- Email: [email protected]
A note on the relationship between octahedral and tetrahedral ligand field splitting parameters
3930
Notes
A c k n o w l e d g e m e n t s - T h e authors thank L. J. Nugent for directing the effort and K. L. Van der Sluis and George Werner for testing the samples for laser action. Also, gratitude is expressed to C. B. Finch for his contribution to the solid laser research. Chemical Technology Division Oak Ridge National Laboratory P.O. Box X, Oak Ridge, Tennessee 3 7830
H. A. F R I E D M A N J. T. BELL
J. inorg,nucl.Chem., •972, Vol.34, pp. 3930-3932. PergamonPress. Printedin Great Britain
A note on the relationship between octahedral and tetrahedral ligand field splitting parameters (Received 23 March 1972) IN EVEN the most elementary accounts of ligand field theory, it is invariably stated that the spectroscopic splitting parameter At for a tetrahedral chromophore MX4 is equal to 4/9 of the corresponding parameter Ao for the octahedral chromophore MXt. Most writers express satisfaction that, experimentally, the ratio AdAo is usually found to be in the range 0-4-0.5. However, it is not always emphasised that the oft-quoted factor of 4/9 is valid only if the metal-ligand distance R~ in MX4 is the same as the corresponding distance Ro in MX,, and Rt is invariably less than Ro. It is well-known that ligand field splitting parameters are strongly dependent on the metal-ligand distance; the most convincing evidence for this comes from the studies of Drickamer et al. [1-4], who measured the d - d spectra of a number of transition metal compounds over a range of pressures up to several hundred kbar. For example, in the case of NiO, where it was possible to measure both Ao and Ro as functions of pressure, Drickamer[4] noted that Ao was very nearly proportional to Ro -5 over a range of about 0.05 ~. This is in excellent agreement with the prediction of the point-charge crystal field model, which expresses the splitting parameters as:
Ao = (5]3)q(r4)/Ro ~ At = (20/27)q(r4)/Rt 5. If we accept the validity of the crystal field R -5 law (bearing in mind that it is followed, experimentally, only by a limited number of systems over a limited range of internuclear distances), the relationship between At and Ao now becomes: At : (4/9) (Ro/Rt)SAo. Inspection of the available structural data suggests that (Ro/Rt) is usually around 1-08-1.10. Thus the point charge crystal field theory actually predicts that At = 0"7Ao, which is in rather poor agreement with experimental data; At is usually closer to 0.5 Ao in practice. The angular overlap model [5] offers an attractive alternative to the point charge crystal field model 1. 2. 3. 4. 5.
S. Minomura and H. G. Drickamer, J. chem. Phys. 35,903 ( 1961 ). D. R. Stephens and H. G. Drickamer, J. chem. Phys. 34, 937 (1961). R. L. Clendenen and H. G. Drickamer, J. chem. Phys. 44, 4223 (1966). H. G. Drickamer, J. chem. Phys. 47, 1880 (1967). C. K. Jergensen, Modern Aspects o f Ligand Field Theory. North-Holland, Amsterdam ( 1971 ).
