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The skeletal vibrations of some cobalt (III) carbonato-, phosphato- and sulphato-complexes
Spectrochimica Aeta, Vol. 24A, pp. 1139 to 1147. Pergamon Press 1968. Printed in Northern Ireland
The skeletal vibrations of some cobalt(IH) carbonato-, phosphatoand sulphato-complexes J. A. GOLDSMITH, A. HEZEL and S. D. R o s s Department of Chemistry, Chelsea College of Science and Technology
(Received 21 October 1967)
Abstract--The infra-red spectra of eighteen complexes have been studied in the region 500-60 cm -1. l~ormal co-ordinate analysis of the systems Co(NHa)sX with C4v symmetry, and eisCo(NHa)4X 2 with C2v symmetry are carried out using a general valence force field; the observed frequencies are assigned to the skeletal and lattice vibrations. INTRODUCTION
SUBSTITUTED cobaltammine skeletons have been studied b y a number of workers [1-7], and normal co-ordinate analyses of Co(NH3)sX [1, 5, 7] and cis-Co(NHa)4X 2 [7] have been carried out, using a modified Urey-Bradley force field; the U B F F force constants have been calculated for systems where X is halogen or NO 2. FUJITA et al. [8] have considered the M - - O stretching and bending vibrations in cobalt (III) carbonato complexes in terms of the systems MO*C02[C~] and MO~*CO [C2~]. In 1961 SHIMANOUCHI et al. [9] suggested the application of the Wilson F G matrix method to the analysis of the vibrations of two and three dimensional lattices, and recently SHIMA~OUCHI and NAKAGAWA [6, 7] have applied this method to eobaltammines. No complete studies of any complexes of these types have previously been made; FUJITA et al. [8] have located the Co--O stretching frequencies in a number of unidentate and bidentate carbonato complexes. These were found in the region 350-365 em -1 in some unidentate complexes, and at 430 and 395 cm -1 in [Co(NH3) 4 C03]C1, the only bidentate complex common to their study and this work. No attempt has been made to differentiate between NCoN, NCo0 and, in the C2~ case, OCoO bending, as considerable coupling between these modes exists. In all cases, there are more than the eight bands (4A 1 -b 4E) predicted from the C4, symmetry. The bands in the last two lines of the table are probably lattice modes; bands at similar frequencies in other compounds [Co(NH3)sX]2+Y 2 have been assigned to lattice modes [2, 5, 6, 7]. Assignments of the internal modes of the Co(NHs)50 skeleton were made on the basis of a normal co-ordinate analysis using G V F F constants, only the diagonal F elements being employed. In the analysis,f~, f R refer SHIMA~OUCHIand I. ~AKAGAWA, Spcctrochim. Acta 18, 89 (1962). SACCO~I, A. SABATINIand P. G . ~ s , Inorg. Chem. 3, 1772 (1964). W. WA~rT and D. S. KLETT, Inorg. Chem. 3, 782 (1964). S H I ~ O U C E I and I. I~AXAG~WA,Inorg. Chem. 3, 1805 (1964). SHI~A~O~CHI and I. NAKAOAW)~,Speetrochim. Aeta 22, 759 (1966). SHI~ANOUCHIand I. I~AKAGAWA,Speetrochim. Acta 22, 1707 (1966). SHnVtANOVCHrand I. NAKAGAWA,Speetrochim. Aeta 23A, 2099 (1967). [8] J . FUJITA, A. ]~. MAI~TELL a n d K . NAKAMOTO, J. Chem. Phys. 36, 339 (1962). [9] T. SHIMANOUCHI,M. TS•BOI and T. MIYAZAWA,J. Chem. Phys. 35, 1597 {1961). 1139 [1] [2] [3] [4] [5] [6] [7]
T. L. G. T. T. T. T.
1140
J.A.
GOLDSMITH,A. HEZEL a n d S. D. R o s s
T a b l e 1. D i s t r i b u t i o n o f v i b r a t i o n s a m o n g s y m m e t r y classes Unidentate complex
Activity
(Caw)
Type VCo--N vco--o
A1 B1 B~ E
Bending
i.r., R R R i.r., R
2 1 0 1
1 0 0 0
1 1 1 3
i.r., R R i.r., R i.r., R
2 0 1 1
1 0 0 1
3 2 2 2
Bidentate complex (C2v) A1 As B1 B2
T a b l e 2. O b s e r v e d frequencies (cm -1) o f u n i d e n t a t e c o m p l e x e s Cation
[Co (Ntta)5CO3] 2+
Anion
NO a-
C1-
Band a b
508 464
496 470
c
442
434
d e
Br-
I-
498 476 sh464 442
502 474 448
Br-
I-
509 482
493 485
497
500 484
438
446
437
437
330
332
329
280 258
264
264
208
210
196
--
191
204 186 / 174!
