Nephelauxetic Effect Revisited ANDREI L. TCHOUGRE´ EFF,1,2 RICHARD DRONSKOWSKI2 1Poncelet Laboratory, Independent University of Moscow, Moscow Center for Continous Mathematical Education, Moscow 119991, Russia 2Institute of Inorganic Chemistry, RWTH Aachen, Aachen D-52056, Germany Received 1 October 2008; accepted 3 November 2008 Published online 10 April 2009 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/qua.21989 ABSTRACT: We readdress the well-known nephelauxetic effect in coordination compounds of transition metal ions and analyze its possible origins presented in the literature. The initial hypothesis was to ascribe the reduction of the effective Racah parameters B and C of the electron–electron interaction in the complexes as compared to their respective free ion values (which is the essence of the nephelauxetic effect) to the expansion of d-orbitals in the complex because of their quantum mechanical mixing with the orbitals of the ligands leading to delocalization. This picture necessarily leads to a rigid positive correlation between the amount of the d-shell splitting controlled by the same delocalization and the amount of the renormalization of the interaction parameters. In fact, such a rigid relation does not exist and the so-called spectrochemical and nephelauxetic series of the ligands composed according to the aforementioned amounts do not coincide in many points. An alternative explanation based not on the delocalization, but on polarization of the ligands had been proposed at the same time as the delocalization based one. Realistic estimates had been obtained on this basis, but the scheme had never been implemented on the atomic scale, which is necessary to enable renormalization of the aforementioned interaction parameters as a “built-in” function of quantum chemical software. The required atomic resolution formulation of the polarization-based model of the nephelauxetic effect is constructed in this work, in which a relation of such an approach to the general problematics of the “next generation” of semiempirical methods of quantum chemistry is also discussed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 2606–2621, 2009 Key words: effective Hamiltonian crystal filed theory; nephelauxetic effect; next generation of semiempirical methods; transition metal complexes Correspondence to: A. Tchougre´eff; e-mail: [email protected] Contract grant sponsor: RFBR. Contract grant number: 07-03-01128. Contract grant sponsor: DFG. Contract grant number: DR 342/20-1. International Journal of Quantum Chemistry, Vol 109, 2606–2621 (2009) © 2009 Wiley Periodicals, Inc. NEPHELAUXETIC EFFECT REVISITED ligands according to the strengths of the crystal 1. Introduction fields induced by them (the 10Dq parameter) to the so-called spectrochemical series [3–6] having (with mong the words to be learned by heart by many omissions) the following form: A first-year inorganic chemistry students fasci- nated by the bright colors of the coordination com- Ϫ Ϫ 2Ϫ 3Ϫ Ϫ Ϫ Ϫ I Ͻ Br Ͻ S Ͻ N Ͻ F ϽOH Ͻ Cl pounds of transition elements, the term “neph- elauxetic” (effect) is one of the most intriguing, but 1 Ͻ Ox2Ϫ Ͻ O2Ϫ Ͻ (1) unfortunately being rarely readdressed during fur- 2 ther years of studies or even professional carriers. 1 This beautiful Greek word introduced into theoret- Ͻ H O Ͻ SCNϪ Ͻ NH ,py Ͻ En ical inorganic chemistry by Jaurgensen [1] follow- 2 3 2 Ϫ Ϫ ing the advice of Kaj Barr—the prominent Danish Ͻ SO2 Ͻ NO Ͻ CNϪ Ͻ CO. orientalist—refers to the mental picture according 3 2 to which the cloud (␯␧␸␧´␭␩)ofd-electrons expands (␣␷␰␧␫␯) when a transition metal ion (TMI) becomes From this one can see that the crystal fields split- a central one in a coordination compound, where it tings are systematically weaker for charged ligands is surrounded by various other inorganic or organic than for the uncharged ones with the utter example ions or molecules, rather a free one. The conse- of CO inducing the strongest crystal field, but bear- quences of the coordination process for the d-shell ing neither charge nor even noticeable dipole mo- are in principle twofold: before the already men- ment. Thus, the relative strengths of the crystal tioned expansion of the d-orbitals the splitting of fields observed in the experiment cannot be ex- the d-levels degenerate in the free ions takes place, plained by the ionic model of the environment. being much more important both qualitatively and These observations clearly indicate that purely elec- energetically, namely, the splitting is ultimately re- trostatic