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Ligand-field theory and metal-ligand force constants
2558
Notes
Examination of cation exchanger beads before treatment with sol showed X-ray counts due to S (functional SO3- groups) which were higher by a factor of about two on the cut surface compared with the spherical surface, and uniform on both surfaces. The anion exchanger in contrast shows X-ray count rates due to CI (CIO4- counter-ion) on the spherical surface, at the edge of the plane surface and in the centre of the plane surface, in the ratios 3.0:1.5 : 1.0-lower on the cut surface. Adsorption of Fe(OH)3 from sols of suitable pH (2.85 for the cation exchanger and 11.5 for the anion exchanger) showed about double the adsorption (characteristic Fe X-ray count rate) on the cation exchanger cut surface, as compared with the spherical s u r f a c e - a l m o s t exactly comparable with the variation in the concentration of SO3- groups. The adsorption of Fe(OH)3 on the anion exchanger surfaces was in the ratios 1.2 : 1.2 : 1.0 for the spherical surface, the edge of the plane surface and the centre of the plane surface-which show less pronounced differences than the CIO4- counter ion distribution, but are again broadly in line with it. No X-ray count rate due to Fe was obtained from any surface of the anion exchanger from sols at pH 2-85, or of the cation exchanger from sols at pH 11"5.
Resin capacity in colloid absorption The capacity of Na+-form cation exchanger for Fe(OH)a from a sol at pH 3-85 was below the limit of detection of the volumetric method used ( < 0.033 meq/g). The uptake of the H + -form cation exchanger however, at room temperature, was 0.096 meq/g after 15 d and 0.133 meq/g after 41 days. At 100°C the H+-form cation exchanger achieved uptakes of 0.156 meq/g after 8 hr, and 2" 17 meq/g after 16 days in contact with the Fe(OH)3 sol. These figures represent 3.2 and 44 per cent of the resin ionic capacity as determined by titration with alkali. The second figure is an advance of nearly two orders of magnitude on the capacity of the purely surface process, and since the only figure available for the latter is an upper limit the advance is likely in fact to be much higher still. Applied Chemistry Division Building 220 Atomic Energy Research Establishment Harwell Didcot, Berks.
P. B1DDLE J. H. MILES
J. inorg,nucl.Chem.,1973.Vol.35. pp. 2558-2561. PergamonPress. Printedin GreatBritain
Ligand-fieid theory and metal-ligand force constants (Received 1 February 1972) SEVERAL authors[I, 2] in the recent literature have noted that there is a relationship between the strengths of metal-ligand bonds indicated by the vibrational spectra of the particular complexes, and by crystal-field expectations on the relative bond strengths in these complexes. These observations have, however, been confined to series of complexes in which the ligand remained constant while the central cation was replaced successively by a number of different metal ions. An example of such a relationship is seen in Fig. 1, in which the metal-carbon stretching force constants, all calculated using the Urey-Bradley field (UBF), are plotted against the crystal-field stabilization energies for a series of octahedral hexacyanide complexes. The crystal-field stabilization energies have been calculated, where possible, from experimental values of 10Dq, B, and C, or by use of Jergensen's approximations[3] 10 Dq =f.g. and/335 = (1 --hk). 1. K. Nakamoto, Infrared Spectra of Inorganic and Coordination Compounds. Wiley, New York (1963). 2. R. D. Hancock and D. A. Thornton, J. Molec. Struct. 4, 361 (1969). 3. C. K.Jergensen, Progr. lnorg. Chem. 4, 73 (1963).
Notes
2559
,%
Os(~) ~ / ~
pt (Ix/')
• °e Ir(lIT)
E 3"0 Q
Co(m)/ Fe(g~
0.
Eo U Z
eRu(IT)
o
2.0 m
~
Crlrnl
i
50 --~'/0
lO0 1 CFSE
lPt
1.5o cflFix i0 -a
Fig. I. No attention, however, has been paid to the effect on the metal-ligand force constant of change of ligand in a series with a constant metal ion. Figure 2 shows the relationship between the metal-ligand force constants, Ku_L, calculated using the UBF field for a series of Pd(ll) square-planar ML~ complexes, against f, the ligand parameter in JCrgensen's fig. = l0 Dq. From Table 1 below, it can be judged that similar relationships between KMlZ. a n d f are observed for several other series of ligands with constant central metal ion. The relationship o f f with Ku-L would not be expected from the crystal-field model, since the crystalfield stabilization energy (CFSE) in this model is only a small part of the total bond-formation energy. However, in molecular orbital theory (MOT), it is seen[3] t h a t f is a measure of the total covalent interaction in the form of tr-plus or-bonding, with f increasing as total w-bonding plus metal-ligand ~r-bonding increases, but decreasing as total ligand-metal or-bonding increases. As the latter type of n--bonding cannot occur to any appreciate extent in the metal ions that have been studied,f should be an almost direct indication of the total covalent metal-ligand interaction. It has been thought
30
_
Q x
_o E 8
c1~,/
S:C(NHz2 )
m v
eBr-
?