139 118 104 88 54
138 112 88 68 54
122 110
120 88
402! 346
377 346
318 288 264
328 -262 2121 202!
f g h
326 284 262
400/ 352 330 t 312J 292 254
i
222
238
232
j
184
182
k 1
134 102
146 106
176 150 130 112
--
C1-
sh418 t
sh396 356
--
1~Oa-
41o / 402 362 sh348 326 282 sh264
m
[Co(NHa)sSOa]~+
86
236 sh196 / 1801 154 124 88
-
-
54
64 50
The skeletal vibrations of some cobalt (III) complexes
to C o - - N , C o - - O s t r e t c h i n g a n d f~, fp to N C o N , NCoO bending, t h e reciprocal m a s s e s of Co, N H 3 And O r e s p e c t i v e l y ;
-
p ~ , PN a n d P x are
1
1
Pl
1141
Pz
-
rCo--N
--
rco-o
W e h a v e t a k e n rco-N = 2"0 A, rco_ o -~ 1-975 A, a n d ~ : fl - - 90 °. U n p r i m e d a n d p r i m e d b e n d i n g i n t e r a c t i o n c o n s t a n t s refer to i n t e r a c t i o n s b e t w e e n coordinates w i t h a n d w i t h o u t a c o m m o n side respectively. F elements: Species A 1 - - F l l : fR,
Species B 1
--
"F2t~----f r '
Fa3 : f , + 3 f .
F55 --- fr - - f .
Fee = ½d2(f~ + fp -- f . , + fpp) Species B z -- FT~ = d~(f, -- 2f~,, + f:~,) Species E - - Fss = fr - - f ~ F99 ~--"½d2(f~ - ~ - ~ - - L a Fl1,11 = d2(f= -- f==')
G elements: Species A1 -G12 = - - ~ M G13 = 0 G14 =
--2%/2 PMP1
Gzz : PM + lUs Gz3 :
0
G~4 ---- --Gla
Gaa =
~N
Ga4 = 0 Ga4 :
2plU(ps + 4pM)
Species B I -- G55 : Gaa G~ = 0 Gee = 2/~spl ~ Species B 2 -- G77 = 4 ~ N p l u
- - ~ , 8 ) = FlO,lO
1142
J . A . GOLDSMITH, A. HEZEL and S. D. Ross Species E - - Gss = /'~N -91-2f.~M
Gae =
a/2~M(m
-
p2)
G8,1o = --%/2/z•(Pl ~- P2)
Gs.11 = G14
G99 = e9,10 =
3flNPl 2 -~- ~txPl 2 "~- ~tM(p2 - - pl) 2 g x p 22
- - /ZNP12 + ffM(pz 2 -- pl 2)
G9,11 ---- 2/tMPl(P2 - - Pl)
Glo,lo : flXP2 2 -}- ]ZNP12 ~- tiM(P1 "~- P2)2 GlO.U ~- 2flMPl(Pl -4- P2) Gl1,11 -~ 2p12(/x N -1- 2ktM)
T h e force c o n s t a n t calculations were carried out on the U n i v e r s i t y of L o n d o n A T L A S c o m p u t e r , using a n E X C H L F p r o g r a m . As T a b l e 2 shows, b a n d s a, b, c, e, h, i, j a n d k were f o u n d in a l m o s t e v e r y c o m p o u n d , a n d t h e a s s i g n m e n t was m a d e using t h e s e as t h e eight f u n d a m e n t a l s . I t a p p e a r e d p r o b a b l e on t h e basis of t h e previous studies [1-8] t h a t b a n d s a, b, c were C o - - N s t r e t c h i n g a n d b a n d e was a C o - - O s t r e t c h i n g mode, leaving b a n d s h, i, j a n d k as b e n d i n g modes. Our calculations led to t h e a s s i g n m e n t g i v e n below: Table 3. Force constants, and calculated and observed frequencies (era-1) in unidentate complexes Species Band A1
E
e b a k c h i j
Description and assignment
F element*
calc.
obs. I
II
Yl VCo--O v2 VCo__N vs VCo_N v4 (~ vs Vco--N % d~ Ulo 6 rll (~
1"1 1"475 2-4 0.225 1"15 0.625 0.625 0"7
352 470 490 138 450 256 230 182
356 470 496 146 434 262 238 182
346 482 509 139 438 262 207 196
* Stretching and bending elements in mdyn/A and mdyn. A respectively. I n T a b l e 3, t h e first set of o b s e r v e d frequencies is t h a t of t h e c a r b o n a t o chloride, a n d t h e second, t h a t of t h e s u l p h a t o nitrate. As T a b l e 2 shows, the b a n d positions in t h e t w o groups of c o m p o u n d s are v e r y similar, a n d we considered it u n n e c e s s a r y to p e r f o r m s e p a r a t e f o r c e c o n s t a n t calculations for t h e e a r b o n a t o a n d s n l p h a t o complexes. Only b a n d i shows a m a r k e d shift. According to o u r calculations, b a n d s d, f a n d g of t h e skeletal v i b r a t i o n s are left unassigned. I t is possible to a c c o u n t for t h e s e a d d i t i o n a l b a n d s if t h e site s y m m e t r y of t h e p e n t a m m i n o a c i d o cobalt ( I I I ) ion is C2~ or lower. U n d e r these c i r c u m s t a n c e s the E frequencies will b e split a n d t h e B 1 a n d B 2 frequencies will b e c o m e infra-red active. F r o m t h e n o r m a l co-ordinate analysis we see t h a t F55(B1) is equal to Fss(E); also Fee c a n n o t
The skeletal vibrations of some cobalt (III) complexes
1143
be very different from F99. I f we assume t h a t Fee ~-- 0.6, then the calculated B 1 frequencies are 330 and 173 cm -1. The first of these agreesvery well with the observed band f; the second is close to t h a t of band j and m a y be overlapped by it; this band is split in two cases, but this m a y be simply due to breakdown of the degeneracy. Bands d and g could arise from this cause, being near to C(VCo_N) and h (bending), which are both of type E according to our assignment. The optical crystallography of two of the pentammine complexes has been studied, and we have found both to be biaxial; these are the sulphate- and carbonate/ nitrates. Since no biaxial crystal can have any sites of higher than twofold symmetry, all degenerate vibrations are totally broken down and the B 1 and B 2 modes will become infra-red active. (ii) Bidentate complexes Of the ten complexes studied, the five carbonato- and the two phosphatocomplexes have a chelate acido group, whereas the sulphate group in the three bidentate complexes is a bridging group. The skeleton in this case is CoN50, four of the nitrogen atoms belonging to ammonia groups and one to an ammino group. The overall s y m m e t r y is C,, as compared with C2~ in the seven complexes where the acido group is chelate. The vibrations of the C, system are 9A' -k 6A", all i.r. and R active. Table 4. Observed frequencies in bidentate complexes (cm-1) Cation
[Cor (NH3)4C0a] s+
Anion
N O a-
SO42-
Band a b c d e f g h i j k 1 m
528 508 488 440 402 332 318 282 202 182 152 130 b d 92
514 484 440 430 400 336 326 286 204 -142 130 106
n
C1-
516 502 458 436 398 318 312 270 198 182 142 122 102 94 86 n o t i n v e s t i g a t e d below 60 e m -1
Br526 496 476 438 396 324 306 276 -188 140 122 94
Cor (NHa)aP0a °
I524 492 460 430 392 324 300 278 204 182 148 125 b d 92
(anhydrous) 490 463 430 420 382 330 296 246 228 200 150 124 .
