Far infrared and Raman spectra, normal coordinate analysis and potential energy distribution for the dimeric rhodium(II) complexes with oxygen and nitrogen donor ligands

Spectrochimlco Am, Vol. 45A, No. 8, pp. 835-843, Printed in Great Britain.

1989. Maxwell

05846539p39 13.00+0.00 Pcrgamon Macmillan plc

Far infrared and Raman spectra, normal coordinate analysis and potential energy distribution for the dimeric rhodium(I1) complexes with oxygen and nitrogen donor ligands F.

PRUCHNIK,*

J. HANUZA,~

K. HERMANOWICZ,~

H. PASTERNAK*

*Institute of Chemistry,

and M.

K. WAJDA-HERMANOWICZ,*

ZUBER*

Wroclaw University, Poland; and tInstitute for Low Temperature and Structure Research, Polish Academy of Sciences, Wroclaw, Poland

(Received 14 February 1989; accepted 23 February 1989) Abstract-Infrared and Raman spectra in the 30-500 cm- 1region have been recorded for solid rhodium(H) complexes with formate, acetate, phenanthroline, dipyridyl and mandelate ligands.1 The normal coordinate analysis and potential energy distribution were performed for the Rh,0,N4C1, dimeric molecular system of Cz. Hymmetri.

INTRODUCTION

A large number of complexes containing metal-metal bonds have been studied and their vibrational spectra reviewed extensively [l-4]. Generally, metal-metal stretches appear in the low-frequency region, 80-3OOcn--‘. For the centrosymmetric systems, v(MM) is forbidden in i.r. and allowed in Raman spectra. The deviation from the centrosymmetric structure activates these modes in the i.r. spectra. Our interest is focused on the vibrational characteristics of the dimeric rhodium(I1) complexes with a noncentrosymmetric metal-metal bond. A structure like this appears in the carboxylatorhodium complexes with phenantroline and dipyridyl ligands (Fig. 1). These compounds attract much attention as catalysts for the hydrogenation of olefms and ketones. A normal coordinate treatment of these complexes has not yet been undertaken although the mid i.r. spectra have been published by us previously [S]. Now we report the far i.r. and Raman spectral data within the region 30-500 cm-’ for several rhodium complexes with two bridging carboxylate and two N-N chelating ligands (Fig. 1). Attempts are being made to obtain a reasonable fit between the observed and calculated frequencies using a modified Urey-Bradley force field of C,, symmetry. The potential energy distribution is determined in order to describe the observed far i.r. and Raman bands. EXPERIMENTAL The 2H,O,

Rh,(HCOO),.ZH,O, Rh,(OAc),.W,O, Rh,(mand),. Rh,Cl,(HCOO),(bpy),4H,O, [Rh,Cl,(HCOO),-

(phen),l, CRh,Cl,(OAc),(phen),l.2H,O, CRWWnandLand [Rh,Cl,(mand),(pher&].4H,O @py),l.2H,O compounds were prepared by the method described previously [6]. $Ligand abbreviationsused: phen, l,lO-phenanthroline; bpy, 2,2-bipyridine; mand(S), PhCHOHCOO, (S), mandelate.

Raman spectra in the 5(r500 cm-’ region were recorded with JEOL Sl and DFS 24 spectrometers using Ar+ laser excitation (488 and 514 nm) from a Coherent Radiation CR4 source operating at 100-200 mW. The rotating disc technique was used. The far i.r. spectra in the 33-500 cm-’ region were measured on a Perkin-Elmer 180 spectrophotometer. Nujol mulls and polyethylene windows were employed. The computations were performed on a MERA 400 (Elwro Ltd., Wroclaw, Poland) computer using the CART, GMAT, UBZM, ZSYM and GFROOT programs [7]. RESULTS AND DISCUSSION

Infrared and Raman studies

Figures 2 and 3 show the far i.r. and Raman spectra of the compounds under investigation. The observed band positions and relative intensities are listed in Tables 1 and 2. The wavenumbers presented there form the input data for the normal coordinate analysis. Normal coordinate analysis input data

