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DOE OSTI2026

When Do Band Gap Calculations Agree with Experiments in Monolayer-Protected Cu 14 and Au 20 Atomically Precise Nanoclusters? A (TD)-DFT Comparison of HOMO–LUMO, Fundamental, Optical, and Electrochemical Energy Gaps

In view of the tremendous progress in atomically precise metal nanoclusters where electrochemical and optical energetics are routinely supported by computations to establish structure−function correlations, we explore the relationship between different protocols for measuring and computing band gaps of two distinct organic ligand-protected nanoclusters: [Cu 14 H 10 (MBN) 3 (PPh 3 ) 8 ] + and Au 20 (TBBT) 16 . Through UV/visible spectroscopy and differential pulse voltammetry, we measure optical and electrochemical band gaps in those systems. We then compare these experimentally determined gaps to HOMO−LUMO gaps, fundamental gaps, vertical excitation energies, and E o ox − E o red potentials computed using different density functional theory (DFT) or time-dependent DFT (TDDFT) methods. Specifically, in both copper and gold nanoclusters, we test the effect of truncating inert ligands from the model and compare density functionals with varying degrees of Hartree−Fock (HF) exchange from 0 to 50%, range-separated hybrids with a varying long-range tuning parameter, different correlation functionals, basis sets, and (equilibrium and nonequilibrium) continuum solvation models. Despite having different frontier orbital characters (the copper nanocluster has a metal-to-ligand charge transfer character while the gold nanocluster has metal-centered frontier orbitals), both nanoclusters display a similar sensitivity of the HOMO−LUMO gap to the HF exchange that is partially mitigated when computing the fundamental, optical, and electrochemical gaps. Other factors, such as the nature of the correlation functional, basis set, and geometry relaxation, have a considerably smaller effect on computed band gaps in these systems. Overall, this work provides guidelines for factors of varied importance for correlating computed and experimental band gap values.

Chemical calculations↗

DOE OSTI2026

Data for Filling the Cellulosic Bio-economy Gap by Utilizing a Wedge Approach Combined with Stakeholder Collaboration

The price gap between the market and breakeven prices of cellulosic biomass for farmers represents a significant barrier to the development of a low-carbon cellulosic bioeconomy. Using a bottom-up, agent-based modeling tool that replicates the behaviors and interactions of key stakeholders, this study analyzes the emergence of a cellulosic bioeconomy at the local scale through a wedge approach that examines an integrated portfolio of multiple policy options, including subsidies for small-scale bioproducts and environmental credits. The role of collaboration among multiple stakeholders, such as biomass producers (farmers), bio-refinery industry, government, and society, is assessed for filling the price gap. Using the Sangamon River Basin as a case study site, we evaluate the effectiveness of the wedge approach by comparing simulation results from multiple scenarios, each incorporating different combinations of bioeconomy wedges, with and without stakeholder collaboration. Results underscore that active collaboration among stakeholders acts as a catalyst enlarging the effectiveness of bioeconomy wedges. Including the carbon credits and environmental value in the policy portfolio is found to bridge the price gap through collective contributions from diverse stakeholders, where the cellulosic biofuel and bioproduct industry plays a pivotal role. Although this study is conducted at the local watershed scale, the methodology and findings offer valuable insights for market development in other watersheds and the potential scaling of local markets to regional and national levels.

Economics↗

DOE OSTI2025

La 3 CuTe 5 : A Narrow-Gap Semiconductor with Indirect Gap and Dual-Regime Thermally Activated Transport

Metal-chalcogenide systems remain a long-standing research topic because of their structural diversity and potential to host emergent phenomena. Here, we report a new compound, La 3 CuTe 5 , synthesized from the halide-flux method. Single-crystal X-ray diffraction studies indicate the structure to be unique among reported ones. Here, the compound crystallizes in a novel structure type adopting the orthorhombic space group Pnma and a unit cell of a = 24.3947(14) Å, b = 4.4232(2) Å, and c = 10.2142(5) Å. The tetrahedral [CuTe 4 ] building blocks form chains along [010] by corner sharing and link [LaTe 7 ] and [LaTe 8 ] polyhedra via edge sharing, resulting in a three-dimensional bulk structure. Thermal analysis results indicate that the material remains stable with a temperature up to 950 °C and decomposable at 1400 °C. First-principles calculations reveal an indirect electronic band gap and flat valence bands dominated by Te p and Cu d states. Optical absorption measurements yield a band gap of ∼0.65 eV, consistent with semiconducting behavior observed in transport measurements. Fittings to the temperature-dependent resistivity reveal two thermally activated regimes associated with Arrhenius-type conduction and three-dimensional variable range hopping, respectively.

