R A L P H G. P E A R S O N
Chemistry Department, Northwestern University, Evanston, Illinois, U.S.A.
a n d
R O G E R J . M A W B Y
Chemistry Department, University of York, Heslington, York, England
\ . Introduction . . 2. E x p e r i m e n t a l
A . Neutral Molecules B . Complex I o n s
3. Tables of Coordinate B o n d Energies A. Neutral Metal H a l i d e s . . B . Metal H a l i d e Complex A n i o n s 4. Other Properties R e l a t e d t o B o n d i n g
A . Electron Spin R e s o n a n c e
B . Nuclear Magnetic R e s o n a n c e Chemical Shifts C. Nuclear Quadrupole R e s o n a n c e
D . Decrease in Spin-Orbit Coupling Constants E . Decrease in Interelectronic R e p u l s i o n Integrals: t h e F . D i p o l e M o m e n t s
G. Force Constants H . X - R a y Diffraction 5. Theoretical . .
A . The H a r d Sphere I o n Model B . Polarizable I o n Model . .
C. Localized Molecular Orbital M e t h o d D . Modified W o l f s b e r g - H e l m h o l z M e t h o d References
N e p h e l a u x e t i c Effect 55 57 57 59 61 61 67 68 68 69 70 70 70 71 72 73 73 73 73 74 76 83
1. Introduction
S y s t e m s composed of m e t a l a t o m s a n d halogen a t o m s c o n s t i t u t e a n u m e r o u s a n d i m p o r t a n t class in inorganic c h e m i s t r y . T h e y m a y be n e u t r a l molecules in t h e gaseous s t a t e or in t h e liquid s t a t e , n e a t or i n solution, or t h e y m a y exist as complex ions, either positively or nega
tively charged. I n t h e l a t t e r case t h e y m a y exist as solids or in solution.
Most c o m m o n l y m e t a l s a n d halogens form ionic solids in which t h e r e is a definite coordination n u m b e r a n d g e o m e t r y w i t h respect t o each
5 5
ion. I n a n y case it is convenient t o use t h e concepts of coordination c h e m i s t r y a n d t o discuss m e t a l - h a l o g e n c o m p o u n d s in t e r m s of a central m e t a l a t o m s u r r o u n d e d b y halide ion ligands.
T h e i m p o r t a n c e of t h e s e s y s t e m s is n o t only in t h e i r practical use
fulness as chemical s u b s t a n c e s , b u t also because t h e y tell u s a g r e a t deal a b o u t t h e n a t u r e of i n t e r a c t i o n s b e t w e e n a t o m s a n d are convenient testing g r o u n d s for theories of b o n d i n g . These v i r t u e s arise from t h e i n h e r e n t simplicity of t h e s y s t e m s . B o t h t h e central a t o m a n d t h e ligands are m o n a t o m i c . T h e y occur in simple ratios, as a rule, a n d form molecules or ions w i t h m a r k e d s y m m e t r y which facilitates theoretical discussion. W i d e v a r i a t i o n s in t h e properties of t h e m e t a l a t o m , t h e halogen a t o m s , t h e s t r u c t u r e a n d t h e stereochemistry are possible.
Finally, t h e b o n d s b e t w e e n m e t a l a n d halogen r e p r e s e n t t h e e x t r e m e of heteropolar, or ionic b o n d i n g , as opposed t o e x t r e m e s of h o m o p o l a r , or covalent b o n d i n g .
I n t h i s c h a p t e r we shall b e concerned chiefly w i t h t h e s t r e n g t h of t h e b o n d s holding t h e a t o m s t o g e t h e r , t h o u g h certain r e l a t e d properties will be discussed. These are chiefly properties which give information on t h e p o l a r i t y of t h e b o n d s . I n t h e theoretical section we shall see t o w h a t e x t e n t a simple, classical ionic model is applicable t o these systems, a n d t o w h a t e x t e n t t h e d a t a forces u s t o i n t r o d u c e a certain a m o u n t of covalent b o n d i n g . Only σ- t y p e covalent b o n d i n g will b e discussed, t h o u g h certainly t h e i m p o r t a n c e of ligand t o m e t a l vr-bonding is well recognized. T h e i m p o r t a n c e of m e t a l t o ligand 7r-bonding, on t h e o t h e r h a n d , r e m a i n s questionable.
T h e r e are t w o w a y s of characterizing t h e b o n d energies of m e t a l halides. One is t h e b o n d energy resulting from a h e m o l y t i c splitting of all b o n d s , e.g.,
CrCl3(g) >Cr(g) + 3Cl(g) (1.1) T h e o t h e r is a heterolytic splitting of t h e b o n d s .
CrCl3(g) Cr3+(g) + 3Cl-(g) (1.2) T h e energy r e q u i r e d for t h e l a t t e r process, p e r b o n d , is called t h e
coordinate b o n d energy (Basolo a n d P e a r s o n , 1958). I n b o t h cases it is usually t h e a v e r a g e b o n d energy which is available from e x p e r i m e n t a l d a t a . T h e energy r e q u i r e d t o b r e a k t h e first, or last, b o n d m a y be q u i t e different, of course.
N o w if one is i n t e r e s t e d in t h e high t e m p e r a t u r e p r o p e r t i e s of m e t a l halides t h e n it is t h e b o n d e n e r g y (1.1) which is of i m p o r t a n c e , since this is t h e k i n d of process t h a t occurs a t high t e m p e r a t u r e . Also in certain r e d o x reactions (atom transfer mechanisms) t h e n o r m a l b o n d
energy is t h e one t o consider. H o w e v e r , for m o s t o t h e r considerations it is t h e coordinate b o n d energy which is t h e useful one t o k n o w a b o u t . T h e r e are several reasons for t h i s s t a t e m e n t . One is t h a t in t h e v e r y c o m m o n s u b s t i t u t i o n reactions of m e t a l halides, or t h e i r complexes, it is t h e coordinate b o n d b r e a k i n g w h i c h occurs. Secondly, it would n o t be possible t o discuss complex ions in t h e s a m e fashion as n e u t r a l molecules if only b o n d energies were allowed. T h a t is, t h e process
CrCle^-(g) > Cr3+(g) + 6Cl-(g) (1.3) is j u s t as logical as is (1.2), b u t n o process e q u i v a l e n t t o (1.1) exists.
Thirdly, t h e ionic n a t u r e of m e t a l - h a l o g e n b o n d s m a k e s i t convenient t o t h i n k of t h e complexes as dissociating i n t o ions.
Opposed t o t h e s e a d v a n t a g e s is t h e fact t h a t t h e k i n d of processes described b y (1.2) a n d (1.3) n e v e r occur in n a t u r e . A t h i g h t e m p e r a t u r e , it is h e m o l y t i c splitting which a c t u a l l y occurs. H e t e r o l y t i c splitting in t h e gas p h a s e w o u l d r e q u i r e m u c h m o r e energy. I n solution w h a t h a p pens, as is well k n o w n , is t h a t a coordinate b o n d t o a halide ion is simply replaced b y one t o a solvent molecule.
CrCl6^-(aq) -f βΗ^Ο > Cr(H20)63+ + 6Cl-(aq) (1.4) This m e a n s t h a t h e a t s of reaction in solution lead only t o differences in coordinate b o n d energies, a n d n o t t o t h e energies themselves.
Nevertheless, i t is clear t h a t in t h e process of forming t h e a q u o complex, t h e coordinate b o n d of chlorine ion t o c h r o m i u m ion m u s t be b r o k e n . Therefore, t h e energy of t h i s b o n d is one of t h e i m p o r t a n t factors which d e t e r m i n e s t h e r a t e s a n d t h e equilibrium c o n s t a n t s of reactions such as (1.4). O u r theories, w h i c h calculate h e a t s of h y p o thetical reactions such as (1.2) a n d (1.3), will h a v e predictive power for real reactions in solution or in t h e solid s t a t e . F u r t h e r m o r e t h e theories m a y be t e s t e d b y comparison t o calculated h e a t s of heterolytic dis
sociation in t h e gas p h a s e o b t a i n e d from e x p e r i m e n t a l results b y suitable cycles. I n t h e n e x t section we will consider t h e e x p e r i m e n t a l m e t h o d s used.