I
.
07
I t 7
f from Jorgensen, ,~ - IODq
2560
Notes Table 1. Metal-ligand stretching force constants (UBF) for squareplanar ML4 and octahedral ML~ complexes. Units are mdyn/A Ligand
Pt(ll)
Pd(ll)
Au(lI1)
CNNOzDipyridyl NH2CH2CHzNH_, NHa AcacCIS=C(NHz)z BrI-
3.43 3.40 2.85 2.64 2"53 2.46 1.99
3.00
3.41
Ligand
f
ML4 complexes
2.64
1.7 1.53 1.49 1.28 1"25 1.20 0.80 0.86 0.76 0.70
2"22 2.15 1.62 1-51 1.28
2.22
Pt(lV)
Ir(Ill)
Rh(lll)
Co(Ill)
f
3.54 2.73
3.28 2.43
3.09 2-24
2.47 1.54 0.90 (1.05)* (0.90) ( 1.03) (0.62)
1.70 1.25 1.00 0.90 0.80 0.76 0.70
1-72 1.19
1-84 0.97
ML6 complexes CNNHz H20 FC1BrI-
3.18 1.80 1.43 (1.06)
1.20
*Brackets indicate that force constant has been obtained from a mixed complex such as M(NH3)4CI2. permissible to use f, derived from octahedral complexes, for the square-planar complexes, since it has been shown [4] that the spectro-chemical series is the same for both types of stereochemistry. The ions in Table 1 are all low spin, and therefore account should be taken of P, the spin-pairing energy, in estimating the stabilization afforded the metal-ligand bond, which the use o f f alone as a measure of metal-ligand bond strength does not do. If, however, the CFSE calculated for Co(Ill) from C FSE = 24 D q - - P
(where P = 5 B + 8 C)
is used instead o f f in plotting Fig. 2, it is found that the linear relationship obtained using f alone becomes curved. The reason for this is not difficult to see, since the above equation applies to the CFT model, in which only the electrons of the metal d-orbital are considered, and the contribution of P is disproportionately large as compared with MOT, where the interaction of a much larger number of electrons is considered. If one makes the rough assumption that the ligand electrons are stabilized by the same amount as the eg~ level is destabilized in On symmetry, then Eqn (1) becomes approximately: -- AH - 100 Dq - P
(where -- AH = total covalent bond-formation energy),
so that the pairing energy makes a much smaller contribution in MOT than it does in CFT. This factor then accounts for the linearity obtained in plottingf alone against KM-L, since P is relatively a much smaller correction than would be supposed from the CFT model. In Fig. 1, inclusion of P does not matter, since P is roughly porportional to Dq for these complexes. The MOT model above does not take into account the ionic contribution to the stabilization of the 4. W. R. Mason and H. B. Gray, J. Am. chem. Soc. 90, 5721 (1968).
Notes
2561
metal-ligand bond. Thus, the only deviation from linearity for K~ /, for Pt(IV) complexes plotted against f is found in the fluoride complex, and to a lesser extent in the other halide complexes, in which platinum atom is bound to the very highly electronegative fluorine atom, or the other halogen atoms. Several indications of the order of magnitude of this contribution can be obtained. I n the original electronegativity scale proposed by Pauling [5], the electronegativity contribution to the bond energy is given by (E,,--E~)2, where Ea and Eb are the electronegativities of the two atoms A and B, forming the bond. The ratios of the ionic contributions F : C I : B r : I thus derived are 11.9:3.3:2-8: 1.0. The relative h values from J Crgensen's hk = (I -/3:~5), which are thought to indicate the degree of covalent character in the bond, are 0.8, 2.0, 2.3, and 2,7, for F, CI, Br, and I, respectively. Both of these approaches indicate that the ionic contribution to Pt-X bonds increases in the order X = 1 < Br < CI ~F. On a more quantitative basis. NQR spectroscopy suggests [6] that the percentage ionic character of the M - X bonds in Pt(IV) halide complexes is Pt-I, 30%: Pt-Br, 38%, Pt-CI, 44%; and, estimated from electronegativities, P t - F , 59%. Correction of these estimates for 7r-bonding will reduce these ionic contributions by about 50 per cent in the Pt-I bond, and by very little in the P t - F bond. The use of these values to correct KM-L, by subtracting the percentage of K~/--Lconsidered to be due to ionic contribution, then removes the discrepancies observed between the value of KM L expected from the MOT model and that observed in practice. Where KM_~, for series of ligands with other metal ions, e.g. Cr(lil), Ni(li), Cu(ll). has been examined, the data, though very sparse, suggest that here too a relationship of Kv-L withfshould be observed. While it is perhaps not clear[l] to what extent force constants can be equated with bonddissociation energies, it seems from the above correlations that K+t ~ does give one a fair picture of bond strengths at the equilibrium position-that, in fact, both the force constant and the MOT model are representations of bond strength at equilibrium position.