54
(3H20) 487 460 419 409 387 320 262 248 232 200 166 130, 121 . .
58
[C°s (NHa)sNHsS04] s+
N O a-
C1-
505 460
490 460
490
332 292 236 221 176 157 138 .
334 294
330 291 232
188 163 146
183 159 136
46
56
58
Br-
.
The complexes with a chelate acido group display more bands t h a n those with a bridging group, which is surprising in view of their higher symmetry. The following normal co-ordinate analysis applies to the C~., skeleton of the carbonate and phosphate complexes, cis-Co(NH3)40 ~. The symbols used are the same as the corresponding symbols in the previous analysis; fy refers to OCoO bending. All molecular parameters are given the same values as in the previous analysis; a = fl = ? = 90 °. These calculations were carried out on the College Elliott 803 computer, using an ALGOL program.
g . A . GOLDSMITH,A. I~ZEL and S. D. Ross
1144 F elements Species A~
-
-
--~II :
F22 : f r
-~-frr
ds d2
F44 = ¥ ( L + 2f, + f . + 2f,, + 2f~, - aft, - % 0 d ~. F55 = -~ (f~ + fp + L= + fpa + 2f==' + 2 f . . ' -- 8f=,)
.Fee
= f~ + fRR
Species A s -- F77 = d~(fp - - f~p - - 2f~p') Fss = d~(f. - - f . Species B 1 -- F99 = f . - - f . . "~10,10 = d~(f~ + f .
-- 2 f d ) -- 2 f d )
k~11,11 = dS(fp + fpp - - 2 f p / )
Species B~ -- FlS.12 = -~99 "~13,13 = d~(fp - fpp) -~14,14
=f~ - f ~
d~ F15.15 = ~ (f~ + f p
-f~
-fpp)
Species A 1 -- Gll Gz2 = 0 GlS = - - / ~ ( P l + P2) = --~/2~M(p~ -- p~) G15 ----- - - 2 p M p l Gle ----- --PM G22 G2a Gs3 :
a3~ = a35 :
f l N P l '~ -l- ~Xp2 s +
~M(PI + PP.)s
V2~[~Mp12 - - V2~,~KR2 2 -J[- V~,/.~M(P12 - - p2 2)
2pMpI(P1 + P2)
:/~M(PI + P2)
a.
= 2/ZNpl ~ + 2~txP2 s + 2/x~(p 1 _ p~)9. ----- 2%/2g}~P1(Pl -- P2)
am. =
- - ~14
2~NPlS + 4pMpI~ =
--G15
d/e6 = P x + ,uM
The skeletal vibrations of some cobalt (III) complexes
1145
Species A 2 -- G77 ---- 3pNpl 2 G7s = juNpl 2 G88 ~--- ~tNPl 2 -~- 2pxp~ ~
Species B 1 -- G99 = gN -t- 2pM G9.1o = --2V~2gMpl G9,11 = 2~¢/2~uMp2 Gloao = 3/~NPl 2 -4- 4tip2 ~
Species B2:
4flMPlP2
GlO,11 =
--~NPl 2 +
Gll,11 =
2#Np22 -4- 4pMp22 A- ~ x P l 2
G12.1~.= Gll G12.13 = G15 G12,14 :
G13
G12,15 = Gle G13,1 a = G55 G13.14 = G35 G13,15 :
G15
G14,14 :
Gee
G14.15 = G13 G15,15 :
Ga3
As with the u n i d e n t a t e complexes, there are six bands (a-f) identifiable with stretching modes. FUTJITX'S s t u d y places these a t 430 a n d 395 cm -1 in [Co(NHs)4C03]C1 , a n d our bands d a n d e in this c o m p o u n d occur a t 436 a n d 398 cm -1. H o w e v e r , the force c o n s t a n t calculations based on the n o r m a l co-ordinate analysis above do n o t entirely s u p p o r t this assignment. W e prefer to assign bands d a n d f to C o - - O stretching, b a n d d being the A 1 stretch a n d b a n d f, which occurs at 318 cm -1 in the t e t r a m m i n e chloride, the B e stretch. I n Table 5, ~obs I a n d I I are, respectively, t h e highest a n d lowest frequencies observed for the b a n d in the c a r b o n a t e complexes. A t t e n t i o n has been c o n c e n t r a t e d on these since t h e y afford a basis for comparison of force constants on going from a u n i d e n t a t e to a b i d e n t a t e structure. T h e r e are no u n i d e n t a t e p h o s p h a t e complexes, a n d the b i d e n t a t e sulphate complexes are binuclear. I t is not possible to evaluate all the force constants used, since there are m a n y more force constants t h a n frequencies; the principal stretching force constants can, however, be u n a m b i g u o u s l y evaluated. T h e r e are v e r y few o t h e r calculated force constants which are at all comparable; in studies of [Co(NHa)5X] ~+ where X is a halogen, SHIMA~OUCHI a n d NAKAGAWA [1], f o u n d Fdia(Co_N) = 1"25 m d y n / A , while in a later s t u d y of the [Co(NH3)sN02] 2+
1146
g. A. GOLDSMITH, A. HEZEL and S. D. R o s s
Table 5. Constants, and calculated and observed frequencies (em 5x) in bidentate carbanato complexes Description and assignment
Species
Band
A1
a d g k
vl, v2, va, v4,
--
v 5,
~
e b h i c j f 1
%, r9, vl0, vii , v12, v13, v14, v15,
vCo_o VCo_N 6 ~ VCo--~¢ ~ Vco_0 6
B1 B2
F element* talc.