Notes
3931
as an empirical method for the computation of ligand field splittings. The orbitals of the partly-filled shell (the ~d-orbitals' of crystal field theory) are considered to be split by the effects of covalent bonding, and their relative energies can be expressed in terms of the parameters e~ and e~. Thus in an octahedral complex where the ligands are regarded as ~r-donors, each with two equivalent orbitals available for 7r-bonding (e.g. halide ions), the angular overlap model gives: ~,, = 3e,~ - 4e~. The corresponding expression for a tetrahedral chromophore is: 21,= (4/31e,,- (16/91e=. Thus. as in the crystal field approach, we can sa~¢ that ~t = (4/9)',-ko provided that the internuclear distances R,, and R, are the same. We can take account of the shorter bond lengths in tetrahedral M X , by assuming the proportionality of e~ and e~ to the squares of the diatomic overlap integrals S%., and S~,,~. respectively, in accordance with the formulation of the angular overlap model in terms of second order perturbation theory[5]. If we further assume that each ligand offers a set of three equivalent p-orbitals for bonding to the metal (i.e. the ligand s-orbitals are ignored), the proportionality constants relating e,, to (S',,.,.)~ and e~, to (S~I,,~.)~ should be the same. Hence the values of 21,,and at appropriate to any values of R, and Rt can be expressed in terms of a single parameter, and the relative magnitudes of &, and At for M X , and MX4 can be found by simply evaluating the overlap integrals at the internuclear distances R,, and R~. in Table l, we have compared the values of the ratio 2~JA,, as calculated by the point charge crystal field model and the angular overlap model with the experimental values for MC[, and MC[~ chromophores. Most of the available experimental comparisons ofA o and A~come from studies of halides, and in the case of a monatomic ligand the assumptions of the previous paragraph are most likely to be approximately ~alid. In the cases of M = Mn(ll), Co(Ill and Ni(ll). the anhydrous chlorides MCI~ were taken as representative of the octahedral chromophores MCI,. while data for the tetrahedral Table 1. Comparison of experimental values of ~t/&o with values calculated by crystal field theory (CF) and angular overlap theory (AO) for MCI~ and MCI, M
2idA,, (calc. CF)
At~A<,(calc. AO)
&IA° (exp.)
V(IV) Mn(ll) Co(l I) Ni(ll)
0.71 0.76 0.71 0.66
0-35 0.57 0.58 0-56
0.51 0.44 0.46 (1-49
chromophores MCI4 refer to the well-known discrete anions MCI~~ . Crystallographic and spectroscopic data were taken from Canterford and Colton[6]; in the cases of MnCI2 and CoCle, R, was estimated from the hexagonal unit cell parameters, assuming the chromophores to be regular octahedra. For M = V(IV), the data refer to the discrete anion VCI6'-' and gaseous VCI4. No crystallographic data are available for VCI~-~-: Ro was estimated as 2-35 A by comparison with published data for other MCI6 systems. The radial wave functions of Richardson et ul.[7] for M ~ and of Clementil8] for CI were used in the computation of overlap integrals. Although the angular overlap results are not in particularly good agreement with experiment, they are much better than those obtained by the crystal field method. It must be borne in mind that the overlap integrals are rather sensitive to the choice of wave functions. However. what is really significant is 6. J. H. CanCerford and R. Colton, Halides of the First Row Transition Metals. Wiley-lnterscience. New York ( 19691. 7. J. W. Richardson, W. C. Nieupoort, R. R. Powell and W. F. Edgell../. chem. Phys. 36, 1(/57 (19621. 8. E. Clementi. Supplement to I B M Journal o f Research and D~.uelopment 9, 2 ( 1965 ).
3932
Notes
that the angular overlap model gives us some insight into the problem, and offers at least some qualitative explanations for the fact that At/Ao is smaller than might be expected. The splittings are expressed as differences between two quantities which vary differently with the internuclear distance. We have previously shown [9] that over a relatively small range of internuclear distances close to Ro, e~ often varies roughly as R -5, in agreement with the crystal field model. But 7r-overlap integrals increase more sharply with decreasing internuclear distance than o--overlap integrals [ 10]. Thus for purely o--bonding ligands the angular overlap and crystal field methods predict similar radial variations in the cubic splitting parameters, but with 7r-donor ligands the increasing importance of the term in e= with decreasing internuclear distance (making a negative contribution to A) leads to smaller values of the ratio At/Ao than those predicted by the crystal field model, in agreement with observation. These results strengthen our conviction [ 11, 12] that the angular overlap method is superior to the crystal field model in circumstances where the radial dependence of splitting parameters is of paramount importance. D E R E K W. S M I T H
Department o f Chemistry The University Sheffield S 3 7HF
9. 10. 11. 12.
D. W. D. W. D. W. D.W.
Smith, J. chem. Phys. 50, 2784 (1969). Smith,J. chem. Soc. (A) 1498 (1970). Smith, J. chem. Soc. (A) 1024 (1971). Smith,J. chem. Soc. (A) 1209 (1971).
J. inorg, nucl. Chem., 1972, Vol. 34, pp. 3932-3935.
Pergamon Press.
