First-principles approach to the calculation of electronic spectra in clusters (original) (raw)
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Journal of Physics and Chemistry of Solids, 2011
We present a systematic study of the photo-absorption spectra of various Si n H m clusters (n=1-10, m=1-14) using the time-dependent density functional theory (TDDFT). The method uses a real-time, real-space implementation of TDDFT involving full propagation of the time dependent Kohn-Sham equations. Our results for SiH 4 and Si 2 H 6 show good agreement with the earlier calculations and experimental data. We find that for small clusters (n<7) the photo-absorption spectrum is atomic-like while for the larger clusters it shows bulk-like behaviour. We study the photo-absorption spectra of silicon clusters as a function of hydrogenation. For single hydrogenation, we find that in general, the absorption optical gap decreases and as the number of silicon atoms increase the effect of a single hydrogen atom on the optical gap diminishes. For further hydrogenation the optical gap increases and for the fully hydrogenated clusters the optical gap is larger compared to corresponding pure silicon clusters.
Physical Review B, 2003
We present calculations of the optical absorption spectra of clusters SiH 4 , Si 10 H 16 , Si 17 H 36 , Si 29 H 24 , and Si 35 H 36 , as determined from two different methods: the Bethe-Salpeter equation ͑BSE͒ with a model dielectric function, and the time-dependent density-functional theory within the adiabatic local-density approximation ͑TDLDA͒. Single-particle states are obtained from local-density approximation ͑LDA͒ calculations and, for the BSE calculation, a quasiparticle gap correction is provided by quantum Monte Carlo calculations. We find that the exchange-correlation kernel of the TDLDA has almost no effect on the calculated spectra, while the corresponding attractive part of the electron-hole interaction of the BSE produces enhanced absorptive features at low energies. For the smallest cluster SiH 4 , the two methods produce markedly different results, with the TDLDA spectra appearing closer to the experimental result. The gross features of the TDLDA and BSE spectra for larger clusters are however similar, due to the strong repulsive Coulomb kernel present in both treatments.
First-principles calculations of electronic excitations in clusters
International Journal of Quantum Chemistry, 2000
We discuss an approach to calculate electronic excitations in clusters, which starts from the determination of the ground state within density functional theory and the local density approximation, and subsequently yields electronic spectra from Green's function theory. These methods, which were originally developed and used in extended systems, are shown to work well also in clusters. We discuss the theory and the computational implementation, and illustrate the performance and the physical mechanisms of this approach for the example clusters Na 4
Ab initiocalculations on hydrogen-bounded silicon clusters
Physical review, 1981
The unrestricted Hartree-Fock method is applied to tetrahedrally coordinated Si,H"clusters as a function of several different Si-H "saturator" bond lengths. Ground-state and excited-state configurations, representative of the initial and final states of a low-energy optical transition, are studied analyzing the energetics, symmetries, and charge densities. The determination of the "cluster band gap" by Koopmans' theorem versus 3 SCF (self-consistentfield) calculations shows electronic relaxation to be significant compared to the expected transition-energy range. The cluster band gap and other energetic properties are shown to change appreciably for the various Si-H bond lengths, yet the charge densities in the Si-Si bond regions remain similar, exemplifying a minimal environmental effect on the central bonding region. The charge densities obtained are comparable to experimental x-ray and theoretical pseudopotential calculations describing bulk silicon. The adequacy of using an ab initio effective core potential for the five silicon atoms is established by comparison to a calculation allowing relaxation of the core on the one central silicon atom. The concepts underlying cluster simulation of condensed matter are discussed with particular emphasis on the environmental models. The usefulness and formal limitations of the self-consistent saturator environmental model are addressed.
