The Effect of Particle Size and Composition on the Optical and Electronic Properties of CdO and CdS Rocksalt Nanoparticles

Quantum confinement like behaviour in CdO and CdS nanoparticles is demonstrated through explicit ev GW -BSE many-body perturbation theory calculations on 0.6-1.4 nanometre particles of these materials. However, while the lowest optical excited-state, exciton, and the highest occupied and lowest unoccupied quasiparticle states in such nanoparticles are predicted to be delocalised, they are found to be delocalised over the surface of the particle only and not the whole particle volume. The electronic and optical properties of CdO and CdS rocksalt nanoparticles are predicted to differ dramatically from their structurally analogous MgO counterparts, where the lowest exciton and highest occupied and lowest unoccupied quasiparticle states are strongly localised, in contrast. This difference in behaviour between MgO and CdO/CdS is explained in terms of the more polarisable, less ionic, bonding in CdO and CdS. The effect on the optical and fundamental gaps of the particles due to the presence of amine capping agents on the particles’ surface is explored and predicted to be relatively small. However, the highest occupied and lowest unoccupied quasiparticle states are found to consistently shift to more shallow values when increasing the surface density of capping agents. An explanation of this shift, finally, is proposed in terms of the dipole field induced by the aligned dipoles of the capping agents.


Introduction
The effect of nanostructuring a material on its electronic and optical properties is complex. Nanostructures of some materials, such as those of CdO, [1][2][3] CdS, 4 CdSe, [5][6] PbS 7-8 and PbSe, 9 display experimentally a significantly blue-shifted optical gap (see Fig. 1) relative to the corresponding bulk material, i.e. the bulk starts absorbing light at longer wavelengths than the nanostructures. In contrast, nanostructures of other materials, such as MgO, [10][11][12] CaO 11 and SrO, 13 are observed experimentally to have considerably red-shifted optical gaps. The optical gaps of nanostructures of the former materials are also generally observed to shift with particle size, [2][3][4][5][6][7][8][9] where the optical gap and the whole absorption spectrum shifts to the blue with decreasing particle size. For nanoparticles of MgO, in contrast, the optical gap of particles does not change with particle size and only the relative intensities of the peaks in the spectrum changes. 10 The blue shift is often explained in terms of quantum confinement, where the size of a delocalised exciton, the excited electron-hole pair, is constrained in the nanostructure to a value smaller than in the bulk, [14][15] while the red shift is discussed in the experimental literature in terms of the strong localisation of the exciton on surface defect states. 10-11, 13, 16 The exact microscopic picture of how excitons are (de)localised in the nanostructures, how changes in the nature of the chemical bonding in the materials switches between quantum confinement and surface defect localisation, the degree of (de)localisation of free charge carriers, as well as the exact effect of capping agents, is still not well understood.
Materials that in the bulk crystallise in the rocksalt (halite) structure are ideal systems to study to better understand the link between the chemical bonding in materials, nanostructure size and the optical and electronic properties of these nanostructures. In contrast, to materials that crystallise in the zincblende (sphalerite) and wurtzite structures, nanoparticles of which normally only show a blue-shift, both blue-shifts (CdO, PbS, PbSe) and red-shifts (MgO, CaO, SrO) are observed for materials that crystallise under ambient conditions in the rocksalt structure.
Moreover, nanostructures of some of the materials that under ambient conditions crystallise in the wurtzite structure (CdS, CdSe) convert under pressure into the rocksalt structure, which can be subsequently recovered back to ambient conditions. [17][18][19] Another advantage of rocksalt materials as model systems is that even for small nanostructures and even in the absence of capping agents the experimentally relevant nanostructures are generally simple cuts from the bulk crystal structure exposing simple, typical <001>, crystal faces, which is not necessarily true for their wurtzite and zincblende counterparts. Whilst experimental spectroscopy can clearly demonstrate the effect on the electronic and optical properties of materials of reducing the dimensions of materials to the nanoscale, to elucidate the microscopic origin of these changes one needs to combine experiment with theoretical chemistry calculations. Theoretical chemistry calculations also allow one to compare systems like-for-like, eliminating the effect of differences in nanostructure size (distributions) and the presence of capping agents for some materials experimentally and the absence for others. However, to be useful, the calculations should both be accurate and computationally tractable for nanostructures of at least 1 nm in size. (Time-Dependent) Density Functional Theory ((TD-)DFT) would be the ideal methodology in terms of tractability. However, previous work on MgO 29 and TiO 2 30-31 nanostructures demonstrated that the results  of TD-DFT calculations on such structures were very sensitive to the exact density   functional used, because of the well-known issue 32-33 of TD-DFT where charge-transfer (CT) excitations are spuriously stabilised with respect to local, i.e. non-CT, excitations. Well-chosen density functionals with the optimal percentage of exact exchange can reproduce the key features of the experimental spectra including the optical gap (MgO) and the results of high-level quantum chemistry reference calculations (TiO 2 ), but the strong dependency on the percentage of exact exchange makes these calculations more empirical than desirable.
While computationally much more expensive it is inherently more accurate than (TD-)DFT and it has become recently tractable to perform GW-BSE calculations on realistic nanostructures due to a combination of methodological advances and increased computer power. By application of partial self-consistency in the GW part of the calculation, evGW, most of the dependency on the specific density functional used in the underlying DFT calculation is removed and evGW-BSE also has been shown 40 to avoid most pitfalls of TD-DFT, including the description of CT-states.
(ev)GW-BSE, in contrast, to TD-DFT also treats the optical gap, the energy required to generate an interacting exciton, and the fundamental gap (see Fig. 1), the energy required to generate a non-interacting electron-hole pair, at the same footing allowing for the excitonic character of excited-states to be assessed.
Recently, evGW-BSE was used to study the optical and electronic properties of MgO nanoparticles. 41 There it was found that the evGW-BSE predictions of the optical gap of MgO nanoparticles and the characteristic absorption spectrum of such particles agreed well with available experimental data, as well as that evGW-BSE correctly predicts, as discussed above, that the optical gap of MgO nanoparticles does not change with particle size. Here this work is extended to rocksalt nanostructures of two other materials: CdO and CdS.
Well-defined rocksalt MgO nanoparticles, as small as 3 nm in size, can be prepared experimentally in the absence of any capping agents in the gas-phase by chemical vapour synthesis [10][11] and flame spray pyrolysis. 12 [44][45][46] The preparation of rocksalt CdS nanoparticles involves the application of pressures in excess of 5 GPa to 5-10 nm zincblende CdS nanoparticles. [18][19] Using evGW-BSE differences in the optical and electronic properties of ~ 1 nm CdO and CdS rocksalt particles (see Fig. 2) are studied and compared with those predicted for similar MgO nanoparticles in previous work. The (de)localisation of the states responsible for the electronic and optical properties of the nanoparticles and how these properties change with particle composition and size is investigated, as is the effect of capping agents on the electronic and optical properties.

