739
NOTES Crystal Field Activation Energies of Hexaaquo Transition Metal Complexes by Audrey
Table I: S N Crystal ~ Field Activation Energies for Hexaaquo Traneition Metal Complexes Many electron CaV C F 4 E , kcal/mol----
I,. Companion
Department of Chemistry, Illinois Institute of Technology, Chicago, Illinois 60616 (Receioed July 17, 1 9 6 8 )
In recent years the concept of crystal field activation energy (CFAE) has been employed by several investigators‘-7 in attempts to rationalize trends in kinetic data for ligand replacement reactions involving transition metal complexes. The CFAE for an Sn.1 dissociation of a hexacoordinated species, for example, may be easily computed in terms of the relative crystal field stabilization energy (CFSE) of an octahedron (Oh) and square pyramid ((34”) of ligands with the oneelectron formulas as presented by Basolo and Pearson.’ Generally, CFAE’s computed this way have been in only rough agreement with experiment. I n this note we examine the possibility of improving these calculations by using many-electron methods and crystal field parameters in better accord with observed spectra of transition metal ions. For d2 and d7 configurations (for which one-electron formulas may be in considerable error) we computed ground state CFSE’s with the matrices given in the Appendix in terms of parameters Dq, Ds, and Dt, in turn expressed as functions of radial integrals a2 and 014. While in the octahedral species only the parameter a4 is significant in determining the CFSE, in the lower synimetry species knowledge of both a2 and a4 is necessary. Purely theoretical calculations yield values of the ratio p = a2/cqfrom 2 to 6, results believed to be gross exaggerations of the importance of the a2contribution. While spectroscopic studies of noncubic complexes have not yet yielded definitive evidence favoring any specific p, several investigations8-’’ have indicated that a reduction of p to a value of 1 or less is necessary for compatibility of theory with experiment. The oneelectron CFSE’s employed thus far in CFAF: considerations] are based on p = 2. The weak-field one-electron and many-electron CFAE’s computed for bivalent and trivalent aquo ions and the original spectroscopic data used are summarized in Table I. The only ions for which nephelauxetic relaxation influenced the CFAE over the parameter range investigated were V3+ and Co2+, for which the F-P separations 13,200 and 12,800 cm-I were used. Comparison of the results of the one-electron and manyelectron treatments with p = 2 indicate that except for a small increase (about 1 kcal/mol) in the CFAE for d2 and d7 ions the many-electron treatment makes no appreciable correction in the computed CFAE’s, a t least for Sx1 processes. Sote in Table I that in all cases the CFAE’s of both d3 and d8 ions are independent of p, since the ground
7 -
Ion
Vat(da) Cr2+(d4) Mnz+(d6) FeB+(d6) CO~’(d7) NP+(d*) Cu2+(d9) Zna+ (d‘o) Sc3+(do) Tia+(dl) V3+(d2) CraC(d3) 1LIn3+(d4) Fea+ ( dI )
Oneelectron CFAE
Dq,cm-1
p = 0
p = 1
p = 2
p = 2
1180a 1400”
6.8 1.1 0.0 0.9 1.8 4.8 1.1 0.0 0.0 -1.7 4.1 10.0 1.7 0.0
6.8 -5.7 0.0
6.8 -12.6 0.0 -1.7 -2.1 4.8 -11.7 0.0 0.0 -3.3 -4.9 10.0 -18.9 0.0
6.8 -12.6 0.0 -1.7 -3.1 4.8 -11.7 0.0 0.0 -3.3 -5.8 10.0 -18.9 0.0
...
1040* 950a 850a 13000 ,..
... 2030” 1785” 1740a 2100h
...
0.9 1.9 4.8 -5.6 0.0 0.0 1.7 3.3 10.0 -8.6 0.0
a C. J. Ballhausen, “Introduction to Ligand Field Theory,” McGraw-Hill Book Co., Ino., New York, N. Y., 1962. L. E. Orgel, “Transition Metal Chemistry,” Methuen and Co., London, 1960. c D. S. McClure, ref 2, p 82.
