Covalent bonding of Mn2+ ions in octahedral and tetrahedral coordination

Abstract

Hindered rotational energy levels of a linear ion in octahedral and tetrahedral cystalline fieldsThis paper is divided into four parts: The first part (Sec. I) contains a brief review of different assumptions made by several authors for the numerical values of the free Mn H ion parameters. It is shown that if only the Racah parameters Band C are taken into account, then the Orgel-Griffith choice B =960 em-I, C =3325 em-I seems to be the best one. Tanabe and Sugano's figures lead to errors as high as 3800 em-I. Adding only the Racah-Trees correction a does not seriously improve the fitting of levels 4G, 4D, and 4F because a singular set of equations is then obtained. An exact experimental agreement can be obtained for all quartet levels by simultaneously using the Racah-Trees correction a and the seniority correction /3. The best fit values of the adjustable parameters relevant to the Mn H ion are given; it is found that a and /3 do not differ very much from Shadni's values. Section II deals with the well-known use of the two normalization parameters N /' N. for describing covalent bonding. A routine method is developed for performing these calculations by using the three traces of the 4 E, 4 T I' and 4 T 2 matrices (if experimentally available). The interest of using these traces, rather than the energies of individual levels, lies in the fact that the energy sum of 4E(4G) and 4E(4D) levels deviates only slightly from a linear function of the Koide and Pryce covalency parameter, while the energy sum of 4T I and 4T 2 levels does not depend on any assumption upon D q. This method is extensively applied in Sec. IV. In Sec. III is an attempt to obtain condensed analytical expressions by means of Lohr's INDO approximation for covalent bonding. These expressions allow some discussion about the validity of the method described above: It is shown that the use of the conventional D q formalism can still be justified (with a suitable modified value of D q) when only the metal-ligand interaction is taken into account, but it is no longer correct if the ligand-ligand terms are introduced in the calculation. In Sec. IV, we have used the "method of traces" described in Sec. II for deriving tables of covalency and normalization parameters for several manganese-containing crystals: MnF2' MnCl 2 , MnBr2' NaCl:Mn, • .• . We found that the accuracy of the experimental results presently available is in some cases very poor and new measurements by means of more modern techniques are needed. Specifically, an error as high as 6000 cm-I has been found on the 4T I (4p) level in Pappalardo's classical paper on MnCI 2 .Nevertheless, the D q values we obtain are in the right order D q (MNBr 2 ) < D q (MnCI 2 ) < D q (MnF,), while the reverse order was presented in the pioneer paper by Stout. In addition, other materials of interest for luminescence studies are discussed. In ZnF 2 :Mn, covalency parameters are abou t the same as in MnF2' but D q is stronger in zinc fluoride. In ZnS:Mn, it is shown that the first excited level above those iss...

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“…for the d * N ion in a tetrahedral crystal-field [8]. As the covalence increases, the ratio of the two factors N t and N e decreases and the difference between them increases.…”

“…Our calculation shows that the three doublet lines should be 2 T 1c , 2 T 1d , 2 T 2c in this region, the results are in good agreement with the experimental data. For the tetrahedral field such as ZnSe N e is lager than N t [8] since the covalence of the t 2g orbital is stronger than that of the e g orbital. The different between the t 2g and e g orbitals induce that energy level of the Co 2+ ion should be calculated with the d * 7 electron system instead of the d * 3 hole system.…”

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