The Rh,O,NJl, core is common to all the complexes studied here. The structure of this molecular model is described by the Cl0 point group. For this symmetry, 30 normal modes are classified by the 11A, + 5A, +4B, + lOB, irreducible representation. The A,, B, and E, modes are both i.r. and Raman active while the A, ones are Raman active only. The dynam-

ics of the system under study may be described by means of 36 internal coordinates, 11 of which are interatomic distances and 24 are inter-bond angles. The 36th coordinate corresponds to the torsion motion of one Rh-polyhedron with respect to another. Since the values of the torsional frequencies are usually very low, they were assumed to be close to zero and therefore omitted in calculations. The representation derived on the basis of the internal coordinate set is llA, +7A, +7B, + lOB, and contains six redundant cordinates which were included in the calculations which gave rise to the zero frequencies [8]. The 835

F. PRUCHN~Ket al.

836

Fig. 1. The structure of [Rh,(OOCR),L,]

and [Rh,X,(OOCR),(N-N),]

b

,aM 100

I

1

100

where (N-N)= bpy and phen.

200

300

400

I

I

I

200

300

400

500

1

500

Fig. 2. The far i.r. (a, c, e) and Raman spectra (b,d, f) of the Rh,(HCOO),

2H,O (a, b), Rh,(OAc),. 2H,O

(c, d) and Rh,(mand), .2H,O (e, f).

symmetry coordinates applied, suitably normalized and orthogonal, are given in Table 3. The planar internal coordinates are defined in Fig. 4. The molecular parameters used for the numerical construction of the B and G matrices are listed in Table 4. The potential energy F matrix was constructed using the modified Urey-Bradley force field (MUBFF). The 18-parametric space applied was built up from 4 diagonal stretching, 7 diagonal bending and 7 interaction constants. The force constant definitions and notations used are specified in Table 5. The initial MUBFF constants associated with the rhodium-xygen stretching and bending modes were those reported by COTTON et al. [12] for RH,(HCOO), .2H,O. The analogous rhodiumnitrogen force constants were transferred from the

other metal complexes with nitrogen-donor ligands [13-153. The acceptance of the initial values for the rhodium-rhodium interactions was somewhat troublesome. The vibrational spectra of several complexes with Rh-Rh bonds have been discussed [ 161. After all, the assignment of v(Rh-Rh) in binuclear rhodium complexes is still controversial. The initial studies of authors [17-191 favour the range several 12&170cm-’ for v(Rh-Rh) in Rh,(0,CR),L2 type complexes. Other authors assigned the 280-350 cm-’ range for this mode [20]. Recently reported Raman and electronic spectral analysis was based on the lower value [21], whereas CLARK et al. [22], on the basic of electronic, i.r. Raman, resonance Raman studies and 160-180 isotope exchange, have proposed the higher

837

Dimeric rhodium(I1) complexes I

1

I

a & e I 100

I’* I 200

300

1 400

500

100

200

300

400

500

c

Fig. 3. The far i.r. (a,c,e,g,i) and Raman spectra (b,d,f, h, k) of the Rh,(HCOO),phen,Cl, (a, b), Rhz(HCOO),bpy,Cl, .4H,O (c, d), Rh,(OAc),phen,Cl,. 2H,O (e, f), Rh,(mand),phen,Cl, .4H,O (g, h) and Rh,(mand),bpy,.ZH,O (i, k).

values for the v(Rh-Rh)---near 290 cm-i. These two sets of vibrational frequencies were accepted by us as input data for a full normal coordinate analysis of the dimeric rhodium complexes. We have undertaken the NCA and PED calculations in the conviction that in such a way we would resolve this problem definitively. The initial values of the force constants associated with the Rh-Rh stretching mode were taken from those obtained for a simple diatomic model and the frequencies discussed above. PED and NCA results and discussion