VCo_N VCo_N (~ 6
1-85 1-85 0.90 0"40 0.30 1-25 1.45 0.80 0.40 1.45 0-40 1.20 0.30
* F stretching elements in mdyn/•;
527 430 308 149 38 396 496 273 201 459 191 318 129
obs. I
II
528 440 318 152 -402 508 282 204 488 188 336 130
516 430 300 140 -392 492 270 198 458 182 318 122
bending elements in mdyn. ~ .
Table 6. Principal stretching force constants in carbonate complexes (md3m/A)
fCo-N = f~ fCo-O = f R
Unidentate
Bidentate
1.475 1.1
1.6 1'25
i o n [7] t h e c o r r e s p o n d i n g v a l u e is 1.14 m d y n / A . N o v a l u e s o f t h e C o - - O s t r e t c h i n g f o r c e c o n s t a n t e x i s t e x c e p t t h a t c a l c u l a t e d b y F U J I T A e t a l . [8]; s i n c e in t h i s c a s e t h e C o - - O b o n d s a r e r e g a r d e d p u r e l y a s p a r t o f t h e c o m p l e x e d c a r b o n a t e ion, t h e i r U B F F f o r c e c o n s t a n t o f 2.00 m y d n / A f o r K c o _ o is i n n o w a y c o m p a r a b l e w i t h o u r values. T h e so f a r u n a s s i g n e d b a n d s m , n i n T a b l e 4 a r e o f s i m i l a r f r e q u e n c y t o b a n d s 1, m i n T a b l e 2, a n d , l i k e t h e m , c a n r e a s o n a b l y b e a t t r i b u t e d t o l a t t i c e v i b r a t i o n s .
EXPERIMENTAL T h e s p e c t r a w e r e r u n , a s R i g i d e x d i s c s , c o n t a i n i n g 20 m g s a m p l e t o 200 m g R i g i d e x , o n a R e s e a r c h a n d I n d u s t r i a l I n s t r u m e n t s Co. F S - 6 2 0 - E L F o u r i e r s p e c t r o m e t e r . D e t a i l s o f t h e p r e p a r a t i o n o f t h e s a m p l e h a v e b e e n g i v e n p r e v i o u s l y [10]. T h e s p e c t r a w e r e c o m p u t e d o v e r t h e r e g i o n 4 0 - 5 0 0 c m -1, o r in s o m e c a s e s 6 0 - 5 0 0 c m -1, o n t h e U n i v e r s i t y o f L o n d o n A T L A S c o m p u t e r .
CONCLUSIONS The spectra of eighteen cobalt (III) acido complexes have been recorded, and bands assigned to the skeletal vibrations of both the unidentate and bidentate [10] A. HEZEL and S. D. Ross, S p e c t r o c h i m A c t a . 24A, 131 (1968).
The skeletal vibrations of some cobalt (III) complexes
1147
complexes, by means of a normal co-ordinate analysis employing a GVFF potential function. Bands additional to the eight expected fundamentals in the unidentate complexes may arise due to site symmetry effects; optical crystallography showed that this explanation is possible, some of the complexes being biaxial. Some low frequency bands are assigned to lattice vibrations. The spectra of the bidentate carbonate complexes were also assigned, the majority of the compounds showing all the predicted bands. Again some bands assignable to the lattice were found. Separate force constant calculations were not made for the phosphate complexes, since it is clear that only quite small adjustments of the force constants are required to fit the same assignments. No analysis was carried out on the binuclear sulphate complexes; there are less bands in their spectra than would be expected from the effective Cs symmetry of the eobaltammine skeleton.
Acknowledgements--The authors
are grateful to the Science Research Council for a grant for the purchase of the Fourier spectrometer (to S. D. R.) and for a research studentship (to A. H.). The authors also wish to th a n k Mr. D. BROWN of the College Computer Unit for devising the ALGOL program, and Mr. H. Zv~ev, of the Geology Department for carrying out the optical crystallographic work.