A c k n o w l e d g e m e n t s - T h e authors would like to thank the Director of the National Institute for Metallurgy for permission to publish this work. National lnstituteofMetallurgy Johannesburg South Africa
R.D. HANCOCK A. EVERS
5. L. Pauling. The Nature o f the Chemical Bond, Cornel l University Press. Ithaca, N.Y. (1960). 6. H. A. O. Hill and P. Day, Physical Methods in Advanced Inorganic" Chemistry, p. 456. Interscience, New York (1968).
.I. inorg,nucl. Chem., 1973,Vol.35, pp. 2561-2564. PergamonPress. Printedin Great Britain
Thermal decomposition of coordination polymers, KM(II) [Co(CN)6].xH20 (First received 14September 1972; in revised form 3 October 1972) IN SPITE of considerable interest in the thermal properties of coordination compounds containing N H3, CO32- and C2042- as ligand, there have been relatively few studies on the thermal decomposition of polynuclear transition metal cyanides. Recently differential thermal analysis (DTA) and dynamic gas evolution analysis have been reported on the salts of hexacyano- and penta-cyanonitrosyl-metalates [1]. Furthermore, a series of compounds of the type M3[Co(CN)6]2'xH20 (M=Mn, Ni, Zn or Cd) 1. A. Greene, Jr. and M. Chamberlain, J. inorg, nucl. Chem. 25, 1471 (1963).
Notes
Examination of cation exchanger beads before treatment with sol showed X-ray counts due to S (functional SO3- groups) which were higher by a factor of about two on the cut surface compared with the spherical surface, and uniform on both surfaces. The anion exchanger in contrast shows X-ray count rates due to CI (CIO4- counter-ion) on the spherical surface, at the edge of the plane surface and in the centre of the plane surface, in the ratios 3.0:1.5 : 1.0-lower on the cut surface. Adsorption of Fe(OH)3 from sols of suitable pH (2.85 for the cation exchanger and 11.5 for the anion exchanger) showed about double the adsorption (characteristic Fe X-ray count rate) on the cation exchanger cut surface, as compared with the spherical s u r f a c e - a l m o s t exactly comparable with the variation in the concentration of SO3- groups. The adsorption of Fe(OH)3 on the anion exchanger surfaces was in the ratios 1.2 : 1.2 : 1.0 for the spherical surface, the edge of the plane surface and the centre of the plane surface-which show less pronounced differences than the CIO4- counter ion distribution, but are again broadly in line with it. No X-ray count rate due to Fe was obtained from any surface of the anion exchanger from sols at pH 2-85, or of the cation exchanger from sols at pH 11"5.
Resin capacity in colloid absorption The capacity of Na+-form cation exchanger for Fe(OH)a from a sol at pH 3-85 was below the limit of detection of the volumetric method used ( < 0.033 meq/g). The uptake of the H + -form cation exchanger however, at room temperature, was 0.096 meq/g after 15 d and 0.133 meq/g after 41 days. At 100°C the H+-form cation exchanger achieved uptakes of 0.156 meq/g after 8 hr, and 2" 17 meq/g after 16 days in contact with the Fe(OH)3 sol. These figures represent 3.2 and 44 per cent of the resin ionic capacity as determined by titration with alkali. The second figure is an advance of nearly two orders of magnitude on the capacity of the purely surface process, and since the only figure available for the latter is an upper limit the advance is likely in fact to be much higher still. Applied Chemistry Division Building 220 Atomic Energy Research Establishment Harwell Didcot, Berks.