Printed in Great Britain
Study in some heterochelates-- I Zn(II) + nitrilotriacetic acid + mercapto acid systems (First received 18 January 1972; in revised form 16 March 1972)
FORMATION constants of mixed ligand complexes, log KMAI.MA(where M = Z n ( I I ) , A = N T A and L = mercapto acid), have been determined by using a modified form of lrving-Rossotti titration technique. The values have been interpreted in terms of electrostatic repulsion indicating that the contribution due to 7r-interaction in M - S bond is not significant. Study of ternary systems, M,4L (where M = Ni(lI), Zn(ll), Cu(II), A = Nitrilotriacetic acid (henceforth to be represented as NTA), and L = amino acids or polyhydroxy aromatic compounds), have been carried out by earlier workers[I-4]. Mercapto acids are known to combine with bivalent zinc[5-9] at higher pH. The systems are interesting because the M - S bond is observed to be quite stable in cases where M is a class B type[10] of metal ion. This stability has been attributed to either of the two factors (1) 7r interaction in the M - S bond[l 1] (2) increase in the M - S o'-bonding due to 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
D. Hopgood and R. J. Angelici, J. A m. chem. Soc. 90, 2508 (1968). A. L. Beauchamp, J. Israeli and H. Saulinier, Can. J. Chem. 47, 1269 (1969). M. V. Chidambaram and P. K. Bhattacharya, ,4cta, Chim. Hung. In press. I. P. Mavani, C. R. Jejurkar and P. K. Bhattacharya, Ind. J. Chem. In press. D. I. Leussing, J. Am. chem. Soc. 80, 4180 (1958). Q. Fernando and H. Freiser, J. A m. chem. Soc. 80, 4928 (1958). D. D. Perrin and I. G. Sayce, J. chem. Soc. 82 (1967). R. S. Saxena, K. C. Gupta and M. L. Mittal, Can.J. Chem. 46, 311 (1968). D. D. Perrin and L. J. Porter, Aust. J. Chem. 22, 267 (1969). S. Ahrland, J. Chatt and N. R. Davies, Q, Rev. chem. Soc. 12, 265 (1958). S. E. Livingstone, Q. Rev. chem. Soc. 19,386 (1965).
Notes
A c k n o w l e d g e m e n t s - T h e authors thank L. J. Nugent for directing the effort and K. L. Van der Sluis and George Werner for testing the samples for laser action. Also, gratitude is expressed to C. B. Finch for his contribution to the solid laser research. Chemical Technology Division Oak Ridge National Laboratory P.O. Box X, Oak Ridge, Tennessee 3 7830
H. A. F R I E D M A N J. T. BELL
J. inorg,nucl.Chem., •972, Vol.34, pp. 3930-3932. PergamonPress. Printedin Great Britain
A note on the relationship between octahedral and tetrahedral ligand field splitting parameters (Received 23 March 1972) IN EVEN the most elementary accounts of ligand field theory, it is invariably stated that the spectroscopic splitting parameter At for a tetrahedral chromophore MX4 is equal to 4/9 of the corresponding parameter Ao for the octahedral chromophore MXt. Most writers express satisfaction that, experimentally, the ratio AdAo is usually found to be in the range 0-4-0.5. However, it is not always emphasised that the oft-quoted factor of 4/9 is valid only if the metal-ligand distance R~ in MX4 is the same as the corresponding distance Ro in MX,, and Rt is invariably less than Ro. It is well-known that ligand field splitting parameters are strongly dependent on the metal-ligand distance; the most convincing evidence for this comes from the studies of Drickamer et al. [1-4], who measured the d - d spectra of a number of transition metal compounds over a range of pressures up to several hundred kbar. For example, in the case of NiO, where it was possible to measure both Ao and Ro as functions of pressure, Drickamer[4] noted that Ao was very nearly proportional to Ro -5 over a range of about 0.05 ~. This is in excellent agreement with the prediction of the point-charge crystal field model, which expresses the splitting parameters as:
Ao = (5]3)q(r4)/Ro ~ At = (20/27)q(r4)/Rt 5. If we accept the validity of the crystal field R -5 law (bearing in mind that it is followed, experimentally, only by a limited number of systems over a limited range of internuclear distances), the relationship between At and Ao now becomes: At : (4/9) (Ro/Rt)SAo. Inspection of the available structural data suggests that (Ro/Rt) is usually around 1-08-1.10. Thus the point charge crystal field theory actually predicts that At = 0"7Ao, which is in rather poor agreement with experimental data; At is usually closer to 0.5 Ao in practice. The angular overlap model [5] offers an attractive alternative to the point charge crystal field model 1. 2. 3. 4. 5.