13
The skeletal vibrations of some cobalt(IH) carbonato-, phosphatoand sulphato-complexes J. A. GOLDSMITH, A. HEZEL and S. D. R o s s Department of Chemistry, Chelsea College of Science and Technology
(Received 21 October 1967)
Abstract--The infra-red spectra of eighteen complexes have been studied in the region 500-60 cm -1. l~ormal co-ordinate analysis of the systems Co(NHa)sX with C4v symmetry, and eisCo(NHa)4X 2 with C2v symmetry are carried out using a general valence force field; the observed frequencies are assigned to the skeletal and lattice vibrations. INTRODUCTION
SUBSTITUTED cobaltammine skeletons have been studied b y a number of workers [1-7], and normal co-ordinate analyses of Co(NH3)sX [1, 5, 7] and cis-Co(NHa)4X 2 [7] have been carried out, using a modified Urey-Bradley force field; the U B F F force constants have been calculated for systems where X is halogen or NO 2. FUJITA et al. [8] have considered the M - - O stretching and bending vibrations in cobalt (III) carbonato complexes in terms of the systems MO*C02[C~] and MO~*CO [C2~]. In 1961 SHIMANOUCHI et al. [9] suggested the application of the Wilson F G matrix method to the analysis of the vibrations of two and three dimensional lattices, and recently SHIMA~OUCHI and NAKAGAWA [6, 7] have applied this method to eobaltammines. No complete studies of any complexes of these types have previously been made; FUJITA et al. [8] have located the Co--O stretching frequencies in a number of unidentate and bidentate carbonato complexes. These were found in the region 350-365 em -1 in some unidentate complexes, and at 430 and 395 cm -1 in [Co(NH3) 4 C03]C1, the only bidentate complex common to their study and this work. No attempt has been made to differentiate between NCoN, NCo0 and, in the C2~ case, OCoO bending, as considerable coupling between these modes exists. In all cases, there are more than the eight bands (4A 1 -b 4E) predicted from the C4, symmetry. The bands in the last two lines of the table are probably lattice modes; bands at similar frequencies in other compounds [Co(NH3)sX]2+Y 2 have been assigned to lattice modes [2, 5, 6, 7]. Assignments of the internal modes of the Co(NHs)50 skeleton were made on the basis of a normal co-ordinate analysis using G V F F constants, only the diagonal F elements being employed. In the analysis,f~, f R refer SHIMA~OUCHIand I. ~AKAGAWA, Spcctrochim. Acta 18, 89 (1962). SACCO~I, A. SABATINIand P. G . ~ s , Inorg. Chem. 3, 1772 (1964). W. WA~rT and D. S. KLETT, Inorg. Chem. 3, 782 (1964). S H I ~ O U C E I and I. I~AXAG~WA,Inorg. Chem. 3, 1805 (1964). SHI~A~O~CHI and I. NAKAOAW)~,Speetrochim. Aeta 22, 759 (1966). SHI~ANOUCHIand I. I~AKAGAWA,Speetrochim. Acta 22, 1707 (1966). SHnVtANOVCHrand I. NAKAGAWA,Speetrochim. Aeta 23A, 2099 (1967). [8] J . FUJITA, A. ]~. MAI~TELL a n d K . NAKAMOTO, J. Chem. Phys. 36, 339 (1962). [9] T. SHIMANOUCHI,M. TS•BOI and T. MIYAZAWA,J. Chem. Phys. 35, 1597 {1961). 1139 [1] [2] [3] [4] [5] [6] [7]
T. L. G. T. T. T. T.
1140
J.A.
GOLDSMITH,A. HEZEL a n d S. D. R o s s
T a b l e 1. D i s t r i b u t i o n o f v i b r a t i o n s a m o n g s y m m e t r y classes Unidentate complex
Activity
(Caw)
Type VCo--N vco--o
A1 B1 B~ E
Bending
i.r., R R R i.r., R
2 1 0 1
1 0 0 0
1 1 1 3
i.r., R R i.r., R i.r., R
2 0 1 1
1 0 0 1
3 2 2 2
Bidentate complex (C2v) A1 As B1 B2
T a b l e 2. O b s e r v e d frequencies (cm -1) o f u n i d e n t a t e c o m p l e x e s Cation
[Co (Ntta)5CO3] 2+
Anion
NO a-
C1-
Band a b
508 464
496 470
c
442
434
d e
Br-
I-
498 476 sh464 442
502 474 448
Br-
I-
509 482
493 485
497
500 484
438
446
437
437
330
332
329
280 258
264
264
208
210
196
--
191
204 186 / 174!
139 118 104 88 54
138 112 88 68 54
122 110
120 88
402! 346
377 346
318 288 264
328 -262 2121 202!
f g h
326 284 262
400/ 352 330 t 312J 292 254
i
222
238
232
j
184
182
k 1
134 102
146 106
176 150 130 112
--
C1-
sh418 t
sh396 356
--
1~Oa-
41o / 402 362 sh348 326 282 sh264
m
[Co(NHa)sSOa]~+
86
236 sh196 / 1801 154 124 88
-
-
54
64 50
The skeletal vibrations of some cobalt (III) complexes
to C o - - N , C o - - O s t r e t c h i n g a n d f~, fp to N C o N , NCoO bending, t h e reciprocal m a s s e s of Co, N H 3 And O r e s p e c t i v e l y ;
-
p ~ , PN a n d P x are
1
1
Pl
1141
Pz
-
rCo--N
--
rco-o
W e h a v e t a k e n rco-N = 2"0 A, rco_ o -~ 1-975 A, a n d ~ : fl - - 90 °. U n p r i m e d a n d p r i m e d b e n d i n g i n t e r a c t i o n c o n s t a n t s refer to i n t e r a c t i o n s b e t w e e n coordinates w i t h a n d w i t h o u t a c o m m o n side respectively. F elements: Species A 1 - - F l l : fR,
Species B 1
--
"F2t~----f r '
Fa3 : f , + 3 f .
