o d e n o u g h (1963) also uses a semi-empirical a p p r o a c h a n d found t h a t t h e critical d i s t a n c e b e y o n d which m e t a l - m e t a l b o n d i n g c a n n o t occur for a first r o w t r a n s i t i o n m e t a l is given b y :

R,{U) - [3-05 - 0·03(Ζ - Ζτι)] Â

w h e r e a n d Ζ a r e t h e a t o m i c n u m b e r s of t i t a n i u m a n d t h e o t h e r 3d-element in question, respectively. ( I t is a s s u m e d in t h i s expression t h a t t h e electrons d o n o t b e c o m e completely delocalized on m e t a l - m e t a l b o n d formation.)

Similarly,

i? e( 4 d ) - R,{U) + 0-88 Â Rci^d) - Roi^d) + 1-36 Â

T h e s e schemes h a v e a limited p r e d i c t i v e ability for c o m p o u n d s b a s e d o n close p a c k i n g of t h e non-polarizable oxide or chloride ions w h e r e t h e d i s t a n c e b e t w e e n t h e m e t a l a t o m s is p a r t l y g o v e r n e d b y a n i o n p a c k i n g , for e x a m p l e for t h e clusters t h a t occur in NbgClg a n d ZnaMogOg. H o w ­ ever, t h e a b o v e criteria h a v e n o p r e d i c t i v e ability for t h e f o r m a t i o n of clusters of m e t a l a t o m s w h e r e t h e r e is n o r e s t r a i n t o n t h e m e t a l a t o m s a p p r o a c h i n g e a c h o t h e r .

T h e factors influencing t h e size of t h e m e t a l orbitals a n d c o n s e q u e n t l y t h e m e t a l o r b i t a l - m e t a l o r b i t a l o v e r l a p are t h e effective nuclear charge on t h e m e t a l a t o m , w h i c h is d e p e n d e n t u p o n t h e o x i d a t i o n s t a t e , a n d t h e ligands b o n d e d t o t h e m e t a l a t o m . F o r e x a m p l e , a single σ electron pair m e t a l - m e t a l b o n d is f o u n d in t h e isoelectronic [Fe^^(C0)8]^~, Co§(CO)8 a n d [Ni2(CN)6]^-, w h e r e a s t h e isoelectronic Cu^^ forms n o m e t a l - m e t a l b o n d s of t h i s t y p e d u e t o its higher o x i d a t i o n s t a t e a n d smaller orbital size.

I f a n isovalent series is n o w considered, for e x a m p l e TigOg, VgOg, CrgOg, t h e progressively poorer shielding of t h e increasing n u c l e a r charge b y t h e a d d i t i o n a l cZ-electrons will r e s u l t in a c o n t r a c t i o n of t h e iZ-electron cloud. T h u s t h e first t w o m e m b e r s of t h i s series form m e t a l - m e t a l b o n d s , b u t n o t CrgOg. Similarly, TiOg c o n t a i n s infinite strings of t i t a n ­ i u m a t o m s close t o g e t h e r a n d shows metallic b o n d i n g w h e n d o p e d w i t h T i ( I I I ) . VO2 h a s V - V p a i r s which a r e easily b r o k e n b y h e a t i n g t o a b o u t 70'', while n o m e t a l - m e t a l b o n d i n g occurs in CrOg (Morin, 1959).

T h e d i s t a n c e over which m e t a l - m e t a l b o n d s can s p a n is also s t r o n g l y d e p e n d e n t u p o n t h e anion. A n increase in polarizability of t h e a n i o n s

increases t h e screening of t h e ίί-electrons from t h e nucleus, allowing t h e d-orbitals t o e x p a n d . On t h e o t h e r h a n d in close p a c k e d anion lattices, t h e larger m o r e polarizable anions force t h e cations further a p a r t . W h i c h of t h e t w o factors is m o r e i m p o r t a n t is difficult t o d e t e r m i n e . H o w e v e r , t h e y seem t o cancel each o t h e r fairly well, as is shown b y t h e fairly large r a n g e of i n t e r n u c l e a r distances over which m e t a l - m e t a l b o n d i n g can occur. F o r e x a m p l e , T i ( I I I ) - T i ( I I I ) b o n d i n g isfoundinTigOgiTi—Ti

= 2 - 5 9 Â ) , jS-TiClg (2-96 A), TiBrg (3-05 Â), Tilg (3-23 A), c o m p a r e d w i t h 2-90 A in t h e m e t a l . This feature is also found w i t h o t h e r polariz­

able anions, for e x a m p l e t h e t r i a n g u l a r clusters of iron a t o m s in F e S are 3-08 A from each other, c o m p a r e d w i t h 2-48 A in t h e m e t a l .

T h e combined effect of increasing size of orbitals, a n d m o r e impor­

t a n t l y t h e increasing n u m b e r of electrons available for m e t a l - m e t a l bonding, is shown in t h e series NbCI^, a n d MoCl^; as χ is decreased. T h u s m e t a l a t o m s occur as pairs in NbCl4, t r i a n g u l a r triplets in NbClg-e? a n d o c t a h e d r a l clusters in NbClggg. Similarly no m e t a l - m e t a l b o n d s are found in M0CI5, pairs of m o l y b d e n u m a t o m s occur in M0CI4 a n d MoClg, while o c t a h e d r a l clusters of m e t a l a t o m s occur in MoClg. T h e ability t o form m e t a l - m e t a l b o n d s , however, will reach a m a x i m u m a n d t h e n decrease as t h e n u m b e r of electrons in t h e valence shell increases. This can be seen from t h e series TaClg, ReClg, OsClg, IrClg, which h a v e 2, 4, 5 a n d 6 iZ-electrons p e r m e t a l a t o m respectively. T h e first t w o m e m b e r s contain m e t a l - m e t a l b o n d s while IrClg h a s a filled dc shell which c a n n o t be used for m e t a l - m e t a l b o n d i n g .

