Semi-empirical Tight-binding Method Research Articles

Low-temperature electron transport in [110] and [100] silicon nanowires: a DFT-Monte Carlo study

The effects of very low temperature on the electron transport in a [110] and [100] axially aligned unstrained silicon nanowires (SiNWs) are investigated. A combination of semi-empirical 10-orbital tight-binding method, density functional theory and Ensemble Monte Carlo (EMC) methods are used. Both acoustic and optical phonons are included in the electron-phonon scattering rate calculations covering both intra-subband and inter-subband events. A comparison with room temperature (300 K) characteristics shows that for both nanowires, the average electron steady-state drift velocity increases at least 2 times at relatively moderate electric fields and lower temperatures. Furthermore, the average drift velocity in [110] nanowires is 50 percent more than that of [100] nanowires, explained by the difference in their conduction subband effective mass. Transient average electron velocity suggests that there is a pronounced streaming electron motion at low temperature which is attributed to the reduced electron-phonon scattering rates.

Dxtb-An efficient and fully differentiable framework for extended tight-binding.

Automatic differentiation (AD) emerged as an integral part of machine learning, accelerating model development by enabling gradient-based optimization without explicit analytical derivatives. Recently, the benefits of AD and computing arbitrary-order derivatives with respect to any variable were also recognized in the field of quantum chemistry. In this work, we present dxtb-an open-source, fully differentiable framework for semiempirical extended tight-binding (xTB) methods. Developed entirely in Python and leveraging PyTorch for array operations, dxtb facilitates extensibility and rapid prototyping while maintaining computational efficiency. Through comprehensive code vectorization and optimization, we essentially reach the speed of compiled xTB programs for high-throughput calculations of small molecules. The excellent performance also scales to large systems, and batch operability yields additional benefits for execution on parallel hardware. In particular, energy evaluations are on par with existing programs, whereas the speed of automatically differentiated nuclear derivatives is only 2 to 5 times slower compared to their analytical counterparts. We showcase the utility of AD in dxtb by calculating various molecular and spectroscopic properties, highlighting its capacity to enhance and simplify such evaluations. Furthermore, the framework streamlines optimization tasks and offers seamless integration of semiempirical quantum chemistry in machine learning, paving the way for physics-inspired end-to-end differentiable models. Ultimately, dxtb aims to further advance the capabilities of semiempirical methods, providing an extensible foundation for future developments and hybrid machine learning applications. The framework is accessible at https://github.com/grimme-lab/dxtb.

Exploring the potential of boron-nitride nanobelts in environmental applications: Greenhouse gases capture

This study examines boron-nitride nanobelts, including Möbius-type, for capturing and detecting nine greenhouse gases (ammonia, carbon dioxide, carbon monoxide, hydrogen sulfide, methane, methanol, nitric dioxide, nitric oxide, and phosgene). Negative adsorption energies indicate favorable adsorption on both nanobelt types. The systems show recovery times ranging between 2 h to few nanoseconds. Only nitric oxide forms covalent bonds; other gases interact non-covalently. Molecular dynamics simulations reveal consistent single-molecule interactions and attractive forces with multiple molecules. Semi-empirical tight-binding methods, as implemented in the xTB software were used for computational efficiency. Results demonstrate the potential of boron-nitride nanobelts for environmental monitoring and remediation of industrial toxic gas emissions, addressing concerns about human health and environmental impact.

Multi-electron transfer mechanism and band structures of CNTs in MOF-derived CNTs/Co hybrids for enhanced electromagnetic wave absorption property

Metal-organic framework (MOF)-derived magnetic metal/carbon nanocomposites have received widespread attention for electromagnetic wave (EMW) absorption. The present study introduces a novel approach to MOF composite material design by constructing composites modified with carbon nanotubes (CNTs) and magnetic Co nanoparticles. The carbon confinement effect in CNT/Co not only regulates the electronic structure of Co-C bonds, but also maintains the redox cycle of Co0/2→Co3+→Co0/2+, improving electronic activity and exhibiting synergistic integration characteristics of efficient electromagnetic wave absorption. Particularly, the maximum reflection loss (RLmin) of CNTs/Co-900 reached −52.7 dB at 4.67 GHz in the case of an absorber thickness of 1.6 mm. The excellent microwave absorption performance may be attributed to the interwoven structure formed by novel ZIF-67, CNTs, and Co metal nanoparticles and the double loss of magnetic Co and dielectric CNTs. In addition, the band gap of CNTs was calculated to be Eg = 0.27 eV by the semi-empirical tight-binding method with DFTB+. It is confirmed that CNTs have high electron migration ability, which is beneficial to conductive loss. It is confirmed that CNTs have high electron migration ability, which is beneficial to conductive loss. This study provides a novel strategy for the development of metal-organic framework-based magnetic particles/carbon nanocomposites for electromagnetic wave absorption.