2. Experimental
T h e m e t h o d s of o b t a i n i n g t h e coordinate b o n d energies of n e u t r a l m e t a l halides are s o m e w h a t different from t h o s e for complex ions, a n d t h e t w o will be considered separately.
A. Neutral molecules
(i) Spectroscopic Methods
W h e r e a s t h e coordinate b o n d energy (c.b.e.) of a m e t a l halide is t h e
e n e r g y required t o split a gaseous m e t a l halide into its c o m p o n e n t ions,
M X , ( g ) — ^ M-+(g) + ^ X - ( g ) (2.1) t h e energies o b t a i n e d from spectroscopic studies n o r m a l l y relate t o
dissociation t o a t o m s , a n d hence t h e a p p r o p r i a t e ionization p o t e n t i a l s a n d electron affinities m u s t also be k n o w n . I n m a n y cases t h e p r o d u c t s of dissociation are a t o m s in excited electronic s t a t e s , a n d t h e results m u s t be altered t o allow for t h e difference in energy b e t w e e n t h e g r o u n d s t a t e s of t h e a t o m s a n d their excited s t a t e s .
Spectroscopic m e t h o d s h a v e m a i n l y been used for d i a t o m i c m e t a l halides, a l t h o u g h some b o n d energies for t r i a t o m i c halides h a v e been o b t a i n e d as t h e s u m of t h e energies of t h e t w o processes
M X 2 > M X + X (2.2)
a n d
M X > M + X (2.3) A m o n g t h e spectroscopic m e t h o d s t h a t h a v e been used are (a) lower
limit of c o n t i n u o u s s p e c t r u m , (b) a t o m i c fluorescence, (c) convergence limit, (d) B i r g e - S p o n e r e x t r a p o l a t i o n a n d (e) predissociation.
Discussions of t h e s e m e t h o d s , t o g e t h e r w i t h large n u m b e r s of refer
ences t o original work, a r e given b y G a y d o n (1953) a n d Cottrell (1958).
(ii) Thermochemical Methods
T h e q u a n t i t y n o r m a l l y o b t a i n e d from t h e r m o c h e m i c a l m e a s u r e m e n t s is t h e h e a t of f o r m a t i o n of t h e m e t a l halide in its s t a n d a r d s t a t e from t h e elements in t h e i r s t a n d a r d s t a t e s a t 298·16°Κ. This h e a t of forma
t i o n m a y sometimes be m e a s u r e d directly b u t is frequently o b t a i n e d indirectly from a H e s s ' s law cycle, involving t h e h e a t s of several reactions. A t y p i c a l cycle for t h e h e a t of formation of sodium chloride is shown below. T h e h e a t s of t h e reactions involved are listed b y Bichowski a n d Rossini (1936).
Na(c) + H2O + a q — N a O H ( a q ) + ^H^ig) (2.4)
i H , ( g ) + iCl,(g) - ^ - > HCl(g) (2.5) HCl(g) + a q — H C l ( a q ) (2.6) N a O H ( a q ) + HCl(aq) — N a C l ( a q ) + H20(aq) (2.7)
NaCl(c) + a q NaCl(aq) (2.8) Na(c) + iCUg) ^ ^ - > NaCl(c) (2.9) AHf = AH^ + AH^ + AH^ + AH^ - AH^ (2.10)
Several corrections h a v e t o be m a d e t o c o n v e r t such h e a t s of forma
t i o n t o c o o r d i n a t e b o n d energies (c.b.e.). T h u s , for t h e c.b.e. of a halide MX^,
c.b.e. ^ - Δ ^ , ( Μ Χ , ) - Δ ^ , , , ι ( Μ Χ , ) + AH,,^,{M)
+ i IP,(M) + i^Aiïat(X2) - ^ E A ( X ) (2.11)
i = l
w h e r e t h e t e r m s on t h e r i g h t h a n d side of t h e e q u a t i o n are h e a t of f o r m a t i o n of MX^, h e a t of s u b l i m a t i o n of MX^, h e a t of s u b l i m a t i o n of M, t h e s u m of t h e first η ionization p o t e n t i a l s I P of M, h e a t of a t o m i z a t i o n of t h e halogen molecule a n d t h e electron afl&nity Ε A of t h e halogen a t o m , respectively.
H e a t s of s u b l i m a t i o n of m e t a l halides can b e o b t a i n e d from v a p o r pressure m e a s u r e m e n t s , usually a t higher t e m p e r a t u r e s . A review of m e t h o d s used in high t e m p e r a t u r e v a p o r pressure m e a s u r e m e n t s h a s been m a d e b y M a r g r a v e (1959).
T h e t r e a t m e n t of high t e m p e r a t u r e v a p o r pressure d a t a t o o b t a i n h e a t s of s u b l i m a t i o n a t 298·16°Κ is discussed b y Brewer a n d B r a c k e t (1961) a n d b y Brewer et al. (1963) for t h e alkali m e t a l a n d alkaline e a r t h halides a n d o t h e r dihalides. Similar m e t h o d s m a y b e used t o o b t a i n h e a t s of s u b l i m a t i o n of t h e m e t a l s .
B. Complex ions
A t t e m p t s t o o b t a i n t h e e n e r g y of t h e process
( M X , ) ( - - ) - ( g ) '-^'"· . M-+(g) + r X - ( g ) (2.12) involve t h e use of a H e s s ' s law cycle. One such cycle is t h e following.
M + | r X , + a q
.^MZ^ÎTIUK^ ^
( M X , ) ( - " ) - ( a q ) ( 2. 1 3 )M^ ^ i m? L^ M " + ( g ) ( 2. 1 4 )
irX, ^ ^ ^ < ^ " ' f e U r X - ( g ) ( 2. 1 5 ) w h e r e M a n d Χ2 a r e in t h e i r s t a n d a r d s t a t e s a t 2 9 8· 1 6 ° Κ , a n d
(MX,)('-")-(g) ^ g» ' y d r( M X . ) ' ^ - " ) - ^ (MX^)(r-«)-(aq) ( 2. 1 6 ) T h e c o o r d i n a t e b o n d e n e r g y is t h e n g i v e n b y
c.b.e. = - A i i , ( M X , ) < ' - " > - ( a q ) + A^,(M«+)(g) + rAHf(X-)(g) +
AH,,yrt.(MX,)<-«>- ( 2. 1 7 )
L a t i m e r ( 1 9 5 2 ) l i s t s m a n y h e a t s o f f o r m a t i o n o f c o m p l e x i o n s in a q u e o u s s o l u t i o n . T h e h e a t s o f s o l u t i o n o f c o m p l e x i o n s , i f t h e y a r e l a r g e a n d a p p r o x i m a t e l y s p h e r i c a l ( a r e a s o n a b l e a p p r o x i m a t i o n f o r t e t r a h e d r a l a n d o c t a h e d r a l c o m p l e x i o n s ) , c a n b e o b t a i n e d ( B a s o l o a n d P e a r s o n , 1 9 5 8 ) f r o m t h e B o r n h y d r a t i o n e q u a t i o n
A i ^ « = - | ( l - i ) ( 2 . 1 8 )
a n d t h e v a r i a t i o n o f t h e d i e l e c t r i c c o n s t a n t o f w a t e r w i t h t e m p e r a t u r e
a n d t h u s
AH^^^ = AFB + Τ AS Β ( 2 . 2 0 )
T h e r a d i u s r o f t h e i o n i s t a k e n t o e q u a l t h e s u m o f t h e m e t a l i o n r a d i u s a n d t h e d i a m e t e r o f t h e h a l o g e n i o n . T h i s m e t h o d h a s b e e n u s e d t o c a l c u l a t e t h e c o o r d i n a t e b o n d e n e r g y o f T i F ^ ^ - , a n d v a r i a n t s o f t h i s m e t h o d h a v e b e e n u s e d f o r HgBr^^-, Ugl^^^- a n d A l F g ^ - ( s e e S e c t i o n 3 ) . A s o m e w h a t d i f f e r e n t c y c l e h a s b e e n e m p l o y e d b y B l a k e a n d C o t t o n ( 1 9 6 3 ) t o o b t a i n c o o r d i n a t e b o n d e n e r g i e s o f t h e s p e c i e s MCl^^-, w h e r e
M = C o , C u a n d Z n .