Chalcogenides↗

DOE OSTI2025

Soft costs and EVSE – Knowledge gaps as a barrier to successful projects

There has been a recent push to increase access to electric vehicle (EV) charging infrastructure. The National Electric Vehicle Infrastructure (NEVI) program, part of the Bipartisan Infrastructure Law (BIL) has made significant funding available for major charging infrastructure projects along state thruways, and many state and local incentives exist for EV owners to install chargers in their homes. However, deployment of these chargers has not kept up with demand, primarily due to issues in project planning, permitting processes, and unforeseen delays. This paper serves as a review of the current understanding of these and other non-hardware costs in EV charging infrastructure projects (collectively known as “soft costs”). We found that soft costs in EV charging infrastructure projects are not well understood. Specifically, there is little agreement on how soft costs should be categorized and tracked, and less agreement still on best practices for controlling these costs and lowering barriers to infrastructure deployment. A broader review of EV charging infrastructure cost analyses shows that these costs can have significant impacts on project outcomes. EV charging infrastructure projects may be able to examine the success of the solar industry in lowering soft costs, and a similar effort may lower project costs significantly. Further work on standardizing and collecting data on EV charging infrastructure costs is required to begin addressing and controlling these costs.

32 - ENERGY CONSERVATION, CONSUMPTION, AND UTILIZA↗

DOE OSTI2025

Gas-Gap Calorimeter Sizing and Rating Tools for Heat Pipe Experimentation

Effective gas-gap calorimeter sizing and rating tools are required to design calorimeters that enable well-defined operating conditions, high cooling powers, and accurate calorimetry. The present report describes two tools utilizing Microsoft Excel and MathWorks MATLAB that enable the sizing and rating of gas-gap calorimeters with a He-Ar binary gas mixture in the gap. The Excel tools are two easy-to-use spreadsheets for calculating heat pipe operating temperature or He-Ar mole fractions given the required inputs. The MATLAB tool includes similar models with more robust solution algorithms along with sub-options for full-vacuum, static gas-gap, and forced circulation in the gas-gap. The accuracy of the developed tools were demonstrated by comparing with existing work in literature. The MATLAB tool was used for a parametric study to determine the gas-gap thickness, coolant gap thickness, coolant flow rate, and coolant inlet temperatures for the testing of a 3/4 in outer diameter heat pipe up to powers of 10 kW and temperatures of 1,000°C. The effects of heat pipe and calorimeter inner shell surface emissivities were investigated, considering the inability to control or accurately measure surface emissivities in most applications. It was found that controlling the He-Ar mole fractions provides a wide operating range for gas-gap thicknesses around ~ 0.042--0.090 in (~ 1.07--2.29 mm) for a surface emissivity range of 0.4--0.8, since conduction heat transfer is a significant fraction of the heat transfer across the gas-gap. In addition, it was found that turbulent flow in the coolant gap is needed at high input powers to prevent shell temperatures from approaching the boiling temperature of the water coolant. The parametric study resulted in choosing stainless steel tubes with an outer diameter and thickness of 1 x 0.065 in as the inner shell, and a 1-1/2 x 0.156 in as the outer shell of the calorimeter. Overall, this report presents the necessary information for the sizing and rating of gas-gap calorimeters with He-Ar mixtures for the testing of high-temperature heat pipes (~ 500--1,000°C).

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Impact of symmetry breaking and spin-orbit coupling on the band gap of halide perovskites

Halide perovskite (HP) materials have recently emerged as a class of semiconductors with immense promise for various optoelectronic applications, ranging from solar cells to light-emitting diodes. One of the unique attributes of HPs is their tunable band gaps with different factors governing their value. Furthermore, the first factor is related to relativistic corrections [“mass-Darwin,” connected to the ns 2 lone pairs, and spin-orbit coupling (SOC)] that induce an orbital shift or degeneracy splitting, resulting in a band-gap reduction. The second factor involves the structural configuration: in HPs the local symmetry of each Wyckoff position tends to be broken, inducing an opening of the band gap. Based on high-throughput density functional theory calculations, this paper systematically studies a possible self-cancelation on the band-gap correction for HPs when the polymorphous configuration—structural effects—and the SOC—electronic effects—are included. Our results indicate that the nature of interplay between SOC and symmetry breaking (SB) is that they are independent decoupling effects to describe the band-gap magnitude in halide perovskites. As a result of that, we observe a transitivity of the band-gap description; i.e., if we know the band gap of halide perovskites without SB and SOC, we can independently add the effects of band-gap reduction due to SOC and band-gap opening due to SB, regardless of the order in which these effects are considered.