Atomistic origins of compound semiconductor synthesis with computational neuromorphic engineering

We propose the usage of multi-element bulk materials to mimic neural dynamics instead of atomically thin materials via the modeling of group II–IV compound semiconductor growth using vacancy defects and dopants by creating and annihilating one another like a complex artificial neural network, where each atom itself is the device in analogy to crossbar memory arrays, where each node is a device. We quantify the effects of atomistic variations in the electronic structure of an alloy semiconductor using a hybrid method composed of a semiempirical tight-binding method, density functional theory, Boltzmann transport theory, and a transfer-matrix method. We find that the artificial neural network resembles the neural transmission dynamics and, by proposing resistive switching in small areas with low energy consumption, we can increase the integration density similar to the human brain.

Electronic and structural properties of Möbius boron-nitride and carbon nanobelts

For the development of nanofilters and nanosensors, we wish to know the impact of size on their geometric, electronic, and thermal stabilities. Using the semiempirical tight binding method as implemented in the xTB program, we characterized Möbius boron-nitride and carbon-based nanobelts with different sizes and compared them to each other and to normal nanobelts. The calculated properties include the infrared spectra, the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), the energy gap, the chemical potential, and the molecular hardness. The agreement between the peak positions from theoretical infrared spectra compared with experimental ones for all systems validates the methodology that we used. Our findings show that for the boron-nitride-based nanobelts, the calculated properties have an opposite monotonic relationship with the size of the systems, whereas for the carbon-based nanobelts, the properties show the same monotonic relationship for both types of nanobelts. Also, the torsion presented on the Möbius nanobelts, in the case of boron-nitride, induced an inhomogeneous surface distribution for the HOMO orbitals. High-temperature molecular dynamics also allowed us to contrast carbon-based systems with boron-nitride systems at various temperatures. In all cases, the properties vary with the increase in size of the nanobelts, indicating that it is possible to choose the desired values by changing the size and type of the systems. This work has many implications for future studies, for example our results show that carbon-based nanobelts did not break as we increased the temperature, whereas boron-nitride nanobelts had a rupture temperature that varied with their size; this is a meaningful result that can be tested when the use of more accurate simulation methods become practical for such systems in the future.

Multilevel Framework for Analysis of Protein Folding Involving Disulfide Bond Formation.

In this study, a three-layered multicenter ONIOM approach is implemented to characterize the naive folding pathway of bovine pancreatic trypsin inhibitor (BPTI). Each layer represents a distinct level of theory, where the initial layer, encompassing the entire protein, is modeled by a general all-atom force-field GFN-FF. An intermediate electronic structure layer consisting of three multicenter fragments is introduced with the state-of-the-art semiempirical tight-binding method GFN2-xTB. Higher accuracy, specifically addressing the breaking and formation of the three disulfide bonds, is achieved at the innermost layer using the composite DFT method r2SCAN-3c. Our analysis sheds light on the structural stability of BPTI, particularly the significance of interlinking disulfide bonds. The accuracy and efficiency of the multicenter QM/SQM/MM approach are benchmarked using the oxidative formation of cystine. For the folding pathway of BPTI, relative stabilities are investigated through the calculation of free energy contributions for selected intermediates, focusing on the impact of the disulfide bond. Our results highlight the intricate trade-off between accuracy and computational cost, demonstrating that the multicenter ONIOM approach provides a well-balanced and comprehensive solution to describe electronic structure effects in biomolecular systems. We conclude that multiscale energy landscape exploration provides a robust methodology for the study of intriguing biological targets.