F55 --- fr - - f .
Fee = ½d2(f~ + fp -- f . , + fpp) Species B z -- FT~ = d~(f, -- 2f~,, + f:~,) Species E - - Fss = fr - - f ~ F99 ~--"½d2(f~ - ~ - ~ - - L a Fl1,11 = d2(f= -- f==')
G elements: Species A1 -G12 = - - ~ M G13 = 0 G14 =
--2%/2 PMP1
Gzz : PM + lUs Gz3 :
0
G~4 ---- --Gla
Gaa =
~N
Ga4 = 0 Ga4 :
2plU(ps + 4pM)
Species B I -- G55 : Gaa G~ = 0 Gee = 2/~spl ~ Species B 2 -- G77 = 4 ~ N p l u
- - ~ , 8 ) = FlO,lO
1142
J . A . GOLDSMITH, A. HEZEL and S. D. Ross Species E - - Gss = /'~N -91-2f.~M
Gae =
a/2~M(m
-
p2)
G8,1o = --%/2/z•(Pl ~- P2)
Gs.11 = G14
G99 = e9,10 =
3flNPl 2 -~- ~txPl 2 "~- ~tM(p2 - - pl) 2 g x p 22
- - /ZNP12 + ffM(pz 2 -- pl 2)
G9,11 ---- 2/tMPl(P2 - - Pl)
Glo,lo : flXP2 2 -}- ]ZNP12 ~- tiM(P1 "~- P2)2 GlO.U ~- 2flMPl(Pl -4- P2) Gl1,11 -~ 2p12(/x N -1- 2ktM)
T h e force c o n s t a n t calculations were carried out on the U n i v e r s i t y of L o n d o n A T L A S c o m p u t e r , using a n E X C H L F p r o g r a m . As T a b l e 2 shows, b a n d s a, b, c, e, h, i, j a n d k were f o u n d in a l m o s t e v e r y c o m p o u n d , a n d t h e a s s i g n m e n t was m a d e using t h e s e as t h e eight f u n d a m e n t a l s . I t a p p e a r e d p r o b a b l e on t h e basis of t h e previous studies [1-8] t h a t b a n d s a, b, c were C o - - N s t r e t c h i n g a n d b a n d e was a C o - - O s t r e t c h i n g mode, leaving b a n d s h, i, j a n d k as b e n d i n g modes. Our calculations led to t h e a s s i g n m e n t g i v e n below: Table 3. Force constants, and calculated and observed frequencies (era-1) in unidentate complexes Species Band A1
E
e b a k c h i j
Description and assignment
F element*
calc.
obs. I
II
Yl VCo--O v2 VCo__N vs VCo_N v4 (~ vs Vco--N % d~ Ulo 6 rll (~
1"1 1"475 2-4 0.225 1"15 0.625 0.625 0"7
352 470 490 138 450 256 230 182
356 470 496 146 434 262 238 182
346 482 509 139 438 262 207 196
* Stretching and bending elements in mdyn/A and mdyn. A respectively. I n T a b l e 3, t h e first set of o b s e r v e d frequencies is t h a t of t h e c a r b o n a t o chloride, a n d t h e second, t h a t of t h e s u l p h a t o nitrate. As T a b l e 2 shows, the b a n d positions in t h e t w o groups of c o m p o u n d s are v e r y similar, a n d we considered it u n n e c e s s a r y to p e r f o r m s e p a r a t e f o r c e c o n s t a n t calculations for t h e e a r b o n a t o a n d s n l p h a t o complexes. Only b a n d i shows a m a r k e d shift. According to o u r calculations, b a n d s d, f a n d g of t h e skeletal v i b r a t i o n s are left unassigned. I t is possible to a c c o u n t for t h e s e a d d i t i o n a l b a n d s if t h e site s y m m e t r y of t h e p e n t a m m i n o a c i d o cobalt ( I I I ) ion is C2~ or lower. U n d e r these c i r c u m s t a n c e s the E frequencies will b e split a n d t h e B 1 a n d B 2 frequencies will b e c o m e infra-red active. F r o m t h e n o r m a l co-ordinate analysis we see t h a t F55(B1) is equal to Fss(E); also Fee c a n n o t
The skeletal vibrations of some cobalt (III) complexes
1143
be very different from F99. I f we assume t h a t Fee ~-- 0.6, then the calculated B 1 frequencies are 330 and 173 cm -1. The first of these agreesvery well with the observed band f; the second is close to t h a t of band j and m a y be overlapped by it; this band is split in two cases, but this m a y be simply due to breakdown of the degeneracy. Bands d and g could arise from this cause, being near to C(VCo_N) and h (bending), which are both of type E according to our assignment. The optical crystallography of two of the pentammine complexes has been studied, and we have found both to be biaxial; these are the sulphate- and carbonate/ nitrates. Since no biaxial crystal can have any sites of higher than twofold symmetry, all degenerate vibrations are totally broken down and the B 1 and B 2 modes will become infra-red active. (ii) Bidentate complexes Of the ten complexes studied, the five carbonato- and the two phosphatocomplexes have a chelate acido group, whereas the sulphate group in the three bidentate complexes is a bridging group. The skeleton in this case is CoN50, four of the nitrogen atoms belonging to ammonia groups and one to an ammino group. The overall s y m m e t r y is C,, as compared with C2~ in the seven complexes where the acido group is chelate. The vibrations of the C, system are 9A' -k 6A", all i.r. and R active. Table 4. Observed frequencies in bidentate complexes (cm-1) Cation
[Cor (NH3)4C0a] s+
Anion
N O a-
SO42-
Band a b c d e f g h i j k 1 m
528 508 488 440 402 332 318 282 202 182 152 130 b d 92
514 484 440 430 400 336 326 286 204 -142 130 106
n
C1-
516 502 458 436 398 318 312 270 198 182 142 122 102 94 86 n o t i n v e s t i g a t e d below 60 e m -1
Br526 496 476 438 396 324 306 276 -188 140 122 94
Cor (NHa)aP0a °
I524 492 460 430 392 324 300 278 204 182 148 125 b d 92
(anhydrous) 490 463 430 420 382 330 296 246 228 200 150 124 .
