2-D Semiconductors are novel materials in the field of nano-electronics. Their unusual transport properties have led to an extensive research attention towards similar ma- terials. Graphene has carriers that exhibit an effective "speed of light" (10 6 m/s) in the low **energy** range of <0.5 eV. These massless fermions exhibit various quantum electrodynamics(QED) in the low **energy** range that can be explored. It is therefore of interest to understand and simulate the nature of the bands and understand their interactions along the edges and corners of the first brillouin zone. Various forms of monolayer graphene exist - A Graphene nano-ribbon is a sheet of graphene of narrow width and high aspect ratio existing in 2 different edge orientations. This variation in the band gap of different morphologies is known to affect the On current characteristics for corresponding GNRFETs and other applications.

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1. Introduction
Progress in describing of disordered systems is strongly connected with develop- ment of electron **theory**. Substitution alloys are best described among disordered systems. Traditional knowledge about physical properties of alloys is based on Born approximation of the scattering **theory**. But this approach obviously cannot be ap- plied in case of a large scattering potential difference of components that holds for the description of alloys with simple, transition, and rare-earth elements. The same difficulty relates the pseudopotential method. 1 Because of non-local nature of pseudopotential, the problem of pseudopotential transferability exists. It is im- possible to use nuclear potentials determined by the properties of some systems to describe other systems. Because of **using** **theory** of Vanderbilt ultra-soft potentials 2,3 and method of projector-augmented waves proposed by Blochl, 3,4 in investigations of electronic structure and properties of the system have been achieved fundamen- tal progress. Significant success in the study of electronic structure and properties of the systems achieved recently because of the use of ultra-soft pseudopotential Vanderbilt 2,3 and the method of projector-augmented waves in density functional **theory** proposed by Blochl. 3,4 This approach was developed further because of use of the generalized gradient approximation in density functional **theory** of multi- electron systems, developed at Perdew works. 5 – 9 In projector-augmented waves approach, the wave function of valence states of electron (all-electron orbital) is expressed by **using** the conversion through the pseudo orbital. Pseudo orbital ex- pands to pseudo partial waves in the augment area. Even so all-electron orbital in the same area is expanded with the same coefficients via partial waves, described by Kohn–Sham equation. Expression for pseudo Hamiltonian which we have in equa- tion for pseudo wave function is derived by minimizing the full **energy** functional.

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II. M ODEL A ND N UMERICAL M ETHOD
As earlier mentioned, graphene is a two dimensional sheet consisting of connected carbon atoms in hexagons like the benzene molecule. The electronic structure of a carbon nanotube (CNT) can be acquired from that of graphene. The wave vector related with the chiral vector C h , in the circumferential direction gets quantized. On the other wave-vector associated the direction of the translation vector T along the CNT axis remains continuous for an infinite carbon nanotube. These are the boundary conditions of the carbon nanotube. This sets the **energy** bands in one-dimensional **dispersion** relationship cross sections of those of graphene. The reciprocal lattice vectors

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Abstract—The **tight** **binding** **model** is one of the strong theoretical techniques to calculate the band gap of the materials. The band structures of some semiconductors and the semiconductors made by their combination is calculated here **using** simulation technique. The basic **theory** of **Tight** **Binding** **Model** is presented since beginning to the final matrix formulation. Band structure of the four semiconductors AlAs, AlP, GaAs and GaSb and their corresponding alloys Al𝐴𝑠 𝑥 𝑃 1−𝑥 & Ga 𝐴𝑠 𝑥 𝑆𝑏 1−𝑥 is

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Abstract
Planar carbon-based electronic devices, including metal/semiconductor junctions, transistors and interconnects, can now be formed from patterned sheets of graphene. Most simulations of charge transport within graphene-based electronic devices assume an **energy** band structure based on a nearest-neighbour **tight** **binding** analysis. In this paper, the **energy** band structure and conductance of graphene nanoribbons and metal/semiconductor junctions are obtained **using** a third nearest-neighbour **tight** **binding** analysis in conjunction with an efficient nonequilibrium Green ’ s function formalism. We find significant differences in both the **energy** band structure and conductance obtained with the two approximations.