Which molecules can challenge density-functional tight-binding methods in evaluating the energies of conformers? investigation with machine-learning toolset

Large organic molecules and biomolecules can adopt multiple conformations, with the occurrences determined by their relative energies. Identifying the energetically most favorable conformations is crucial, especially when interpreting spectroscopic experiments conducted under cryogenic conditions. When the effects of irregular surrounding medium, such as noble gas matrices, on the vibrational properties of molecules become important, semi-empirical (SE) quantum-chemical methods are often employed for computational simulations. Although SE methods are computationally more efficient than first-principle quantum-chemical methods, they can be inaccurate in determining the energies of conformers in some molecules while displaying good accuracy in others. In this study, we employ a combination of advanced machine learning techniques, such as graph neural networks, to identify molecules with the highest errors in the relative energies of conformers computed by the semi-empirical tight-binding method GFN1-xTB. The performance of three different machine learning models is assessed by comparing their predicted errors with the actual errors in conformer energies obtained via the GFN1-xTB method. We further applied the ensemble machine-learning model to a larger collection of molecules from the ChEMBL database and identified a set of molecules as being challenging for the GFN1-xTB method. These molecules hold potential for further improvement of the GFN1-xTB method, showcasing the capability of machine learning models in identifying molecules that can challenge its physical model.

Phase-dependent polymerization isomerism in the coordination complexes of a flexible bis(β-diketonato) ligand.

First prepared in the late 70s, the pro-ligand 1,3-bis(3,5-dioxo-1-hexyl)benzene (H2bdhb) contains two acetoacetyl terminations linked to a central 1,3-phenylene unit through dimethylene bridges. Since each termination can be either in diketonic or keto-enolic form, in organic solution it exists as a mixture of three spectroscopically resolvable tautomers. In the presence of pyridine, Co2+ and the bdhb2- anion form a crystalline dimeric compound with formula [Co2(bdhb)2(py)4] (2) and a Co⋯Co separation of more than 11 Å. Complex 2 contains two pseudo-octahedrally coordinated and non-interacting high-spin cobalt(II) ions (S = 3/2) displaying a large easy-plane anisotropy (D ∼ 70 cm-1), as consistently indicated by magnetic measurements, X-band EPR spectra, and complete active space self-consistent field/N-electron valence state perturbation theory (CASSCF/NEVPT2) calculations. At cryogenic temperatures (T < 7 K) and in an applied static magnetic field, the compound shows detectably slow magnetic relaxation, which occurs through direct and Raman mechanisms. Combined mass spectrometry, UV-Vis, and 1H/2H NMR data, including an isotopic labelling experiment and a determination of molecular weight by diffusion ordered spectroscopy (DOSY), show that 2 rearranges to monomeric high-spin [Co(bdhb)(py)x] species (x = 0, 1, or 2) in organic solution (CH2Cl2, THF) with concomitant partial dissociation of the py ligands. The X-band EPR spectra in a frozen CH2Cl2/toluene matrix concurrently suggest a significant alteration of the coordination environment upon dissolution. These observations are fairly well reproduced by density functional theory (DFT) and CASSCF/NEVPT2 calculations on the lowest Gibbs free energy conformers of each species, as provided by an extensive conformational search based on meta-dynamics simulations and semiempirical tight-binding methods. After the vanadyl analogue, compound 2 provides the second example of polymerization isomerism in the 1 : 1 adducts of bdhb2- with divalent metal ions.

Excited state properties of an A-D-A non-fullerene electron acceptor: a LC-TD-DFTB study.

Understanding charge transfer processes is essential to estimate the performance of organic photovoltaic technologies. Although experimental production is on the rise, predictability strongly relies on theoretical modeling, which is limited to the size of semiconductors. As a computationally favorable approach, we benchmarked the long-range corrected (LC) time-dependent (TD) formulation of the semi-empirical density functional-based tight-binding method (DFTB) for three polycyclic aromatic hydrocarbons (PAHs) and studied the DTP-IC-4Ph molecule, a PAH-based non-fullerene electron acceptor (NFA) with an A-D-A backbone structure. After a thorough investigation into the long-range parameter (ω) tuning for naphthalene, anthracene and pyrene, the excitation energies, oscillator strengths and Natural Transition Orbitals (NTOs) were compared with the standard ωB97X-D/6-31G(d,p) level of theory and the ADC2/6-31G(d,p) multiconfigurational method. We estimated mobility-related properties of the NFA and considered 1000 thermally accessible configurations to qualitatively reproduce the experimental absorption profile and investigate the energetic disorder. Finally, we conducted a fragment-based analysis using the one-electron transition density matrix (1TDM) to determine the character of the excited states and investigate the effect of side chains on exciton formation. Our results are sensitive to the level of theory and highly dependent on the long-range parameter but suggest that the presence of alkyl chains promotes a higher average charge delocalization and allows for additional hopping mechanisms, favoring the charge transfer dynamics.