Iteraction of the adjustable parameters for the molecular system studied was carried out up to the point where the average error in frequencies did not exceed 5 cm - 1 and the percentage error was 5%. At that time the iteration was continued for the K,,,, force constant only. This force constant changed from 1.85 to 0.35 mdyne A-’ gradually by steps of 0.1. The

remaining force constants were fixed at the following values: K,,, = 1.15, K,,, = 0.85, Z&-i = 0.65; HORhO =0.12, H,,,,=O.ll, H,,,,=O.lO, Ho,, =O.W, H NRhC, = 0.08, Ho,,,, = 0.075, H,,,,, = 0.073, F, =0.25, F,,=0.22, F,,=0.20, Fc,,=0.07, Fc,,=O.O6, F ORh= 0.10 and F,,, = 0.09. Full results obtained from a value of K,,,= 1.85

are listed in Tables 69, together with the calculated wavenumbers. Table 10 illustrates the variations of the PED and frequencies with K,,,, for the selected symmetry coordinates and vibrational modes. The results presented in Tables 6-10 show a high degree of coupling inside the Rh,0,N,C12 core as far as vibrational properties are concerned. The strongest mixing occurs between v(Rh-Rh) and v(Rh-X) modes of the linear X-Rh-Rh-X skeleton. The stretching vibrations of this system are characterized by three modes. For the CZVsymmetry used here these modes correspond to the v3-v,+ and v,..vs species of A,

F. PRUCHNIK et al.

838

Table 1. The far i.r. and Raman Rh,(HCOO),

Far i.r. 499 483 460 455

m m sh vs

.2H,O Raman

wavenumbers

Rh,(OAc),.2H,O

Far. i.r.

452 w

341 s

260 w 246 m

270 m 240m

158 m 155 m

438 w 383 m 372 m 334 m 326 m 311 m

285 vs 279 s

285 s

m m m sh s s

492 m 477 m 462 m 450 sh

386 s 372 s

242 m 237 m

215 m 187 m

194 w

398 m 364w 358 w 332 s

309w 292 w 287 m 281 m 270 m

168 s

171 vs 166 s 133 VW

439m 423 m 395 m 363 m 329 321 315 295

w m s, b w

282 m 273 s

239 m 235 w 218 w 199 w 190m

180 m 175 sh 172 s 158 sh

type compounds

Rh, mand, .2H,O Raman Far i.r.

480 m, b

364m

221 212 198 190 179 176

Raman

for Rh,OsO”

189 w 178 w

170 VW 164m 145 m

132 m 115w 99 w 87 sh 79 w

11ow

110m 82 w

84 m

symmetry and v2s of B, symmetry. For the extremely strong rhodium-rhodium force constant equal to K s,,s,,= 1.85 the v&4J mode arises from the coupling of the 30% RhCl stretching, 62% Rh-Rh stretching and 1% Ss, S,, S,, and S,, coordinates, which describe ORhCl, NRhCl, ORhRh and NRhRh bending vibrations. The wavenumber calculated for this force constant value is 293 cm-‘. Then, because of the greater contribution of the S,(RhRh) coordinate, this mode should be considered as a rhodium-rhodium stretching mode. When the strength of the rhodium-rhodium bond 1.15-1.25, the calculated frequendeclines to K,,,,= cies reach a value close to 260 cm- ’ and vj transforms into vq, i.e. it becomes the fourth frequency in the A, block. For values of K,,,,, within the range 1.25-1.15, the domination of the S, coordinate disappears and the S, coordinate becomes predominant. Further reduction of the K,,,, value below 1 mdyne A-’ leads to the gradual increase of the S,(RhCl) coordinate contribution. Then the vq mode becomes an RhCl stretching vibration. For the hypothetical value KRhRh=0.35, the v., mode arises from 81% S, (Rh-Cl) and 16% S,(Rh-Rh).