54
(3H20) 487 460 419 409 387 320 262 248 232 200 166 130, 121 . .
58
[C°s (NHa)sNHsS04] s+
N O a-
C1-
505 460
490 460
490
332 292 236 221 176 157 138 .
334 294
330 291 232
188 163 146
183 159 136
46
56
58
Br-
.
The complexes with a chelate acido group display more bands t h a n those with a bridging group, which is surprising in view of their higher symmetry. The following normal co-ordinate analysis applies to the C~., skeleton of the carbonate and phosphate complexes, cis-Co(NH3)40 ~. The symbols used are the same as the corresponding symbols in the previous analysis; fy refers to OCoO bending. All molecular parameters are given the same values as in the previous analysis; a = fl = ? = 90 °. These calculations were carried out on the College Elliott 803 computer, using an ALGOL program.
g . A . GOLDSMITH,A. I~ZEL and S. D. Ross
1144 F elements Species A~
-
-
--~II :
F22 : f r
-~-frr
ds d2
F44 = ¥ ( L + 2f, + f . + 2f,, + 2f~, - aft, - % 0 d ~. F55 = -~ (f~ + fp + L= + fpa + 2f==' + 2 f . . ' -- 8f=,)
.Fee
= f~ + fRR
Species A s -- F77 = d~(fp - - f~p - - 2f~p') Fss = d~(f. - - f . Species B 1 -- F99 = f . - - f . . "~10,10 = d~(f~ + f .
-- 2 f d ) -- 2 f d )
k~11,11 = dS(fp + fpp - - 2 f p / )
Species B~ -- FlS.12 = -~99 "~13,13 = d~(fp - fpp) -~14,14
=f~ - f ~
d~ F15.15 = ~ (f~ + f p
-f~
-fpp)
Species A 1 -- Gll Gz2 = 0 GlS = - - / ~ ( P l + P2) = --~/2~M(p~ -- p~) G15 ----- - - 2 p M p l Gle ----- --PM G22 G2a Gs3 :
a3~ = a35 :
f l N P l '~ -l- ~Xp2 s +
~M(PI + PP.)s
V2~[~Mp12 - - V2~,~KR2 2 -J[- V~,/.~M(P12 - - p2 2)
2pMpI(P1 + P2)
:/~M(PI + P2)
a.
= 2/ZNpl ~ + 2~txP2 s + 2/x~(p 1 _ p~)9. ----- 2%/2g}~P1(Pl -- P2)
am. =
- - ~14
2~NPlS + 4pMpI~ =
--G15
d/e6 = P x + ,uM
The skeletal vibrations of some cobalt (III) complexes
1145
Species A 2 -- G77 ---- 3pNpl 2 G7s = juNpl 2 G88 ~--- ~tNPl 2 -~- 2pxp~ ~
Species B 1 -- G99 = gN -t- 2pM G9.1o = --2V~2gMpl G9,11 = 2~¢/2~uMp2 Gloao = 3/~NPl 2 -4- 4tip2 ~
Species B2:
4flMPlP2
GlO,11 =
--~NPl 2 +
Gll,11 =
2#Np22 -4- 4pMp22 A- ~ x P l 2
G12.1~.= Gll G12.13 = G15 G12,14 :
G13
G12,15 = Gle G13,1 a = G55 G13.14 = G35 G13,15 :
G15
G14,14 :
Gee
G14.15 = G13 G15,15 :
Ga3
As with the u n i d e n t a t e complexes, there are six bands (a-f) identifiable with stretching modes. FUTJITX'S s t u d y places these a t 430 a n d 395 cm -1 in [Co(NHs)4C03]C1 , a n d our bands d a n d e in this c o m p o u n d occur a t 436 a n d 398 cm -1. H o w e v e r , the force c o n s t a n t calculations based on the n o r m a l co-ordinate analysis above do n o t entirely s u p p o r t this assignment. W e prefer to assign bands d a n d f to C o - - O stretching, b a n d d being the A 1 stretch a n d b a n d f, which occurs at 318 cm -1 in the t e t r a m m i n e chloride, the B e stretch. I n Table 5, ~obs I a n d I I are, respectively, t h e highest a n d lowest frequencies observed for the b a n d in the c a r b o n a t e complexes. A t t e n t i o n has been c o n c e n t r a t e d on these since t h e y afford a basis for comparison of force constants on going from a u n i d e n t a t e to a b i d e n t a t e structure. T h e r e are no u n i d e n t a t e p h o s p h a t e complexes, a n d the b i d e n t a t e sulphate complexes are binuclear. I t is not possible to evaluate all the force constants used, since there are m a n y more force constants t h a n frequencies; the principal stretching force constants can, however, be u n a m b i g u o u s l y evaluated. T h e r e are v e r y few o t h e r calculated force constants which are at all comparable; in studies of [Co(NHa)5X] ~+ where X is a halogen, SHIMA~OUCHI a n d NAKAGAWA [1], f o u n d Fdia(Co_N) = 1"25 m d y n / A , while in a later s t u d y of the [Co(NH3)sN02] 2+
1146
g. A. GOLDSMITH, A. HEZEL and S. D. R o s s
Table 5. Constants, and calculated and observed frequencies (em 5x) in bidentate carbanato complexes Description and assignment
Species
Band
A1
a d g k
vl, v2, va, v4,
--
v 5,
~
e b h i c j f 1
%, r9, vl0, vii , v12, v13, v14, v15,
vCo_o VCo_N 6 ~ VCo--~¢ ~ Vco_0 6
B1 B2
F element* talc.