2 C s ( c ) + M ( c ) + 2 C l 2 ( g ) ^ g , ( C s , M C l , ( c ) ) ^ C s 2 M C l 4 ( c ) ( 2 . 2 1 )
C s 2 M C l 4 ( c ) - ^ ^ - - ^ 2 C s + ( g ) + M C l , 2 - ( g ) ( 2 . 2 2 )
2 C s ( c ) - ^ ^ ^ ^ i ^ ^ - > 2 C s + ( g ) ( 2 . 2 3 ) M ( c ) - ^ M ! ! K g ) _ _ ^ M 2 + ( g ) ( 2 . 2 4 ) 2 C l , ( g ) ^ ^ g . ( C i - ) ( g ) ^ ^ ^ j . ^ g j ^ 2 . 2 5 ) M C I 4 2 - M 2 + ( g ) + 4 C l - ( g ) ( 2 . 2 6 ) c . b . e . = - A i i ^ ( C s 2 M C l 4 ) ( c ) - AHL + 2AHF{Gs+)(g)
+ A ^ , ( M 2 + ) ( g ) + 4 A f f , ( C l - ) ( g ) ( 2 . 2 7 )
T h e h e a t o f f o r m a t i o n o f t h e s o l i d c o m p l e x w a s o b t a i n e d b y s t a n d a r d c a l o r i m e t r i c t e c h n i q u e s ( B l a k e a n d C o t t o n , 1 9 6 4 ) w h i l e t h e * ' p s e u d o - l a t t i c e e n e r g y " AHL, w h i c h r e p r e s e n t s t h e e n e r g y r e q u i r e d t o b r e a k
t h e lattice d o w n t o Cs+ a n d MCl^^- u n i t s , w a s o b t a i n e d b y c o m p u t e r t e c h n i q u e s , using a n a s s u m e d charge d i s t r i b u t i o n in t h e MCl4^- u n i t of
]\I+0.5 Ql-0.625^
A similar b u t less sophisticated calculation h a s b e e n carried o u t (see Section 3) t o o b t a i n t h e coordinate b o n d energy of FeCl4~, using t h e s a m e cycle b u t e s t i m a t i n g t h e pseudo-lattice energies of NaFeCl4 a n d KFeCl4 b y t h e m e t h o d of K a p u s t i n s k i i (1956).
3. Tables of Coordinate Bond Energies A. Neutral metal halides
T h e coordinate b o n d energies of all m e t a l halides listed in Tables I - I V (except those of l i t h i u m , sodium, beryllium, m a g n e s i u m a n d a l u m i n u m ) were o b t a i n e d b y combining t h e d a t a of F e b e r (1965) o n h e a t s of a t o m i z a t i o n of gaseous m e t a l halides w i t h t h e a p p r o p r i a t e ionization p o t e n t i a l s (Moore, 1949-1958) a n d electron affinities (Berry a n d R e i m a n n , 1963). T h e references given beside t h e values for t h e coordinate b o n d energies of t h e halides of L i , N a , B e , Mg a n d Al a r e either t o t h e sources of t h e h e a t s of formation of t h e m e t a l halides from t h e elements, all in their s t a n d a r d s t a t e s a t 298·16°Κ, a n d of t h e h e a t s of sublimation of t h e m e t a l halides a t this t e m p e r a t u r e ; or t o t h e sources of t h e h e a t s of formation of gaseous m e t a l halides from t h e elements in t h e i r s t a n d a r d s t a t e s a t 298·16°Κ.
T h e r e m a i n i n g d a t a necessary t o calculate t h e s e coordinate b o n d energies were ionization potentials, electron affinities, h e a t s of sublima
t i o n of m e t a l s a n d h e a t s of a t o m i z a t i o n of t h e halogens (Lewis a n d R a n d a l l , 1961). T h e absence of ionization p o t e n t i a l d a t a ruled o u t t h e l a n t h a n i d e s a n d actinides for consideration.
A s t u d y of Tables I - I V shows t h a t in v i r t u a l l y e v e r y case, t h e order of decreasing coordinate b o n d energy for t h e four halides of a m e t a l ion is F > CI > B r > I . Closer inspection, however, shows t h a t t h e e x t e n t of t h i s decrease varies considerably from o n e m e t a l ion t o a n o t h e r . I n T a b l e V , t h e p a r a m e t e r
(c.b.e. of fluoride) — (c.b.e. of iodide) c.b.e. of fluoride
is listed for m a n y of t h e m e t a l ions included in t h e earlier tables. F o r m e t a l ions of a given charge, i t will b e seen t h a t large values of t h e p a r a m e t e r a r e found for t h o s e m e t a l ions n o r m a l l y r e g a r d e d a s ' ' h a r d "
(Pearson, 1963) or class (a) (Ahrland et al., 1958) while smaller values are found for " s o f t " or class (b) m e t a l ions.
F CI B r I
L i 7.97l),e 6-63C 6-37C 6-OOc
N a 6-63C 5-75C 5-53C 5-23C
Κ 5-99 5-11 4 - 9 1 4 - 6 0
R b 5-76 4 - 9 3 4 - 7 3 4 - 4 4
Cs 5-63 4 - 8 8 4 - 7 1 4 - 4 0
Cu (8-61) 7-85 7-78 (7-65)
A g 7-75 7-21 7-20 7-18
A u 8-93 8-42 8 - 4 5 8-54
Ga 8 - 8 4 7-34 6-97 6 - 4 8
I n 7-84 6-67 6 - 4 4 6-17
T l 7-45 6-31 6 - 1 8 5-85
^ V a l u e s in parentheses are b a s e d on e s t i m a t e d h e a t s of vaporization of t h e m e t a l halides concerned.
^ A r m s t r o n g a n d B r a c k e n (1964).
c Brewer a n d B r a c k e t t (1961).
T A B L E I I . T o t a l c o o r d i n a t e b o n d e n e r g i e s ( e V ) o f d i h a l i d e s ^ a t 2 9 8 · 1 6 ° Κ
F CI B r I
B e 3 3 - 7 c . d 29-9^ 29-0^ 27-9t>
Mg 26-4c.e 23-6b.e 23-0t> 22·0ΐ>
Ca 2 2 - 7 2 0 - 1 1 9 - 5 (18-6)
Sr 2 1 - 3 1 9 - 0 18-4 (17-6)
B a 2 0 - 2 1 7 - 9 17-4 (16-5)
Zn 2 8 - 8 2 6 - 8 2 6 - 2 2 5 - 5
Cd 2 5 - 8 2 4 - 5 2 4 - 2 2 3 - 7
H g (27-9) 2 6 - 6 2 6 - 3 2 6 - 1
Ge 2 6 - 9 (24-6) 2 3 - 8 2 3 - 2
S n (25-0) 2 2 - 7 2 2 - 1 2 1 - 3
P b 2 3 - 7 2 1 - 5 2 M 2 0 - 6
Sc (24-8) (22-2) (21-5) (20-6)
Ti (26-1) 2 3 - 6 (22-9) 2 2 0
v (26-6) 2 4 - 3 2 3 - 7 2 2 - 9
Cr (26-1) 2 4 - 0 2 3 - 3 2 2 - 4
Mn 2 5 - 7 2 4 - 0 2 3 - 2 2 2 - 5
F e (27-2) 2 5 - 2 2 4 - 4 2 3 - 7
Co (27-7) 2 5 - 5 2 4 - 9 (24-1)
N i 2 8 - 5 2 6 - 2 2 5 - 5 2 4 - 9
Cu (28-9) 2 6 - 9 (26-6) (25-9)
* Values in parentheses are b a s e d o n e s t i m a t e d h e a t s of vaporization of t h e m e t a l halides concerned.
to Brewer et al. (1963).
c Armstrong a n d B r a c k e n (1964).
d Blauer et al. (1965).
e Hildenbrand et al. (1964).
D i v i d e b y t w o t o g e t c.b.e. per b o n d .