state in O h , becomes under the p values considered, the ground state B1 in C4”, which has no dependence on Ds (see Appendix). This fact, along with the known zero CFSE of do, d5, and d10 ions in any weak field, was used in positioning what we call a “classical” activation energy curve (without crystal field effects) for a series, on which computed CFAE’s mere superimposed. As an illustration, consider the free energies of activation’2 determined by Swift and Connick3 by nmr methods for the exchange of ligand and solvent water molecules in hexaaquo bivalent complexes, shown as open circles in Figure 1. Comparison of the difference between the experimental activation energies of A h 2 + and Ni2+ (1) F. Basolo and R. G. Pearson, “Mechanisms of Inorganic Reactions,” 2nd ed, John Wiley and Sons, Inc., New York, N. Y., 1967, Chapters 2 and 3. (2) R. G. Pearson in “Some Aspects of Crystal Field Theory,” T. Dunn, D. S. McClure, and R. G. Pearson, Harper and Row, New York, N. Y., 1965. (3) T. J. Swift and R. E. Connick, J . Chem. Phys., 37, 307 (1962): 41, 2553 (1964). (4) 3%.Eigen in “Advances of the Chemistry of Coordination Compounds,“ The Macmillan Co., New York, N. Y., 1961, p 371. (5) R. Hogg, G. A. Melson, and R. G. Wilkins, ref 4 p 39. (6) D. Fiat and R. E. Connick, J . Amer. Chem. Soc., 90, 608 (1968). (7) W. Kruse and D. Thusius, Inorg. Chem., 7 , 464 (1968). ( 8 ) J. A. Anysas and A. Companion, J. Chem. Phys., 40, 1205 (1964). (9) D. S, McClure, { b i d . , 36, 2757 (1962). (10) 0.K. Jorgensen, “Absorption Spectra and Chemical Bonding in Complexes,” Pergamon Press, New York, N. Y., 1962, p 55. (11) R. A. D. Wentworth and T. S. Piper, Inorg. Chem., 4, 709 (1965). (12) Association of CFAE with free energies of activation rather than with the less accurately known enthalpies is a common procedure, although of questionable validity. The implicit assumption of regularly varying entropy changes within a series, although logically appealing, is not well founded. A t worst the crystal fleld model used in this way may be regarded as a heavily empiriciaed method with which one may make reasonably good flrst guesses about trends in rate constants. Volume 73, Number 3 March I969
NOTES
740
14t
R
II O2 l I
V
Cr
Mn
Fa
Co
NI
Cu
Zn
Figure 1. Activation energies for SKI dissociations of bivalent transition metal ions: p = 0, - - -; p = 1, --; p = 2, --. Open circles represent experimental points of Swift and Connick;3 open aquares, experimental points of Eigen.x3
(4.2 kcal/mol) with the computed difference in CFAE's for these ions (4.8 kcal/mol) makes it reasonable to assume that the classical activation energy is essentially constant across the series. This near-constancy is again illustrated by Eigen's datal3 for dissociation of a ligand water molecule from a hydrated ion involved in an ion pair, [M (H20).2+, SO,z-]. The theoretical total activation energies for bivalent ions computed under the assumption of a constant classical activation energy across the series C7.2 kcal/mol, the Swift and Connick result for ILIn2+] are plotted in Figure 1 for p values of 0, 1, and 2 . The open squares represent Eigen's rate coiistants corrected for classical contributions and with the scale adjusted such that -1ogk values for >'In2+ and Xi2+correspond to the computed activation energies (both independent of p) . For both sets of experimental data, agreement between theory and experiment is obviously better for the lower p values over the whole range of ions from V2+ to Zn2+; in particular, the lower p values correctly predict the observed trend from Mn2+ to Wf, for which the usual p = 2 fails completely. The largest deviations between theory and experiment occur for Cr2+and Cu2+ions, both of which undergo strong Jahn-Teller distortions in six coordination, an effect not included in our calculations. The Journal of Physical Chemistry
No rate studies by a given group of investigators using a consistent method have yet been reported for the whole series of trivalent transition metal ions. However, Fiat and Connick6 and Kruse and Thusius7 have summarized available substitution rate data indicating that for aquo complexes rate constants for Ti3+, Fe3+, and V3+ are of the same order of magnitude, ordering approximately as k(Ti) > k(Fe) > k ( V ) . Hexaaquo Cr3+ ion is considerably less labile than these three. Assuming that reactions of these ions do proceed through an s N 1 elimination of water (a fact not yet definitively established) one may see from the CFAE's in Table I that p values of 1 or less describe the trend much more properly than the ratio commonly used. (For example, p = 2 predicts that Va+ should be considerably more labile than Fe3+.) Based primarily on improved agreement between theoretical and experimental activation energies for S N 1 processes of hexaaquo transition metal ions, the suggestion is made that radial parameter ratios of 1 or less, rather than 2, be used in calculations of crystal field activation energies. One-electron formulas comparable to those of Basolo and Pearson' may be easily derived for any geometry chosen for an intermediate (including complexes with mixed ligands) with the simple approach presented earlier b y Companion and K~marynsky.'~In addition, Spees, Perumareddi, and hdamson15 have recently recalculated one-electron energy levels for some of the Rnsolo-Pearson intrrmediates. Aclcnozuledymenl. The author is grateful t,o the donors of the American Chemical Society Prtmleum Research Fund for support of t,his work.
Appendix: Clv Crystal Field Energy Matrices
d 2 J Configurations
(13) M. Eigen, Ber. Bunsenges. Physik. Chem., 67, 753 (1963); see also G.Geier, i b i d . , 69, 615 (1965). (14) A. Companion and 111. Komarynsky, J . Chem. Educ., 41, 257 (1964). (15) S. T. Spees, Jr., J. R. Perumareddi, and A. W. Adamson, J . P h y s . Chem., 72, 1822 (1968).