P. B1DDLE J. H. MILES
J. inorg,nucl.Chem.,1973.Vol.35. pp. 2558-2561. PergamonPress. Printedin GreatBritain
Ligand-fieid theory and metal-ligand force constants (Received 1 February 1972) SEVERAL authors[I, 2] in the recent literature have noted that there is a relationship between the strengths of metal-ligand bonds indicated by the vibrational spectra of the particular complexes, and by crystal-field expectations on the relative bond strengths in these complexes. These observations have, however, been confined to series of complexes in which the ligand remained constant while the central cation was replaced successively by a number of different metal ions. An example of such a relationship is seen in Fig. 1, in which the metal-carbon stretching force constants, all calculated using the Urey-Bradley field (UBF), are plotted against the crystal-field stabilization energies for a series of octahedral hexacyanide complexes. The crystal-field stabilization energies have been calculated, where possible, from experimental values of 10Dq, B, and C, or by use of Jergensen's approximations[3] 10 Dq =f.g. and/335 = (1 --hk). 1. K. Nakamoto, Infrared Spectra of Inorganic and Coordination Compounds. Wiley, New York (1963). 2. R. D. Hancock and D. A. Thornton, J. Molec. Struct. 4, 361 (1969). 3. C. K.Jergensen, Progr. lnorg. Chem. 4, 73 (1963).
Notes
2559
,%
Os(~) ~ / ~
pt (Ix/')
• °e Ir(lIT)
E 3"0 Q
Co(m)/ Fe(g~
0.
Eo U Z
eRu(IT)
o
2.0 m
~
Crlrnl
i
50 --~'/0
lO0 1 CFSE
lPt
1.5o cflFix i0 -a
Fig. I. No attention, however, has been paid to the effect on the metal-ligand force constant of change of ligand in a series with a constant metal ion. Figure 2 shows the relationship between the metal-ligand force constants, Ku_L, calculated using the UBF field for a series of Pd(ll) square-planar ML~ complexes, against f, the ligand parameter in JCrgensen's fig. = l0 Dq. From Table 1 below, it can be judged that similar relationships between KMlZ. a n d f are observed for several other series of ligands with constant central metal ion. The relationship o f f with Ku-L would not be expected from the crystal-field model, since the crystalfield stabilization energy (CFSE) in this model is only a small part of the total bond-formation energy. However, in molecular orbital theory (MOT), it is seen[3] t h a t f is a measure of the total covalent interaction in the form of tr-plus or-bonding, with f increasing as total w-bonding plus metal-ligand ~r-bonding increases, but decreasing as total ligand-metal or-bonding increases. As the latter type of n--bonding cannot occur to any appreciate extent in the metal ions that have been studied,f should be an almost direct indication of the total covalent metal-ligand interaction. It has been thought
30
_
Q x
_o E 8
c1~,/
S:C(NHz2 )
m v
eBr-
?
I
.
07
I t 7
f from Jorgensen, ,~ - IODq
2560
Notes Table 1. Metal-ligand stretching force constants (UBF) for squareplanar ML4 and octahedral ML~ complexes. Units are mdyn/A Ligand
Pt(ll)
Pd(ll)
Au(lI1)
CNNOzDipyridyl NH2CH2CHzNH_, NHa AcacCIS=C(NHz)z BrI-
3.43 3.40 2.85 2.64 2"53 2.46 1.99
3.00
3.41
Ligand
f
ML4 complexes
2.64
1.7 1.53 1.49 1.28 1"25 1.20 0.80 0.86 0.76 0.70
2"22 2.15 1.62 1-51 1.28
2.22
Pt(lV)
Ir(Ill)
Rh(lll)
Co(Ill)
f
3.54 2.73
3.28 2.43
3.09 2-24
2.47 1.54 0.90 (1.05)* (0.90) ( 1.03) (0.62)
1.70 1.25 1.00 0.90 0.80 0.76 0.70
1-72 1.19
1-84 0.97
ML6 complexes CNNHz H20 FC1BrI-
3.18 1.80 1.43 (1.06)
1.20
*Brackets indicate that force constant has been obtained from a mixed complex such as M(NH3)4CI2. permissible to use f, derived from octahedral complexes, for the square-planar complexes, since it has been shown [4] that the spectro-chemical series is the same for both types of stereochemistry. The ions in Table 1 are all low spin, and therefore account should be taken of P, the spin-pairing energy, in estimating the stabilization afforded the metal-ligand bond, which the use o f f alone as a measure of metal-ligand bond strength does not do. If, however, the CFSE calculated for Co(Ill) from C FSE = 24 D q - - P
(where P = 5 B + 8 C)
is used instead o f f in plotting Fig. 2, it is found that the linear relationship obtained using f alone becomes curved. The reason for this is not difficult to see, since the above equation applies to the CFT model, in which only the electrons of the metal d-orbital are considered, and the contribution of P is disproportionately large as compared with MOT, where the interaction of a much larger number of electrons is considered. If one makes the rough assumption that the ligand electrons are stabilized by the same amount as the eg~ level is destabilized in On symmetry, then Eqn (1) becomes approximately: -- AH - 100 Dq - P
(where -- AH = total covalent bond-formation energy),
so that the pairing energy makes a much smaller contribution in MOT than it does in CFT. This factor then accounts for the linearity obtained in plottingf alone against KM-L, since P is relatively a much smaller correction than would be supposed from the CFT model. In Fig. 1, inclusion of P does not matter, since P is roughly porportional to Dq for these complexes. The MOT model above does not take into account the ionic contribution to the stabilization of the 4. W. R. Mason and H. B. Gray, J. Am. chem. Soc. 90, 5721 (1968).
