Quantum Monte Carlo calculations of nanostructure optical gaps: application to silicon quantum dots

The effect of particle size on the optical and electronic properties of hydrogenated silicon nanoparticles

We use a combination of many-body perturbation theory and time-dependent density functional theory to study the optical and electronic properties of hydrogen terminated silicon nanoparticles. We predict that the lowest excited states of these silicon nanoparticles are excitonic in character and that the corresponding excitons are completely delocalised over the volume of the particle. The size of the excitons is predicted to increase proportionally with the particle size. Conversely, we predict that the fundamental gap, the optical gap, and the exciton binding energy increase with decreasing particle size. The exciton binding energy is predicted to counter-act the variation in the fundamental gap and hence to reduce the variation of the optical gap with particle size. The variation in the exciton binding energy itself is probably caused by a reduction in the dielectric screening with decreasing particle size. The intensity of the excited state corresponding to the optical gap and other low energy excitations are predicted to increase with decreasing particle size. We explain this increase in terms of the 'band structure' becoming smeared out in reciprocal space with decreasing particle size, increasing the 'overlap' between the occupied and unoccupied quasiparticle states and thus, the oscillator strength. Fourier transforms of the lowest excitons show that they inherit the periodicity of the frontier quasiparticle states. This, combined with the delocalisation of the exciton and the large exciton binding energy, means that the excitons in silicon nanoparticles combine aspects of Wannier-Mott, delocalisation and effect of periodicity of the underlying structure, and Frenkel, large exciton binding energy, excitons.

Quantum Chemical Characterization and Design of Quantum Dots for Sensing Applications

The ability to tune the optoelectronic properties of quantum dots (QDs) makes them ideally suited for the use as fluorescence sensing probes. The vast structural diversity in terms of the composition and size of QDs can make designing a QD for a specific sensing application a challenging process. Quantum chemical calculations have the potential to aid this process through the characterization of the properties of QDs, leading to their in silico design. This is explored in the context of QDs for the fluorescence sensing of dopamine based upon density functional theory and time-dependent density functional theory (TDDFT) calculations. The excited states of hydrogenated carbon, silicon, and germanium QDs are characterized through TDDFT calculations. Analysis of the molecular orbital diagrams for the isolated molecules and calculations of the excited states of the dopamine-functionalized quantum dots establish the possibility of a photoinduced electron-transfer process by determining the relative energies of the electronic states formed from a local excitation on the QD and the lowest QD → dopamine electron-transfer state. The results suggest that the Si₁₆₅H₁₀₀ and Ge₈₄H₆₄ QDs have the potential to act as fluorescent markers that could distinguish between the oxidized and reduced forms of dopamine, where the fluorescence would be quenched for the oxidized form. The work contributes to a better understanding of the optical and electronic behavior of QD-based sensors and illustrates how quantum chemical calculations can be used to inform the design of QDs for specific fluorescent sensing applications.

Excitation Energies of Localized Correlated Defects via Quantum Monte Carlo: A Case Study of Mn4+-Doped Phosphors

Accurate excitation energies of localized defects have been a long-standing problem for electronic structure calculation methods. Using Mn⁴⁺-doped solids as our proof of principle, we show that diffusion quantum Monte Carlo (DMC) is able to predict phosphorescence emission energies within statistical error. To demonstrate the generality of our DMC approach for other possible localized defects, we conduct charge density analyses using DMC and density functional theory (DFT). We also identify a new material with an emission energy of 1.97(8) eV, which is close to the optimum of 2.03 eV for a red-emitting phosphor. To our knowledge, our work is the first report on studying excitation energies of a transition metal impurity using an ab initio many-body electronic structure method. In contrast, semilocal and hybrid-DFT largely underestimates, and fails to reproduce, some of the trends in the emission energies. Our work underscores the importance of an accurate account of exchange, correlation, and excitonic effects for localized excitations in defective solids.

Machine learning unifies the modeling of materials and molecules

Determining the stability of molecules and condensed phases is the cornerstone of atomistic modeling, underpinning our understanding of chemical and materials properties and transformations. We show that a machine-learning model, based on a local description of chemical environments and Bayesian statistical learning, provides a unified framework to predict atomic-scale properties. It captures the quantum mechanical effects governing the complex surface reconstructions of silicon, predicts the stability of different classes of molecules with chemical accuracy, and distinguishes active and inactive protein ligands with more than 99% reliability. The universality and the systematic nature of our framework provide new insight into the potential energy surface of materials and molecules.