741
NOTES
F (TI,)
A2
F (Tld
[- 30Dq
-~
P(Td
+
D s 30Dt]/5
p (TI,)
F (TI,)
E F (Tld
C-120Dq
+ ~ D +s 45Dt]/20
F (T2,)
[20Dq
- 12Ds - 20Dt]/5
[14Ds
+ 5(P - F ) ] / 5
F (T2d
[4Ds [BDq
+ 5Dt](15)'12/20
+ 7Dt]/4
p (TI,) Dq = ~ 4 6 Ds ; = a 2 / 7 ; Dt = 4 2 1 ; 012 = qe2(r2)/R3; 014 = qe2(r4)/R5; where qe is the ligand charge, R the ligand-metal distance and ( r n ) the expectation value of the nth power of the d-electron distance from the metal nucleus. The above formulas also describe d4l9 and d3sSconfigurations if the signs of Dq, Ds, and Dt are changed everywhere.
Transference Numbers and Ionic Solvation of Lithium Chloride in Dimethylformamide by Ram Chand Paul, Jai Parkash Singla, and Suraj Prakash Narula Department of Chemistry, Panjah University, Chandigarh-I 4, India (Received August 20, 1 9 6 8 )
In a number of publications, the potentialities of dimethylf~rmamide'-~as a protonic solvent have been highlighted. Sherrington and Prue5 have briefly mentioned the measurement of cation transference number of potassium thiocyanate in DhIF. However, no attempt has been made to calculate the solvation of the ions on the basis of transference data. Gopal and Hussain6have calculated the solvation number of many alkali ions in different solvents from the available conductance data. In the absence of transference data of various ions, they have claimed only a limited accuracy of their results. Lithium ion being small in size is generally solvated in solutions. Lithium chloride is appreciably soluble in D M F and accurate conductance data for it are available in the l i t e r a t ~ r e . ~It has, therefore, been selected as the electrolyte for the present investigations. The ionic conductance and the solvation number of lithium ion as calculated on the basis of transference data are reported here.
Experimental Section Materials. Lithium chloride (BDH AnalaR) was fused in a platinum crucible under a stream of dry hydrogen chloride, cooled in a desiccator, and lumps of
p (TI,) [.iODq - 12Ds - 15Dt]/lO
+ 5Dt](15)1'2/10 [-7Ds + 5 ( P - F ) ] / 5
C4Ds
the fused salt were powdered and reheated in a weighing bottle to 300" for 3 hr, cooled, and kept in a vacuum desiccator for use. Silver nitrate and potassium thiocyanate (both BDH AnalaR) were used as received. Silver (commercial) was purified by electrolysis in the laboratory and converted into wire for use. Solvent. Dimethylformamide (Baker Analyzed) was purified by keeping it over anhydrous sodium carbonate (BDH AnalaR) for about 48 hr with occasional shaking. It was fractionally distilled. The middle fraction ohm-' cm-l) (bp 148.5-149.5", sp. cond. < 2 X was taken for use. As far as possible all transference of materials was carried out in a drybox and solutions were protected from moisture by silica gel guard tubes. Determination of Transference Numbers. A weighed amount of lithium chloride was dissolved in D M F (250 ml) . A modified Hittorf transference cell with three compartments separated with well-greased stopcocks was used. The experimental technique for the measurement of transference number is exactly the same as described by Amis and cou~orkers.~J There was no evolution of gas at the cathode when a current of 3-10mA was employed. A current stabilizer (Gelman Instrument Co.) was used along with a Richard coulometer to measure the amount of current passed, Each experiment was continued for about 12-24 hr depending upon the concentration of the solution. The time of experiment was increased with the dilute solutions. Because of the solubility of the silver chloride (formed at the anode during electrolysis) in D I I F , the solutions of cathode and middle compartments were analyzed. The chloride ion concentrations of the solutions were estimated by Volhard's method. Two (1) R. C. Paul, P. S. Guraya, and R. R . Sreenathan, Indian J . Chem., 1, 335 (1963). (2) R. 0. Paul, S . Sharda, and B . R . Sreenathan, ihid., 2 , 97 (1964). (3) R. 0. Paul, S. C. Ahluwalia, and 8. R. Pahil, d h i d . , 3 , 300, 306 (1965). (4) R . 0. Paul and B . R. Sreenathan, ihid., 4, 348, 382 (1966). (5) J. E. Prue and P. J. Sherrington, Trans. Faraday Soc., 57, 1795 (1961).
(6) R. Gopal and M . M. Hussain, (1963).
J. Indian Chcm. Soc.,
40, 981
(7) W. Ves Chjlds and E. 13. Amis, J . Inorg. Nucl. Chem., 16, 114 (1960). (8) J. 0. Wear, 0. V. McNully, and E . S. Amis, i h i d . , 18, 48 (1961).
Volume Y9,Number 9 March 1060