Finally, Cotton a n d H a a s (1964) h a v e p o i n t e d o u t t h a t t h e t y p e of m u l t i c e n t r e - b o n d e d m e t a l - m e t a l cluster will be limited if t h e species a r e n o t t o a t t a i n w h a t t h e y consider t o b e a n i m p r o b a b l y large charge.

F o r e x a m p l e , if t h e formally d^ Mo(II) a n d R e ( I I I ) in t h e cores (MogClg)^"^ a n d (RegClg)^+ were t o a d o p t each o t h e r ' s s t r u c t u r e , we would h a v e t h e h y p o t h e t i c a l cores (MogClg)'^^ a n d (RegCig)^^"^. T h e former would be unlikely t o form [(Mo3Cl3)Cl9]^~ w i t h t h e negatively charged chloride ion, while t h e charge on t h e l a t t e r was considered t o b e i m p r o b a b l y high.

3. Compounds Based on the {M^X-^^)^^ Core A. Introduction

T h e lowest halides formed b y t h e r e d u c t i o n of n i o b i u m a n d t a n t a l u m p e n t a h a l i d e s u n d e r fairly vigorous conditions a r e :

NbFa-s NbCl2.33 NbBrg Nbia?

— TaClg.s TaBr^.s Tal2.33

T h e formulation a n d s t r u c t u r e of t h e s e halides h a v e only r e c e n t l y been d e t e r m i n e d (Schafer a n d Schnering, 1964), a l t h o u g h t h e i r reactions h a v e b e e n s t u d i e d for some t i m e . F o r a n u n d e r s t a n d i n g of t h e n a t u r e of these c o m p o u n d s , a n d for historical reasons, it is c o n v e n i e n t t o discuss t h e n a t u r e of t h e d e r i v a t i v e s before dealing w i t h t h e halides t h e m s e l v e s . F o r t h e p r e p a r a t i o n of t h e d e r i v a t i v e s it is n o t necessary t o isolate t h e p u r e halides t h e m s e l v e s , a n d n o r m a l l y t h e r e d u c e d m a s s of t h e chlorides or b r o m i d e s is e x t r a c t e d a n d recrystallized from a q u e o u s hydrochloric or h y d r o b r o m i c acids respectively, yielding t h e c o m p o u n d s NbgCli4.

7H2O, NbgBri^.VHaO, Ta6Cli4.7H20 a n d Ta6Bri4.7H20 respectively.

Metallic c a d m i u m a p p e a r s t o be a p a r t i c u l a r l y suitable reducing a g e n t for t h e p e n t a c h l o r i d e s a n d p e n t a b r o m i d e s , a n d w i t h t h e exception of t h e b r o m o n i o b i u m c o m p o u n d , a b o u t 3 0 % yields h a v e been o b t a i n e d ( H a r n e d et al,, 1960). T h e only r e a c t i o n w i t h o t h e r halides a p p e a r s t o be t h e o b s e r v a t i o n t h a t Talg-aa is stable in acid solution w i t h a green colour b u t decomposes in alkaline solution w i t h t h e evolution of h y d r o ­ gen, in a n e x a c t l y analogous m a n n e r t o t h e chloro a n d b r o m o com­

p o u n d s i K o r o s y , 1939). A l t h o u g h t h e s t r u c t u r e of t h e s e p a r t i c u l a r species h a v e n o t b e e n d e t e r m i n e d , t h e r e is n o d o u b t t h a t t h e s t r u c t u r e is b a s e d on t h e (MeXi2)^+ core s h o w n in Fig. 1, where t h e six m e t a l a t o m s are s i t u a t e d a t t h e corners of a n o c t a h e d r o n , w i t h a halogen a t o m a b o v e each o c t a h e d r a l edge, each halogen bridging t w o m e t a l a t o m s .

A v a r i e t y of d o n o r molecules can a p p a r e n t l y a d d o n t o t h e (NL^^^'^+

cage, one t o each m e t a l a t o m , in a similar m a n n e r as h a s b e e n m o r e conclusively d e m o n s t r a t e d w i t h t h e c o m p o u n d s containing t h e analo­

gous (MoeClg)^^ a n d (Re3Cl3)^+ cages, indicating t h a t t h e c o m p o u n d s should be considered t o b e composed of [(M6Xi2)L6]'^- ions, where L h a s been found t o be a n e u t r a l or negatively charged ligand (Fig. 5).

T h e c o m p o u n d s of t h e t y p e Nb6Cli4.7H20 r e t a i n t h e i r w a t e r t e n a ­ ciously, a n d do n o t completely d e h y d r a t e even a t 300°, suggesting t h a t some of t h e w a t e r is strongly b o n d e d t o t h e m e t a l a t o m s . H o w e v e r , care m u s t be t a k e n a b o u t t h e formulation of t h e s e c o m p o u n d s a n d t h e i r derivatives, as m a n y of t h e essential properties h a v e n o t been m e a s u r e d . F o r e x a m p l e , a l t h o u g h t h e a b o v e c o m p o u n d is conveniently f o r m u l a t e d as [(Nb6Cli2)Cl2(H20)4]3H20, t h e necessary chemical a n d physical properties h a v e n o t b e e n d e t e r m i n e d .

I t should b e n o t e d t h a t t h e d e r i v a t i v e s p r e p a r e d h a v e t h e a v e r a g e m e t a l a t o m in t h e formal o x i d a t i o n s t a t e of 2-33. H o w e v e r , t h e y a p p e a r t o b e p r e p a r e d from b i n a r y halides where t h e m e t a l a t o m s h a v e formal o x i d a t i o n s t a t e s of 2-00, 2-33 a n d 2-50. A s t u d y of t h e o x i d a t i o n - r e d u c t i o n processes is therefore clearly i n d i c a t e d , a n d it should also b e possible t o p r e p a r e d e r i v a t i v e s w i t h o t h e r formal o x i d a t i o n s t a t e s . I t

F I G . 5. T h e structure of [(M6Xi2)(Hgand)6]^". One Hgand a t o m (hatched ch-cle) is a t t a c h e d t o each m e t a l a t o m of Fig. 1 in a centrifugal position.