VCo_N VCo_N (~ 6
1-85 1-85 0.90 0"40 0.30 1-25 1.45 0.80 0.40 1.45 0-40 1.20 0.30
* F stretching elements in mdyn/•;
527 430 308 149 38 396 496 273 201 459 191 318 129
obs. I
II
528 440 318 152 -402 508 282 204 488 188 336 130
516 430 300 140 -392 492 270 198 458 182 318 122
bending elements in mdyn. ~ .
Table 6. Principal stretching force constants in carbonate complexes (md3m/A)
fCo-N = f~ fCo-O = f R
Unidentate
Bidentate
1.475 1.1
1.6 1'25
i o n [7] t h e c o r r e s p o n d i n g v a l u e is 1.14 m d y n / A . N o v a l u e s o f t h e C o - - O s t r e t c h i n g f o r c e c o n s t a n t e x i s t e x c e p t t h a t c a l c u l a t e d b y F U J I T A e t a l . [8]; s i n c e in t h i s c a s e t h e C o - - O b o n d s a r e r e g a r d e d p u r e l y a s p a r t o f t h e c o m p l e x e d c a r b o n a t e ion, t h e i r U B F F f o r c e c o n s t a n t o f 2.00 m y d n / A f o r K c o _ o is i n n o w a y c o m p a r a b l e w i t h o u r values. T h e so f a r u n a s s i g n e d b a n d s m , n i n T a b l e 4 a r e o f s i m i l a r f r e q u e n c y t o b a n d s 1, m i n T a b l e 2, a n d , l i k e t h e m , c a n r e a s o n a b l y b e a t t r i b u t e d t o l a t t i c e v i b r a t i o n s .
EXPERIMENTAL T h e s p e c t r a w e r e r u n , a s R i g i d e x d i s c s , c o n t a i n i n g 20 m g s a m p l e t o 200 m g R i g i d e x , o n a R e s e a r c h a n d I n d u s t r i a l I n s t r u m e n t s Co. F S - 6 2 0 - E L F o u r i e r s p e c t r o m e t e r . D e t a i l s o f t h e p r e p a r a t i o n o f t h e s a m p l e h a v e b e e n g i v e n p r e v i o u s l y [10]. T h e s p e c t r a w e r e c o m p u t e d o v e r t h e r e g i o n 4 0 - 5 0 0 c m -1, o r in s o m e c a s e s 6 0 - 5 0 0 c m -1, o n t h e U n i v e r s i t y o f L o n d o n A T L A S c o m p u t e r .
CONCLUSIONS The spectra of eighteen cobalt (III) acido complexes have been recorded, and bands assigned to the skeletal vibrations of both the unidentate and bidentate [10] A. HEZEL and S. D. Ross, S p e c t r o c h i m A c t a . 24A, 131 (1968).
The skeletal vibrations of some cobalt (III) complexes
1147
complexes, by means of a normal co-ordinate analysis employing a GVFF potential function. Bands additional to the eight expected fundamentals in the unidentate complexes may arise due to site symmetry effects; optical crystallography showed that this explanation is possible, some of the complexes being biaxial. Some low frequency bands are assigned to lattice vibrations. The spectra of the bidentate carbonate complexes were also assigned, the majority of the compounds showing all the predicted bands. Again some bands assignable to the lattice were found. Separate force constant calculations were not made for the phosphate complexes, since it is clear that only quite small adjustments of the force constants are required to fit the same assignments. No analysis was carried out on the binuclear sulphate complexes; there are less bands in their spectra than would be expected from the effective Cs symmetry of the eobaltammine skeleton.
Acknowledgements--The authors
are grateful to the Science Research Council for a grant for the purchase of the Fourier spectrometer (to S. D. R.) and for a research studentship (to A. H.). The authors also wish to th a n k Mr. D. BROWN of the College Computer Unit for devising the ALGOL program, and Mr. H. Zv~ev, of the Geology Department for carrying out the optical crystallographic work.
13