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The parameters are optimized to minimize the mean squared error. We use the nonlinear least-squares minimiza- tion method of Levenberg-Marquardt with a numerical Jacobian. 24 We weight each k point by unity, and the result- ing total **energy** by 200; accordingly the total energies are weighted approximately the same as the k-point data. We initialize our parameters **using** the Hamiltonian and overlap values for Ti from Ref. 20 adapted to our functional form. We then fit only the environment-dependent on-site terms to the band structure of the cubic elements. After an initial fit is found, we include the hopping terms in the optimization. We proceed **using** only the cubic band structure, then the cubic band structure and total energies, and finally all structures and energies. After a new minimum is found, we check each function to see if the minimization has made the exponential term g 共ll ⬘ m 兲 too large; this corresponds to making the entire

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When replacing PBE+vdW with DFTB3+vdW in the description of lattice energies, regard- less of vdW method, we find lattice energies with minimum MARE as high as 15% corre- sponding to minimum MAE of 13 kJ mol −1 compared to experiment (see second column in Fig. S2a of SI). While this may disqualify the DFTB3+vdW methods in their current formu- lation as outright stability prediction methods, following the scheme of Fig. 1, we can use the higher quality of crystal structure prediction at the DFTB3+vdW level in order to perform structural prescreening. Thereby, we identify stable structures **using** DFTB3+vdW and eval- uate improved energetics at the DFT+vdW level. ∗ The evaluation of lattice energies at the DFT level i.e. PBE+MBD on top of DFTB3+MBD structures improves the lat- tice **energy** prediction significantly as shown in Table 1 and Fig. 2c. In fact, the relative error of PBE+MBD//DFTB3+TS/MBD en- ergies is comparable in performance with the full DFT+MBD i.e. PBE+MBD//PBE+MBD when compared to experiment. This means that replacing optimized PBE+MBD crystal structures with DFTB3+TS/MBD structures does not significantly affect the lattice **energy** prediction compared to experiment.

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In summary, we coupled pairwise **dispersion** corrections and the many-body **dispersion** method with DFTB3 **using** charge population analysis and optimally tuned range-separation parameters for the current state-of-the-art 3ob parameter set for organic molecules. We examined the applicability of this approach for organic crystals **using** the X23 benchmark set of molecular crystals and two highly polymorphic systems, ﬁnding encouraging results. The proposed method yields signi ﬁcantly improved geometries compared with bare DFTB, whereas energetics can still be improved. 52 We suggest to improve the lattice **energy** prediction by calculating single-point PBE+MBD energies on top of DFTB3+vdW geometries, which were found to be very close to the full DFT calculations. We identi ﬁed remaining issues in the DFTB description potentially stemming from the parametrization of the 3ob parameter set. As more suitable DFTB parametrizations become available, the here- presented approach will become even more eﬀective for complex molecular materials. Further studies are necessary to con ﬁrm the transferability of our results to other systems, such as carbon nanostructures, larger ﬂexible molecules, and hybrid organic −inorganic materials. Additionally, applications beyond structure search, such as the calculation of thermal corrections

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Keywords: Graphene; Plasmon; **Tight**-**Binding** **Model**
1. Introduction
Graphene, a single layer of carbon atoms arranged as a honeycomb lattice, is a semimetal with remarkable phy- sical properties [2,3]. This is due to the band structure of the material which consists of two bands touching each other at two nodes. The electronic spectrum around these two nodes is linear and can be approximated by Dirac cones. However, calculations of many physical proper- ties demand the knowledge of the full electron **dispersion** in the entire Brillouin zone, not only in the vicinity of the nodes. This statement becomes particularly relevant when we take into account the fact that graphene can be gated or doped, such that the Fermi **energy** can be freely tuned.

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18]. Nevertheless, very few interacting fermionic models that give rise to BF **theory** are available.
Here we make another step into the exploration of
interactions-driven phases of matter. Our starting point is a cubic lattice of spinless fermions. For particular val- ues of the couplings and in the absence of interactions the system becomes a chiral topological insulator [19]. Our approach is similar in spirit to Haldane’s Chern insula- tor [20], which gives us the ability to arbitrarily tune the asymmetry in the **energy** spectrum of the **theory**.

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The trends shown in Fig. 2 and the values of our fitted parameters in Table I are in general agreement with previ- ously published work. 8–14 What is unique to this study, how- ever, is that we show that a single TB parameter set can be used to **model** both AGNR and ZGNR systems. Without edge-hopping perturbation, the combination of the required AGNR and ZGNR parameters leads to a minimal, general- ized TB **model** 共set D, Table I兲 that adequately reproduces the band-structure features about the Fermi **energy** and gap trends of the ab initio results—note that the gaps for both the AGNR and ZGNR have been adequately obtained **using** the t 3 term 共 see also Refs. 10 and 14 兲 and the Hubbard U, re-

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Figure 1. Ab initio eigenvalues of the 6p states of the bismuth atom as a function of the spin–orbit strength computed **using** the FP-LAPW method and **using** TM and HGH pseudopotentials.
a millihartree for all pseudopotentials. The same spacing was used for the bismuth dimer, but in this case the simulation box was built by taking two spheres of radius 11.5 au centred around each atom. In the case of ABINIT, the wavefunctions are expanded in a plane-wave basis set and periodic boundary conditions are used in all cases. We found that an **energy** cut- off of 10 Ha and a super-cell of 50 ×50 × 50 au was necessary to fulfil the same convergence criteria. As for the FP-LAPW calculations, the radius of the muffin-tin spheres, R MT , was chosen to be 2.4 au, so that there were no overlapping spheres in our calculations. The plane-wave cut-off, k max , was chosen such that R MT k max =7.0. Finally, the size of the super-cell used was the same as for the ABINIT calculations.

