Theoretical Challenges in Electronic Structure of Clusters and Nanoparticles
- Vijay Kumar (Dr. Vijay Kumar Foundation, Haryana, India)
- Angel Rubio (University of the Basque Country, San Sebastian, Spain)
- Puru Jena (Virginia Commonwealth University, USA)
Clusters and nanoparticles have been used for centuries e.g. in artwork (stained glasses and paints), photography, and medicine (colloidal gold). However, it is only in the past three decades that attention has been focused on a fundamental understanding of their properties as a function of size, shape, and composition. Advancement of theoretical techniques and computer hardware and software has made it possible to study the structure-property relationships of matter containing from a few to a few thousand atoms. The accuracy with which theory can predict some of the properties as well as new species has made it an invaluable tool in the design of new materials and in guiding experiments in their focussed discovery. Computational materials science, therefore, has been the third pillar in exploring the new frontiers of nanoscience. In spite of the successes many challenges remain in developing a seamless multi-scale approach that can treat matter from molecules and small clusters to large nanoparticles and modelling the interaction from very weak van der Waals to strong covalent bonding, correlations and finally the excitations. This is particularly important when dealing with material problems in biology, energy science, catalysis, and device applications. This Workshop will bring some of the top experimental and theoretical experts in the area of cluster science and focus on hard questions and challenges that could lead to future developments for the applications of clusters and nanoparticles in catalysis, optical, magnetic, sustainable energy, device science, and biological systems.
We summarize the status of the electronic structure of clusters and nanoparticles in two parts: 1) The calculation of the ground state properties in which structure and bonding play dominant role and 2) optical and other excitation properties that are important for applications.
1) Structure and bonding
The most common approach to understand the ground state structure and properties of clusters and nanoparticles is using Kohn-Sham density functional theory approach within local density approximation (LDA) or generalized gradient approximation (GGA) that has many variants to describe exchange and correlations in the system. These calculations have been highly successful in many cases in understanding experimental results such as those obtained from mass abundance spectroscopy, measurements of IP, EA, electric dipole moments, IR and Raman modes, and photoemission experiments. Such studies have not only helped the development of cluster science but in some cases led to the prediction of novel structures such as silicon fullerenes and other polyhedral forms  that have been subsequently realized in laboratory  as well as the findings of planar and other novel structures of gold clusters  that are attracting great interest in catalysis and nanomedicine as well as molecular assemblies. Such predictive ability of the computational methods is going to play a very important role in the development of cluster science. However, such striking findings are few and in some cases such as clusters of transition metals which are very important in catalysis and optical properties, our understanding needs to be improved because recent experiments of IR spectra  have been found to agree with one form of exchange-correlation functional while another exchange correlation functional gives very different energies of isomers. These experiments highlight the need for the development of theoretical and computational methods to treat these high-spin transition metal clusters. Such difficulties are also expected for partially occupied f electron systems such as rare earth doped semiconductor quantum dots for use in LED and it is important that good understanding be evolved for clusters and nanoparticles of such systems. Such developments would have a profound effect in understanding the catalytic behavior and magnetic as well as optical applications and in designing new species for cluster assembly.
While in most above cases the interactions within clusters and nanoparticles are generally strong, past few years have seen emergence of the applications of clusters and nanoparticles in hydrogen storage  and biological systems . However, these involve weak interaction of some molecules such as hydrogen (for hydrogen storage) and organic molecules (for biological applications) on clusters and nanoparticles. Research in these areas is currently evolving. Recently there have been developments of treating van der Waals interaction using the ground state density obtained from the DFT programs based on GGA approach  and these are promising. Such studies are also very important for studying clusters and nanostructures on graphene which is currently a very important area of research. Another area in which both weak and strong interactions play a very important role is reactions and the developments of the treatment of weak interactions as well as strong interactions in the case of partially occupied d shells will help to obtain better understanding of the reaction barriers. While reactions have been simulated on clusters for quite a long time, theoretical tools often used in these calculations were not sufficient to treat weak and strong interactions.
2) Optical spectra and other excitation properties
Understanding of the optical and other excitation properties is important for many applications of clusters and nanoparticles. The above mentioned theoretical formulations of the ground state properties suffer from the deficiency that even for the weakly correlated systems such as s-p bonded metals and semiconductors, the band gap is underestimated by 20-50% and thus it is difficult to describe the optical and other excitation properties of nanoclusters properly. This problem is more severe for systems with atoms involving open d or f shells where electron correlations become more important. Often different variants of GGA or hybrid exchange-correlation functionals are used within the time dependent (TD) DFT framework for optical absorption calculation. However, their success may be limited to particular systems. What is the correct description is an important question and one needs to find better ways to describe such systems. While Bethe-Saltpeter equations for electron and hole using two particle Green's function is an appropriate approach , it is computationally very demanding and often used for small systems and this could be used for benchmaking approximate methods. There are also recent reports of simplifying this method for applications to large systems of the order of 1 nm size .
For sp bonded systems, the so-called GW method has been very successful and has been the method of choice for quantitative description of quasi-particle excitations. However, its applications to d and f systems are much fewer and these are not as successful as anticipated. Recently GW method has been used together with LDA+U [10 ] to treat localised d and f electrons and it is referred to GW@LDA+U, but this is just the beginning and much more work would be required to develop computational approaches to treat correlations and excitations in clusters and nanoparticles of such systems. There are efforts to treat correlations for the calculation of electronic and optical spectra of small systems  and treat excitations in metal-molecular interfaces .
An important application of nanoparticles such as those of CdTe, PbSe, PbTe is in solar energy area which is currently a very important area for sustainable energy solutions. This would require the calculation of excitonic properties such as exciton binding energies and optical absorption spectra. Such efforts are going on in some laboratories. For increased efficiency, important developments are taking place on the ways to have multiple exciton formation and breaking of exciton in to electron and hole to drive current. In order to obtain vital insight into the electronic processes involving excited states, efforts are now going on to extend the powerful techniques of electronic structure theory to include electron dynamics in clusters and nanparticles to describe the excited electron motion in such systems . This is an emerging area for theoretical studies.
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