Calculations of molecular properties of 2-(2'-hydroxyphenyl)benzoxazole by semi-empirical tight-binding methods

The semi-empirical tight-binding methods GFN1-xTB and GFN2-xTB are applied to calculations of structure, energy and normal vibrations of the molecule of 2-(2'-hydroxyphenyl)benzoxazole undergoing excited state intramolecular proton transfer. The results are compared with ones obtained by the density-functional tight-binding methods with hydrogen interaction corrections and density functional theory. The GFN2-xTB method is found to provide good correspondence to the results obtained by more accurate but much slower density functional theory method for geometrical parameters of hydrogen bond, relative energy of molecular conformations and potential energy surface.

Reduction pathway of glutaredoxin 1 investigated with QM/MM molecular dynamics using a neural network correction.

Glutaredoxins are small enzymes that catalyze the oxidation and reduction of protein disulfide bonds by the thiol-disulfide exchange mechanism. They have either one or two cysteines in their active site, resulting in different catalytic reaction cycles that have been investigated in many experimental studies. However, the exact mechanisms are not yet fully known, and to our knowledge, no theoretical studies have been performed to elucidate the underlying mechanism. In this study, we investigated a proposed mechanism for the reduction of the disulfide bond in the protein HMA4n by a mutated monothiol Homo sapiens glutaredoxin and the co-substrate glutathione. The catalytic cycle involves three successive thiol-disulfide exchanges that occur between the molecules. To estimate the regioselectivity of the different attacks, classical molecular dynamics simulations were performed and the trajectories analyzed regarding the sulfur-sulfur distances and the attack angles between the sulfurs. The free energy profile of each reaction was obtained with hybrid quantum mechanical/molecular mechanical metadynamics simulations. Since this required extensive phase space sampling, the semi-empirical density functional tight-binding method was used to describe the reactive cysteines. For an accurate description, we used specific reaction parameters fitted to B3LYP energies of the thiol-disulfide exchange and a machine learned energy correction that was trained on coupled-cluster single double perturbative triple [CCSD(T)] energies of thiol-disulfide exchanges. Our calculations show the same regiospecificity as observed in the experiment, and the obtained barrier heights are about 12 and 20 kcal/mol for the different reaction steps, which confirms the proposed pathway.

Molecular Mechanisms of Phosphoester Bond Formation in Water Using Tight-Binding Ab Initio Molecular Dynamics.

Phosphate groups are ubiquitous in biomolecules and are usually incorporated through phosphoester bonds between alcohol groups and orthophosphate. The formation of this bond is exceptionally difficult, with associated barriers of 30-45 kcal/mol in the absence of catalysts. In abiotic conditions, polymerizing nucleic acids without enzymes remains very challenging and is still a partly unsolved problem that severely questions the RNA World hypothesis for the origins of life. Offering a solution to this problem would involve a detailed knowledge of the reaction energetics and mechanisms, yet these remain not fully understood at a molecular level, especially because of the very slow reaction rates that represent a significant challenge for the experiments. The number of involved reaction coordinates and the possible role of the solvent in assisting the reaction are challenging for computational studies. Here, we use extensive ab initio molecular dynamics simulations using semiempirical tight-binding methods and enhanced sampling to address these issues. We first show that the choice of the tight-binding method is greatly limited by the instability of the water liquid phase for most DFTB generations and parameter sets that are widely available. We then focus on a model reaction involving methanol and orthophosphate, for which the two protonation states (mono- and dianionic) that are dominant around neutral pH are considered. We compare different proton coordinates that enable (or not) the participation of solvent water molecules. Our simulations suggest that in all cases, a dissociative associative mechanism, with an intermediate metaphosphate, is favored. The main difference between the two phosphate species is that reaction with the monoanion is assisted by the substrate, while that with the dianion involves solvent water molecules. Our results are in agreement with early experimental measurements, but the reaction barriers are underestimated in our framework. We believe that our approach provides an interesting perspective on how to sample the reaction phase space efficiently, but it calls for future studies using more accurate descriptions of chemical reactivity.

Theoretical calculations of formation and reactivity of o-quinomethide derivatives of resorcin[4]arene with reference to empirical data.