93 s 83 m 48 m

88 m 58 sh

The v&4,) mode is another which characterizes the vibrational motions of the X-Rh-Rh-X skeleton (X=Cl). For the extreme value of K,,,,=1.85 this mode arises from the coupling of 54% S,(RhCl), 29% S,(Rh-Rh) and 17% nearly equal contribution of S,, Sg, S,, and S,, coordinates. Therefore, for the very strong Rh-Rh bonds, the frequency at about 180 cm- ’ should be discussed as an RhCl stretching mode. Because of the reduction of K,,,, below 1.55 mdyne A-’ the contribution of the S,(Rh-Rh) coordinate becomes more significant and the band at should be considered as a about 173 cm-’ rhodium-rhodium stretching vibration. For K,,,, = 1.35, the vg mode arises from 35% S,, 39% S, and 25% bending S,, S,, S,, and S,, coordinates. After a further reduction of the K,,,, value below 0.75, what corresponds to the very weak Rh-Rh bond, the S,, S,, S,, and S, 1 contributions become predominant. For value, equal to 0.35, the vs mode the lowest K,,,, transforms into v7 and thus the frequency at about 137 cm- ’ should be discussed as a mixing of the bending vibration since it arises from 19% S, and 80% (S, + S, + S,, + S, r). It should be noted that for the very weak rhodium-rhodium bonds (K,,,, =0.84.35) the v&f,) mode activated at about