T h e correct formulation of t h e s e c o m p o u n d s h a s always been a n interesting problem, d u e t o t h e non-integral n u m b e r of t h e valency of t h e average m e t a l a t o m . T h e m a g n e t i s m a n d m o d e of b o n d i n g in these c o m p o u n d s will be discussed separately after t h e chemistry h a s been summarized.

B. Monomeric complexes

T h e ' ' h y d r a t e d t a n t a l u m dichloride" was first p r e p a r e d b y Chabrie (1907) who r e d u c e d t a n t a l u m pentachloride w i t h 3 % sodium a m a l g a m a t red h e a t , a n d e x t r a c t e d t h e m i x t u r e w i t h hydrochloric acid. T h e c o m p o u n d is green, b u t t u r n s b r o w n on prolonged exposure t o air, a n d was formulated as TaCl2.2H20.

Chapin (1910) similarly p r e p a r e d this c o m p o u n d a n d no less t h a n 20 g of t h e corresponding b r o m i d e b y reduction w i t h h y d r o g e n , b u t formu­

lated t h e p r o d u c t s as Ta6Cli4.7H20 a n d Ta6Bri4.7H20 respectively. T h e h a s recently been shown (McCarley et al, 1964) t h a t Τ8ϋοΒτΐ2^+ can b e oxidized w i t h h y d r o g e n peroxide t o form Ta>QBr^2^+,

compounds were correctly described as h e x a m e r i c species on the basis of a molecular weight determination on the bromo compound in boiling propanol (found 1750, TagBri4.7H20 requires 2332). A molecular weight determination in freezing water (found 720) indicated that this com­

pound dissociated into three ions. This was confirmed b y showing t h a t only t w o of the bromide ions in Ta6Bri4.7H20 could be precipitated with silver nitrate from cold aqueous solutions, and also that only t w o bromide ions were replaceable after repeated evaporation with hydro­

chloric acid. T h e compounds Ta6Bri2(OH)2.10H2O and Ta6Bri2l2.71120 were similarly obtained. More recently (Allen and Sheldon, 1965) it has been shown that these compounds are 2:1 electrolytes in water and ethanol.

H a r n e d ( 1 9 1 3 ) similarly prepared the green chloroniobium compound, which is also obtained as the green heptahydrate Nb6Cli4.7H20. I t was again found that two of these chlorine atoms could be replaced, and Nb6Cli2(OH)2.8H20 and Nb6Cli2Br2.7H20 were prepared. H a r n e d noted that the green N b 6 C l i 4. 7 H 2 0 dissolved in alkali forming a green-brown solution, which on addition of concentrated hydrochloric acid produced a brown crystalline material thought to be N b 6 C l i 4. 9 H 2 0 . H o w e v e r , the relationship between the t w o species was not understood; the hepta­

hydrate could not be formed b y dehydrating the enneahydrate, but was formed if aqueous solutions of the enneahydrate were boiled. T h e enneahydrate was less soluble than the heptahydrate. I t has been suggested (Allen and Sheldon, 1 9 6 5 ) that the brown form is similar to t h e green form, e x c e p t t h a t t h e r e is a slight r e p l a c e m e n t of t h e bridging chloride groups w i t h hydroxide groups.

L i n d n e r and F e i t (1924) again prepared the chlorotantalum com­

pound, b y reduction of t h e p e n t a c h l o r i d e w i t h lead at 600°. R a t h e r t h a n formulate t h e compound in terms of t h e metal atom having a non- integral valence number, t h e y preferred t h e formula H(TaÇCl7.H20).

3H2O. T h e y found that only 1/14 of the chloride was precipitated from ethanolic solution, but 4/14 was precipitated from aqueous solution under vigorous conditions. These authors produced a number of com­

plexes which appear largely analogous to the better known molybdenum compounds, but which were formulated as derivatives of the acid H(Ta3Cl7.H20).3H20, a few examples of which are shown on the left hand side of the following reaction scheme. I n the absence of critical measurements such as conductivity and molecular weight, these com­

pounds can be reformulated as shown on the right hand side of t h e reaction scheme. Six centrifugal ligands have tentatively been used with compounds obtained from solution, but the compounds obtained on heating must be polymeric with bridging centrifugal ligands.

L i n d n e r a n d F e i t Possible reformulation H(Ta3Cl7.H20).3H20

1 A q u e o u s H B r

H(Ta3Cle.Br.H20).3H20

I H e a t

HiTasCle-Br.H^O)

p y in E t O H l sat. w i t h HCl

pyH(Ta3Cl,) Η(Τα3θΐ7.Η2θ).3Η2θ

ivy

(pyH)[Ta3Cl,py]

H(Ta3Cl7.H20).3H20

j E t O H

H(Ta3Cl,.EtOH).EtOH

[(TaeCl,,)Cl,(H,0)4].3H,0

I A q u e o u s H B r

[(TaeCl,2)Br,(H,0)J.3H,0

j H e a t

(TaeCli,)Br,(H,0), [(TaeCli,)Cl2(H20)J.3H,0

p y in E t O H j sat. w i t h HCl

H2(pyH)2[(TaeCli2)Cle]

j 2 9 0 °

(TaeCli2)Cl2py2

[(TaeCl,2)Cl2py4]

[(TaeCli2)Cl2(H20)4].3H20

j E t O H

[(TaeCli2)Cl2(EtOH)J

Similar c o m p o u n d s were o b t a i n e d b y r e p l a c e m e n t of t h e o u t e r centri­

fugal chlorine a t o m s w i t h b r o m i n e , w h i c h can b e r e f o r m u l a t e d H2(pyH)2 [(TaeCli2)Bre], (TaeCli2)Br2py2 a n d [(TaeCli2)Br2pyJ.