T A B L E I . C o o r d i n a t e b o n d e n e r g i e s ( e V ) o f m o n o b a l i d e s » a t 2 9 8 · 1 6 ° Κ for t h e p r o c e s s M X ( g ) > M + ( g ) + X - ( g )
F Cl B r I
Al 61.2to 5 4 - 3 b 52-9^
Se (52-2) 4 7 - 6 4 6 - 2 (44-9)
Y ( 4 8 . 3 ) (43-7) (42-5) 4 1 - 2
L a (46-2) 4 1 - 3 (39-8) 3 8 3
Ga (61-5) 57 4 5 6 - 5 5 5 - 4
I n (56-1) 5 2 - 0 5 1 - 3 5 0 - 5
A s 6 1 - 5 5 5 - 9 5 4 - 7 5 3 - 8
Sb (53-7) 4 9 - 4 4 8 - 4 4 7 3
B i (51-4) 4 7 - 2 4 6 - 7 4 5 - 6
Ti (56-0) 5 1 - 3 5 0 - 0 (48-9)
V (57-6) 5 2 - 8 5 1 - 8 (50-7)
Cr (58-1) 5 4 - 3 (53-1) (51-9)
Mn (59-5) (55-8) (54-6) (53-5)
F e (58-5) 5 4 - 5 5 3 - 7 5 2 - 8
Co (61-1) 5 7 - 4 (56-3) (55-3)
N i (63-1) (59-4) (58-3) (57-4)
8- Values in parentheses are b a s e d on estiraated h e a t s of vaporization of t h e m e t a l halides concerned.
to J A N A F Thermochemical Tables, T h e D o w Chemical Company, Midland, Michigan.
D i v i d e b y three t o get c.b.e. per b o n d .
T A B L E I V . T o t a l c o o r d i n a t e b o n d e n e r g i e s ( e V ) o f h i g h e r h a l i d e s » a t 2 9 8 · 1 6 ° Κ
F Cl B r I
Tetrahalides
Ti 1 0 1 - 6 9 4 - 5 9 2 - 9 9 1 - 2
Zr 9 0 - 3 83-1 8 1 - 4 7 9 - 4 -
Ge ( 1 0 8 - 7 ) 103-7 101-7 1 0 0 - 2
Sn (96-6) 9 2 - 2 9 1 - 1 (89-4)
P b (96-7) (92-3) (91-5) (90-5)
P e n t a h a l i d e s
V 170-6
— — —
N b 1 4 6 - 9 1 3 7 - 6 1 3 5 - 5 ( 1 3 3 - 6 )
a Values in parentheses are b a s e d o n e s t i m a t e d h e a t s of vaporization of t h e m e t a l halides concerned.
D i v i d e b y four or five t o g e t c.b.e. per b o n d .
T h e observed t r e n d s in p a r a m e t e r values m a y therefore be rational
ized on t h e basis t h a t h a r d acids (such as t h e alkali a n d alkaline e a r t h m e t a l ions) form their m o s t stable c o m p o u n d s w i t h h a r d bases such as fluoride ion, t h u s p r o d u c i n g large values of t h e p a r a m e t e r in T a b l e V.
Soft acids like t h e G r o u p I Β a n d I I Β m e t a l ions prefer soft bases such as iodide ion, a n d hence h a v e small p a r a m e t e r values. T h e results m i g h t be explained on t h e basis of t h e availability (class (a)) or absence
T A B L E I I I . T o t a l c o o r d i n a t e b o n d e n e r g i e s ( e V ) o f t r i h a l i d e s ^ a t 2 9 8 · 1 6 ° Κ
M+ M2+ M3+
Li 0-247 B e 0-172
N a 0-211 Mg 0-167 Al 0 1 3 6
Κ 0-232 Ca 0-181 Sc 0-140
R b 0-229 Sr 0-172 Y 0-147
Cs 0-218 B a 0-183 L a 0-171
Cu 0-112 Zn 0-115 Ga 0-099
A g 0-074 Cd 0-081 I n 0-100
A u 0-044 H g 0-065
G a 0-267 Ge 0-138 A s 0-125
I n 0-213 Sn 0-148 Sb 0-119
Tl 0-215 P b 0-131 B i 0-113
Sc 0-169 Ti 0-127
Ti 0-157 V 0-120
V 0-139 Cr 0-107
Cr 0-142 Mn 0-101
Mn 0-125 F e 0-097
F e 0-129 Co 0-095
Co 0-130 N i 0-089
N i 0-126 Cu 0-104
(class (b)) in a m e t a l ion of electrons in d-orbitals of suitable energy for d a t i v e 7r-bonding (to halide ions in t h i s instance). Such d a t i v e 7r-bonding will lead t o stronger b o n d s t o t h e heavier halide ions, b u t n o t t o fluoride ion, which lacks t h e necessary acceptor orbitals. T h u s , high p a r a m e t e r values are o b t a i n e d for alkali a n d alkaline e a r t h ions w i t h n o available d-electrons, v e r y low values for t h e nd^^-metal ions Cu+, Ag+, Au+, Zn^+, Ca^+ a n d Jlg^+ a n d steadily decreasing values for t h e t r a n s i t i o n m e t a l ions as t h e n u m b e r of available d-electrons increases. I t is also noticeable t h a t t h e values for Ga+, I n + a n d T1+ are considerably higher t h a n t h o s e for Cu+, Ag+ a n d Au+, since t h e TicZ-electrons are n o w p a r t l y shielded from t h e halide ions b y t h e (n + l)s-electrons. Similar con
siderations a p p l y t o Ge^^, Sn2+ a n d Pb2+, which h a v e higher p a r a m e t e r values t h a n Zn2+, Cd^^ a n d IIg2+, a n d h e n c e a r e h a r d e r .
Since t h e r e is little evidence from spectroscopy t h a t 7r-bonding from m e t a l t o halide ion occurs (Jorgensen, 1964), i t is p e r h a p s b e t t e r t o i n v e r t t h e a r g u m e n t a n d stress t h a t fluoride ion forms stronger ligand t o m e t a l 7r-bonding t h a n iodide ion does. Such 7r-bonding would lead t o
TABLE V . V a l u e s f o r v a r i o u s m e t a l i o n s o f t h e p a r a m e t e r c . b . e . o f fluoride — c . b . e . o f i o d i d e
c . b . e . o f fluoride
increased stability for m e t a l ions w i t h e m p t y cZ-orbitals, b u t w o u l d actually cause a n a n t i b o n d i n g effect w i t h m e t a l ions t h a t h a d filled d-shells.
T h e r e are also several o t h e r theories which predict increased b o n d i n g s t r e n g t h w h e n a soft m e t a l ion combines w i t h a soft ligand. These include increased covalent c h a r a c t e r in t h e σ-bonds, L o n d o n a t t r a c t i v e forces, a n d electron correlation effects (Pearson, 1963). T h e i n t e r a c t i o n of a h a r d m e t a l ion w i t h a h a r d ligand would b e chiefly electrostatic in n a t u r e . Simple size considerations will t h e n lead t o a m u c h higher stability for fluorides t h a n for iodides.
A plot of t h e coordinate b o n d energies of t h e t r a n s i t i o n m e t a l di- a n d trihalides against a t o m i c n u m b e r of t h e m e t a l (Figs. 1, 2) shows t h a t t h e y do n o t lie on a s m o o t h curve, as w o u l d b e p r e d i c t e d b y a simple ionic model. I t is e v i d e n t t h a t , for t h e dihalides, curves can b e d r a w n t h r o u g h t h e p o i n t s for t h e 3 d ^ , 3d^ a n d Sd^^-metal ions, Ca2+, M.n^+ a n d Zn2+, w i t h t h e r e m a i n i n g t r a n s i t i o n m e t a l ions showing positive devia
tions from t h e s e lines. This h a s b e e n n o t e d b y Brewer a n d B r a c k e t t (1963), a n d is evidently a t t r i b u t a b l e t o ligand field stabilization effects
" C a S c Ti V Cr Mn Fe Co Ni Cu Z n
F I G . 1. Total coordinate b o n d energies of divalent halides of first transition series.
which increase t h e s t a b i h t y of all t h e t r a n s i t i o n m e t a l dihalides e x c e p t those of calcium, m a n g a n e s e a n d zinc. As i n d i c a t e d b y Berg a n d Sinanoglu (1960), t h e ligand field of t h e t w o halide ions (assuming t h e molecule t o be linear) would split t h e m e t a l 3(i-orbitals i n t o t h r e e groups of different energies. If t h e i n t e r n u c l e a r axis is t a k e n as t h e ;2-axis, t h e lowest energy g r o u p is t h e dr^^_y^ a n d d^^y, t h e n e x t g r o u p contains t h e d^^- a n d d^^-orbitals, w i t h t h e cZ^a-orbital h a v i n g t h e highest energy. A splitting p a t t e r n of t h i s t y p e is in q u a l i t a t i v e a g r e e m e n t , a t a n y r a t e , w i t h t h e v a r i a t i o n s in coordinate b o n d energies observed in Fig. 1.