Il Nuovo Cimento D, 1998
A method for the inclusion of self-energy and excitonic effects in firstprinciples calculations of absorption spectra, within the state-of-the-art plane-wave pseudopotential approach, is discussed, Self-energy effects are computed within GW, and the electron-hole interaction is treated solving an effective two-particle equation which is derived from the relevant Bethe-Salpeter equation, We review numerical results for three systems; a small sodium cluster, the lithium oxyde insulating crystal, and bulk silicon, the prototype semiconductor, In the case of silicon, we present new results obtained considering additional approximations intended to reduce the computational effort and generally employed in Wannier-Mott exciton calculations, and discuss their reliability, PACS 71 ,35,Cc-Intrinsic properties of excitons; optical absorption spectra, PACS 71,10-Theories and models of many electron systems, PACS 78,20-Optical properties of bulk materials and thin films, PACS OL30,Ee-Monographs and collections, L-Introduction Density-functional theory (DFT) in the Local Density Approximation (LDA) is widely and successfully used as a state-of-the-art tool to compute the ground-state electronic properties of many-electron systems [1], It is feasible to apply DFT to systems as complex as surfaces, defects, and clusters, However, while the ground-state properties can in principle be obtained exactly within DFT, many spectroscopic properties are in general not directly accessible in such a calculation, In fact, it is well known that the use of the DFT-LDA eigenvalues as the physical energies entering in the absorption process relies on several approximations, First of C*) In honour of Prof Gianfranco Chiarotti on the occasion of his 70th birthday,
Density-functional-based predictions of Raman and IR spectra for small Si clusters
Physical Review B, 1997
We have used a density-functional-based approach to study the response of silicon clusters to applied electric fields. For the dynamical response, we have calculated the Raman activities and infrared ͑IR͒ intensities for all of the vibrational modes of several clusters ͑Si N with Nϭ3Ϫ8, 10, 13, 20, and 21͒ using the local density approximation ͑LDA͒. For the smaller clusters (Nϭ3Ϫ8) our results are in good agreement with previous quantum-chemical calculations and experimental measurements, establishing that LDA-based IR and Raman data can be used in conjunction with measured spectra to determine the structure of clusters observed in experiment. To illustrate the potential of the method for larger clusters, we present calculated IR and Raman data for two low-energy isomers of Si 10 and for the lowest-energy structure of Si 13 found to date. For the static response, we compare our calculated polarizabilities for Nϭ10, 13, 20, and 21 to recent experimental measurements. The calculated results are in rough agreement with experiment, but show less variation with cluster size than the measurements. Taken together, our results show that LDA calculations can offer a powerful means for establishing the structures of experimentally fabricated clusters and nanoscale systems. ͓S0163-1829͑97͒01303-9͔
Local-basis quasiparticle calculations and the dielectric response function of Si clusters
Physical Review B, 2000
We present an ab initio computational scheme for evaluating the dielectric response function of Si clusters. All calculations are carried out employing a basis of localized atomiclike orbitals and including quasiparticle corrections. The self-energy operator is evaluated in the GW approximation, with a full frequency dependence for the dielectric matrix. The approach is convenient and computationally optimal for the calculation of optical properties of complex systems lacking full periodicity, such as surfaces and clusters. We present here the quasiparticle-level structure for Si 20 and Si 60 clusters and discuss the sensitivity of their optical properties to quasiparticle corrections. We find that the optical gap is larger than in bulk silicon, clearly the net result of size quantization over structural disorder.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2001
We find that for simple metal clusters a single-electron description of the ground state employing self-interaction correction (SIC) in the framework of localdensity approximation strongly contaminates the high-energy photoionization cross sections with spurious oscillations for a subshell containing node(s). This effect is shown connected to the unphysical structure that SIC generates in ensuing state-dependent radial potentials around a position where the respective orbital density attains nodal zero. Non-local Hartree-Fock that exactly eliminates the electron self-interaction is found entirely free from this effect. It is inferred that while SIC is largely unimportant in high photon energies, any implementation of it within the local frame can induce unphysical oscillations in the high-energy photospectra of metal clusters pointing to a general need for caution in choosing appropriate theoretical tools. The local-density approximation (LDA), along with its time-dependent version, is a standard theoretical technique to describe the structure and dynamics of large systems. From a practical standpoint, LDA is typically preferred to other conventional many-body methods (such as, Hartree-Fock (HF) or techniques based on configuration-interactions) because of its relatively low computational costs. In the context of the studies involving static and dynamical properties of simple metal clusters, LDA has proved to be particularly successful [1-3]. However, a well known drawback of LDA is that it only partially accounts for unphysical electron selfinteractions. As a consequence, the resulting potential for a finite system decays exponentially at a large distance instead of producing the physical 1/r behaviour. To render the long distance behaviour of the LDA potential realistic, therefore, approximation schemes have been suggested [4]. The most general and widely applied to remedy the error is the one proposed by Perdew and Zunger [5], which concerns an orbit-by-orbit elimination of self-interaction, although the scheme immediately makes the potential state-dependent. The self-interaction corrected LDA (LDA-SIC) improves remarkably the vast variety of results related to many structural properties of physical systems: for instance, improvements in total energies of