Notes
2561
metal-ligand bond. Thus, the only deviation from linearity for K~ /, for Pt(IV) complexes plotted against f is found in the fluoride complex, and to a lesser extent in the other halide complexes, in which platinum atom is bound to the very highly electronegative fluorine atom, or the other halogen atoms. Several indications of the order of magnitude of this contribution can be obtained. I n the original electronegativity scale proposed by Pauling [5], the electronegativity contribution to the bond energy is given by (E,,--E~)2, where Ea and Eb are the electronegativities of the two atoms A and B, forming the bond. The ratios of the ionic contributions F : C I : B r : I thus derived are 11.9:3.3:2-8: 1.0. The relative h values from J Crgensen's hk = (I -/3:~5), which are thought to indicate the degree of covalent character in the bond, are 0.8, 2.0, 2.3, and 2,7, for F, CI, Br, and I, respectively. Both of these approaches indicate that the ionic contribution to Pt-X bonds increases in the order X = 1 < Br < CI ~F. On a more quantitative basis. NQR spectroscopy suggests [6] that the percentage ionic character of the M - X bonds in Pt(IV) halide complexes is Pt-I, 30%: Pt-Br, 38%, Pt-CI, 44%; and, estimated from electronegativities, P t - F , 59%. Correction of these estimates for 7r-bonding will reduce these ionic contributions by about 50 per cent in the Pt-I bond, and by very little in the P t - F bond. The use of these values to correct KM-L, by subtracting the percentage of K~/--Lconsidered to be due to ionic contribution, then removes the discrepancies observed between the value of KM L expected from the MOT model and that observed in practice. Where KM_~, for series of ligands with other metal ions, e.g. Cr(lil), Ni(li), Cu(ll). has been examined, the data, though very sparse, suggest that here too a relationship of Kv-L withfshould be observed. While it is perhaps not clear[l] to what extent force constants can be equated with bonddissociation energies, it seems from the above correlations that K+t ~ does give one a fair picture of bond strengths at the equilibrium position-that, in fact, both the force constant and the MOT model are representations of bond strength at equilibrium position.
A c k n o w l e d g e m e n t s - T h e authors would like to thank the Director of the National Institute for Metallurgy for permission to publish this work. National lnstituteofMetallurgy Johannesburg South Africa
R.D. HANCOCK A. EVERS
5. L. Pauling. The Nature o f the Chemical Bond, Cornel l University Press. Ithaca, N.Y. (1960). 6. H. A. O. Hill and P. Day, Physical Methods in Advanced Inorganic" Chemistry, p. 456. Interscience, New York (1968).
.I. inorg,nucl. Chem., 1973,Vol.35, pp. 2561-2564. PergamonPress. Printedin Great Britain
Thermal decomposition of coordination polymers, KM(II) [Co(CN)6].xH20 (First received 14September 1972; in revised form 3 October 1972) IN SPITE of considerable interest in the thermal properties of coordination compounds containing N H3, CO32- and C2042- as ligand, there have been relatively few studies on the thermal decomposition of polynuclear transition metal cyanides. Recently differential thermal analysis (DTA) and dynamic gas evolution analysis have been reported on the salts of hexacyano- and penta-cyanonitrosyl-metalates [1]. Furthermore, a series of compounds of the type M3[Co(CN)6]2'xH20 (M=Mn, Ni, Zn or Cd) 1. A. Greene, Jr. and M. Chamberlain, J. inorg, nucl. Chem. 25, 1471 (1963).