300s 281 m 265 s

297 291 286 265 259

297 w 288 w 278 s 260s

167 m 131 m

82 sh

113 m 98 m 93 m

208 m 194 m

179 m 166 m 131 m

235 vs 202 vs 193 sh

sh s vs m m

330 m

323 w

318 m

116m 102 m

166 m

180 s, b

232 m 199 sh

336 sh

330 m

w w s sh s m

331 m

445s

435 w 417 s 397 s

472 452 428 416 410 377 m m s s m

m w w s vs s sh

84 w

129 w

161 s

172 m

187 w

230 m 214 m

329 322 311 291 282 267 248

335 m

475 454 427 415 403

Rh,(HCOO),bpy,Cl,.4H,O Far i.r. Raman

447s 434 m 422 m 397 m 342 m

Rh,(HCOO),phen,Cl, Far i.r. Raman

frequencies

11ow

180m

225 s 203 s

295 sh 276 s

306 vs. b

433 m 378 s 356 m

110m 105 m

168 m

210 m

288 m

305 w

430 w 385 s

m w sh vs, b

128 w 1OOm

165 sh

238 220 199 188

284 s, b

328 m

340m

377 w

4QOm

122 w

168 m 164s.b 127 w

m m s m

109m

128 w

195 vs, b 170 m

225 w 212 w

250 w 240w

276 s 258 m 241 237 198 180

288 m 275 m

330 m

418 s 395 m, b

281 m

326 s 311 m 306 m

335 m

434 s 388 m

93 sh

16Os.b 130 m

240w 209 m 204m 182 sh 170 sh

280 s

314 m 300m

335 s

415 m

444m

464m,b

478 w 445 w

474 m 440W

Rh,mand,bpy,Cl,.2H,O Far i.r. Raman

type. complexes

Rh,mand,phen,Cl,.4H,O Far i.r. Raman

for the Rh,O,N,CI,

Rh,(OAc),phen,Cl,.2H,O Far i.r. Raman

Table 2. The i.r. and Raman

840

F. PRUCHNIK et al.

1l&120 cm- 1 includes a large contribution from the S,(Rh-Rh) coordinates (20-30%). For the extreme force constant K,,,,, this share makes a 77% S, contribution. Therefore, depending on the strength of the Rh-Rh bonds, the vj, vg, ir, or v&l,) modes could be considered as rhodium-rhodium stretching vibrations. The v2#,) mode corresponds to the third characteristic frequency of the X-Rh-Rh-X skeleton. Since 94.5% of this mode is dominated by a single 5,s coordinate, the frequency at about 221 cm- ’ is a pure rhodiumchlorine stretching. The potential energy distribution in Tables 6-9 indicates that very few of the normal modes of the system studied are dominated by a single internal coordinate. The examples are: v,(A,) and vz2(B,) modes corresponding to v(Rh-0) at 427-429 cm-‘, v&4 ,) and vzJ(B,) modes assigned to v(Rh-N) at 398 cm-‘, vr,(A,) and vls(B,) ones corresponding to the 8(0-Rh-N) at 196_199cm-’ and the v2JB,) mode being v(RhhC1). It is the rule rather, that most of the vibrations consist of concerted motions (stretching or bending) of connected groups of internal coordinates. At this stage of the discussion we can settle the controversial problem of the energetic position of the v(Rh-Rh) vibration. It is obvious that both the low frequency range favored by SAN FILLIPPO and SNIADOCH [ 173, KHARITONOV et al. [ 181, KIREEVA et al. [ 191, MISKOWSKI et al. [21] and the high frequency region assigned by KETTERINGHAM and OLDPIAM [20] and CLARK et al. [22] to this mode are correct. The low and high values of the v(Rh-Rh) frequency correspond to two separate normal modes of the X-Rh-Rh-X skeleton. Each of them has a different PED contribution of vibrations which occur primarily along the Rh-Rh bond and along the bonds nearly orthogonal to the former. The contribution of the Rh-Rh internal coordinate varies in a wide range depending on the strength of the rhodium-rhodium bond and restoring force brought about by the chelating groups. A consequence of this is the broad energetic range of two characteristic modes of the X-Rh-Rh-X skeleton. These results indicate that the energetic position of the (Rh-Rh) mode depends primarily on the nature and influence of axial ligands and somewhat less on orthogonal ligands, which can also modify the metal-metal frequency. Based on the results of the NCA and PED calculations presented here, the bands in the far i.r. region observed for dimeric rhodium complexes with an N,O-donor ligand may be classified in the following manner: 427430 cm333415 cm-’

1

230-295 cm-’ 255-260 cm-

’

v(Rh-O) v(Rh-0) and v(Rh-N) mixing v(Rh-Rh) and v(Rh-Cl) coupling 6(0-Rh-N) coupled with 6(0-Rh-0) G(N-Rh-N)

and

Dimeric rhodium(H) complexes

841

Fig. 4. Internal coordinates for the RhaO.,N,Cl, molecular system.

ca 220 cm-’

198-200 cm-’ llO-lSOcm_’ 40-155 cm-’

v(Rh-CI) 6(0-Rh-N) and 6(0-Rh-O)/ G(N-Rh-N) mixing v(Rh-Rh) and v(Rh-CI) coupling 6(0-Rh-CI), G(N-RhCl), d(O-Rh-Rh) and &N-Rh-Rh) equivalent mixing

After extrapolation of the relation between the K,,,, force constant and the calculated frequencies, and after comparison of the obtained results with observed

Table 4. Structural data for the complexes under investigation Rh,O,N,Cl, [9] Internal coordinate R

: 4

Average value (A) 2.578 2.049 2.007 2.509

Rh-Rh Rht3 Rh-N Rh-Cl

wavenumbers, the best fitting of these values was found for K,,,, = 1.55-1.69 and v~,~ 271-284 and vg,, 175-178 cm-r. In Table 11 the assignment of bands observed for the X-Rh-Rh-X skeleton is proposed. The comparability of the observed and calculated data should be emphasized. The structural parameters used in the calculations were transferred from the literature on similar molecules. This could be the reason for small discrepancies between the real and extrapolated values. The limitation of the Rh20,N,Cl, system, and an omission of the complete ligands could produce the same effect. This being so, the v(Rh-N) frequency values could be too high. Our goal however, was to find evidence for the existence of a coupling within the central X-Rh-Rh-X arrangement, and that particular quantitative and qualitative aim has been achieved. The set of data collected in our paper is the initial set for the NCA of the complete molecule.