Hybrid silicon–carbon nanostructures for broadband optical absorption

Superposition of the optical spectra of the assemble of Sim@C_2nwhich exhibit a broadband optical absorption and the spectrum of solar radiation.

Molecular Origin of Properties of Organic-Inorganic Hybrid Perovskites: The Big Picture from Small Clusters

We show that the electronic properties, including the band gap, the gap deformation potential, and the exciton binding energy as well as the chemical stability of organic-inorganic hybrid perovskites can be traced back to their corresponding molecular motifs. This understanding allows one to quickly estimate the properties of the bulk semiconductors from their corresponding molecular building blocks. New hybrid perovskite admixtures are proposed by replacing halogens with superhalogens having compatible ionic radii. The mechanism of the boron-hydride based hybrid perovskite reacting with water is investigated by using a cluster model.

Quasiparticle and excitonic gaps of one-dimensional carbon chains

The charge density of a one-dimensional sp-bonded chain composed of 26 carbon atoms terminated by H with alternating single and triple bonds.

Colloidal Nanoparticles for Intermediate Band Solar Cells

The Intermediate Band (IB) solar cell concept is a promising idea to transcend the Shockley-Queisser limit. Using the results of first-principles calculations, we propose that colloidal nanoparticles (CNPs) are a viable and efficient platform for the implementation of the IB solar cell concept. We focused on CdSe CNPs and we showed that intragap states present in the isolated CNPs with reconstructed surfaces combine to form an IB in arrays of CNPs, which is well separated from the valence and conduction band edges. We demonstrated that optical transitions to and from the IB are active. We also showed that the IB can be electron doped in a solution, e.g., by decamethylcobaltocene, thus activating an IB-induced absorption process. Our results, together with the recent report of a nearly 10% efficient CNP solar cell, indicate that colloidal nanoparticle intermediate band solar cells are a promising platform to overcome the Shockley-Queisser limit.

Negative Differential Resistance Probe for Interdot Interactions in a Double Quantum Dot Array

Colloidal quantum dots are free-standing nanostructures with chemically tunable electronic properties. In this work, we consider a new STM tip-double quantum dot (DQD)-surface setup with a unique connectivity, in which the tip is coupled to a single dot and the coupling to the surface is shared by both dots. Our theoretical analysis reveals a unique negative differential resistance (NDR) effect attributed to destructive interference during charge transfer from the DQD to the surface. This NDR can be used as a sensitive probe for interdot interactions in DQD arrays.

Density functional theory study on boron- and phosphorus-doped hydrogen-passivated silicene

When silicene is passivated by hydrogen, a bandgap occurs so that it becomes a semiconductor.

Density functional theory study on organically surface-modified silicene

The geometrical structures, band structures and optical absorption of organically surface-modified silicene have been investigated by density functional theory.

Size dependence of the structural, electronic, and optical properties of (CdSe)n, n = 6–60, nanocrystals

HOMO–LUMO and optical gaps of (CdSe)_n nanocrystals appear to have controversial magnitudes and size dependence, which we have rationalized.

High-pressure core structures of Si nanoparticles for solar energy conversion

We present density functional and many body perturbation theory calculations of the electronic, optical, and impact ionization properties of Si nanoparticles (NPs) with core structures based on high-pressure bulk Si phases. Si particles with a BC8 core structure exhibit significantly lower optical gaps and multiple exciton generation (MEG) thresholds, and an order of magnitude higher MEG rate than diamondlike ones of the same size. Several mechanisms are discussed to further reduce the gap, including surface reconstruction and chemistry, excitonic effects, and embedding pressure. Experiments reported the formation of BC8 NPs embedded in amorphous Si and in amorphous regions of femtosecond-laser doped "black silicon." For all these reasons, BC8 nanoparticles may be promising candidates for MEG-based solar energy conversion.

