Theoretical Modelling of Photoelectron Spectroscopy of Transition Metal Clusters
Open Access
- Author:
- Iordanov, Ivan Olegov
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- August 20, 2012
- Committee Members:
- Jorge Osvaldo Sofo, Dissertation Advisor/Co-Advisor
Jorge Osvaldo Sofo, Committee Chair/Co-Chair
Vincent Henry Crespi, Committee Member
Gerald Dennis Mahan, Committee Member
Albert Welford Castleman Jr., Committee Member - Keywords:
- Photo-electron Spectroscopy
Density Functional Theory
Molecular Clusters
Franck-Condon Factors
Vibrational States - Abstract:
- The interaction between light and electrons is one of the most widely studied physical phenomena, and a primary means of characterizing the properties of condensed matter systems. Many experimental techniques have been developed which make use of light to probe materials in bulk, on substrates and in the gas phase. Photoelectron spectroscopy (PES) is one such technique, in which monochromatic photons are used to photodetach electrons whose kinetic energy is then measured. Through energy conservation, the difference between the energy of the incoming photons and outgoing electrons is then equal to the difference in energy between the initial and final state of the molecule from which the electron was ejected. This difference is defined as the binding energy of the electron, a spectrum of the number of electrons versus their binding energy can be plotted. With sufficient resolution, PES can be used to determine both the electronic and vibrational structure of clusters, however the price of this versatility is that it is difficult to interpret PES without complementary theoretical investigation. In this thesis we first present background information on PES theory and our ab initio calculations, and then delve into our use of theoretical techniques to interpret the PES spectra of three different types of transition metal clusters. We first examine the case of the NbCn (n=2-7) clusters. DFT calculations show that these clusters are stable in both a linear and cyclic configuration, although the cycle is the ground state for all but NbC6. We use the DFT density of states to obtain theoretical PES spectra that can be compared to the experimental results. We find that to explain the full experimental PES spectrum of this cluster series, it is necessary to combine the spectra of both linear and cyclic structural isomers, even in cases where the higher energy isomer is up to 0.8eV above the ground state. This result is confirmed through calculating the excited states of the neutral clusters using the SAC-CI method. The conclusion is that since the clusters are produced in a high energy environment far from equilibrium, they can remain trapped in metastable states during the PES measurement. In Chapter 4, we examine the curious case of the ZnO and ZnOH clusters. The spectrum of the ZnO cluster consists of a single narrow peak with a well-defined vibrational progression. It is easily explained through a DFT calculation of its detachment energy and vibrational state, coupled with a Franck-Condon calculation. The experimental spectrum of ZnOH consists of a single broad peak without a resolved vibrational progression. DFT calculations of the detachment energy match well with the experimental value of the position of the peak. The source of the width of the peak remains unclear, despite our investigation of all the common sources of unusual large peak width in PES – electronic excited states, rotational transitions and vibrational transitions. In the last chapter, we consider two series of valence isoelectronic clusters, TiO2, ZrO2, HfO2 and CoO2, RhO2, and IrO2. DFT calculations show that the Ti-Hf series has a cyclic ground state structure with bending angles on the order of 110˚. The ground state structure of the Co-Ir series is more unusual – CoO2 and RhO2 are nearly linear with a bending angle of 165˚, while IrO2 is linear. More importantly the Co-Ir clusters have a very flat potential with respect to changes in angle – the difference in energy between the linear and 165˚configuration for CoO2 is a mere 0.003eV. The flat potential is also reflected in their vibrational bending mode frequencies which are on the order of 100 cm-1, compared to ~400 cm-1 for the Ti-Hf series. An examination of the molecular orbitals of the two series suggests that the reason for this difference is in the five extra electrons of the Co-Ir series, four of which occupy two d orbitals that are unbonded in the linear configuration and become anti-bonding as the molecule is bent. In order to confirm that the electronic occupation is the primary factor behind the properties of the two series, we implement a simple Hubbard model to model the clusters, using parameters acquired by matching against the DFT orbitals of the linear CoO2. This simple model is then applied to the whole series of transition metal dioxide clusters along the same row as Ti and Co – FeO2, MnO2, CrO2, VO2. We find that even if we keep the parameters matched against CoO2, the model correctly predicts the angle of the ground state structure determined in DFT for all the clusters examined (except for FeO2). Unfortunately, the method only matches the rough order of magnitude of the curvature of the potential energy surface found in DFT, in particular it does not match the abnormally low curvature of the CoO2 cluster. In future work, we plan to refine this simple model to allow us to understand the unusually flat potential of CoO2.