Similar considerations a p p l y t o t h e trihalides. H e r e t h e halides of Sc^+ {d^), Fe^+ {d^) a n d Ga^+ (ήλ^) lie o n a curve, w i t h t h e r e m a i n i n g halides showing positive d e v i a t i o n s . On t h e basis of a n a s s u m e d p l a n a r s t r u c t u r e (in t h e a;?/-plane) for t h e trihalides, t h e ligand field of t h e halide ions would again split t h e d-orbitals i n t o t h r e e groups, w i t h t h e dz^- as t h e orbital of lowest energy, t h e n t h e d^^- a n d dy^-, a n d finally t h e da.^_y^- a n d iZa.^-orbitals. Again, a splitting of t h i s t y p e yields q u a l i t a t i v e a g r e e m e n t w i t h t h e observed results.
S c Ti V Cr Mn Fe Co Ni Cu Zn Ga
F i Q . 2. T o t a l c o o r d i n a t e b o n d e n e r g i e s o f t r i v a l e n t h a l i d e s o f first t r a n s i t i o n s e r i e s .
F e C l ^ - 5 9 - 7 F e C l g 5 4 - 5
C0CI42- 2 7 - 8 C0CI2 2 5 - 5
CUCI42- 2 8 - 5 C u C l a 2 6 - 9
Z n C l ^ ^ - 2 8 - 4 Z n C l g 2 6 - 8
H g B r, 2 - 2 6 - 7 H g B r , 2 6 - 3
H g l 4 ^ - 2 5 - 7 H g l , 2 6 - 1
T i F e ^ - 1 0 4 - 4 TiF4 1 0 1 - 6
6 0 - 8 AIF3 6 1 - 2
D i v i d e b y c o o r d i n a t i o n n u m b e r t o g e t c . b . e . p e r b o n d .
A comparison of t h e coordinate b o n d energies of t h e G r o u p l A a n d I I A h a h d e s w i t h those of t h e corresponding G r o u p I B a n d I I B h a h d e s shows t h a t t h e l a t t e r are in all cases m o r e stable t h a n t h e former, t h e difference being p a r t i c u l a r l y m a r k e d for t h e G r o u p I I halides. This m a y be a t t r i b u t e d t o incomplete shielding of t h e nuclei of t h e G r o u p s I B a n d I I B m e t a l ions b y t h e full nd-shell (n = 3, 4 a n d 5 for t h e first, second a n d t h i r d t r a n s i t i o n series, respectively).
I t is also noticeable t h a t t h e regular t r e n d t o smaller coordinate b o n d energies on descending, for e x a m p l e , groups I A a n d I I A of t h e periodic t a b l e , is n o t always followed elsewhere. I n p a r t i c u l a r one m a y n o t e t h e values for ions in t h e second a n d t h i r d t r a n s i t i o n series w i t h t h e electron configuration . . . n d ^ ^ . T h u s t h e coordinate b o n d energies for t h e halides of Au+ are larger t h a n t h o s e for Ag+, a n d similarly Hg^+ > Cd2+ a n d Pb^+ > Sn^+. T h i s reversal m a y p e r h a p s b e associated with t h e contraction in ionic r a d i u s caused b y t h e poor shielding of t h e
14 4/-electrons in t h e configurations of Au+, Jlg^+ a n d Pb^+.
B. Metal halide complex anions
T h e coordinate b o n d energies listed in T a b l e V I h a v e been o b t a i n e d b y t h e following m e t h o d s .
F e C l 4 - — F r o m t h e h e a t s of reaction of KCl a n d NaCl w i t h FeClg (to form M F e C l 4 ) (Cook a n d D u n n , 1961), t h e h e a t s of formation of KCl, NaCl a n d FeClg, a n d t h e pseudo-lattice energies of N a F e C l 4 a n d K F e C l 4
as calculated b y t h e m e t h o d of K a p u s t i n s k i i (1956) using 4-00 Â as t h e r a d i u s (Zaslow a n d R u n d l e , 1957) of F e C l 4 - a n d 0-95 a n d 1-33 Â for N a + a n d K + respectively. H e a t s of formation of t h e gaseous ions Na+, K + , Fe^+ a n d CI", from t h e elements in t h e i r s t a n d a r d s t a t e s were o b t a i n e d from w o r k s referred t o in Section 3A. T h e values o b t a i n e d for t h e coordinate b o n d energy of F e C l 4 - from N a F e C l 4 a n d K F e C l 4 were in excellent a g r e e m e n t w i t h one a n o t h e r .
T A B L E V I . T o t a l c o o r d i n a t e b o n d e n e r g i e s o f c o m p l e x i o n s a t 2 9 8 · 1 6 ° Κ , a n d c o r r e s p o n d i n g v a l u e s for n e u t r a l m o l e c u l e s ( e V )
C0CI42-, CuCl4^"- a n d ZnCl42- — F r o m t h e h e a t s of formation of crystal- Hne
CS2MCI4
a n d t h e pseudo-lattice energies ofCS2MCI4,
plus t h e h e a t s of formation of gaseous Cs+, M.^+ a n d CI".HgBr42-, Hgl42- — F r o m t h e h e a t s of formation of HgX42-(aq), Hg^+(aq) a n d X ~ ( a q ) , t h e h e a t s of h y d r a t i o n of Hg^+ a n d X ~ , a n d t h e B o r n h e a t s of h y d r a t i o n of HgX42-, using t h e radii (Sutton, 1958) 4-52 a n d 4-94 Â for HgBr42- a n d ï i g i i ^ ~ respectively.
TiFg^- — F r o m t h e h e a t of f o r m a t i o n of TiFQ^-{3ùq), t h e h e a t of forma
tion of gaseous Ti^+ a n d F - from t h e elements in t h e i r s t a n d a r d s t a t e s a n d t h e B o r n h e a t of h y d r a t i o n of TiFg^-, using as r a d i u s 3-27 Â.
AlFg^- — B y a slight v a r i a n t of t h e m e t h o d used for K g X ^ ^ - , See Basolo a n d P e a r s o n (1958) for details.
Table V I illustrates t h e comparison b e t w e e n t h e coordinate b o n d energies of m e t a l halide complexes w i t h those for t h e corresponding n e u t r a l halides. I t is e v i d e n t t h a t t h e h e a t s of t h e reactions
Μ Χ , + α Χ - >MX«-(,+«) (3.2) a r e v e r y small for a g r e a t e r t h a n 1. E v i d e n t l y a n y e x o t h e r m i c character
of t h e reaction
M X , + X - > M X- ( , + i ) (3.3) is v i r t u a l l y cancelled b y t h e e n d o t h e r m i c n a t u r e of t h e steps in which
further halide ions are a d d e d . I n t h e cases w h e r e a = 2 a n d X = I or α — 3 a n d X = F in reaction (3.2) it will be seen t h a t t h e complex anion is actually u n s t a b l e w i t h respect t o t h e corresponding m e t a l halide a n d free halide ion, b u t w h e r e a = 2 a n d X = F , CI or B r , reaction (3.2) is slightly e x o t h e r m i c .
4 . Other Properties Related to Bonding A. Electron spin resonance
Hyperfine s t r u c t u r e in t h e electron spin resonance s p e c t r u m of a p a r a m a g n e t i c ion can arise from t h e effect of t h e m a g n e t i c m o m e n t of t h e nucleus on t h e electrons of t h e ion. E a c h allowed o r i e n t a t i o n of t h e nuclear m o m e n t gives rise t o a slightly different t o t a l field (nuclear + external) on t h e electron a n d , where t h e nuclear spin is / , (21 + 1) lines a r e observed for each electronic t r a n s i t i o n (Bleaney a n d Stevens, 1953).