Table 5. The notation used for the MUBFF parameters Rh,O,N,CI, molecular system Stretching force constants K IthO KNIN

K RbCl KrMh

Bending force constants Ho,,, H oRbN H,s,,

Hoa,cr

&a,,,

Interactions (repulsion) force constants Foe Fo, F,, Foci FIW FORh FW.,

Hoasru, &ass,,

of the

F. PRUCHNIK et al.

842

Table 6. The calculated Symmetry

S, S, S, S, S, S, S, Ss S, S 10 S 11

29?28

26zM

19y808

18249

13769

12229

Y (Rho) v (RhN) v (RhCl) Y (RhRh) 6 (ORhO) 6 (ORhN) 6 (NRhN) 6 (ORhCl) 6 (NRhCl) 6 (ORhRh) 6 (NRhRh)

0.9813 0.0165 0.0000 0.0003 0.0005 MOoO 0.0005 0.0004 0.0005 0.0000 0.0000

0.0006 0.9974 0.0000 0.0007 0.0003 0.0000 0.0003 0.0005 0.0002 0.0000 0.0000

0.0006 0.0009 0.3007 0.6240 0.0000 0.0000 0.0000 0.0171 0.0152 0.02 15 0.0201

0.0004 0.0002 0.0000 0.0000 0.2683 0.4962 0.2350 0.0000 0.0000 0.0500 0.0000

0.047 1 0.0392 0.0000 0.0000 0.4638 0.0015 0.4334 0.0074 0.0062 0.0007 0.0006

0.0038 0.0049 0.5361 0.2869 0.0001 0.0000 0.0001 0.0405 0.033 1 0.0490 0.0456

0.003 1 0.0036 0.0000 0.0000 0.0096 0.0000 0.0082 0.2531 0.3045 0.1733 0.2445

0.0022 0.0020 0.1427 0.0342 0.0001 0.0000 0.0000 0.2130 0.1466 0.2496 0.2096

v (Rho) v (RhN) 5 (ORhN) 6 (ORhCl) 6 (NRhCl) 6 (ORhRh) 6 (NRhRh)

v (Rho) v (RhN) 6 (ORhN) 6 (ORhCl) 6 (NRhCl) 6 (ORhRh) 6 (NRhRh)

Table 9. The calculated Symmetry

S28 S 29 S 30 S 31 S 32 S 33 S 34 S 35

for the A, block

39240

Symmetry coordinate S”

_I

obtained

42V8t80

Table 8. The calculated

S 26 S ,,

and per cent PED matrix elements

coordinate

Symmetry coordinate S”

S 19 S 20 S 21 S 22 S 23 S 24 S 25

(in cm-‘)

S”

Table 7. The calculated

S 12 S 13 S 14 S 15 S 16 S 17 S 1s

wavenumbers

coordinate

wavenumbers

(in cm-r)

and per cent PED matrix

elements

obtained

48yp26 0.0092 0.0099 0.0002 0.0000 0.0000 0.0000 0.0000 0.2120 0.1969 0.3107 0.2609

for the A, block

VlO 415.32

VI1 334.06

“12 199.17

VI3 138.16

v14 129.00

“IS 79.37

0.6876 0.3029 0.0017 0.0006 0.0005 0.0035 0.0032

0.3402 0.6594 0.0003 0.0000 0.0000 0.0001 0.0000

0.0276 0.05 13 0.8681 0.0014 0.0011 0.0263 0.0244

0.0015 0.0013 0.0214 0.1983 0.2645 0.2087 0.3043

0.0005 0.0011 0.0002 0.2636 0.1746 0.3163 0.2438

0.0004 0.0001 0.0284 0.2786 0.2582 0.2384 0.1959

wavenumbers

(in cm-‘)

and per cent PED matrix

elements

obtained

for the B, block

VI6 418.06

“17 334.12

VIB 196.79

VI9 137.68

“20 129.02

v21 48.26

0.6874 0.3091 0.0020 0.0009 0.0007 0.0000 0.0000

0.3454 0.6543 0.0002 0.0000 0.0000 0.0000 0.0000

0.0255 0.0481 0.9109 0.0074 0.0067 O.ooO6 0.0007

0.0020 0.0037 0.0186 0.2487 0.3086 0.1694 0.2490

0.0008 0.0006 0.0001 0.2622 0.1766 0.3061 0.2536

0.0080 0.0077 0.0000 0.2135 0.1968 0.3109 0.2630

wavenumbers

(in cm-‘)

and per cent PED matrix

elements

obtained

for the B, block

S”

