Analysis of the Spectra of Tripositive Praseodymium in Ethylsulfate Crystals

In the first portion of this paper a theoretical calculation is presented for the ``free-ion'' spectrum of Pr3+ (4f2). A least-squares calculation is made to obtain a set of Slater and spin-orbit parameters that gives a theoretical spectrum in closest possible agreement with the observed absorption spectrum of Pr3+ (4f2) in ethylsulfate crystals. The disagreement between the calculated and observed spectrum may be explained as due primarily to the neglect of the configuration interaction in the ``free-ion'' calculation, and to a much smaller extent as due to the effect of the lattice environment surrounding the Pr3+ (4f2) ion. In comparing the spectrum of Pr3+ (4f2) in ethylsulfate crystals with the spectrum of the same ion in other crystals, the shift in energy of the J levels may be explained as due to the difference in chemical bonding in the various crystals. This ``chemical bonding'' shift may be accounted for by a simple change in the Slater and spin-orbit parameters. Assuming that the local symmetry about the Pr3+ (4f2) ion is D3h, a first-order perturbation calculation is carried out for the crystal-field split components of the Pr3+ (4f2) ion J-levels, 3P2, 1I6, 3P1, 3P0, 1D2, 1G4, 3F4, 3F3, and 3H4. The following set of lattice parameters, Anm 〈rn〉, obtained by a least-squares calculation, gives the best over-all agreement between the theoretical and observed spectrum: A20 〈r2〉=16.32 cm—1, A40 〈r4〉=—83.46 cm—1, A60 〈r6〉=—45.76 cm—1, and A66 〈r6〉=530.21 cm—1. A more complete calculation is then made using an IBM 7090 program that diagonalizes the entire intermediate-coupling and D3h crystal-field-splitting matrix. Again, from a least-squares calculation, the following ``best'' set of parameters is found: F2=307.4 cm—1, F4=49.44 cm—1, F6=5.138 cm—1, ξ=727.9 cm—1, A20 〈r2〉=15.31 cm—1, A40 〈r4〉=—88.32 cm—1, A60 〈r6〉=—48.76 cm—1, and A66 〈r6〉=548.48 cm—1. When one compares the theoretical energy spectrum based on these parameters with the observed spectrum, one finds an average deviation of 3.0 cm—1, and a standard deviation of only 1.0 cm—1.