#### Title

Ab Initio RCI Calculations of Atomic Properties of Selected Transition Metal Ions

#### Date of Award

2008

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (Ph.D.)

#### Institution Granting Degree

Michigan Technological University

#### Cedarville University School or Department

Science and Mathematics

#### First Advisor

Donald R. Beck

#### Keywords

Pure sciences, Transition metal ions, Relativistic configuration interaction, Strontium, Molybdenum

#### Abstract

In this dissertation, the relativistic configuration interaction (RCI) method has been applied to some selected transition metal ions. These include the three strontium isoelectronic ions (Zr III, Nb IV and Mo V), Mo VI and Hf^{-} . While the most crucial part in any RCI calculation is to generate an effective basis set and correspondingly an adequate radial set, these projects provide some experience in what consists of such a basis set for the specific kind of system.

In the strontium isoelectronic case, the energy levels of 4d^{2 }, 5s^{2} *J* =0 state, the 4d5p, 5s5p *J* =1 state are computed with correlation in the valence and from the shallow core. Our results for the *J* =0 levels of Zr III are in good agreement with the experiment, with an average absolute error of 190 cm^{-1} . For the *J* =1 levels, the average absolute error is 249 cm^{-1} . By including the important second order effect, we are able to extract from the energy matrix 12 more levels of 4d4f, 4d5f, 4d6p and 4d7p with an average absolute error of 896 cm^{-1} . Our calculation for the *J* =0 state of Nb IV suggests a reposition of the 5s^{2} level, which has been confirmed later by the new experiment. For the *J* =1 levels, we obtain similar accuracy to Zr III with an average absolute error of 215 cm^{-1} in the 4d5p, 5s5p levels, and 878 cm^{-1} in the 4d4f, 4d6p levels. We have also calculated the oscillator strength for the electric dipole transitions between the *J* =0 and *J* =1 state and have obtained good gauge agreement. The gauge agreement is 3.2% on average for Zr III and 2.7% for Nb IV. For Mo V, we use a larger reference space and calculate the *J* =0 energy levels of 4d^{2} , 5s^{2} , 4d5d, 4d6d and 5p^{2} . We find excellent agreement with the most recent measurement in the levels of 4d^{2} and 4d5d, the average absolute error being 85 cm^{-1} .

For Mo VI, the*J* =5/2 energy levels of the Rydberg series 4p^{6}*n* f (*n* =4,5,6) and its strong perturber 4p^{5} 4d^{2} are calculated. Due to the different occupation number in the core-like 4p subshell, accurate positioning of these levels is still computationally challenging. This challenge exists also experimentally, as is manifested by the large discrepancies between the energy values measured by two groups. Most of our calculated level energies agree with the most recent measurement, but large discrepancies in a few upper levels do exist. The possible causes to these large disagreements, such as the second-order effect, the Breit operator effect, adequacy in radial space etc., are discussed. The oscillator strength of all the electric dipole transitions from the 4p ^{6} nd ^{2} D (*n* =4,5,6) states to these a *J* =5/2 states are computed and 36 of the large (*f* > 0.001) ones are presented. The gauge agreement is 6.6% for ^{2} D_{3/2} [arrow right] *J* =5/2 and 5.0% for ^{2} D_{5/2} [arrow right] *J* =5/2. Most of them have been computed for the first time.

For Hf^{-} , calculations show it has only one bound state 5d^{2} 6s^{6p} *J* =5/2. The electron affinity is determined to be 0.114 eV by combining valence calculation with a separate estimate for the core-correlation effect. Our value falls within the limits estimated by two experimental groups. The partial cross sections for photodetachment into the energetically reachable neutral thresholds are calculated. We infer from Fano's theory that the important resonance states are 5d ^{3} 6s^{2} , 5d6s^{2} 6p^{2} and 5d^{2} 6s6p^{2} . Mies's theory is employed to mix these resonance states with the continuum channels. While the mixing of 5d^{ 3} 6s^{2} into the 6p detachment has a trivial impact, the mixing of 5d6s^{2}6p^{2} , 5d^{2} 6s6p^{ 2} into the 5d detachment results in increase by two to three orders of magnitude in the cross sections.

In the future, our calculation for cross sections can be improved in two aspects. The first is the evaluation of the energy matrix element between a continuum state and a discrete state. The non-orthonormality effect has been treated only partially, but a complete treatment is inevitable if higher accuracy and efficiency are to be achieved. The second aspect is the direct interaction between two continuum states, i.e. interchannel coupling. So far there is no relativistic code for this purpose.

#### Recommended Citation

Pan, Lin, "Ab Initio RCI Calculations of Atomic Properties of Selected Transition Metal Ions" (2008). *Faculty Dissertations*. 42.

https://digitalcommons.cedarville.edu/faculty_dissertations/42