“22 427.20

v23 397.18

“24 260.05

v25 220.58

v26 200.44

y27 154.53

v2s 138.12

V29 79.35

v (Rho) Y (RhN) v (RhCi) 6 (ORhO) S (ORhN) S (NRhN) 6 (ORhCl) 6 (NRhCl) 6 (ORhRh) 6 (NRhRh)

0.9873 0.0076 0.0003 0.0004 0.0000 O.OOiM 0.00&I 0.0002 0.0015 0.0019

0.0006 0.9949 0.0006 0.0003 O.OOOfl o.OQO3 0.0002 O.OOtM 0.0019 0.0011

0.0004 0.0002 0.0000 0.2689 0.4960 0.2344 0.0000 0.0000 0.0000 0.0000

0.0041 0.0043 0.945 1 0.0000

0.0493 0.0428 0.0001 0.4409 0.0015 0.4140 0.0015 0.0011 0.0251 0.0238

0.0003 o.ooo5 0.0000 0.0000 O.OOOCl 0.0000 0.2216 0.2146 0.2731 0.2898

0.0015 0.0001 0.0113 0.0000 0.0097 0.2388 0.2254 0.2554 0.2559

0.0002 0.0004 0.0004 0.0155 0.0001 0.0123 0.2829 0.2544 0.2340 0.1997

0.0000

0.0000 0.0102 0.0101 0.0138 0.0125

Dimeric rhodium(H) complexes

843

Table 10. The variation of the PED and calculated wavenumbers with respect to the K,,,, symmetry coordinates v in cm-’

K Rhllh 0.95

0.65

0.35

264.46 45.21 47.71 7.03

vq: 251.23 56.27 37.52 6.19

239.75 68.91 26.25 4.84

230.59 80.98 15.74 3.26

176.44 43.36 34.74 21.00

170.62 30.55 41.41 27.16

162.20 16.48 46.32 36.40

150.54 4.61 43.63 51.15

122.29 14.27 3.42 81.88

121.92 14.84 4.65 80.03

121.34 15.71 6.97 76.86

120.25 17.14 12.30 69.80

117.71 19.13 28.83 50.79

109.55 14.32 77.19 6.19

220.58 94.51

220.58 94.51

220.58 94.51

220.58 94.51

220.58 94.51

220.58 94.51

PED in %

1.85

1.55

1.25

v3+v.dA,)

v3: 293.38 30.07 62.40 7.39

278.68 36.54 55.98 7.38

vg: 180.49 53.61 28.69 16.82

vs (A,) S, S4 S,+S,+SI,+~,, “25 (82) S28 v (RbCI)

S, S,

v (RhCl) v (RhRh)

S*+S,+S,,+S,, out-of-plane bending vs+v7 (A,) S, v (RhCI) S, v (RhRh) S*+S9+SI,+S,I

value change for selected

v,:

137.49 0.01 19.29 79.79

Table 11. The comparison between the calculated and observed wavenumbers for vibration of the X-Rh-Rh-X Force constants in mdyne di- ’ K Rhlb K llhCl

Complex Rh,(HCOO),phen,CI, Rh,(HC00)2bpy,C12.4H,0 Rh,(OAc),phen,C1,.2H,O Rh,mand,phen,Cl,.4H,O Rh,mand,bpy,C1,.2H,O

1.69 1.62 1.68 1.60 1.55

0.65 0.65 0.65 0.65 0.65

284 281 283 279.5 278.7

va,,(AJ 177 176.5 178 176 175

REFERENCES

WI [l]

[2] [3] [4] [S] [6]