14 SOLAR ENERGY↗

DOE OSTI2026

Upward band gap bowing and negative mixing enthalpy in multi-component cubic halide perovskite alloys

Physical properties intermediate between constituents of alloys can be achieved as downward convex positive bowing, upward concave negative bowing, or zero bowing. Such bowing effects are essential for band gap engineering in semiconductor alloys. Upward band gap bowing effects are rather rare, hindering the exploration on half of the available physical property space of alloys. Part of this being a rare event is related to the need to stabilize an alloy with low mixing enthalpy, so it does not phase separate. Here, in this paper, we find via density functional theory that one can satisfy the simultaneous conditions of negative mixing enthalpy and upward band gap bowing in four-component AB⁢X 3 halide perovskite alloys in the cubic perovskite structure. Such perovskite alloys have the B-site occupied by a mixture of group IVB and IIB elements that have the IVB-𝑠 and IIB-s states in the valence bands and conduction bands, respectively, leaving the delocalized 𝑠 states to strongly repel each other. This 𝑠−𝑠 repulsion leads to the upward band gap bowing and negative mixing enthalpies simultaneously. Remarkably, we identify a perovskite alloy that has a band gap much larger than all its components. Analogous trends of upward band gap bowing and negative mixing enthalpy also appear in the corresponding three-component and two-component AB⁢X 3 halide perovskite alloys. These observations of upward band gap bowing and negative mixing enthalpy will significantly accelerate the design of stable upward band gap bowing alloys in a broad range of material families.

14 SOLAR ENERGY↗

DOE OSTI2025

Alloying multiple halide perovskites on the same sublattice in search of stability and target band gaps

Single-component halide perovskites (HPs) rarely satisfy all the necessary criteria for optoelectronic applications, such as achieving an optimal band gap while maintaining high chemical and structural stability. Alloying halide perovskites has emerged as a promising strategy, not only to enhance stability but also to fine-tune their electronic and optical properties. In this work, we explore multiple degrees of freedom in alloy design, considering different substitution sublattices sites (A, B, or X in ABX3 perovskites), various chemical species (isovalent and hetero-valent elements), and multi-component compositions on a given sublattice. Using first-principles calculations based on density functional theory (DFT), we investigate how compositional variations influence the electronic (band gap) and structural properties (mixing enthalpy) of HP alloys. Our approach employs the polymorphous cell model, allowing full local relaxation which breaks local symmetry while preserving global cubic symmetry—an essential framework for accurately modeling HPs. Our results reveal that X-site mixing (halogen substitution) primarily affects the valence band maximum, allowing target band gap engineering. Additionally, variations in halogen radii introduce internal strain through octahedral distortions, influencing the mixing enthalpy. A-site substitution, while not directly contributing to the band edge states, modifies structural stability via volume effects, indirectly impacting the band gap. B-site alloying plays a dominant role in band gap modulation, leading to either positive or negative band gap bowing. Specifically, isovalent B-site mixing (Sn–Pb) induces strong positive bowing, where the alloy band gap is smaller than the average gap of parent compounds, whereas hetero-valent mixing (Cd–Pb) results in pronounced negative bowing. As an aside, we investigate the competition between the excess energy of disordered alloys vs. that of long-range ordered double perovskites of the same compositions, seeking examples of ordered phases emerging from disordered alloys. Furthermore, our findings provide fundamental insights into the electronic and structural behavior of HP alloys, offering valuable design principles for the development of stable and efficient materials for next-generation photovoltaic and optoelectronic devices.

14 SOLAR ENERGY↗

DOE OSTI2025

Exact spectral gaps of random one-dimensional quantum circuits

The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. Here, by focusing on the second moment of one-dimensional unitary circuits where nearest-neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Development of thin-gap GEM- μ RWELL hybrid detectors