S. Minomura and H. G. Drickamer, J. chem. Phys. 35,903 ( 1961 ). D. R. Stephens and H. G. Drickamer, J. chem. Phys. 34, 937 (1961). R. L. Clendenen and H. G. Drickamer, J. chem. Phys. 44, 4223 (1966). H. G. Drickamer, J. chem. Phys. 47, 1880 (1967). C. K. Jergensen, Modern Aspects o f Ligand Field Theory. North-Holland, Amsterdam ( 1971 ).
Notes
3931
as an empirical method for the computation of ligand field splittings. The orbitals of the partly-filled shell (the ~d-orbitals' of crystal field theory) are considered to be split by the effects of covalent bonding, and their relative energies can be expressed in terms of the parameters e~ and e~. Thus in an octahedral complex where the ligands are regarded as ~r-donors, each with two equivalent orbitals available for 7r-bonding (e.g. halide ions), the angular overlap model gives: ~,, = 3e,~ - 4e~. The corresponding expression for a tetrahedral chromophore is: 21,= (4/31e,,- (16/91e=. Thus. as in the crystal field approach, we can sa~¢ that ~t = (4/9)',-ko provided that the internuclear distances R,, and R, are the same. We can take account of the shorter bond lengths in tetrahedral M X , by assuming the proportionality of e~ and e~ to the squares of the diatomic overlap integrals S%., and S~,,~. respectively, in accordance with the formulation of the angular overlap model in terms of second order perturbation theory[5]. If we further assume that each ligand offers a set of three equivalent p-orbitals for bonding to the metal (i.e. the ligand s-orbitals are ignored), the proportionality constants relating e,, to (S',,.,.)~ and e~, to (S~I,,~.)~ should be the same. Hence the values of 21,,and at appropriate to any values of R, and Rt can be expressed in terms of a single parameter, and the relative magnitudes of &, and At for M X , and MX4 can be found by simply evaluating the overlap integrals at the internuclear distances R,, and R~. in Table l, we have compared the values of the ratio 2~JA,, as calculated by the point charge crystal field model and the angular overlap model with the experimental values for MC[, and MC[~ chromophores. Most of the available experimental comparisons ofA o and A~come from studies of halides, and in the case of a monatomic ligand the assumptions of the previous paragraph are most likely to be approximately ~alid. In the cases of M = Mn(ll), Co(Ill and Ni(ll). the anhydrous chlorides MCI~ were taken as representative of the octahedral chromophores MCI,. while data for the tetrahedral Table 1. Comparison of experimental values of ~t/&o with values calculated by crystal field theory (CF) and angular overlap theory (AO) for MCI~ and MCI, M
2idA,, (calc. CF)
At~A<,(calc. AO)
&IA° (exp.)
V(IV) Mn(ll) Co(l I) Ni(ll)
0.71 0.76 0.71 0.66
0-35 0.57 0.58 0-56
0.51 0.44 0.46 (1-49
chromophores MCI4 refer to the well-known discrete anions MCI~~ . Crystallographic and spectroscopic data were taken from Canterford and Colton[6]; in the cases of MnCI2 and CoCle, R, was estimated from the hexagonal unit cell parameters, assuming the chromophores to be regular octahedra. For M = V(IV), the data refer to the discrete anion VCI6'-' and gaseous VCI4. No crystallographic data are available for VCI~-~-: Ro was estimated as 2-35 A by comparison with published data for other MCI6 systems. The radial wave functions of Richardson et ul.[7] for M ~ and of Clementil8] for CI were used in the computation of overlap integrals. Although the angular overlap results are not in particularly good agreement with experiment, they are much better than those obtained by the crystal field method. It must be borne in mind that the overlap integrals are rather sensitive to the choice of wave functions. However. what is really significant is 6. J. H. CanCerford and R. Colton, Halides of the First Row Transition Metals. Wiley-lnterscience. New York ( 19691. 7. J. W. Richardson, W. C. Nieupoort, R. R. Powell and W. F. Edgell../. chem. Phys. 36, 1(/57 (19621. 8. E. Clementi. Supplement to I B M Journal o f Research and D~.uelopment 9, 2 ( 1965 ).