I n investigating t h e hyperfine s t r u c t u r e in a crystal of (NH4)2lrCl6 diluted w i t h d i a m a g n e t i c (NH4)2PtCl6, Owen a n d Stevens found n o t four lines (as e x p e c t e d from t h e nuclear spin of 3/2 for I r ) b u t sixteen lines (Owen a n d Stevens, 1953). This suggested t h a t t h e r e w a s also a n i n t e r a c t i o n w i t h t h e chlorine nuclei (/ = 3/2) causing further hyperfine splitting. F r o m t h e size of t h e splitting a n d t h e decrease in t h e size of
t h e spectroscopic s p h t t i n g factor g, t h e ' ' h o l e " in t h e formally n o n - b o n d i n g m e t a l orbitals s p e n t 3 % of i t s t i m e on each of t h e six chlorine a t o m s , showing t h a t t h e hole a n d t h e five electrons were a c t u a l l y in orbitals consisting of c o m b i n a t i o n s of t h e m e t a l 5d^y-, d^^- a n d dy^-orbitals a n d suitable 7r-type chlorine orbitals. Similar results h a v e since been o b t a i n e d for t h e IrBrg^- ion (Griffiths a n d Owen, 1954) a n d for MnFg, FeFg a n d CoFg (all d i l u t e d in ZnFg) w h e r e T m k h a m (1956) finds t h a t t h e u n p a i r e d electrons are t o some e x t e n t delocalized i n t o 2S' a n d 2^-fluorine orbitals. Some further information on b o n d i n g in m e t a l halide complex anions, o b t a i n e d b y e.s.r., is included in T a b l e V I I .
T A B L E V I I . C h a r g e d i s t r i b u t i o n a n d p e r c e n t a g e i o n i c c h a r a c t e r i n c o m p l e x i o n s , a s o b t a i n e d b y v a r i o u s e x p e r i m e n t a l t e c h n i q u e s
Technique
Charge on m e t a l a t o m
% Ionic character
e.s.r.^ 1-76 96
CoBre*- e.s.r. a 1-70 95
Cole*- e.s.r.a 1-52 92
NiFe*- n.m.r.^ 1-76 96
CUCI42- e.s.r.c 1-68 92
PdCle^- n.q.r.d 0-58 43
PdBre^- n.q.r.d 0-22 37
PdBr42- n.q.r.d 0-40 60
V^Cle^- n.q.r.e 0-58 43
ReCle^- n.q.r.e 0-70 45
ReBre^- n.q.r.e 0-34 39
Rele^- n.q.r.e - 0 - 0 8 32
OsCle^- n.q.r.i 0-80 47
IrCle^- n.q.r.f 0-80 47
p t c i e ^ - n.q.r.d 0-64 44
PtBre^- n.q.r.d 0-28 38
P t i e ^ - n.q.vA - 0 - 2 0 30
PtBr^^- 0-28 57
a Windsor et al. (1962).
to S h u l m a n a n d K n o x (1960).
c Thornley et al. (1962).
d N a k a m u r a et al. (1961).
e I k e d a et al. (1965).
f I t o et al. (1963).
B. Nuclear magnetic resonance chemical shifts
T h e i n t e r a c t i o n s b e t w e e n fiuorine nuclei a n d t h e m a g n e t i c electrons of t r a n s i t i o n m e t a l ions w h i c h result in t h e hyperfine s t r u c t u r e o b s e r v e d in t h e e.s.r. s p e c t r a of MnFg a n d FeFg also result in large shifts in t h e nuclear m a g n e t i c r e s o n a n c e of ^^F. T h e fact t h a t t h e fiuorine resonance is n o t g r e a t l y b r o a d e n e d b y t h e field of t h e p a r a m a g n e t i c ion is a t t r i b u t e d t o e x c h a n g e i n t e r a c t i o n s , which lead t o t h e formation of a n t i - ferromagnetic MnFg below 68°K ( S h u l m a n et al., 1957, 1960).
D a t a on chemical shifts in these a n d o t h e r fiuorides allow a n estima
tion of t h e fraction of u n p a i r e d electrons in fluorine 2 5 - , 2p^- a n d
2^^-orbitals. S h u l m a n a n d J a c c a r i n o (1957) c o m p a r e their results for MnFa w i t h t h o s e of T i n k h a m (1956) a n d find good a g r e e m e n t .
C. Nuclear quadrupole resonance
A non-spherical a t o m i c nucleus in a non-spherical electric field will h a v e a n energy which varies according t o its o r i e n t a t i o n a b o u t some fixed axis. T h e i n t e r a c t i o n b e t w e e n nucleus a n d field gives rise t o nuclear q u a d r u p o l e coupling. A non-spherical electric field is p r o v i d e d for e x a m p l e b y a n incompletely filled ^-shell such as is found in halogen a t o m s . I n a molecule t h e electrostatic p o t e n t i a l d u e t o all molecular charges outside t h e nucleus m u s t be considered, b u t Townes a n d Dailey (1949) showed t h a t efifects d u e t o electrons a n d ions a t distances of a n a t o m i c r a d i u s or m o r e from t h e nucleus u n d e r consideration are small.
Since all t h e halogens except fiuorine h a v e non-zero n u c l e a r q u a d rupole m o m e n t s , t h e size of t h e q u a d r u p o l e coupling c o n s t a n t for t h e halogen in a m e t a l halide relative t o t h a t for t h e free halogen can be used t o assess t h e degree of ionic or covalent c h a r a c t e r in m e t a l - h a l o g e n b o n d s . T h u s t h e coupling c o n s t a n t for a t o m i c ^^Cl is —110-4 c/s, whereas t h a t for ^^Cl in NaCl is close t o zero. This is i n t e r p r e t e d as indicating v i r t u a l l y completely ionic binding w i t h a S^^S^^-electron configuration r o u n d t h e chlorine.
T h e relationship b e t w e e n decrease in coupling c o n s t a n t a n d degree of ionic c h a r a c t e r is complicated b y t h e effect of ^ ^ - h y b r i d i z a t i o n a n d TT-bonding on t h e coupling c o n s t a n t . H o w e v e r , w i t h t h e aid of some a s s u m p t i o n s (Ito et al., 1963; N a k a m u r a et al., 1961), t h e results in T a b l e V I I h a v e been o b t a i n e d .
D. Decrease in spin-orbit coupling constants
Owen (1955) h a s p o i n t e d o u t t h a t t h e s p i n - o r b i t coupling c o n s t a n t s λ " of m e t a l ions in complexes are often considerably lower t h a n t h o s e , λ, for free m e t a l ions. These c o n s t a n t s can b e d e t e r m i n e d from p a r a m a g n e t i c resonance studies, a n d Owen used t h e r a t i o λ' 7 λ as a m e a s u r e of covalent c h a r a c t e r in t h e m e t a l - l i g a n d b o n d i n g . D u n n (1959) h a s also discussed t h i s effect, w h i c h h e considers t o b e d u e t o p a r t i a l screen
ing of t h e m e t a l d-electrons from t h e nuclear charge b y t r a n s f e r of σ-bonding ligand electrons from ligand t o m e t a l (i.e. covalent σ-bond
ing). H e suggests, however, t h a t W'jX c a n n o t be i n t e r p r e t e d as simply as Owen describes.
E. Decrease in interelectronic repulsion integrals : the nephelauxetic effect A comparison of t h e s p e c t r a of complexes of a given t r a n s i t i o n m e t a l ion w i t h t h a t of t h e free gaseous m e t a l ion h a s shown (Orgel, 1955;
T a n a b e a n d Sugano, 1954) t h a t the parameters of interelectronic repul
sion ( R a c a h parameters) are smaller for the complexes t h a n for the free ion, demonstrating t h a t complex f o r m a t i o n decreases t h e repulsions between d-electrons on the transition m e t a l ion.
Jorgensen (1962a) describes t h e effect as one of cloud-expansion (the nephelauxetic effect). H e proposes t h a t decrease of the effective nuclear charge on the m e t a l d-electrons due to covalent σ-bonding w i t h the ligands causes a n expansion of the orbitals of the iZ-electrons, a n d t h a t the effect m a y be enhanced b y metal-to-ligand 7r-bonding which de- localizes the cZ-electrons on to t h e ligands. B o t h effects m u s t increase the average distance between m e t a l cî-electrons a n d hence reduce inter
electronic repulsions. T h u s the decrease i n the R a c a h parameters can be used as a n indication of the n a t u r e of the m e t a l - l i g a n d bonding.
Schaffer a n d Jorgensen (1958) list a series of m e t a l ions i n order of increasing nephelauxetic effect for complexes w i t h a given ligand
Mn2+ < Ni2+ < Cr3+ < Co^+ < Rh^+ < lr^+ (4.1) a n d a series of ligands i n order of increasing nephelauxetic effect for
complexes w i t h a given m e t a l ion
F - < H2O < NH3 < en < S C N - < C I " < C N " < B r - (4.2) a n d Jorgensen (1962b) has since extended these series.