[7]

[8] [9] [lo] [ll]

Lines observed near the calculated values

Calculated wavenumbers ~w.,(AJ

T. G. SPIRO, Prog. inorg. Chem. 11, 1 (1970); C. 0. QUICKSALLand T. G. SPIRO, Inorg. Chem. 8, 2363 (1969); 9, 1045 (1970). K. L. WATTERSand W. M. RISENJR, Inorg. chim. Acta Rev. 3, 129 (1969). E. MASLOVSKYJR, Chem. Reo. 71, 507 (1971). W. P. GRIFFITHand A. J. WICKHAM,.I. them. Sot. A 834 (1969). F. PRLJCHNIK, M. ZUBER, H. PASTERNAK and K. WAJDA, Spectrochim. Acta 34A, 1111 (1978). F. PRUCHNIK,B. R. JAMESand P. KVINTOVICS,Can. .I. Chem. 64, 936 (1986); F. PRUCHNIKand M. ZUBER, Roczniki Chemii 51, 1813 (1977); H. PASTERNAKand F. PRUCHNIK,Inorg. nucl. them. L.&t. 12, 591 (1976). J. H. SCHACHTSCHNEIDER and F. S. MORTIMER, Vibrational Analysis of Polyatomic Molecules, Fortran IV and Programs for Setting up the Vibrational Seqular Equation. Technical Report No. 231-64 (1964). J. OVERENDand J. R. SCHERER,J. &em. Phys. 32, 1289 (1960). T. G~OWIAK, H. PASTERNAKand F. PRUCHNIK,Acta crystallogr. C34, 1038 (1987). A. S. ANCYSKINA,Acta crystallogr. ZlA, 135 (1966). E. M. SHUSTOROVICH,M. A. PORAY-KOSHITSand

Cl31 Cl41 Cl51 Cl61

lx71 WI Cl91 c-w PI

c-m

v&4) 220.6 220.6 22&6 220.6 220.6

skeleton

v314 278, 286 281,282 276, 288 276, 284 275, 280

v.517 166, 166, 168, 168, 170,

179 180 180 180 182

v25 202, 214, 210, 220, 209,

235 232 225 237 225

Y. A. BUSLAYEV,Coord. Chem. Rev. 17 1 (1975). F. A. COTTON, B. G. DE BOER, M. LA PRADE, J. P. PIPALand D. A. UCKO, J. Am. them. Sot. 92,2026 (1970). G. BORCH,P. H. NILSEN,P. KLABOE,Acta them. stand. A31, 109 (1977). T. J. THAMANNand T. M. LOEHR, Spectrochim. Acta 36A, 751 (1980). D. T. JAWORTH,B. Y. LIN and J. D. BROWN, Spectrochim. Acta 34A, 371 (1978). E. B. BOYARand S. D. ROBINSON, Coord. Chem. Rev. SO, 109 (1983); T. R. FELTHOUSE, Prog. inorg. Chem. 29,73 (1982). J. SAN FILIPPOand H. J. SNIADOCH,Inorg. Chem. 12, 2326 (1973). Y. Y..KHA~ITONOV, G. MAZO and N. A. KNYAZEVA, Russ. J. inorg. Chem. 15, 739 (1970). I. K. KIREEVA,G. MAZO and R. N. SHCHELOKOV, Russ. J. inorg. Chem. 24, 220 (1979). A. P. KETTERINGHAM and C. J. OLDHAM,J. them. Sot. Dalton Trans. 1067 (1972). V. M. MISKOWSKI,W. P. SCHAEFER,B. SADEGHI, B. D. SANTERSIARO and H. GRAY, Inorg. Chem. 23,1954 (1984); V. M. MISKOWSKI,T. P. SMITH,T. M. LOEHR and H. B. GRAY, J. Am. them. Sot. 107, 7925 (1985). R. J. H. CLARK, A. J. HEMPLEMANand C. D. FLINT,J. Am. them. Sot. 108, 518 (1986).