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a) Electronic mail: a.horsfield@imperial.ac.uk
Here we formulate an extended DFTB approach including self-consistent polarized charges and polarization orbitals.
The electrostatic integrals are evaluated analytically for the chosen basis set by **using** Gaussian expansions, resulting in an internally consistent **theory** without the need for a fitting procedure. The resulting Gaussian **Tight** **Binding** (GTB) **model** gives molecular polarizabilities in excellent agreement with experimental data for hydrocarbons, having errors of the same order as DFT **using** the PBE 4 exchange- correlation functional. Various empirical extensions to **tight**- **binding** with a self-consistent description of ion polarizability have previously been formulated and tested, such as the polarizable-ion **tight**-**binding** **model**, 5,6 or parametrically extended DFTB 7–9 models. We present a systematically improvable **model** derived from first-principles within the DFTB formalism.

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2 Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin, Germany 共Received 27 January 2010; accepted 4 May 2010; published online 17 June 2010兲
We present numerical estimates of the leading two- and three-body **dispersion** **energy** terms in van der Waals interactions for a broad variety of molecules and solids. The calculations are based on London and Axilrod–Teller–Muto expressions where the required interatomic **dispersion** **energy** coefficients, C 6 and C 9 , are computed “on the fly” from the electron density. Inter- and intramolecular **energy** contributions are obtained **using** the Tang–Toennies 共TT兲 damping function for short interatomic distances. The TT range parameters are equally extracted on the fly from the electron density **using** their linear relationship to van der Waals radii. This relationship is empiricially determined for all the combinations of He–Xe rare gas dimers, as well as for the He and Ar trimers. The investigated systems include the S22 database of noncovalent interactions, Ar, benzene and ice crystals, bilayer graphene, C 60 dimer, a peptide 共Ala 10 兲, an intercalated drug-DNA **model** 关ellipticine-d共CG兲 2 兴, 42 DNA base pairs, a protein 共DHFR, 2616 atoms兲, double stranded DNA 共1905 atoms兲, and 12 molecular crystal polymorphs from crystal structure prediction blind test studies. The two- and three-body interatomic **dispersion** energies are found to contribute significantly to **binding** and cohesive energies, for bilayer graphene the latter reaches 50% of experimentally derived **binding** **energy**. These results suggest that interatomic three-body **dispersion** potentials should be accounted for in atomistic simulations when modeling bulky molecules or condensed phase systems. © 2010 American Institute of Physics. 关doi:10.1063/1.3432765兴

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computationally expensive and impractical even with the latest state-of-the-art computing resources. In this study, we therefore develop an efficient **model** in which a **tight**- **binding** Dirac equation (TBDE), calibrated with para- meters from the **tight**-**binding** π -bond **model** (TB- π ) [10-13], is used together with the non-equilibrium Green ’ s function approach (NEGF) [14] to investigate transport properties of GNRs. We compare the density of states, DOS(E), and the transmission, T(E), of selected GNR devices for our TBDE **model** with that of the more expen- sive TB- π **model**. Good agreement is found within the relevant **energy** range for flat band, Laplace and single barrier bias condition. We believe that our **model** and cali- brated data for a side selection of GNR widths presented in this article provided researchers in the quantum trans- port an accurate and practical framework to study the properties, particularly quantum transport in arbitrary bias conditions, of GNR-based devices.

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One particularly attractive feature of TD-DFT +TB is that it does not rely at all on the DFTB parametrization. The only parameters used for the construction of the TD-DFTB coupling matrix are the chemical hardness η A (for singlet excitations) and the magnetic Hubbard W A parameter (for triplet excitations). These are just physical properties of the atoms that can be calculated and tabulated for the entire periodic table. We use the chemical hardness as tabulated by Ghosh and Islam 47 and have calculated the values for the magnetic Hubbard parameter W A **using** the same details as specified earlier. 12 The numerical values of W A are given in Table I. All other parameters entering DFTB which are needed for describing the ground state, i.e., the form of the basis functions, the e ffective potential, and the repulsive potential needed for calculating the total **energy** and its gradients are not needed to build the TD-DFTB coupling matrix. TD- DFT +TB is therefore directly applicable to systems containing any combination of elements without the need of further parameterization.