Environmental photostability of SF6-etched silicon nanocrystals

We report on the long-term environmental stability of the photoluminescent (PL) properties of silicon nanocrystals (SiNCs). We prepared sulfur hexafluoride (SF(6)) etched SiNCs in a two-stage plasma reactor and investigated their PL stability against UV irradiation in air. Unlike SiNCs with hydrogen-passivated surfaces, the SF(6)-etched SiNCs exhibit no photobleaching upon extended UV irradiation despite surface oxidation. Furthermore, the PL quantum yield also remains stable upon heating the SF(6)-etched SiNCs up to 160 °C. The observed thermal and UV stability of SF(6)-etched SiNCs combined with their PL quantum yields of up to ~50% make them attractive candidates for UV downshifting to enhance the efficiency of solar cells. Electron paramagnetic spin resonance indicates that the SF(6)-etched SiNCs have a lowered density of defect states, both as-formed and after room temperature oxidation in air.

Excitation Gaps of Finite-Sized Systems from Optimally Tuned Range-Separated Hybrid Functionals

Excitation gaps are of considerable significance in electronic structure theory. Two different gaps are of particular interest. The fundamental gap is defined by charged excitations, as the difference between the first ionization potential and the first electron affinity. The optical gap is defined by a neutral excitation, as the difference between the energies of the lowest dipole-allowed excited state and the ground state. Within many-body perturbation theory, the fundamental gap is the difference between the corresponding lowest quasi-hole and quasi-electron excitation energies, and the optical gap is addressed by including the interaction between a quasi-electron and a quasi-hole. A long-standing challenge has been the attainment of a similar description within density functional theory (DFT), with much debate on whether this is an achievable goal even in principle. Recently, we have constructed and applied a new approach to this problem. Anchored in the rigorous theoretical framework of the generalized Kohn-Sham equation, our method is based on a range-split hybrid functional that uses exact long-range exchange. Its main novel feature is that the range-splitting parameter is not a universal constant but rather is determined from first principles, per system, based on satisfaction of the ionization potential theorem. For finite-sized objects, this DFT approach mimics successfully, to the best of our knowledge for the first time, the quasi-particle picture of many-body theory. Specifically, it allows for the extraction of both the fundamental and the optical gap from one underlying functional, based on the HOMO-LUMO gap of a ground-state DFT calculation and the lowest excitation energy of a linear-response time-dependent DFT calculation, respectively. In particular, it produces the correct optical gap for the difficult case of charge-transfer and charge-transfer-like scenarios, where conventional functionals are known to fail. In this perspective, we overview the formal and practical challenges associated with gap calculations, explain our new approach and how it overcomes previous difficulties, and survey its application to a variety of systems.

Spin-polarized density functional investigation into ferromagnetism in C-doped (ZnO)n clusters; n = 1-12, 16

We investigate the ferromagnetism in ZnO clusters due to vacancy defects and C impurities doped at substitutional O or Zn sites, and interstitial sites. The total energy calculations suggest C at the O site is more stable than that at the Zn site in ZnO clusters. The total magnetic moments of Zn(n)O(n-m)C(m) clusters are 2.0 μ(B)/C. However, when two C atoms are bonded to the same Zn atom they interact antiferromagnetically and the total magnetic moment becomes less than 2.0 μ(B)/C. The interstitial C defects in ZnO clusters induce small magnetic moments. The combination of substitutional and interstitial C defects in ZnO clusters leads to magnetic moments of 0.0-2.0 μ(B)/C. The presence of vacancy defects in addition to substitutional C defects gives magnetic moments of greater than 2.0 μ(B)/C. These results suggest that the experimentally observed sample dependence of magnetic moments in ZnO systems is largely due to the different concentrations of substitutional and interstitial C impurities and the presence of vacancy defects in ZnO samples prepared under different growth conditions.