Ruff a n d T h o m a s (1925) also preferred t h a t t h e m e t a l a t o m s in t h e s e c o m p o u n d s h a v e a n integral valence, b u t preferred t r i v a l e n t t a n t a l u m . F o r e x a m p l e , t h e y r e w r o t e t h e H(Ta^3Cl7.H20)3H20 of L i n d n e r a n d F e i t as ( T a | " C l 7 0) 3 H 2 0 .

T h e formulae a n d s t r u c t u r e of t h e s e c o m p o u n d s r e m a i n e d in d o u b t u n t i l V a u g h a n et al. (1950) m e a s u r e d t h e X - r a y diffraction of alcoholic solutions of NbgCli^.VHgO, TaeCli^.THgO a n d Ta6Bri4.7H20, a n d d e d u c e d t h a t t h e s t r u c t u r e s were b a s e d on a ( M 6 X i 2 ) ^ + core, w i t h t h e m e t a l a t o m s in t h e form of a n o c t a h e d r o n a n d w i t h a halogen a t o m a b o v e each edge (Fig. 1). T h e i n t e r a t o m i c distances are given below.

M — M (A) M — X (A)

Nb6Cli4.7H20 2-85 2-41

TaeCl^.TH^O 2-88 2-44

TaeBrj^.VHaO 2-92 2-62

NbeFis NbeCli4 NbeBr^^ mj.^^

(NbF^.so) (NbCl2.33) (NbBr^.oo) (Nbl^.oo)

— TaeCli5 TaeBr^s Tagl^^

— (TaCla.so) (TaBr^.^o) (Tal^.ga)

T h e s t r u c t u r e of NbgFis shows t h e presence of (NbgFia) cores s h o w n in Fig. 1 (Schafer a n d Schnering, 1964). T h e centrifugal fluorine a t o m o n e a c h n i o b i u m a t o m is s h a r e d w i t h a centrifugal position of t h e neighbouring (NbgFig) core, so t h a t a three-dimensional n e t w o r k is formed. T h e formula c a n b e conveniently w r i t t e n [(Nb6Fi2)F6/2]- N o distortion of t h e cage from regular g e o m e t r y w a s n o t e d , t h e i n t e r a t o m i c distances being: N b — N b = 2 - 8 0 Â , N b — b r i d g i n g F 2-05 Â, N b — centrifugal F = 2-11 Â. T h e lowest t a n t a l u m chloride a n d b r o m i d e also h a v e t h i s stoichiometry, a n d a r e i s o m o r p h o u s w i t h each o t h e r (Schafer et al, 1964, 1965). T h e existence of TaCl2 which h a s b e e n claimed b y earlier workers could n o t be confirmed (e.g. see Y o u n g a n d B r u b a k e r (1952); F r e r e a n d Michel (1961, 1962) ).

T h e s t r u c t u r e of NbeCli4 also shows t h e presence of Nb^ o c t a h e d r a , b u t it is interesting t o n o t e t h a t in t h i s case t h e o c t a h e d r o n is flattened along one of its fourfold axes, such t h a t t h e r e a r e four n i o b i u m - n i o b i u m distances of 2-95 Â, a n d eight n i o b i u m - n i o b i u m distances of 2-89 Â (Schafer a n d Schnering, 1964). I n a d d i t i o n t o t h e six centrifugal chlorine a t o m s a c t i n g as bridges b e t w e e n different (Nb6Cli2)^+ cores, t w o of t h e inner chlorine a t o m s of t h e core itself a r e s h a r e d w i t h t h e centrifugal positions of a d j a c e n t (NbeClig)^"*" clusters. E a c h Nbg cluster is therefore linked t o eight n e i g h b o u r s in a three-dimensional n e t w o r k , a n d Nb6Cli4 can b e conveniently f o r m u l a t e d [(Nb6ClioCl2/2)Cl6/2]- E o r t h e t w o n i o b i u m a t o m s a t t h e flattened corners of t h e o c t a h e d r o n , N b — b r i d g i n g CI = 2 · 3 6 - 2 · 3 9 A, a n d N b — c e n t r i f u g a l CI = 3-04 Â, while for t h e o t h e r four n i o b i u m a t o m s , Nb—^bridging CI = 2 - 4 0 - 2-47 Â, a n d Nb—centrifugal CI = 2-58. Earlier r e p o r t s of a lower C. Binary halides

T h e r e h a v e been n o crystal s t r u c t u r e d e t e r m i n a t i o n s of t h e n u m e r o u s solid crystalline d e r i v a t i v e s referred t o a b o v e . Confirmation of t h e existence of t h e (MgXja)^"^ cage a w a i t e d t h e p r e p a r a t i o n of single crystals of t h e b i n a r y halides b y r e d u c t i o n of t h e higher halides w i t h t h e m e t a l in a t e m p e r a t u r e g r a d i e n t . W h e r e a s all t h e d e r i v a t i v e s referred t o a b o v e h a v e t h e a v e r a g e m e t a l a t o m in t h e formal o x i d a t i o n s t a t e of t h e lowest halides which h a v e been p r e p a r e d h a v e stoichiometry d e p e n d e n t b o t h on t h e m e t a l a n d t h e halogen:

90°K 195°K 2 9 5 ° K 2 9 7 ° K

10«x(TaCl2.5) ^{295 178 129}

10«x(TaBr2.5) ^{113 89 70}

These values for t h e susceptibility are consistent w i t h a single u n p a i r e d electron for t h e six t a n t a l u m a t o m s (/Xeff(Ta6Xi5) ' ^ 1 - 5 B), w h i c h is in a g r e e m e n t w i t h t h e o d d n u m b e r of electrons which m u s t b e p r e s e n t in t h e s e c o m p o u n d s .