This paper describes theoretical reaction pathways of alkoxybenzyl derivatives of resorcin[4]arene leading to the formation of o-quinomethide derivatives of resorcin[4]arene (o-QMR[4]A). For each case, the activation energies for the formation of one o-QMR[4]A unit and the activation energies for the backward reaction were calculated. Based on the calculated reaction pathways, the reaction mechanism of o-QMR[4]A formation was proposed. Using the example of o-QMR[4]A generated from a methoxy derivative of resorcin[4]arene, the activation energies with selected nucleophiles were calculated and the reaction mechanisms discussed. Reaction path calculations were performed using the nudged elastic band method and semiempirical extended tight-binding method (GFN2-xTB). Using hydroxybenzyl derivatives of resorcin[4]arene as an example, a comparison of calculated activation energies by selected density-functional theory methods with GFN2-xTB and B97-3c geometries was performed. B97-3c and wB97XD methods were used to calculate the energies of the reactants (R), transition states (TS) and products (P) of the analysed reactions. Theoretical reaction mechanisms were discussed with respect to the orbital-weighted Fukui dual descriptor (Δfw) and experimental data.

Geometrical benchmarking and analysis of redox potentials of copper(I/II) guanidine-quinoline complexes: Comparison of semi-empirical tight-binding and DFT methods and the challenge of describing the entatic state (part III).

Copper guanidine-quinoline complexes are an important class of bioinorganic complexes that find utilization in electron and atom transfer processes. By substitution of functional groups on the quinoline moiety the electron transfer abilities of these complexes can be tuned. In order to explore the full substitution space by simulations, the accurate theoretical description of the effect of functional groups is essential. In this study, we compare three different methods for the theoretical description of the structures. We use the semi-empirical tight-binding method GFN2-xTB, the density functional TPSSh and the double-hybrid functional B2PLYP. We evaluate the methods on five different complex pairs (Cu(I) and Cu(II) complexes), and compare how well calculated energies can predict the redox potentials. We find even though B2PLYP and TPSSh yield better accordance with the experimental structures. GFN2-xTB performs surprisingly well in the geometry optimization at a fraction of the computational cost. TPSSh offers a good compromise between computational cost and accuracy of the redox potential for real-life complexes.

Computer Generated Realistic Interstellar Icy Grain Models: Physicochemical Properties and Interaction with NH3.

Interstellar grains are composed by a rocky core (usually amorphous silicates) covered by an icy mantle, the most abundant molecule being H2O followed by CO, CO2, NH3, and also radicals in minor quantities. In dense molecular clouds, gas-phase chemical species freeze onto the grain surface, making it an important reservoir of molecular diversity/complexity whose evolution leads to interstellar complex organic molecules (iCOMs). Many different models of water clusters have appeared in the literature, but without a systematic study on the properties of the grain (such as the H-bonds features, the oxygen radial distribution function, the dangling species present on the mantle surface, the surface electrostatic potential, etc.). In this work, we present a computer procedure (ACO-FROST) grounded on the newly developed semiempirical GFN2 tight-binding quantum mechanical method and the GFN-FF force field method to build-up structures of amorphous ice of large size. These methods show a very favorable accuracy/cost ratio as they are ideally designed to take noncovalent interactions into account. ACO-FROST program can be tuned to build grains of different composition mimicking dirty icy grains. These icy grain models allow studying the adsorption features (structure, binding energy, vibrational frequencies, etc.) of relevant species on a large variety of adsorption sites so to obtain a statistically meaningful distribution of the physicochemical properties of interest to be transferred in numerical models. As a test case, we computed the binding energy of ammonia adsorbed at the different sites of the icy grain surface, showing a broad distribution not easily accounted for by other more size limited icy grain models. Our method is also the base for further refinements, adopting the present grain in a more rigorous QM:MM treatment, capable of giving binding energies within the chemical accuracy.

Virtual screening of norbornadiene-based molecular solar thermal energy storage systems using a genetic algorithm.

We present a computational methodology for the screening of a chemical space of 1025 substituted norbornadiene molecules for promising kinetically stable molecular solar thermal (MOST) energy storage systems with high energy densities that absorb in the visible part of the solar spectrum. We use semiempirical tight-binding methods to construct a dataset of nearly 34000 molecules and train graph convolutional networks to predict energy densities, kinetic stability, and absorption spectra and then use the models together with a genetic algorithm to search the chemical space for promising MOST energy storage systems. We identify 15 kinetically stable molecules, five of which have energy densities greater than 0.45 MJ/kg, and the main conclusion of this study is that the largest energy density that can be obtained for a single norbornadiene moiety with the substituents considered here, while maintaining a long half-life and absorption in the visible spectrum, is around 0.55 MJ/kg.

