R. Acevedo

Vibronic intensities in centrosymmetric lanthanide complex ions. I: A combined crystal field-ligand polarisation approach

SummaryA theoretical model to calculate the vibronic intensities induced by the odd vibrational modes in centrosymmetric lanthanide complexes is developed and applied to octahedral complex ions, LnX63−, such as occur in the hexachloroelpasolites Cs2NaLnCl6. Both the crystal field and the ligand polarisation contributions are evaluated using a standard set of symmetry coordinates. For the crystal field term a truncated expansion of the intermediates states is employed rather than the more conventional closure approximation. Special care is necessary to ensure that the phases of the contributions are correctly determined since the cross-term between the ligand polarisation and crystal field contributions is signed. General equations applicable to anyfn complex ion are derived and an example of their application to the PrCl63− ion is given The agreement with experiment is satisfactory.

Vibronic intensities in the electronic spectra of transition metal complex ions. Part X. Second order Herzberg-Teller contributions to the vibronic intensity of the 4A2g ↔ 4T2g transition in MnF2- 6

A method to estimate the contribution to the vibronic intensity in electronic transitions of inorganic complex ions due to second order terms in the Herzberg-Teller expansion of vibronic wavefunctions is developed and applied to the 4A2g ↔ 4T2g transition of the MnF2- 6 ion. Both crystal field and ligand polarization contributions are derived, the crystal field term being evaluated in the single intermediate p state approximation. Contributions to the intensity of the nine second order terms are evaluated for several force fields and compared with recent experimental data. Although there are some difficulties in this comparison, it provides some support both for the model and the attribution of the intensity mechanism.

Normal coordinate analysis of the 25-atom system Cr(NH3)3+6 octahedral symmetry

Abstract A full normal coordinates analysis of the Cr(NH3)3+6 ion has been carried out in which the complex is treated as a 25-atom system with freely rotating ammine groups. The parameters appropriate to both valence and Urey—Bradley force fields are evaluated using data from i.r., Raman and vibronic spectroscopy and their values discussed. A complete set of symmetry coordinates and the potential energy distribution are given. The calculated vibrational wavenumbers and potential energy distribution for Cr(ND3)3+6 are then compared with experiment. The only modes which are significantly mixed are the T1u CrND bend and CrN stretch of the deuterated species. The agreement between the 13-atom Cr(NX)6 and 25-atom Cr(NH3)6 models of the cation is good except for the T1g CrNH bend.

Vibronic intensities in the electronic spectra of transition metal complex ions. Part IX. Experimental study of the relative vibronic intensities in the 2Eg → 4A2g transition of the MnF2- 6 ion in Cs2SiF6

The relative intensities of about 90 of the more prominent vibronic bands in the 2Eg → 4A2g luminescence spectrum of the MnF2- 6 ion in Cs2SiF6 have been measured at 80K. The reported intensities cover a range of more than 106. Corrected values of the important intensity ratios of the v 3, v 4, v 6 vibronic origins are given as 1:4·02:5·45. Most of the features can be assigned as progressions in the v 1, v 2 even parity vibrational modes based on the magnetic dipole allowed electronic origin and the v 3, v 4, v 6 odd parity vibronic origins, up to four members of the progressions being observed. Prominent features also include combinations of the three odd vibrational modes. Anharmonic effects are small. The intensity mechanisms of these features are briefly discussed. It is likely that second order and third order Herzberg-Teller vibronic coupling makes a significant contribution to the intensity mechanism. These data will be used in subsequent theoretical models of the intensity mechanism.

The calculation of electric dipole vibronic intensities in centrosymmetric coordination compounds using the crystal field-closure-ligand polarization model

Equations are derived for the evaluation of the contribution to the electric dipole vibronic intensity of d-d and f-f transitions in octahedral complex ions. Expressions for the evaluation of the crystal-field and ligand polarization terms and the cross term between are presented in symmetry adapted form and tables of the required coupling constants are given.