Optical excitation energies, Stokes shift, and spin-splitting of C24H72Si14

As an initial step toward the synthesis and characterization of sila-diamondoids, such as sila-adamantane (Si(10)H(16),T(d)), the synthesis of a fourfold silylated sila-adamantane molecule (C(24)H(72)Si(14),T(d)) has been reported in literature [Fischer et al., Science 310, 825 (2005)]. We present the electronic structure, ionization energies, quasiparticle gap, and the excitation energies for the Si(14)(CH(3))(24) and the exact silicon analog of adamantane Si(10)H(16) obtained at the all-electron level using the delta-self-consistent-field and transitional state methods within two different density functional models: (i) Perdew-Burke-Ernzerhof generalized gradient approximation and (ii) fully analytic density functional (ADFT) implementation with atom dependent potential. The ADFT is designed so that molecules separate into atoms having exact atomic energies. The calculations within the two models agree well, to within 0.25 eV for optical excitations. The effect of structural relaxation in the presence of electron-hole-pair excitations is examined to obtain its contribution to the luminescence Stokes shift. The spin-influence on exciton energies is also determined. Our calculations indicate overall decrease in the absorption, emission, quasiparticle, and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps, ionization energies, Stokes shift, and exciton binding energy when passivating hydrogens in the Si(10)H(16) are replaced with electron donating groups such as methyl (Me) and trimehylsilyl (-Si(Me)(3)).

Novel Computational Methods for Nanostructure Electronic Structure Calculations

Experimentally relevant nanocrystals often contain a few thousands to hundreds of thousands of atoms. Yet, to understand their electronic structures, surface and impurity effects, atomic relaxations, interior electric fields, carrier dynamics, and transports, it is often necessary to carry out atomistic simulations. Owing to the advance of recent algorithm developments and improved supercomputer powers, it is now possible to calculate such nanocrystals based on ab initio methods. In this review, we discuss the numerical algorithms (the plane-wave pseudopotential method and the real-space finite-difference method) used in conventional density-functional-theory calculations, which enable the simulations of systems up to one or two thousand atoms. We also introduce methods designed specifically for nanostructure calculations. These methods [the charge-patching method (CPM) and the linear scaling three-dimensional fragment method (LS3DF)] can be used to calculate systems with hundreds of thousands of atoms. Whereas CPM is an approximation with ab initio quality, the LS3DF method is an O(N) method with essentially the same results as the direct methods. The computational aspects of the algorithms, especially for their parallelization scalability, are also emphasized in the review.

Methods for calculating forces within quantum Monte Carlo simulations

Atomic force calculations within the variational and diffusion quantum Monte Carlo methods are described. The advantages of calculating diffusion quantum Monte Carlo forces with the 'pure' rather than the 'mixed' probability distribution are discussed. An accurate and practical method for calculating forces using the pure distribution is presented and tested for the SiH molecule. The statistics of force estimators are explored and violations of the central limit theorem are found in some cases.

Continuum variational and diffusion quantum Monte Carlo calculations

This topical review describes the methodology of continuum variational and diffusion quantum Monte Carlo calculations. These stochastic methods are based on many-body wavefunctions and are capable of achieving very high accuracy. The algorithms are intrinsically parallel and well suited to implementation on petascale computers, and the computational cost scales as a polynomial in the number of particles. A guide to the systems and topics which have been investigated using these methods is given. The bulk of the article is devoted to an overview of the basic quantum Monte Carlo methods, the forms and optimization of wavefunctions, performing calculations under periodic boundary conditions, using pseudopotentials, excited-state calculations, sources of calculational inaccuracy, and calculating energy differences and forces.

Altering the electronic properties of diamondoids through encapsulating small particles

The stability, optimized structure, and electronic gap of four diamondoid complexes, adamantane, C(10)H(16), diamantane, C(14)H(20), triamantane, C(18)H(24) and the T(d)-symmetry isomer of pentamantane, C(26)H(32), incorporating cage-centered small atoms and ions (X@cage, where X = H(+), Li(0,+), Be(0,+,2+), Na(0,+), Mg(0,2+), He, Ne, and F(-)) have been studied at the B3LYP hybrid level of theory. All adamantane complexes, except those encapsulating H(+) and Mg, are endohedral minima. In contrast no diamantane complexes are minima. A wide variety of atoms and ions can be encapsulated by triamantane and pentamantane molecules. The complexes are more stable for smaller and more highly charged metallic guest species. The electronic HOMO-LUMO gaps of diamondoid complexes are significantly affected by the inclusion of charged particles. The stability of the structures, the amount of the charges which are transferred between small particles and diamondoids cages, and the change in the HOMO-LUMO gaps of diamondoids are nearly the same for the corresponding possible complexes. All these features mostly depend on the charge, the size and the type of the encapsulated particle, and not on the type of diamondoid.