Methodology
The geometry of the nanoparticles was optimised in DFT calculations, using the

Effect of composition -(CdO) 32 , (CdS) 32 and (MgO) 32
First, we consider the predicted quasiparticle and optical absorption spectra of (CdO) 32 , (CdS) 32 and (MgO) 32 , data for the latter taken from previous work. 41 These particles are the smallest rocksalt cuts that preserve most of the symmetry of the infinite material and contain a number of atoms with bulk, 6-fold, coordination. shows the quasiparticle spectrum around the highest occupied and lowest unoccupied quasiparticle state for the three different particles as calculated using evGW(AC)/def2-TZVPP, data for other method combination can be found in the supporting information (See Table S1-S4). From Fig. 3 it can be seen that, as expected from the bulk, the fundamental gaps of (CdS) 32 and (CdO) 32 is much smaller than that of (MgO) 32 . It is also from clear from Fig. 3  A and A in the case of (CdS) 32 and T and A in the case of (CdO) 32 and (MgO) 32 .
Because the GW calculations are performed in the D 2 subgroup instead of the full Td point group, we cannot further distinguish between A 1 and A 2 or between T 1 and T 2 .
However, DFT calculations in the full Td point group suggests that the symmetry of the highest occupied and lowest unoccupied quasiparticle states is A 2 and A 1 in the case of (CdS) 32 and T 2 and A 1 for (CdO) 32 . evGW(SR)/def2-SVP and evGW(CD)/def2-TZVPP calculations, see Table S1, demonstrate that this difference in the character of the states involved is not an artefact of the fact that in evGW(AC) only the highest occupied and lowest unoccupied quasiparticle states are explicitly calculated with evGW. Finally, the results in Fig. 3 were obtained from non-relativistic calculations. 2c-GW calculations that include spin-orbit coupling on smaller (CdO) 4 and (CdS) 4 particle, see Tables S1 and S2, suggest that including relativistic effects does not significantly change the predictions.  lowest unoccupied quasiparticle state is delocalised over only the 3-and 4coordinated the cadmium atoms on the corner and edges of the particle.   Change in the predicted optical spectra of (CdS) 32
Adsorbing four methylamine molecules on the cadmium corner atoms of (CdO) 32 forming (CdO) 32 (NH 2 (CH 3 )) 4 results in no significant structural changes in the inorganic part of the nanoparticle. In contrast, adsorption of four methylamine molecules on the cadmium corner atoms of (CdS) 32   surface levels off for high surface coverage. Another change, partially caused by a reduction in symmetry, is that for the particles with methylamines adsorbed all singlet vertical excitations are now optically allowed, including the lowest excited state which for the naked (CdO) 32 and (CdS) 32 particle, as discussed above, is dark for symmetry reasons. evGW-BSE calculations on particles where the ligands have been removed but the geometry of the inorganic part of the particle has not been allowed to relax back, suggest that the majority of the change in the particles' electronic and optical properties upon adsorption of capping agents is a direct electronic effect of the presence of the ligands rather than the structural distortions caused by their adsorption. Visualising the DFT orbitals also suggests no or limited direct contribution to the highest occupied and lowest unoccupied quasiparticle states by the amine capping agent. functional to obtain the starting Kohn-Sham orbitals as used by Schleife and coworkers for the bulk, yields an optical gap value that is smaller than the bulk (see Table S6). This could be an issue with the underlying G 0 W 0 description, related to the fact that, as discussed above, no optical gap reduction with particle size is  The presence of capping agents on the surface and increasing the surface coverage of these capping agents clearly and consistently results in upward shift of the highest occupied and lowest unoccupied quasiparticle states. As discussed above, these quasiparticle states do not appear to directly involve the capping agents and the change in these states neither appears to be caused by the structural distortion of the inorganic core of the particles induced by adsorption of the capping agents.
Dielectric contrast, where the capping agent changes the screening of the electric field outside the nanoparticles, is naively also unlikely to be the origin of the observed change because both the occupied and unoccupied quasiparticle states shift upwards, although dielectric contrast might be relevant for realistic capping agents with longer alkyl chains. There is also very limited evidence of chargetransfer between the amines and the inorganic core, with e.g. for

Acknowledgements
Dr. Christof Holzer is kindly acknowledged for discussion. The UK Engineering and Physical Sciences Research Council (EPSRC) is thanked for funding part of this work through grants EP/I004424/1 and EP/N004884/1.

Supporting information
Tables with predicted quasiparticle energies and excitation energies,