Theoretical Calculation of Electronic Structures and 4f→5d Transitions of Lanthanide Ions Doped in Crystals
My work mainly consists of two parts as follows:a) The ab initio self-consistent DV-Xα(discrete variational Xα)method was used to computate the ground-state electronic structures,the f-d transition energies of the whole series of rare earth ions doped in crystal YPO_4b) After a brief review of the simple model for analysing the f-d transition spectra of lanthanide and actinide ions in crystals, this model is successfully applied to the configurations f~(12)d as a supplementary study.In the first part, the ab initio self-consistent DV-Xα(discrete variational Xα) method was used in it\'s relativistic , spin-polarized and embedded cluster version to computate the ground-state electronic structures, the f-d transition energies of the series (4f)~1-(4f)~(13) of rare earth ions doped in crystals YPO4 The ground-state calculation gave the molecular-orbital energy spectra, the curve of total and the partial density of states and the corresponding occupation numbers etc., the 4f and 5d crystal-field one-electron levels of Ln~(3+) relative to the valence and conduction bands of host,and their variation trends across the Ln~(3+) series . Compared with the others theoretical results(empirical equation or other ab initio calculation), the calculated variation trends fit well with theirs while our calculated characteristic energiesε_f,ε_d are better and more completed.In the transition-state calculation aspect, usually each transition-state calculated 4f→5d excitation energies should be compared to a average energy of several experimentally observed ones for a (4f)~N ions with N>1, However, we found that under our low symmetry circumstances, the orbital degenerate is totally relieved, simultaneously spin degenerate is also relieved in the spin-polarized calculation version, each single-electron energy level corresponds to a unique single-electron state, each electron occupation configuration corresponds to a unique many-electron state, so each transition-state calculated 4f→5d excitation energies can be directly compared to zero-phonon line of a 4f→5d transition peaks. In this thesis, the transition-state calculated 4f→5d excitation energies was compared to observed excitation peaks of YPO_4:Ln~(3+) so that each peak was identified. The identified results fit well with the results given by M. F. Reid based on parameter-fitting method and the results proposed by Duan C. K. and Xia S. D based on the simple model method. In the mean while, the lattice distortion caused by the differences between radials of the doped lanthanide ions and Y ions was also optimized. The 4f-5d transitions which have not been or can not be observed through experiment can also be predicted using the transition-state calculation mentioned above. This method can also be applied in other calculations of f-f, f-d transition and charge-transfer for other Ln~(3+) doped low symmetry systems.In the second part, the development and extension of the simple model for analysing f-d transitions of lanthanide and actinide ions in crystals was reviewed. The model had already been successfully applied to f-d transition spectra of rare-earth ions (4f~3-4f~(12)) in crystals. As a supplementary study, this model was further applied to the remaining configurations f~(12)d in this thesis, where the parameterized energy matrix elements of this configuration were obtained and tabulated. As an example of it, the excitation spectrum of Yb~(3+) doped in crystal CaF_2 was well explained.