J . Am. Chem. SOC.1988, 110, 8341-8343 110 K that are too large. These results are in qualitative agreement with Smedarchina et a1.k golden rule tunneling calculation for tetraphenylp~rphyrin.’~ Considering the simplicity of the tunneling model, the barrier parameters cannot be taken too literally. Reasonable fits can be obtained for barrier heights of 4400-5700 cm-I, depending on the classical pre-exponential factor. The porphine isomer with the inner hydrogens on adjacent nitrogens has a calculated energy of 1670-1960 cm-’ above the energy of the isomer with hydrogens on opposite nitrogens. The calculated rate for the mono-deuteriaied porphine-is very close to the rate for the di-deuteriated
8341
porphine, which is consistent with experimental results for tetraphenylporphyrin.I0
Acknowledgment. We thank Hans Limbach for helpful discussions and encouragement. This research was by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S.Department of Energy under Contract No. DE-AC03-76SF00098. T.J.B. acknowledges support from the National Science Foundation in the form of a predoctoral fellowship. Registry No. Porphine, 101-60-0; deuterium, 7782-39-0.
Nephelauxetic Effect in Paramagnetic Shielding of Transition-Metal Nuclei in Octahedral d6 Complexes Nenad JuraniC Contribution from the Department of Chemistry and Physical Chemistry, Faculty of Sciences, University of Belgrade, P.O. Box 550. 11001 Belgrade, Yugoslavia. Received February 1 , 1988
Abstract: For transition metals, using reliable d electron radial wave functions, it was calculated that the d electron radial parameters, BRacshand (rd-3), are equally influenced by change in the d-orbital occupancy. On this basis, introduction of the first power of the nephelauxetic ratio into the paramagnetic shielding term of octahedral d6-complex transition-metal nuclei is justified. Interpretations of rhodium NMR chemical shifts in rhodium(II1) complexes were analyzed.
In the recent interpretation of metal N M R chemical shifts in octahedral d6 transition metal complexes,’ the paramagnetic shielding term (up) has been expressed by the ligand field parameters in the following way:
(where ho is the vacuum permeability, p~ the Bohr magneton, ( rd-3)Fthe free-ion(atom) expectation value of d electron inverse cube distance, f13s the nephelauxetic ratio, and A E the energy of the ‘ A l g f T i electronic transition). Some arguments for incorporation of the nephelauxetic ratio into the paramagnetic shielding term, based on molecular orbital analysis of the covalency effects, have been put forward.2 However, the general validity of the proposed relationship has been questioned by Bramley et since they would rather expect the third power of the nephelauxetic parameter to be incorporated in the paramagnetic shielding term. They suggested that rhodium chemical shifts in rhodium(II1) complexes are in accordance with that expectation. Therefore, I undertook further investigation of the theoretical foundation of eq 1, the results of which are presented here.
Results Ramsey’s theory of nuclear paramagnetic shielding, applied to a metal with d6 configuration in a strong octahedral ligand field$J leads, in the molecular orbital to the expression:
(where 1, is orbital angular momentum operator). Molecular orbitals e,(t2g5eg:1T1g) and t2&t2‘?‘Alg), which in the ionic limit are reduced to the metal d,+$ and d, orbitals, respectively, contain information on the metal-ligand bond covalency. As a measure of the impact of covalency on the paramagnetic shielding term, the following ratio may be introd~ced:~?’
which allows eq 2 to be put into the form: (4) The theoretical foundation of eq 1 depends on whether the covalency ratio qur in eq 4 could be replaced by the nephelauxetic ratio P35. One may compare these two ratios by expressing relevant molecular orbitals as a linear combination of the corresponding atomic orbitals and, under the assumption of a small admixing of ligand into metal orbitals, obtain for qrr:2 ltrr
= a,2a,Z((rd-3)C/(rd-3)F)
or for the nephelauxetic 635
= au2a,Z(Bc/Bd
(7) Note also that: (1) (a) JuraniC, N.Inorg. Chem. 1980, 19, 1093. (b) JuraniE, N. Inorg. Chem. 1985, 24, 1599. (c) JuraniC, N. J . Magn. Reson. 1987, 71, 144. (2) JuraniE, N. Inorg. Chem. 1983, 22, 521. (3) Bramley, R.; Brorson, M.; Sargenson, A. M.; Schiffer, C. F. J . Am. Chem. SOC.1985, 107, 2780. (4) Griffith, J. S.; Orgel, L. E. Trans. Faraday SOC.1957, 53, 601. (5) Freeman, R.; Murray, G. R.; Richardson, R. E. Proc. R. Soc. London, Ser. A 1957, 242, 455. (6) Walstedt, R. E.; Wernick, J. M.; Jaccarino, V. Phys. Rev. 1967, 162,
301.