Micro Pattern Gaseous Detectors (MPGDs) are used for tracking in High Energy Physics and Nuclear Physics because of their large area, excellent spatial resolution capabilities and low cost. However, for high energy charged particles impacting at a large angle with respect to the axis perpendicular to detector plane, the spatial resolution degrades significantly because of the long trail of ionization charges produced in clusters all along the track in the drift region of the detector. The long ionization charge trail results in registering hits from large number of strips in the readout plane which makes it challenging to precisely reconstruct the particle’s position using simple center of gravity algorithm. As a result, the larger the drift gap, the more severe the deterioration of spatial resolution for inclined tracks. For the same reason, the position resolution is also severely degraded in a large magnetic field, where the Lorentz E x B effect causes the ionization charges to follow a curved and longer path in the detector gas volume. In this paper, we report on the development of thin-gap MPGDs as a way to maintain excellent spatial resolution capabilities of MPGD detectors over a wide angular range of incoming particles. In a thin-gap MPGD, the thickness of the gas volume in the drift region is reduced from typically 3 mm to 1 mm or less. We present preliminary test beam results demonstrating the improvement in spatial resolution from 400 m with a standard 3 mm gap μ RWELL prototype to ~140 μ m with a double amplification GEM- μ RWELL thin-gap hybrid detector. Here, we also discuss the impact of a thin-gap drift volume on other aspects of the performance of MPGD technologies such as the efficiency and detector stability.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

Enhanced power density in zero-vacuum-gap thermophotovoltaic devices

Thermophotovoltaic (TPV) devices, which convert infrared thermal radiation from a hot emitter into electricity, hold great promise for applications in energy storage and waste heat recovery. While recent advancements have developed TPV devices with high efficiency, much less attention has been focused on improving the power density. Current TPV methods face challenges in significantly boosting the power density using emitters at very high temperatures (>2000 °C) or using complex, costly architectures such as near-field TPV. Here, we present the first experimental demonstration of a novel far-field TPV concept called “zero-vacuum-gap TPV” that eliminates the vacuum or gas-filled gap in conventional designs. By incorporating a high-index, infrared-transparent, and thermally insulating fused quartz spacer, we achieved a two-fold increase in power density compared to the far-field counterpart under identical conditions. Notably, in our experiment, the zero-vacuum-gap far-field design transforms a less-optimized, low-power-density far-field device into one with one of the highest power densities reported at moderate temperatures (700–1100 °C). Moreover, our measurements using a graphite emitter surpass the blackbody limit for gap-integrated far-field devices and match the performance of near-field TPV devices with an ultrathin 200-nm gap. Our findings suggest that zero-vacuum-gap TPV offers potential for cost-effective, scalable manufacturing using current technologies. Additionally, our modelling predicts that further power enhancements over one order of magnitude are possible with other spacer materials.

14 SOLAR ENERGY↗

DOE OSTI2025

Filling the Gaps: A Bayesian Mixture Model for Imputing Missing Soil Water Content Data

ABSTRACT Soil water content (SWC) data are central to evaluating how soil moisture varies over time and space and influences critical plant and ecosystem functions, especially in water‐limited drylands. However, sensors that record SWC at high frequencies often malfunction, leading to incomplete timeseries and limiting our understanding of dryland ecosystem dynamics. We developed an analytical approach to impute missing SWC data, which we tested at six eddy flux tower sites along an elevation gradient in the southwestern United States. We impute missing data as a mixture of linearly interpolated SWC between the observed endpoints of a missing data gap and SWC simulated by an ecosystem water balance model (SOILWAT2). Within a Bayesian framework, we allowed the relative utility (mixture weight) of each component (linearly interpolated vs. SOILWAT2) to vary by depth, site and gap characteristics. We explored “fixed” weights versus “dynamic” weights that vary as a function of cumulative precipitation, average temperature, and time since the start of the gap. Both models estimated missing SWC data well ( R 2 = 0.70–0.88 vs. 0.75–0.91 for fixed vs. dynamic weights, respectively), but the utility of linearly interpolated versus SOILWAT2 values depended on site and depth. SOILWAT2 was more useful for more arid sites, shallower depths, longer and warmer gaps and gaps that received greater precipitation. Overall, the mixture model reliably gap‐fills SWC, while lending insight into processes governing SWC dynamics. This approach to impute missing data could be adapted to accommodate more than two mixture components and other types of environmental timeseries.