3932
Notes
that the angular overlap model gives us some insight into the problem, and offers at least some qualitative explanations for the fact that At/Ao is smaller than might be expected. The splittings are expressed as differences between two quantities which vary differently with the internuclear distance. We have previously shown [9] that over a relatively small range of internuclear distances close to Ro, e~ often varies roughly as R -5, in agreement with the crystal field model. But 7r-overlap integrals increase more sharply with decreasing internuclear distance than o--overlap integrals [ 10]. Thus for purely o--bonding ligands the angular overlap and crystal field methods predict similar radial variations in the cubic splitting parameters, but with 7r-donor ligands the increasing importance of the term in e= with decreasing internuclear distance (making a negative contribution to A) leads to smaller values of the ratio At/Ao than those predicted by the crystal field model, in agreement with observation. These results strengthen our conviction [ 11, 12] that the angular overlap method is superior to the crystal field model in circumstances where the radial dependence of splitting parameters is of paramount importance. D E R E K W. S M I T H
Department o f Chemistry The University Sheffield S 3 7HF
9. 10. 11. 12.
D. W. D. W. D. W. D.W.
Smith, J. chem. Phys. 50, 2784 (1969). Smith,J. chem. Soc. (A) 1498 (1970). Smith, J. chem. Soc. (A) 1024 (1971). Smith,J. chem. Soc. (A) 1209 (1971).
J. inorg, nucl. Chem., 1972, Vol. 34, pp. 3932-3935.
Pergamon Press.
Printed in Great Britain
Study in some heterochelates-- I Zn(II) + nitrilotriacetic acid + mercapto acid systems (First received 18 January 1972; in revised form 16 March 1972)
FORMATION constants of mixed ligand complexes, log KMAI.MA(where M = Z n ( I I ) , A = N T A and L = mercapto acid), have been determined by using a modified form of lrving-Rossotti titration technique. The values have been interpreted in terms of electrostatic repulsion indicating that the contribution due to 7r-interaction in M - S bond is not significant. Study of ternary systems, M,4L (where M = Ni(lI), Zn(ll), Cu(II), A = Nitrilotriacetic acid (henceforth to be represented as NTA), and L = amino acids or polyhydroxy aromatic compounds), have been carried out by earlier workers[I-4]. Mercapto acids are known to combine with bivalent zinc[5-9] at higher pH. The systems are interesting because the M - S bond is observed to be quite stable in cases where M is a class B type[10] of metal ion. This stability has been attributed to either of the two factors (1) 7r interaction in the M - S bond[l 1] (2) increase in the M - S o'-bonding due to 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
D. Hopgood and R. J. Angelici, J. A m. chem. Soc. 90, 2508 (1968). A. L. Beauchamp, J. Israeli and H. Saulinier, Can. J. Chem. 47, 1269 (1969). M. V. Chidambaram and P. K. Bhattacharya, ,4cta, Chim. Hung. In press. I. P. Mavani, C. R. Jejurkar and P. K. Bhattacharya, Ind. J. Chem. In press. D. I. Leussing, J. Am. chem. Soc. 80, 4180 (1958). Q. Fernando and H. Freiser, J. A m. chem. Soc. 80, 4928 (1958). D. D. Perrin and I. G. Sayce, J. chem. Soc. 82 (1967). R. S. Saxena, K. C. Gupta and M. L. Mittal, Can.J. Chem. 46, 311 (1968). D. D. Perrin and L. J. Porter, Aust. J. Chem. 22, 267 (1969). S. Ahrland, J. Chatt and N. R. Davies, Q, Rev. chem. Soc. 12, 265 (1958). S. E. Livingstone, Q. Rev. chem. Soc. 19,386 (1965).