effects may be only of minor significance in sponsible for the mentioned colors of the transition determining the strength of the effective crystal metal complexes (TMCs). Its qualitative picture is field felt by the d-shell. explained by the crystal filed theory (CFT) origi- The unsatisfactory situation with the CFT esti- nally proposed by Bethe [2] and numerously rep- mates called for the development of the ligand field resented in various other sources adjusted for the theory (LFT) [3, 4], trying to include the ligands on chemical problem setting [3–6] (originally CFT had a more realistic basis. In its simplest version, it been developed for the transition metal impurity assumes that it is enough to consider the valence ions in the crystals). The CFT bases on the very shell of the TMI, containing 3d-, 4s-, and 4p-orbitals natural picture of what happens in TMCs—all in- and to include one lone pair orbital per donor atom teresting events (low- energy excitations)—are lo- of the ligand thus giving the following picture of calized in the d-shell of a central TMI, whereas one-electronic states of the closest ligand shell other atoms or groups provide some external, orig- (CLS) of a TMI in a TMC which the octahedral local inally purely electrostatic, field responsible for the symmetry: splitting. In such a formulation of the CFT known as its ionic model, and treating the splitting of the ye a g ␺ ͑e ͒ ϭϪx ␾͑d 2͒ ϩ ͑2␹ ϩ 2␹Ϫ Ϫ ␹ Ϫ ␹Ϫ d-shell as a pure electrostatic effect, the CFT faces a gc eg z ͱ12 z z x x serious problem: the splitting parameters cannot be Ϫ ␹ Ϫ ␹ ͒ correctly estimated. Although the symmetry is per- y Ϫy fectly reproduced even by this simplistic scheme, it xe b g turns out that quantitatively the ionic model gives ␺ ͑e ͒ ϭ y ␾͑d 2͒ ϩ ͑2␹ ϩ 2␹Ϫ Ϫ ␹ Ϫ ␹Ϫ gc eg z ͱ z z x x at best 20% of the observed splitting even if unre- 12 alistically large effective charges are ascribed to the Ϫ ␹ Ϫ ␹ ͒ y Ϫy ligands. This happens due to the oversimplified ye description of the TMI’s environment (ligands). It is a g ␺ ͑e ͒ ϭϪx ␾͑d 2Ϫ 2͒ ϩ ͑␹ ϩ ␹Ϫ Ϫ ␹ Ϫ ␹Ϫ ͒ not thus surprising that the heaviest strike upon the gs eg x y 2 x x y y CFT from the (semi)quantitative side was given by xe TMC spectroscopy in 30s of the last century. Spec- b g ␺ ͑e ͒ ϭ y ␾͑d 2Ϫ 2͒ ϩ ͑␹ ϩ ␹Ϫ Ϫ ␹ Ϫ ␹Ϫ ͒ troscopic experiments allowed to range different gs eg x y 2 x x y y VOL. 109, NO. 11 DOI 10.1002/qua INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2607 TCHOUGRE´ EFF AND DRONSKOWSKI ya from the (effective) charges localized on the li- a 1g ␺ ͑ ͒ ϭ ␾͑ ͒ ϩ ͑␹ ϩ ␹ ϩ ␹ ϩ ␹Ϫ ϩ ␹Ϫ a1g xa1g 4s x y z x y gands, but is a consequence of covalent interac- ͱ6 tions—ultimately of the interplay between the de- ϩ ␹ ͒ Ϫz localization of the d-electronic states to the ligands and of the ligand electronic states to the d-shell. xa ␺b͑ ͒ ϭ ␾͑ ͒ ϩ 1g͑␹ ϩ ␹ ϩ ␹ ϩ ␹ ϩ ␹ Spectrochemical series Eq. (1) then can be thought a1g ya 4s x y z Ϫx Ϫy 1g ͱ6 to be arranged in the order of increase of not only ϩ ␹ ͒ 10Dq but also of the characteristic delocalization Ϫz 2 2 parameters xegyeg, describing the strength of the co- yt valent metal–ligand interaction and determined by a 1u ␺ ͑t ␥͒ ϭϪx ␾͑4p␥͒ ϩ ͑␹␥ Ϫ ␹Ϫ␥͒ 1u t1u ͱ2 the same Hamiltonian matrix elements as the split- ting through the relations: xt ␺b͑ ͒ ϭ ␾͑ ͒ ϩ 1u͑␹ Ϫ ␹ ͒ t1u␥ yt1u 4p␥ ␥ Ϫ␥ . (2) ͱ2 2 2 1 1 x y ϭ ͩ Ϫ ͪ eg eg 1 ϩ ␨2 , (6) 4 1 eg The Stevens’ coefficients x⌫, y⌫ subject to the normalization condition: H ␹ ␨ ϭ d eg . (7) Ϫ ␹␹ 2 2 Hdd H x⌫ ϩ y⌫ ϭ 1 (3) Getting very large ␨ yields the highest possible give the amount of the delocalization of the TMI- eg value of x2 y2 ϭ 1/4 referring to the maximal pos- centered states and have to be determined (ideally) eg eg sible delocalization of the d-orbital. from a self-consistent field procedure applied to the These considerations dating back to 30s qualita- effective Fock operator describing the CLS of the tively explain pretty much of the spectroscopy of TMI. By this, the one-electron states of both the TMI TMCs in terms of the 10Dq splitting parameter for and of the surrounding ligand atoms are explicitly the one-electron d-levels (although the consistent included into consideration. In a symmetric envi- estimation of these and similar quantities through a ronment assumed in Eq. (2), the d-orbitals of the kind of quantum chemical procedure—from the t -symmetry neither get any admixture nor expe- 2g information on chemical composition and geome- rience any change of their energy (␲-orbitals on the try of the TMC—was not possible).