C o m p o u n d s of t h e G r o u p V m e t a l s of t h e general formulae (MeXig)^^

h a v e 30 electrons on t h e six m e t a l a t o m s . Of t h e s e , 12 will b e used for binding t h e 12 halogen a t o m s , a n d t w o t o p r o v i d e t h e n e t charge, leaving 16 electrons p o t e n t i a l l y available for m e t a l - m e t a l b o n d i n g . H o w e v e r , if electron p a i r m e t a l - m e t a l b o n d s are considered t o lie along chloride NbClg (Schafer a n d D o h m a n n , 1959; F r e r e a n d Michel, 1961, 1962) h a v e n o t been confirmed.

Ta6li4 h a s a similar s t r u c t u r e t o Nb6Cli4, t h e Tag o c t a h e d r o n again being d i s t o r t e d b y a flattening along one of t h e principal axes. T h e r e a r e four t a n t a l u m - t a n t a l u m distances of 3-10 Â, a n d eight of 2-82 Â. T h e centrifugal iodine a t o m s are again significantly further a w a y from t h e t w o fiattened corners of t h e o c t a h e d r o n t h a n from t h e o t h e r four corners, t h e distances being 4-33 a n d 3-12 Â respectively. T h e t a n t a l u m - i o d i n e distances w i t h i n t h e (Ta^Iia)^^ core r a n g e from 2-72 t o 2-82 Â (Schafer a n d Schnering, 1964).

T h e s t r u c t u r e s of NbBrg ( G u t m a n n a n d T a n n e n b e r g e r , 1956) a n d N b i g (Chaigneau, 1957b) are n o t k n o w n .

D. Magnetism, spectra and bonding

T h e formally 2-33-valent Nb6Cli4.7H20 e x h i b i t s a t e m p e r a t u r e - i n d e p e n d e n t p a r a m a g n e t i s m of 10^x(Nb6Cli4.7H2O) = 240 c.g.s.u. from 42 t o 290°K (Robin a n d K u e b l e r , 1965). A lower r o o m t e m p e r a t u r e susceptibility of 102 c.g.s.u. h a s been r e p o r t e d for t h e c h l o r o t a n t a l u m analogue (Schafer a n d Schnering, 1964). T h e higher t e m p e r a t u r e d e p e n d e n t values found earlier are p r e s u m a b l y d u e t o p a r a m a g n e t i c impurities (Krylov, 1958). A slight p a r a m a g n e t i s m h a s also been found for Nb6Cli4, w h e r e a s Ta6li4 is d i a m a g n e t i c (Schafer a n d Schnering, 1964).

T h e formally 2-5-valent TagClis (Schafer et al,, 1964) a n d TagBrig (Schafer et al., 1965), show a slight p a r a m a g n e t i s m ; t h e v a l u e s e x t r a ­ p o l a t e d t o infinite field s t r e n g t h b u t n o t corrected for d i a m a g n e t i s m a r e :

F I G . 6. Square antiprismatic hybridization s h o w n o n one of t h e m e t a l a t o m s in (M6Xi2)2+. T h e hybrid orbitals are at angles β a n d γ t o t h e eight fold inversion a x i s of t h e square antiprism.

each of t h e o c t a h e d r a l edges, 24 b o n d i n g electrons are required. These c o m p o u n d s are therefore a p p a r e n t l y electron deficient, a n d a n y descrip­

t i o n of t h e b o n d i n g m u s t t a k e t h i s i n t o a c c o u n t , m u s t also a c c o u n t for t h e observed d i a m a g n e t i s m (or t e m p e r a t u r e i n d e p e n d e n t p a r a m a g ­ n e t i s m ) , a n d should also b e of some assistance in t h e i n t e r p r e t a t i o n of t h e visible a n d u l t r a v i o l e t spectra.

T h e valence b o n d a p p r o a c h will b e briefly discussed first. H o w e v e r , for t h i s p a r t i c u l a r class of inorganic c o m p o u n d s , t h e r e are considerable a d v a n t a g e s in using a molecular orbital a p p r o a c h , a n d t h i s will b e discussed in m o r e detail.

I n t h e simplest valence b o n d a p p r o a c h each m e t a l a t o m would b e considered t o be b o n d e d t o four m e t a l a t o m s a n d four halogen a t o m s . T h e p r o b l e m is therefore raised of t h e existence of a n electron deficient system as i n d i c a t e d a b o v e , b u t in a d d i t i o n t h e m e t a l a t o m would require a stereochemistry which would b e related t o cubic stereo­

chemistry, a n d suitable h y b r i d orbitals could only be formed b y t h e utilization of/-orbitals, which would n o t be e x p e c t e d t o be energetically favourable for n i o b i u m or t a n t a l u m .

Dufffey (1951), however, suggested t h a t t h e h y b r i d orbitals projected t o w a r d s t h e centres of t h e o c t a h e d r a l faces r a t h e r t h a n along t h e octa­

hedral edges (Fig. 6). T h e h y b r i d i z a t i o n required is n o w r e l a t e d t o t h e square a n t i p r i s m r a t h e r t h a n t o t h e cube, a n d such h y b r i d i z a t i o n can b e o b t a i n e d using only s-, ρ- a n d cZ-orbitals. T h a t is, t h e r e is overlap of orbitals from t h r e e different m e t a l a t o m s a t t h e c e n t r e of each octa­

hedral face, a n d t h e 16 available electrons are j u s t a c c o m m o d a t e d if t w o b o n d i n g electrons a r e placed in each set of t h r e e overlapping orbitals. Dufffey also p o i n t e d o u t t h a t t h e s q u a r e a n t i p r i s m considered

here is considerably d i s t o r t e d from t h a t e x p e c t e d for n o r m a l s q u a r e a n t i p r i s m a t i c coordination. F o r (NbgClia)^"'', t h e angles t o t h e principal axis which are m a d e b y t h e lines joining t h e m e t a l t o t h e chlorine a t o m a n d t o t h e centre of t h e o c t a h e d r a l face, ή a n d γ respectively in Fig. 6 are 81° a n d 145° respectively, c o m p a r e d w i t h 33° a n d 147° e x p e c t e d for n o r m a l s q u a r e a n t i p r i s m a t i c coordination (Kepert, 1965). I t h a s therefore been suggested t h a t t h e m e t a l - h a l o g e n σ-bonds are consider­

a b l y b e n t (Gillespie, 1961), b u t t h e degree of overlap still a p p e a r s favourable (Duffey, loc. cit.).