Ogle, Kiona [School of Informatics, Computing, and↗

DOE OSTI2025

Role of effective mass and long-range interactions in the band-gap renormalization of photoexcited semiconductors

Understanding how to control changes in the electronic structure and related dynamical renormalizations by external driving fields is the key for understanding ultrafast spectroscopy and applications in electronics. Here, we focus on the band gap's modulation by external electric fields and uncover the effect of band dispersion on the gap renormalization. We employ the Green's function formalism using the real-time Dyson expansion to account for dynamical correlations induced by photodoping. The many-body formalism captures the dynamics of systems with long-range interactions, carrier mobility, and variable electron and hole effective mass. We also demonstrate that mean-field simulations based on the Hartree-Fock Hamiltonian, which lacks dynamical correlations, yields a qualitatively incorrect picture of band-gap renormalization. We find the trend that increasing effective mass, thus decreasing mobility, leads to as much as a 6% enhancement in band-gap renormalization. Further, the renormalization is strongly dependent on the degree of photodoping. As the screening induced by free electrons and holes effectively reduces any long-range and interband interactions for highly excited systems, we show that there is a specific turnover point with a minimal band gap. Here, we further demonstrate that the optical gap renormalization follows the same trend though its magnitude is altered by the Moss-Burstein effect.

Approximation methods for many-body systems↗

DOE OSTI2024

Topological phase transition without single particle gap closing in strongly correlated systems

Here, in this study, we show two models where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard noninteracting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that, for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does, in fact, close. These two gaps are the same in the noninteracting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Band-gap reduction and band alignments of dilute bismide III–V alloys

Adding a few atomic percent of Bi to III–V semiconductors leads to significant changes in their electronic structure and optical properties. Bismuth substitution on the pnictogen site leads to a large increase in spin-orbit splitting Δ SO at the top of the valence band (Γ 8⁢𝑣 −Γ 7⁢𝑣 ) and a large reduction in the band gap, creating unique opportunities in semiconductor device applications. Quantifying these changes is key to the design and simulation of electronic and optoelectronic devices. Using hybrid functional calculations, we predict the band gap of III–Vs (III = Al, Ga, In and V = As, Sb) with low concentrations of Bi (3.125% and 6.25%), the effects of adding Bi on the valence- and conduction-band edges, and the band offset between these dilute alloys and their III–V parent compounds. As expected, adding Bi raises the valence-band maximum (VBM). However, contrary to previous assumptions, the conduction-band minimum (CBM) is also significantly lowered, and both effects contribute to the sizable band-gap reduction. Changes in band gap and Δ SO are notably larger in the arsenides than in the antimonides. In conclusion, we also predict cases of band-gap inversion (Γ 6⁢𝑐 below Γ 8⁢𝑣 ), and Δ SO larger than the band gap, which are key parameters for designing topological materials and for minimizing losses due to Auger recombination in infrared lasers.

Saboor, Abdul [Univ. of Delaware, Newark, DE (Unit↗

DOE OSTI2024

Characterization of Fuel and Cladding In and Near the Pellet-Pellet Gap of a High-Burnup Pressurized Water Reactor Fuel Rod

At TopFuel 2021, we reported on metallographic examinations of a high burnup ZIRLO-clad spent fuel rod operated at the North Anna Power Station having a 3-mm gap between pellets at an elevation of ~1,403 mm. The rod was sectioned axially at that elevation to reveal the pellet-pellet interfaces and the pellet-pellet gap. Sections were mounted and polished to reveal the distribution of cladding inner and outer oxide layer thicknesses above, below, and within the gap. Since then, total cladding hydrogen measurements have been performed to quantify the cladding hydrogen content through the gap and above and below the pellet-pellet gap region. This paper provides the cladding hydrogen concentrations and discusses the overall findings regarding cladding waterside oxidation and cladding hydrogen diffusion to a pellet-pellet gap.

Montgomery, Rose↗

DOE OSTI2026

A Proxy Method to Bridge LCA Data Gaps Using Automated Material Classification and Probabilistic Under-Specification

Life cycle assessments (LCAs) are essential for understanding the environmental impacts of material production. However, gaps in life cycle inventory (LCI) data for material and chemical inputs present a key challenge for LCA practitioners, especially in the early design stages. Strategies for filling in these gaps require additional time and expertise, which can hinder the LCA’s completion. This study combined automatic material classification and probabilistic under-specification to create a time-efficient method to fill material LCI data gaps. To illustrate the proposed method, proxy environmental impact distributions were generated using publicly available material LCI data classified into the ChemOnt chemical taxonomy using the open-source chemical classification software ClassyFire. Input materials with data gaps were then classified into the same taxonomy, where proxy environmental impact values could be selected from the available distributions to quickly fill in any data gaps. Although these methods were applied to classify material production processes available in the Federal LCA Commons and Ecoinvent databases, they can be applied to any LCA database. This study shows that classifying materials by their chemical structure produces taxonomies with increased granularity relative to industrial classification, improving the ability of under-specified proxy data to be used for differentiating the environmental impacts of competing designs.

biological databases↗

DOE OSTI2024

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