Normal Coordinates Analysis of the Hexamminochromium (III) Ion. A Simplified M(NX)6 Model

Abstract A normal coordinates analysis for the hexamminochro mium (III) ion, in octahedral symmetry has been underta ken. A simplified M(NX)6 model has been adopted, since many of the gerade vibrational frequencies are still un known. It is found that a very simple and consistent force field is able to reproduce the observed vibratio nal frequencies as well as gives a reasonable set of for ce constant for this complex ion. This calculation sup ports the assignments, made in literature by several workers.

Spectral Intensities in Cubic Stoichiometric Elpasolites: The Cs2NaSmCl6 and Cs2NaEuCl6 Systems

Abstract We report theoretical studies regarding the optical properties of the Cs 2 NaSmCl 6 and the Cs 2 NaEuCl 6 systems, based upon new and updated experimental data from linear and non-linear optics. Vibronic intensity calculations are carried out for a series of selected transitions for which a number of superpositions of various spectral features derived from different excitations are most likely to take place and, as a consequence to play a significant role in both the observed oscillator strengths and in particular, the relative vibronic intensity distributions for a number of selected electronic transitions in these systems. Models and calculation methods are put forward, within the framework of a generalized vibronic model (VCF-LP). Our model calculation is based upon a minimum set of adjustable parameters (six parameters model, without including the force constants needed to build up a short-range interacting vibrational force field to modulate the normal modes of vibrations for the system). The model is developed within the assumption of either a small or a negligible coupling between the internal and the external vibrations for the crystal. In spite of the limitations and assumptions involved, it is shown that this model shows some utility and flexibility to advance our understanding of these complex radiative processes. For the sake of completeness, we discuss the most likely sources for improvement and the latest development in this field of research.

On the theory of radiative transitions in centrosymmetric complexes

The theory of radiative transitions, in centrosymmetric complexes, is examined in great detail, within the framework of the crystal field method.In connection with radiative transitions, the current method of calculations, with and without invoking closure approximation, are considered from a purely theoretical point of view, by taking advantage of the irreducible tensor method put forward by Griffith.Explicit equations are derived throughout the course of this work to account for the vibronic electric dipole moments, associated with d-d and f-f type of excitations.

Vibronic oscillator strengths of Tm3+ in Cs2NaTmCl6

Abstract Direct calculations (without variable fitting parameters) utilizing a symmetry-adapted vibronic crystal field–ligand polarization scheme are presented for the total vibronic oscillator strengths in the 3 H 6 Γ 1 → 3 H 5 , 3 F 4 , 1 G 4 absorption transitions of the Tm 3+ ion in the cubic system Cs 2 NaTmCl 6 , and are in reasonable agreement with the experimental oscillator strengths from the 10 K absorption spectrum. The calculated total vibronic intensities are not particularly sensitive to the detailed compositions of electronic wavefunctions employed in the calculations, as long as the correct phases are employed. Experimental oscillator strengths for individual moiety mode transitions have been calculated, but in many cases these show large deviations from experimental values, particularly for ν 3 and ν 4 vibronic structure. Reasons for the failure of the model in this respect are considered.

Vibronic intensities in the electronic spectra of transition metal complex ions VIII: Vibrational coordinates for octahedral ions and their application to the4A2g ↔2Eg transition of the MnF 6 2− ion

SummaryA reexamination of the vibrational coordinates appropriate in vibronic intensity calculations in octahedral coordination compounds is presented. We derive a complete set of symmetry coordinates that is orthonormal and transforms correctly under the group generators. The vibronic hamiltonian for the crystal field and ligand polarization contributions to the intensity are calculated in the basis of these coordinates. The crystal field term is evaluated both using a truncated basis set for the intermediate electronic states and using the closure approximation. These methods have been applied to the calculation of the vibronic intensity distribution for the4A2g ↔2Eg transition of the MnF62− ion and close agreement wtih experiment achieved.