F. Dipole moments
A n e u t r a l m e t a l halide molecule w i t h o u t a centre of s y m m e t r y will possess a dipole m o m e n t . F o r a diatomic molecule this can be related to er where e is t h e charge on either a t o m a n d r is the interatomic distance. F o r higher halides a bond m o m e n t can be defined for each m e t a l - h a l o g e n b o n d provided t h a t t h e geometry of t h e molecule is k n o w n . Such moments give a n indication of t h e p o l a r i t y of t h e bond.
T h e dipole moments of supposedly ionic molecules like the a l k a l i halides are i n all cases considerably less t h a n t h e values expected for u n i t charges a t t h e interatomic distance, being, for example, 6 0 % of the ' I d e a l ionic" value for CsF. T h e y are also lower t h a n t h e values expected for the a l k a l i halides on the basis of N Q R results, i.e.
xy ^ (4.3) where χ is t h e charge on either a t o m as given b y N Q R . I t m a y be noted
t h a t polarization, overlap a n d h y b r i d i z a t i o n effects will always m a k e the observed bond m o m e n t μ less t h a n exr ( D a i l e y a n d Townes, 1955).
A compilation of dipole m o m e n t d a t a on halides is given b y L a k a t o s etal (1959).
FeCl4- 3 7 8 GeCl4 4 5 3 PCI4+ 6 2 7 reCl,2- 2 8 2 GaCl4- 3 8 6 SiCl4 6 1 0 ZnCl42- 2 7 3 AICI4- 5 7 5
C0CI2 c.n. = 2 4 9 3
C0CI2 2 p y c.n. = 4 3 4 4 , 3 0 4
C0CI42- c.n. = 4 3 0 0
C0CI2 4 p y c.n. = 6 2 3 0
(trans)
Numbers are frequencies in cm"^. From Clark ( 1 9 6 5 ) .
G. Force constants
I n a diatomic molecule, t h e frequency of t h e stretching v i b r a t i o n of t h e molecule is d e t e r m i n e d b y t w o factors, t h e b o n d stretching force c o n s t a n t a n d t h e masses of t h e t w o a t o m s . H e n c e from e x p e r i m e n t a l l y observable v i b r a t i o n a l frequencies one m a y o b t a i n b o n d force c o n s t a n t s , which are m e a s u r e s of t h e resistance of t h e molecule t o stretching. I n p o l y a t o m i c molecules t h e s i t u a t i o n is complicated b y i n t e r a c t i o n s b e t w e e n n o n - b o n d e d a t o m s , a n d b y t h e fact t h a t v i b r a t i o n s of t h e s e molecules involve b o t h b o n d stretching a n d bending. I n molecules of fairly high s y m m e t r y , however, it is often still possible t o o b t a i n u n a m b i g u o u s values of stretching a n d b e n d i n g force c o n s t a n t s .
I t would a t first sight a p p e a r t h a t , like b o n d energies, force c o n s t a n t s are measures of t h e s t r e n g t h s of chemical b o n d s . H o w e v e r , whereas b o n d energies refer t o t h e chemically i m p o r t a n t process of s e p a r a t i o n of t w o b o n d e d a t o m s t o large distances, stretching force c o n s t a n t s refer t o v e r y small changes from t h e equilibrium b o n d distances. T h u s t h e use of t h e relative sizes of force c o n s t a n t s for diflFerent b o n d s as a m e a s u r e of t h e relative s t r e n g t h s of t h e b o n d s would strictly only be justified if t h e curve of p o t e n t i a l energy against i n t e r a t o m i c distance were t h e s a m e for all t h e b o n d s , which it is n o t .
I n spite of this, t h e r e are often correlations observed b e t w e e n stretching frequencies a n d t h e s t r e n g t h s of chemical b o n d s , a t least provided t h e restriction is m a d e t o one k i n d of b o n d only. Table V I I I h a s some d a t a on m e t a l - c h l o r i n e stretching frequencies, v(M—CI), for a n u m b e r of complexes. I t m a y be seen t h a t t h e frequency increases w i t h increasing oxidation n u m b e r of t h e central m e t a l a t o m for a series of t e t r a h e d r a l complexes. Also t h e Co—CI stretching frequency d e creases as t h e coordination n u m b e r changes from t w o t o four t o six.
A n increased b o n d s t r e n g t h w i t h increasing oxidation s t a t e is e x p e c t e d (see Tables I - I V ) . T h e increased coordination n u m b e r is e x p e c t e d t o reduce t h e average b o n d s t r e n g t h because of l i g a n d - l i g a n d repulsions.
F u r t h e r e x a m p l e s are given b y Clark (1965) a n d A d a m s et al. (1963).
T A B L E V I I I . M e t a l - l i g a n d s t r e t c h i n g f r e q u e n c i e s v ( M — C I ) a s a f u n c t i o n o f o x i d a t i o n s t a t e o f m e t a l i o n a n d o f c o o r d i n a t i o n n u m b e r (c.n.)
H. X-Ray diffraction
T h i s m e t h o d , in t h e o r y t h e m o s t direct available for d e t e c t i n g t h e electron d i s t r i b u t i o n in a m e t a l - h a l o g e n b o n d , is n o t a t p r e s e n t suffi
ciently sensitive t o b e u s e d in a q u a n t i t a t i v e w a y . I t is n o t e v e n clear, for e x a m p l e , t h a t t h e electron d i s t r i b u t i o n in t h e crystalline alkali halides is m u c h closer t o N a + C l " t h a n t o Na^CP (Weiss, 1965).
5 . Theoretical
Most of t h e calculations in Sections 5A, Β a n d C were originally carried o u t b y P e a r s o n a n d G r a y (1963). Changes in t h e m e t h o d s u s e d t o calculate v a n d e r W a a l s a t t r a c t i o n a n d repulsions a n d in t h e b o n d l e n g t h s u s e d for t h e alkaline e a r t h halides a n d ZnClg h a v e caused s o m e small differences b e t w e e n t h e v a l u e s given here a n d t h o s e in P e a r s o n a n d G r a y .
A. The hard sphere ion model
B y t r e a t i n g a molecule or complex ion as a n a s s e m b l y of spherical, non-polarizable ions, one m a y w r i t e a n expression for t h e p o t e n t i a l energy function for t h e molecule as a s u m of t h e i n t e r a c t i o n s b e t w e e n each p a i r of ions i a n d j in t h e molecule.
Ε = Σ i^i^^e^R,, - d,,IR% + &,,e-i;%) (5.1) where Ε is in ergs, a n d z^e are t h e charges on t h e ions in e.s.u., a n d
B i j is t h e d i s t a n c e b e t w e e n t h e ions in cm. T h e p a r a m e t e r s α^,,·, b^j a n d dij are o b t a i n e d from virial coefficient d a t a for t h e isoelectronic i n e r t gas a t o m s using t h e rules of Mason (1955). T h e virial coefficient d a t a is from W h a l l e y a n d Schneider (1955) e x c e p t for H e a n d N e (which t h e s e a u t h o r s d o n o t include) w h e r e t h e d a t a is from Mason a n d R i c e (1954). I n t e r i o n i c distances are from S u t t o n (1958) e x c e p t for t h o s e of t h e alkaline e a r t h halides (Akishin a n d Spiridonov, 1957).
T h e results in T a b l e I X (p. 77) show good a g r e e m e n t w i t h t h e experi
m e n t a l values for t h e alkali m e t a l chlorides, s o m e w h a t less satisfactory results for t h e alkaline e a r t h s (especially BeClg) a n d poor results for
A I C I 3 a n d TiCl4, indicating a s t e a d y increase in covalent c h a r a c t e r . A v a l u e is also included for a n anionic complex, AlFg^-.