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to induce rules at different levels of protein information including structure, sequence and molecular interactions.
Later, machine learning algorithms SVM and its ensemble are employed to combine energetic terms such as van der Waals potentials, solvation **energy**, hydrogen bonds and Coulomb electrostatics, and/or other protein sequences and structure information for a better hot spot prediction performance. Recently, Bayesian Networks are used to combine three main sources of information related to con- servation, FoldX-calculated G and atomic contacts for a novel probabilistic **model** of **binding** hot spots prediction [21]. Very recently, random forests have been proposed to predict hot spots [22] by **using** structural neighborhood properties of mutated residues and other conventional physicochemical features [23,24]. Besides alanine muta- tions, hot spots after mutations to any other type of residues are also investigated [6] and their **binding** free **energy** changes can be predicted [13,25] with good per- formance. Several of these methods are also assessed in a community-wide test for predicting mutation effects on protein-protein interaction affinity [26].

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Ames Laboratory, U. S. Department of **Energy**, Ames, Iowa 50011, USA
(Received 29 October 2018; revised manuscript received 25 January 2019; published 19 February 2019) **Using** a realistic **tight**-**binding** Hamiltonian based on maximally localized Wannier functions, we investigate the two-ion magnetocrystalline anisotropy **energy** (MAE) in L1 0 transition metal compounds. MAE contributions from throughout the Brillouin zone are obtained **using** magnetic force theorem calculations with and without perturbation **theory**. The results from both methods agree with each other, and both reflect features of the Fermi surface. The intrasublattice and intersublattice contributions to MAE are evaluated **using** a Green’s function method. We find that the sign of the intersublattice contribution varies among compounds, and that its amplitude may be significant, suggesting MAE can not be resolved accurately in a single-ion manner. The results are further validated by scaling spin-orbit-coupling strength in density functional **theory**. Overall, this realistic **tight**- **binding** method provides an effective approach to evaluate and analyze MAE while retaining the accuracy of corresponding first-principles methods.

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CONCLUSION
In this study, TD-LC-DFTB2 was implemented in conjunction with PCM in GAMESS- US based on an earlier implementation of an LC-DFTB2 method. 22 It was further used to compute excited-state energies and geometries. Analytic first-order derivatives were also implemented by employing the Z-vector method as in the well-known TD-DFT with long- range corrections. The exchange-type term was computed via eﬃcient matrix multiplications and, thus, the scaling of the (TD-)LC-DFTB was expected to be cubic as in the conven- tional (TD-)DFTB. Compared with the conventional DFTB2, LC-DFTB2 for the ground state was 1.4 times more computationally expensive, while TD-LC-DFTB2 for excited states was approximately three times more computationally expensive. However, a single-point gradient calculation for a system consisting of one thousand atoms took only 30 minutes (without PCM) with one CPU core, demonstrating the advantage of the TD-LC-DFTB2 method. Adding PCM increased the computation time significantly. As a pilot example, in the calculations for 3HF, which exhibits dual emission, TD-LC-DFTB2 predicted sim- ilar absorption and enol-form emission energies as TD-LC-BLYP/aug-cc-pVDZ; however, the predicted emission **energy** of the keto form deviated significantly from experiment and TD-LC-BLYP. Further benchmark calculations were performed **using** the other TD-DFTB methods implemented in GAMESS-US, TD-DFTB2, TD-DFTB3, and TD-LC-DFTB2, for a set of molecules that was previously collected and theoretically evaluated by Jacquemin et al. 24 Even though TD-LC-DFTB2 clearly overestimated the absorption and 0–0 transition energies when compared with the experimentally measured values, they agreed well with the results obtained by CAM-B3LYP and significantly reduced the computational cost. Further, when the range-separation parameter ω was decreased from 0.30 to 0.15, the results agreed even more closely with CAM-B3LYP. Therefore, based on these benchmark calculations, TD-LC-DFTB2 can be considered a computationally cost-eﬀective approximation of DFT with long-range corrections.

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2.3 Alpha particle
Calculate the mean **binding** **energy** per nucleon in the alpha particle.
According to the S-SET, the two protons and two neutrons are placed in vertices of square which diagonal is D = A + 4B, where A = 0.6974425 fm is the radius of the core of baryons, whereas B = 0.5018395 fm [1]. The D = 2.7048 fm defines radius of the last shell in baryons for strongly interacting pions [1]. There are 6 directions of strong interactions i.e. the 4 sides of the square and its two diagonal directions. It leads to conclusion that mean distance of strong interactions is

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