Advances in correlated electronic structure methods for solids, surfaces, and nanostructures

Calculations of the electronic structure of solids began decades ago, but only recently have solid-state quantum techniques become sufficiently reliable that their application is nearly as routine as quantum chemistry is for molecules. We aim to introduce chemists to the pros and cons of first-principles methods that can provide atomic-scale insight into the properties and chemistry of bulk materials, interfaces, and nanostructures. The techniques we review include the ubiquitous density functional theory (DFT), which is often sufficient, especially for metals; extensions such as DFT + U and hybrid DFT, which incorporate exact exchange to rid DFT of its spurious self-interactions (critical for some semiconductors and strongly correlated materials); many-body Green's function (GW and Bethe-Salpeter) methods for excited states; quantum Monte Carlo, in principle an exact theory but for which forces (hence structure optimization and dynamics) are problematic; and embedding theories that locally refine the quantum treatment to improve accuracy.

Coupled-cluster studies of the electronic excitation spectra of silanes

The electronic excitation spectra of unsubstituted linear silanes (n-Si(m)H(2m+2), m = 1-6), cyclopentasilane (c-Si5H10), and neopentasilane (neo-Si5H12) have been studied at the coupled-cluster approximate singles and doubles (CC2) level using Dunning's quadruple-zeta basis sets augmented with diffuse functions (aug-cc-pVQZ). Comparisons with measured ultraviolet spectra for Si2H6 and n-Si3H8 show that CC2 calculations using these basis sets yield excitation energies in good agreement with experiment. The calculated excitation thresholds for Si2H6 and n-Si3H8 of 7.61 and 6.68 eV are only 0.05 eV larger than the gas-phase values of 7.56 and 6.63 eV, respectively. For n-Si4H10, n-Si5H12, and neo-Si5H12, the calculated excitation thresholds of 6.51, 6.14, and 6.87 eV for the lowest dipole-allowed transitions are about 0.4 eV larger than the corresponding liquid-phase data of 6.05, 5.77, and 6.53 eV; the discrepancy can mainly be attributed to solvent effects. The obtained excitation thresholds for n-Si6H14 is 5.85 eV, whereas no experimental data are available for its optical gap. Calculations using the Karlsruhe triple-zeta valence basis sets augmented with single and double sets of polarization functions show that very large basis sets augmented with diffuse functions are needed for obtaining accurate excitation energies. The optical gaps for silanes obtained using the triple-zeta polarization basis sets were found to be 0.4 and 0.2 eV larger than those obtained using Dunning's quadruple-zeta basis sets. Excitation thresholds calculated at density functional theory levels using generalized gradient approximation are 0.7-1.0 eV smaller than the experimental values and by employing hybrid functionals they are 0.3-0.4 eV below the experimental thresholds. By adding the present basis-set correction and environmental effects to the previously calculated CC2 value for the excitation threshold of the Si29H36 silicon nanocluster, the extrapolated absorption threshold is 4.0 eV as compared to the recently reported experimental value of 3.7 eV.

The 15N chemical shifts in mixed NB2Si and NBSi2 environments of Si3B3N7--a theoretical investigation

Nuclear magnetic resonance (NMR) chemical shifts in solids may be calculated by ab initio methods approximating the solid state by molecular clusters. We employed this technique to obtain estimates of (15)N chemical shifts in NB(2)Si and NBSi(2) environments in the solid state. Such nitrogen environments are found in amorphous (Si/B/N-)ceramics which exhibit very interesting features such as high thermal and mechanical stability. We based our calculations on cutouts of hypothetical Si(3)B(3)N(7) crystals suggested by Kroll and Hoffmann [Silicon boron nitrides: hypothetical polymorphs of Si(3)B(3)N(7), Angew. Chem. Int. Ed. 37 (1998) 2527]. Taking the systematic errors of our calculations into account we expect the chemical shifts in NBSi(2) environments around -293+/-5ppm. Chemical shifts in NB(2)Si environments are expected at -272+/-6ppm. The range of the calculated chemical shifts in NBSi(2) environments coincides with experimental chemical shifts in molecular compounds. Experimental chemical shifts of NB(2)Si nitrogen in molecules appear at lower field than our calculated chemical shifts in the solid state.