T h e first molecular orbital t r e a t m e n t w a s d u e t o Grossman et al.

(1963), w h o defined t h e axes a b o u t t h e m e t a l a t o m as s h o w n in F i g . 7,

F I G . 7. T h e a x e s chosen for t h e molecular orbital description of (M6Xi2)^''"are s h o w n o n one of t h e m e t a l a t o m s only. E a c h individual 2-axis p o i n t s radially o u t w a r d from t h e centre of t h e octahedron, a n d t h e individual x- a n d y-axes point over t h e edges of t h e octahedron a n d in t h e direction of t h e bridging halogen a t o m s .

a n d t h i s s y s t e m h a s been r e t a i n e d for t h e following discussion. These a u t h o r s considered p r e l i m i n a r y h y b r i d i z a t i o n of t h e a t o m i c orbitals in suitable directions, before c o m b i n a t i o n t o form t h e molecular orbitals.

T h e y found t h e m o s t stable molecular orbital w a s of A^g s y m m e t r y formed from t h o s e orbitals w i t h c o m p o n e n t s along t h e individual 2;-axes {s, p ^ , ά^ή. T h e n e x t m o s t stable w a s formed from t h e six d^y- orbitals w i t h lobes over t h e o c t a h e d r a l faces (A^u)- F i n a l l y {T^g a n d T^u) were formed from t h o s e orbitals w i t h c o m p o n e n t s directed t o w a r d s t h e o c t a h e d r a l edges (p^, py, dr^^ a n d dy^). These molecular orbitals t h e n a c c o m m o d a t e t h e 16 electrons accounting for t h e observed d i a m a g n e t i s m .

T h e general t r e a t m e n t b y Grossman, Olsen a n d Duffey leads t o difficulties in t h e q u a n t i t a t i v e calculations, a n d a simplified a p p r o a c h w a s later used b y C o t t o n a n d H a a s (1964). These a u t h o r s first of all

'Eu /hybrids ^Ligand

X 2u

F i g . 8. Molecular orbital e n e r g y levels for (MeXia)^^, after Cotton a n d H a a s .

i t w a s a s s u m e d t h a t t h e ^^-orbital w a s t o t a l l y involved w i t h t h e b o n d i n g of t h e centrifugally directed ligand, a n d did n o t i n t e r a c t w i t h t h e iZ22-orbital. F i n a l l y l i g a n d - m e t a l 7r-bonding w a s neglected. These last t w o a s s u m p t i o n s could h a r d l y b e e x p e c t e d t o b e justified a n d a r e of critical i m p o r t a n c e ; t h e y will b e discussed in m o r e detail later. T h e r e m a i n i n g a t o m i c orbitals, d^^^ da.z, dy^ a n d d^y, were c o m b i n e d t o form t h e molecular orbitals used for t h e m e t a l - m e t a l b o n d i n g , a n d t h e over­

l a p integrals a n d relative energies calculated. T h e r e s u l t a n t molecular orbital scheme is i l l u s t r a t e d q u a l i t a t i v e l y in F i g . 8. One r a t h e r r e m a r k ­ able feature of t h e r e s u l t a n t molecular orbital d i a g r a m is t h a t t h e r e a r e only eight b o n d i n g orbitals c o m p a r e d w i t h 16 a n t i b o n d i n g orbitals (the

T2g{dxy) is e x p e c t e d t o b e m o r e u n s t a b l e t h a n shown, d u e t o i n t e r a c t i o n w i t h t h e b o n d i n g T^gid^^z, dy^) ). T h e 16 available electrons were t h e n a c c o m m o d a t e d as indicated, w h i c h is in a g r e e m e n t w i t h t h e observed d i a m a g n e t i s m . These filled orbitals are t h e s a m e as t h o s e derived earlier b y Grossman, Olsen a n d Duffey, a l t h o u g h t h e ordering of t h e T^g{daiz, dyzY a n d Τ-^^(^^ζ9 -orbitals w a s reversed.

Allen a n d Sheldon (1965) s t u d i e d t h e s p e c t r a of t h e s e c o m p o u n d s in t h e visible region (8000-45000 cm-^), a n d eight or m o r e b a n d s were observed. T h e y considered t h a t all observed b a n d s were d u e t o m e t a l - a s s u m e d t h a t h y b r i d s from t h e s-, p^-, py- a n d d^j^-i/a-orbitals b o n d e d t h e halogen a t o m s in a s q u a r e p l a n a r a r r a n g e m e n t . A t t h e t i m e t h i s a s s u m p t i o n a p p e a r e d justified, as t h e only s t r u c t u r e w a s b a s e d on t h e analysis of t h e s c a t t e r i n g of X - r a y s b y ethanolic solutions of t h e com­

p o u n d s , b u t since t h i s t i m e a n u m b e r of c o m p o u n d s h a v e h a d t h e i r s t r u c t u r e s a c c u r a t e l y d e t e r m i n e d in t h e solid s t a t e . T h e results show t h a t t h e angle ή (Fig. 6) t h e m e t a l - h a l o g e n b o n d m a k e s w i t h t h e 2;-axis is 88° for Nb6Fi5, 81° for Nb6Cli4 a n d alcohoHc solutions of Nb6Cli2^+