B. Polarizable ion model
T h e coordinate b o n d e n e r g y per bond for a n e u t r a l m e t a l halide can b e w r i t t e n i n t h e form
p, fe' / V a , Β
where / is a geometric factor w i t h t h e values 1·00 for a d i a t o m i c
molecule, 1-75 for a linear t r i a t o m i c , 2-44 for a trigonal planar t e t r a - tomic a n d 3*08 for a tetrahedral pentatomic molecule; ^ is a similar factor w i t h corresponding values of 0, 0-25, 1-01 a n d 1-15. R is t h e metal-halogen distance a n d α the polarizability of the halide ion ( t a k e n as 3-0 X 10-2^ cm^ for C1-). W h e n e, the charge on the electron, is i n e.s.u. a n d R is i n c m , the coordinate bond energy of the molecule Ε is obtained i n ergs.
T h e first t e r m on t h e r i g h t h a n d side is t h e same as for t h e h a r d sphere model. T h e second is a composite of the following terms: energy required to f o r m induced dipoles, induced dipole-charge interactions a n d induced dipole-induced dipole interactions. T h e final t e r m is a repulsion t e r m , the constant Β being evaluated b y differentiating Ε w i t h respect to Β a n d p u t t i n g (dEjdB) equal to zero for the k n o w n equilibrium value of B.
T h e results listed i n T a b l e I X show t h a t this model works compara
t i v e l y well, giving poor results only for L i C l , BeClg a n d TiCl4. T h e high results for L i C l a n d BeClg are probably p a r t l y due to penetration effects (i.e. the cation, because of its small n u m b e r of electrons, pene
trates into the electron cloud of the anion, causing a n overestimation of the coulombic energy t e r m ) .
This model can also be used for complex anions, a n d for octahedral anions of general formula M X ^ ^ - the following relationship is obtained:
T o t a l c.b.e. = ^ - - ^.^,;^^:^^) + i^'^)
T h e c.b.e. calculated for A l F g ^ - , using a value of 0-64 χ lO-^^ cm^
for the polarizability of fiuoride ion (Tessman et al., 1953), is included i n T a b l e I X a n d is seen to be i n reasonable agreement w i t h the experimental value.
C. Localized molecular orbital method
F o r this m e t h o d (Pearson a n d G r a y , 1963), a two-center molecular orbital
Φμο =Φβ+ Η. (5.4) is constructed for each m e t a l - h a l o g e n bond b y linear combination of
an atomic orbital, φ^, of a valence electron on the halogen a t o m , w i t h a n atomic orbital, φ β, on the m e t a l a t o m , λ is a m i x i n g coefficient, related t o x, t h e fractional negative charge on the halogen a t o m b y
Defining Ê as the one-electron H a m i l t o n i a n , the m e t a l a n d halogen
Coulomb integrals a r e
H,, = ^ M A r (5.6)
Ηήή = Ιφβΰφβάτ (5.7)
a n d t h e exchange integral is
Η,β =^ ίΦ,Εφβάτ (5.8)
T h e overlap integral, Ιφ^φβάτ, is a s s u m e d t o b e zero or negligible.
F r o m this, t h e energy of a pair of b o n d i n g electrons m a y b e w r i t t e n a s
TT = (1 + x)H^f + 2(1 - x-^fim,, + (1 - x)H,, (5.9)
T h e integrals j f f a a » Hββ a n d Η^^β a r e e v a l u a t e d from empirical d a t a , a n d a r e functions of x, t h e fraction of ionic c h a r a c t e r i n t h e b o n d . P e a r s o n a n d G r a y p u t H^^ for a d i a t o m i c molecule equal t o t h e n e g a t i v e of t h e ionization p o t e n t i a l of t h e n e u t r a l m e t a l a t o m , t h u s ignoring t h e possibility t h a t b o t h electrons will b e simultaneously o n t h e m e t a l a t o m (a reasonable a s s u m p t i o n in view of t h e high p o l a r i t y of t h e bonds).
F o r higher halides t h e possibility of t h e s i m u l t a n e o u s presence of m o r e t h a n o n e valence electron o n t h e m e t a l h a s t o b e considered, a n d for t h e t r i a t o m i c case o n e c a n w r i t e
H^^ = - xlP, - (1 - χ ή ^ + ^ (5.10)
This implies t h a t for a fraction χ of t h e t i m e t h e only valence electron on t h e m e t a l ion is t h a t t o which H^^ relates, while for t h e r e m a i n i n g t i m e t w o electrons a r e p r e s e n t a n d a m e a n ionization p o t e n t i a l is used.
(To avoid counting electron-electron repulsions twice, t h e energy of t h e electron o n t h e m e t a l a t o m i n t h e field of t h e electrons o n t h e halogen a t o m is not included, b u t t h e energy of t h e halogen electrons in t h e field p r o v i d e d b y electrons o n t h e m e t a l a t o m is included.) Corresponding e q u a t i o n s for H^^ for MXg a n d MX4 are given b y P e a r s o n a n d G r a y (1963).
T h e valence s t a t e p r e p a r a t i o n energy, v.s.p.e., is t h e energy r e q u i r e d t o p r o m o t e a n electron i n t o a valence, or b o n d i n g , s t a t e a s calculated (for sp-, sp^-, a n d 5^^-valence states) b y Mofi&tt (1954).
T h e corresponding Coulomb integral for t h e halogen represents t h e energy of a n electron in t h e field of t h e halogen a t o m a n d t h e fields p r o v i d e d b y t h e a v e r a g e charges o n t h e o t h e r a t o m s .
Ηήή==-(1- ^)v.s.i.p. - X (^'^·ί'Ρ^-ΈΑ) _ (5.11) T h e valence s t a t e ionization p o t e n t i a l v.s.i.p. is t h e ionization p o t e n t i a l
of t h e halogen a t o m t o a n ion with t h e configuration (sy(Px)HPyY{Pzy.
E A is t h e electron affinity of t h e halogen a n d / is t h e s a m e n u m e r i c a l factor as w a s used in t h e polarizable ion model.
T h e exchange integral Η^ή w a s t a k e n t o b e p r o p o r t i o n a l t o t h e geometric m e a n of t h e single b o n d energies, ί / ^ α Ε ήή oi t h e m e t a l a n d t h e halogen.
2Η,ή = -\'2{Ε,,ΕήήΥΐ^ (5.12)
ΕββΘ8 t h e usual b o n d energy of t h e halogen a n d E^a, t h e single b o n d e n e r g y of t h e gaseous molecule Mg, dissociating i n t o valence s t a t e a t o m s . T h e factor of 1-2 is chosen t o allow 2 0 % of t h e covalent b o n d energy in Mg a n d t o be cancelled b y repulsion energy of t h e v a n der W a a l s t y p e .
T o find t h e v a l u e of χ for t h e molecule dWjdx is p u t equal t o zero, t h u s fixing X for t h e b e s t energy of t h e system. Since t h e q u a n t i t y —W refers t o t h e process
MX(g) > M+(g) + X+(g) + 2e (5.13) it differs from t h e coordinate b o n d energy b y t h e ionization p o t e n t i a l
a n d electron afiinity of t h e halogen. Also, repulsion t e r m s h a v e been o m i t t e d . A suitable t e r m of t h i s k i n d is a s s u m e d t o b e t h e v a n der W a a l s repulsion calculated from t h e h a r d sphere model. T h u s t h e energy p e r b o n d is
Ε = -W - (v.s.i.p. + E A ) + be-^^ (5.14) T h e numerical values used for t h e s e calculations are listed in P e a r s o n
a n d G r a y e x c e p t for t h e v a n der W a a l s repulsions which, as m e n t i o n e d earlier, h a v e been calculated for t h i s p a p e r b y a slightly different m e t h o d . T h e results are given in T a b l e I X .
I t is noticeable t h a t t h e r e is a fairly close correspondence b e t w e e n t h e energies calculated b y t h e polarized ion model a n d b y t h e localized molecular orbital model, showing t h a t t h e y are b o t h a p p r o x i m a t e w a y s of calculating t h e s a m e effect, n a m e l y t h e distortion of t h e electron cloud of t h e anion in t h e field of t h e cation. I t is i m p o r t a n t t o n o t e t h a t a model using b o t h polarization effects and covalent b o n d i n g would be incorrect.
D. Modified Wolfsberg-Helmholz method
T h e so-called Wolfsberg-Helmholz ( W H ) m e t h o d is a n L C A O - M O o n e using t h e one-electron a p p r o x i m a t i o n . T h e secular d e t e r m i n a n t
\H^, - G,^e\ = 0 (5.15) is solved after factoring b y g r o u p t h e o r y . T h e diagonal t e r m s for t h e