Closer Look at Inverse Electron Demand Diels–Alder and Nucleophilic Addition Reactions on s-Tetrazines Using Enhanced Sampling Methods

Inverse electron demand [4+2] Diels–Alder (iEDDA) reactions as well as unprecedented nucleophilic (azaphilic) additions of R-substituted silyl-enol ethers (where R is Phenyl, Methyl, and Hydrogen) to 1,2,4,5-tetrazine (s-tetrazine) catalyzed by hbox {BF}_{3} have recently been discovered (Simon et al. in Org Lett 23(7):2426–2430, 2021), where static calculations were employed for calculation of activation energies. In order to have a more realistic dynamic description of these reactions in explicit solution at ambient conditions, in this work we use a semiempirical tight-binding method combined with enhanced sampling techniques to calculate free energy surfaces (FESs) of the iEDDA and azaphilic addition reactions. Relevant products of not only s-tetrazine but also its derivatives such as hbox {BF}_{3}-mediated s-tetrazine adducts are investigated. We reconstruct the FESs of the iEDDA and azaphilic addition reactions using metadynamics and blue moon ensemble, and compare the ability of different collective variables (CVs) including bond distances, Social PeRmutation INvarianT (SPRINT) coordinates, and path-CV to describe the reaction pathway. We find that when a bulky Phenyl is used as a substituent at the dienophile the azaphilic addition is preferred over the iEDDA reaction. In addition, we also investigate the effect of hbox {BF}_{3} in the diene and steric hindrance in the dienophile on the competition between the iEDDA and azaphilic addition reactions, providing chemical insight for reaction design.

Calculations of Energy Band Structure of GaAs, GaSb and GaP Crystals as a Function of Temperature Using the Semiempirical Tight Binding Method

In this paper, the band structure of gallium group of III-V semiconductor has been calculated with temperature, the semi-empirical tight binding method was used to calculate the band structure and the matrix elements were calculated for both models sp^3 and sp^3 s^*. A computer program in MATLAB was designed to calculate the energy eigenvalues for the wave vector points in the first Brillouin zone between high symmetry points to form energy bands. The effect of temperature on the energy band of these group of crystals has been studied by changing the values of the lattice constant under the influence of temperature according to the Pierron relation and thus calculating the change in the length of the bond with temperature, which in turn affects the change in the values of the elements of the Hamiltonian matrix. The energy gap and refractive index were calculated at points of high symmetry as a function of temperature. The results showed a decrease in the energy gap values of GaAs, GaSb and GaP crystals with increasing temperature. Then the experimental Varshni relation was used to calculate the change in the energy gap values of these crystals and the results obtained from current study were compared with the results of Panish and Bellani, where the results showed that a model sp^3 s^* gives better results than the model sp^3.As well as the calculations of the refractive index of these crystals using the Moss formula showed that the refractive index will gradually increase with increasing temperatures.

Calculation of The Electronic Energy Band Structure of GaAs Crystal Using The Semiempirical Tight Binding Method

In this paper, the semi-empirical tight binding method for the nearest neighbors in the first Brillouin zone has been used to calculate the energy band structure of GaAs crystal which have zinc blend ZB structure, the band structure has been calculated by using sp^3 model which have 9 parameters and sp^3 s^* which have 13 parameters, both these models are used to calculate the main characteristic of both valence and conduction bands. The matrix elements were determined using the method followed by Cohen and Vogl, by identifying points in the wave vector space within the reduced Brillouin zone between the points of high symmetry and calculating the eigenvalues of all these points by building a computer program in MATLAB to form the energy band structure. The effective mass m^* along the direction [111] for the lowest conduction bands has been calculated. A comparison between the sp^3 model used by Cohen and the sp^3 s^* model used by Vogl has been made. The energies of the band structure at points the high symmetry Γ and X obtained from the study were compared with the results of the published research. The results showed that there is a difference in the energy gap between sp^3 and sp^3 s^* models and there is good agreement between the band energies at high symmetry points between these two models and the published results.