a n d Ta6Cli22+, 79° for alcohohc solutions of T a 6 B r i 2 ^ + , a n d 73° for Ta6li4; t h i s t r e n d w o u l d b e e x p e c t e d on simple steric g r o u n d s . Secondly

m e t a l b o n d i n g t o m e t a l - m e t a l a n t i b o n d i n g transitions, a n d fitted t h e spectra t o t h e molecular orbital d i a g r a m of C o t t o n a n d H a a s b y assum­

ing t h a t t h e v a l u e of a, t h e Slater orbital e x p o n e n t , h a s a value of 1-7 for t h e (Z^2-orbitals, a n d 1-2 for t h e o t h e r orbitals. All possible transitions were considered t o be allowed. F o r e x a m p l e t h e lowest energy b a n d , which is strong (extinction coefficient '^3000), was assigned t o t h e t r a n s i t i o n ΤΊ„(ίία;ζ? ^yz) — T^g{d^y), while t h e t h i r d lowest energy b a n d which a p p e a r s only as a shoulder (extinction coefficient ^ 7 0 0 ) was assigned t o t h e t r a n s i t i o n A^uidxyyT^gidr^y), a l t h o u g h t h e a b s o r p t i o n d u e t o such a t r a n s i t i o n m a y be e x p e c t e d t o b e m o r e intense. I t is im­

p o r t a n t t o n o t e t h a t t h e s e molecular orbitals derived from different a t o m i c cZ-orbitals do n o t m i x even a l t h o u g h t h e y m a y be of t h e s a m e molecular orbital s y m m e t r y , since t h e y are forbidden b y t h e local a t o m i c orbital s y m m e t r y . Transitions b e t w e e n s u b s y s t e m s are therefore generally forbidden, a n d each set of molecular orbitals can be considered separately (Robin a n d K u e b l e r , 1965). T h e only exceptions are t h e mixing of t h e T^^{dç^'i_y^ w i t h t h e T^uidxz, dy^), or b y mixing t h r o u g h t h e halogen bridges.

R o b i n a n d K u e b l e r (1965) modified t h e C o t t o n a n d H a a s p i c t u r e b y i n t r o d u c i n g those ligand-metal interactions d u e t o t h e 12 halogen a t o m s of t h e (MgXig)^"^ core, a n d derived t h e molecular orbital d i a g r a m shown in F i g . 9. T h e allowed m e t a l - m e t a l t r a n s i t i o n s are shown. F o r t h e

F I G . 9. Molecular orbital energy levels for (Μ^Χ^ί)^^, after R o b i n a n d Kuebler.

molecular orbitals derived from t h e m e t a l d^^y orbitals, if only m e t a l - m e t a l interactions are considered t h e ordering will b e A^u, T^g, E^, b u t if ligand ρ 7r-metal d^^y i n t e r a c t i o n s a r e considered, t h e i n v e r t e d order E^y T^g, A^u is o b t a i n e d . T h e correct order w a s decided b y considering t h e e x p e r i m e n t a l l y d e t e r m i n e d a b s o r p t i o n spectra. (In addition t h e s e a u t h o r s i n t r o d u c e d t h e iZa.2_y2-orbitals i n t o t h e i r calculations, a n d also

reversed t h e order of Εg[dz'^ a n d ^1^(^-52), b u t t h e s e differences a r e u n i m p o r t a n t for t h e p r e s e n t discussion.)

R o b i n a n d K u e b l e r t h e n s e p a r a t e d t h e observed spectral b a n d s of t h e n i o b i u m c o m p o u n d s (in e t h a n o l a t —100°) i n t o t w o g r o u p s : t h o s e w h i c h change only slightly as we go from (NbeClig)^^ t o (NbeBria)^^, a n d t h o s e which are shifted b y t h e order of 1000 cm*^ t o lower energies in t h e n o r m a l m a n n e r for halogen t o m e t a l charge transfer b a n d s (see first t h r e e columna-of T a b l e I ) . T h e first b a n d a t 10,870 cm-^ (underlined in T a b l e I) is therefore assigned t o t h e first m e t a l - m e t a l t r a n s i t i o n , n a m e l y

^u(dxy) — T^gidoiy). A d d i t i o n a l d a t a o b t a i n e d in w a t e r show a slight shift t o higher energy w h e n c o m p a r i n g t h e b r o m o complex w i t h t h e chloro complex, confirming t h a t t h i s is a m e t a l - m e t a l t r a n s i t i o n (last t h r e e columns of T a b l e I ) .

T A B L E I . V i s i b l e s p e c t r a ( c m - ^ ) o f (NbeXi2)^+ i n e t h a n o l a n d w a t e r

(Nb6Xi2)2+ in ethanol»

X = Cl Χ = B r Difference

(Nb6Xi2)2+ in water&

X = CI X = B r Difference

10870 (m) 10640 - 2 3 0 11200 11400 + 200

16670 (w) 15270 - 1 4 0 0 16500 15500 - 1 0 0 0

20410 (w) — — _{21000 21000 0}

24690 (m) 23360 - 1 3 3 0 25200 23700 - 1 5 0 0

31250 (w) 30300 - 9 5 0 31000 31000 0

35650 (m) 35210 - 4 4 0 36500 35300 - 1 2 0 0

46390 (s) 45300 - 1 0 9 0 43000

4 8 2 0 0 α R o b i n a n d K u e b l e r (1965).

» A l l e n a n d Sheldon (1965).

T h e underlined b a n d is t h a t assigned t o a m e t a l - m e t a l b o n d i n g t o m e t a l - m e t a l anti- b o n d i n g transition.

