Model calculations

In order to understand the main changes in the electronic structure between bulk and MoS2I1/3 NTs, electronic structure calculations of model structures were performed. As noted in [16] the most drastic change in the local geometric arrangement of the MoS₂I_1/3 NTs as compared to the bulk is the S-Mo-S bond angle. Only the most simple model structure containing this bond angle as a parameter, namely a three atom S-Mo-S cluster, was considered. Based on the electronic structure calculations the probability of electronic transitions from the 2p core level to the unoccupied states in the CB was computed to simulate SXA spectra and from the valence band to the 2p core hole to simulate SXF spectra. The calculations were made using the software package StoBe, based on the Linear Combination of Gaussian Type Orbitals - MO solution of the Kohn-Sham DFT equations [81].

From the consideration of the proposed structure for the MoS2-I_1/3 NT (see Fig. 5.1 on page 50) the presence of two types of nonequivalent sulfur atoms (belonging to the inner and to the outer shells) is obvious. A shift in the binding energy of the S 2p core electron may exist due to the inequivalent sites. XPS measurements on MoS2-I_1/3 [86]

demonstrated the presence of two S 2p sets of peaks separated by about 1.8 eV. As XPS is very surface sensitive, the identification of the origin of the two XPS peaks is not clear:

58 MoS2 sub-nanometer diameter nanotubes.

Intensity (a.u.)

164 162

160 158

156 154

Emission energy (eV)

163.40

h ω

in= 200 eV

163.60 164.00 164.68 164.95 167.75 168.55

Figure 5.7: RIXS spectra of MoS₂I_1/3 NTs recorded with different excitation energies corresponding to the specific features in the SXA spectrum (see Fig.5.6). For ¯hωin ≤ 164.95 eV the intense elastic peaks have been divided by 25 and clipped.

5.2 Electronic structure of Mo-S-I nanotubes. 59

Intenisty (a.u.)

169 168

167 166

165 164

163 162

161

Photon energy FY-SXA S 2p

MoS₂-I_1/3 NTs

+1.8eV

+1.8eV

0.2eV 0.2eV

Figure 5.8: FY-SXA spectrum of MoS2-I1/3 NTs. The energy positions of the absorption peaks due to the presence of the nonequivalent sulfur atom are marked by dashed lines.

this shift may also be due to sulfur atoms at the surface of NT bundles vs. sulfur atoms inside a bundle. Out FY-SXA spectra are able to provide some insight into this question.

If the different atomic position of the sulfur atom within each NT causes the 1.8 eV shift of the energy of the 2p core electron, two absorption spectra should be observed, shifted relative to each other by 1.8 eV. In Fig. 5.8 the FY-SXA spectrum of MoS2-I_1/3 NTs is shown. Lines mark the position of main peaks which are 1.1 eV separated and thus can not be assigned to non-equivalent S atoms, but to the spin-orbit partners of the each sulfur atom. The positions of the peaks shifted by 1.8 eV are marked by the dashed line: there are no strong features in the experimental spectrum observed at those photon energies.

From this consideration we conclude that the difference in the 2p electron binding energy in two different sulfur atoms is considerably smaller than 1.8 eV. It could be estimated to be 0.3±0.1eV from the presence of shoulders at the high energy side of the absorption peaks. The energy shift observed in the XPS measurements may be due to probing the surface S atoms. This analysis supports the suitability of the model structure for the MoS2-I1/3 NTs with equivalent sulfur atoms for simulation of emission and absorption spectra neglecting an energy shift of the binding energy of the S 2p electron as this small value is not known precisely.

The bulk material was modeled with a S-Mo-S angle of 82⁰ and a S-Mo bond length equal 2.417 ˚A [82]. The MoS2−Ix NTs were modeled with the smaller S-Mo-S angle of 63⁰ suggested in [16], keeping the bond length constant. The calculated spectra were convoluted with a Gaussian function with a FWMH of 0.3 eV for SXA and 0.5 eV for SXF to account for the life-time broadening of the core hole and the experimental energy

60 MoS2 sub-nanometer diameter nanotubes.

resolution. The presence of the core hole in the final state of the absorption process and the hole in the VB in the non-resonant emission process was taken into account in these calculations. The 1.1 eV spin-orbit splitting of the 2p3/2 and 2p1/2 levels was taken into account assuming a 2:1 branching ratio. The resulting theoretical model spectra are plotted in Fig. 5.9 together with the experimental data. The calculations are in rather good agreement with the measured intensities and reproduce the main features of the experimental spectra. The simple model obviously cannot describe effects resulting from the crystalline structure of the bulk and the NTs. Nevertheless, the main trend in the SXA and SXF spectra when going from the bulk to the NTs is predicted: the SXF spectrum exhibits increased spectral weight at the top of the VB whereas the peak at 162.5 eV is absent in the SXA spectrum.

The good agreement between the calculated spectra and both the experimental SXA and SXF spectra suggests that the simple model captures the essential effects in the changes of the local electronic structure between bulk MoS2 and subnanometer MoS2 -I1/3 NTs. The redistribution of electron density in the tubes compared to 2H-MoS2 bulk material is interpreted due to the S-Mo-S bond distortion. A charge distribution analysis in the ground state (see Fig. 5.10) was made. The distribution of the electronic states which would give a contribution to the high energy peak in the SXF spectrum (state with binding energy of 2 eV below the top of the VB) was calculated for both model structures.

The positions of Mo and one of the S atoms were fixed and the second S atom was moved to simulate the bond angle changing in the tube compared to bulk. Thus the electron density between the fixed atoms could be directly compared. This analysis shows that electron density is redistributed from the S atoms toward the Mo atom due to the change in bond angle: the electron density changes locally at the sulfur site with bond angle.

Although the theoretical spectra give correctly the general character of the experimen-tal changes, the relative intensity of different features is not well reproduced. The high energy part of the emission spectra and the low energy peak in the absorption spectra for both models are underestimated by the theory. The simplicity of the model can explain the disagreement. For bulk material spectra simulated on the basis of DFT calculations using the complete structure of Fig. 5.4 is better reproduced the shape of the experimen-tal emission spectrum:a consequence of taking into account all atoms of the unit cell and the strong hybridization between them.