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where k , is the orbital angular momentum reduction factor: Stevans, K. W. H. Proc. R . Soc. London, Ser. A 1953, 219, 542. ( 8 ) Fenske, R. F.; Coulton, K. G.; Radtke, D. D.; Sweeney, C . C. Inorg. Chem. 1966, 5, 960. (9) Jmgensen, C. K. Prog. Inorg. Chem. 1962, 4, 13; Srruct. Bonding (Berlin) 1966, 1, 3 ; Inorg. Chim. Acta Rev. 1968, 2, 65.
0 1988 American Chemical Socie:v
Jurani?
8342 J . Am. Chem. Soc., Vol. 110, No. 25, 1988 Table I. Ratio of Racah Parameters B(dq)/B(d6) = ( B ) and of d Electron Radial Parameters ( r d - 3 ) d ' / ( r d - 3 ) d 3 = ( F 3 )and (r'l), for Selected dq Configurations, Calculated Using "Double-T" Radial Wave Functions of Richardson and Co-workers Mn Fe co dq d7 d8 d9 dI0
(E)
(r-3)
(r-l)
0.892
0.891
0.922
(E) 0.912 0.820
(r-3)
0.910 0.828
(r-l)
(B)
0.940 0.910
0.927 0.858 0.773
The expressions show that the impact of symmetry restricted covalency, a;a: (where a, and a, are the population coefficients of d,z+ and d, metal orbitals, respectively), is the same in both ratios. The central field covalency is contained in the ratio of radial parameters ( r d - 3 ) c / ( r d - 3 )and F &/EF, where B is the Racah parameter and C denotes parameters of complexed metal and F of a free metal ion (atom). In the applied LCAO approximation, parameters of a complexed metal are to be calculated for the dq configuration using free ion (atom) wave functions which correspond to the self-consistent charge on the metal in a complex.8 The parameters of a free ion (atom) are to be calculated for the free ion (atom) d6 configuration. Therefore, the central field covalency ratios may be denoted also as (rd-3)d'l/(rd-3)d6and B(dq)/B(d6). The question is whether these ratios are of approximately the same value for the dq configurations of interest. By using Slater orbitals one would conclude that they are not, because it follows that B = 3 8 9 ( r d - l ) , I 0 and B(dq)/B(d6) = (rd-I)dq/(rd-l)d6;hence the expectation that the third power of the nephelauxetic ratio should be incorporated into the paramagnetic shielding term.3 However, a single Slater orbital cannot describe accurately d orbitals, as has been shown by Watson.]' Moreover, the shape of the d orbital is changing with ionization in a way which cannot be taken into account by changing the orbital exponent of a single Slater-type orbital. Namely, in Watson S C F wave functions, which are composed of four Slater-type orbitals, both orbital exponents and participation of individual Slater-type orbitals change with the degree of ionization. This could have dramatic effect on central field covalency ratios considered here. Richardson and co-workersI* devised simplified 3d wave functions, composed of two Slater-type orbitals, which are almost as accurate as Watson functions in a comparative calculation^.^^ I have, therefore, calculated the considered ratios for different dq configurations of manganese, iron, cobalt, and nickel using "double-zeta (S6+-Ob) rather than as one involving hypervalent S (>S=O). The observed near constancy of the first IP of dithiaspiroalkanes and their m o m and disulfoxide derivatives is shown to be accidental. The trends in the experimental IPSare well reproduced by calculations, and the nature of the through-bond interaction is related to orbital type. An SO bond lying out of the plane of the thiaspiroalkane ring is necessary for nonzero interaction. Implications for electron transfer in metal complexes and relationships with transfer through rigid hydrocarbon chains are discussed. Through-space effects are equally important in the radical cation of the double-ring molecule VI.
The concept of through-space and through-bond interactions was first introduced by Hoffmann and co-workers nearly 20 years 0002-7863/88/1510-8343.$01.50/0
ago, in interpreting the results of their extended Hiickel molecular orbital’*2calculations on diradical systems in terms of these types 0 1988 American Chemical Society