T h e n e x t four b a n d s , which were considered t o show considerable shifts for changing chloride t o b r o m i d e , w e r e assigned t o charge transfer t r a n s i t i o n s (although T a b l e I shows t h a t t h e spectral results o b t a i n e d in w a t e r d o n o t really confirm t h i s view). T h e w e a k b a n d s a t 16,670, 20,410 a n d 31,250 cm-^ were considered t o b e s y m m e t r y forbidden t r a n s i t i o n s , while t h e first intense charge transfer b a n d a t 24,690 cm-^

i n d i c a t e d t h a t t h i s w a s a n allowed t r a n s i t i o n , a n d w a s assigned t o a t r a n s i t i o n from a ligand ^^-orbital t o one of t h e m e t a l molecular orbitals originating from t h e cia-^-atomic orbitals. I t w a s t h e fact t h a t t h i s t r a n s i t i o n w a s observed as a singlet t h a t led R o b i n a n d K u e b l e r t o propose t h a t t h e t r a n s i t i o n w a s d u e t o t h e A^y^{dr^y) o r b i t a l ; for t h i s t o b e e m p t y t h e s e b a n d s m u s t b e i n v e r t e d relative t o t h e order of

C o t t o n a n d H a a s , so t h a t t h e d o u b l y d e g e n e r a t e EJdr^y) was of t h e lowest energy, t h a t is, m e t a l - l i g a n d i n t e r a c t i o n s a r e m o r e i m p o r t a n t t h a n m e t a l - m e t a l i n t e r a c t i o n s (see above). F o r d i a m a g n e t i s m t o b e r e t a i n e d w i t h t h e s a m e n u m b e r of valence electrons this level m u s t b e filled, a n d t h e only place t h e necessary electrons can come from is t h e lowest lying A•^g{dzή, so t h a t t h e stabilization achieved b y filling t h e EJdxy) t o form t h e closed shell configuration w a s t h o u g h t sufficient t o overcome t h e energy r e q u i r e d t o p r o m o t e t h e s e electrons from t h e A-^g{dz^ level.

Again on t h e basis of comparison of t h e chloride a n d b r o m i d e s p e c t r a in e t h a n o l , t h e b a n d a t 35,650 cm~^ w a s assigned t o a m e t a l - m e t a l transition, while t h a t a t 46,390 cm~^ t o a l i g a n d - m e t a l t r a n s i t i o n .

W i t h t h e exception of t h e lowest energy b a n d a t 10,870 cm-^, a l t h o u g h t h e assignment of t h e b a n d s on t h e basis of t h e shifts observed in ethanolic solution is feasible, it is n o t necessarily convincing, as shown, for e x a m p l e , b y a comparison of t h e s p e c t r a o b t a i n e d in w a t e r (see last t h r e e columns of T a b l e I ) .

T A B L E I I . V i s i b l e s p e c t r a (cm-^) o f (TaeXi2)^+ i n w a t e r a n d a l k a l i ( A l l e n a n d S h e l d o n , 1 9 6 5 )

(TaeXia)^+ in w a t e r (TaeXia)^^ in alkaU

X = CI X = B r Difference X = CI X = B r Difference

11600 12000 + 400 11000 11100 + 100

12800

— — — —

14000 13700 - 3 0 0 13900 13900 0

16000 15800 - 2 0 0 18000 ?

—

22000 21000 - 1 0 0 0 23000 21500 - 1 5 0 0

25200 24000 - 1 2 0 0 27800 25800 - 2 0 0 0

30200 28600 - 1 6 0 0 33900 31000 - 2 9 0 0

37000 34000 41000 39000

42500 37000 44500 43400

43200 47200 47500

T h e underlined b a n d s are t h o s e assigned t o m e t a l - m e t a l b o n d i n g t o m e t a l - m e t a l antibonding transitions.

T h e spectra of t h e t a n t a l u m complexes are similar t o those of t h e n i o b i u m c o m p o u n d s ; n e a r l y all b a n d s are shifted t o higher energy w i t h respect t o t h e corresponding n i o b i u m c o m p o u n d . H o w e v e r , t h e r e is one i m p o r t a n t difference. T h e lowest energy b a n d which h a s been assigned t o a m e t a l - m e t a l t r a n s i t i o n is split, b o t h in solution a n d in t h e solid.

F o r e x a m p l e , t h e b a n d a t 10,640 cm*^ for (NbgBria)^"^ in e t h a n o l a t

—100° is split i n t o c o m p o n e n t s a t 13,000 a n d 15,290 cm"^ for (TagBrig)^"^ u n d e r t h e s a m e conditions. T h a t b o t h p o r t i o n s of t h i s split b a n d are d u e t o m e t a l - m e t a l t r a n s i t i o n s can b e confirmed using t h e s a m e criteria as before, n a m e l y t h e small or even positive shift w h e n m o v i n g from t h e chloride t o t h e b r o m i d e (Table I I ) .

R o b i n a n d K u e b l e r a t t r i b u t e d t h i s splitting t o a t e t r a g o n a l distortion resulting from a localization of t h r e e positive u n i t charges on t w o of t h e m e t a l a t o m s , r a t h e r t h a n a uniform d i s t r i b u t i o n of 2-33 positive charges on all m e t a l a t o m s (Fig. 10). T h e i n t e n s i t y of t h e high energy t r a n s i t i o n w a s observed t o b e double t h e i n t e n s i t y of t h e low energy t r a n s i t i o n , which is e x p e c t e d on t h i s model.

F I G . 10. Tetragonal elongation of t h e Mg octahedron in (MgXia)'*"^.

On t h i s basis a t w o electron oxidation would be e x p e c t e d t o form a flattened o c t a h e d r o n (Fig. 11). This flattened o c t a h e d r o n would be e x p e c t e d t o h a v e t h e reverse i n t e n s i t y ratios, a n d t h i s w a s in fact n o t e d

F I G . 11. Tetragonal flattening of t h e Mg octahedron in (MeXja)*"''.