Density Functional Theory Electronic Structure Research Articles

Operando Condition Reaction Modeling Shows Highly Dynamic Attachment of Oligomeric Ruthenium Catalysts

To increase the stability and current density of molecular-catalyst-based electroanodes for water oxidation, immobilization of the catalysts at the electrode surface is a common strategy. A prominent example is the oligomerized Ru(tda) molecular catalyst, which showed outstanding current densities even at neutral pH values. One of the most challenging aspects of immobilized catalysts is to understand the interaction between the catalyst and the surface under operando conditions. Experiments are often performed under model conditions, and computational methods to study reaction steps are typically limited to a few hundred atoms. In this study, we combined three computational methods, density functional theory electronic structure computations, molecular dynamics for large-scale simulations of the catalyst–solid interaction, and empirical valence bond for reaction modeling the catalyst at the interface of a large carbon support and a phosphate water buffer. These techniques allowed us to explore the combined effects of solvent, hydrophobic directionality, and electric field on the attachment and reactivity of a Ru(tda) pentamer at a graphene surface. Our simulations have a perfect agreement with the experimental characterization under model conditions. However, we find that under operando conditions, where the catalyst is oxidized to the active RuV state, with a phosphate-containing electrolyte and an applied electric field, the attachment is completely reversed compared to the model conditions with RuII and organic solvents. This reversed attachment leads to a water-excluded region close to the active RuV═O center. The EVB reaction modeling showed that the reaction could still proceed to form an O–O bond via an oxide relay mechanism, where a dangling carboxylate reacts with the oxo via nucleophilic attack. We find that the activation energies are identical in water solution and at the electrode surface, showing how this mechanism is key to highly active molecular water oxidation catalysts immobilized on surfaces. Since attachment to surfaces could have a strong, and often negative, influence on the reactions, this study provides a guideline on how to model reactions without compromising the complexity of the electrode environment.

Theoretical prediction by DFT on properties of β′-SrTa2O6 crystal

Based on the Density Functional Theory (DFT) electronic band structure, state density, linear optics, elastic, dynamic and thermodynamic properties of ??-SrTa2O6 crystal with P4/mbm (No. 127) space group were investigated with the help of ABINIT and Wien2k code. In the study, it was found that the ??-SrTa2O6 crystal is classified as a semiconductor with an indirect bandgap. For this crystal, the dielectric function was obtained and optical constants such as energy loss function, extinction coefficient, absorption coefficient and reflectivity were calculated. The components of the elastic stiffness tensor, the phonon dispersion, the state density and the contribution of each atom to the state density were obtained. Finally, thermodynamic properties were determined for the ??-SrTa2O6 crystal. Furthermore, the changes in free energy (F), internal energy (E), entropy (S) and heat capacity (C) depending on the temperature were investigated.

Carissa macrocarpa extract (ECM) as a new efficient and ecologically friendly corrosion inhibitor for copper in nitric acid: Experimental and theoretical approach

BackgroundTo prevent metals from corroding faster, corrosion inhibitors form in the environmental medium and emerge at the right concentrations. The current inhibitors on the market have certain shortcomings. It is therefore necessary to find a new type of corrosion inhibitor that is cheaper, ecofriendly and effectively prevents corrosion. MethodsIn this work, an efficient and eco-friendly Carissa macrocarpa leaf extract (ECM) was investigated by weight loss and electrochemical measurement, subsequently; the surface morphology of copper treated with HNO3(with and without ECM) was characterized by SEM coupled with EDS and FTIR Analysis. In order to explore the adsorption potential and the reactive atomic regions of organic compounds in ECM, extensive theoretical explorations at electronic and atomic levels were carried out using electronic-structure density functional theory (DFT) and Monte Carlo (MC). Significant findingsThe experimental findings demonstrate the cathodic type inhibitory properties of the ECM, and the corrosion inhibition effect is above 91%. The mechanism of inhibition of Cu by ECM is described in detail. Furthermore, the ECM extract has good inhibitory efficiency over a broad temperature range, from 298 to 333 K. The computed thermodynamic parameters revealed that the extract's adsorb on the copper surface was spontaneous and under physico-chemical processes control. In addition, it is found that the activation complex is formed by the binding of Cu+ and ECM in the adsorption layer. Molecular modeling highly asserted the preference of the ECM extract molecules for adsorption onto the copper surface and DFT explorations emphasized that oxygen heteroatoms behaved as relevant local sites for molecular adsorption.

Bonding and Electronic Nature of the Anionic Framework in LaPd3S4

Double Dirac materials are a topological phase of matter in which a non-symmorphic symmetry enforces greater electronic degeneracy than normally expected – up to eightfold. The cubic palladium bronzes NaPd3O4 and LaPd3S4 are built of Pd3X4 (X = O, S) anionic frameworks that are ionically bonded to A cations (A = Na, La). These materials were recently identified computationally as harboring eightfold fermions. Here we report the preparation of single crystals and electronic properties of LaPd3S4. Measurements down to T = 0.45 K and in magnetic fields up to μ0H = 65 T are consistent with normal Fermi liquid physics of a Dirac metal in the presence of dilute magnetic impurities. This interpretation is further confirmed by analysis of specific heat, magnetization measurements and comparison to density functional theory (DFT) calculations. Through a bonding analysis of the DFT electronic structure of NaPd3O4 and LaPd3S4, we identify the origin of the stability of the anionic Pd3X4 framework at higher electron counts for X = S than X = O, and propose chemical tuning strategies to enable shifting the 8-fold fermion points to the Fermi level.

Electron and Hole Mobility of SnO2 from Full-Band Electron–Phonon and Ionized Impurity Scattering Computations

Mobility is a key parameter for SnO2, which is extensively studied as a practical transparent oxide n-type semiconductor. In experiments, the mobility of electrons in bulk SnO2 single crystals varies from 70 to 260 cm2V−1s−1 at room temperature. Here, we calculate the mobility as limited by electron–phonon and ionized impurity scattering by coupling the Boltzmann transport equation with density functional theory electronic structures. The linearized Boltzmann transport equation is solved numerically beyond the commonly employed constant relaxation-time approximation by taking into account all energy and momentum dependencies of the scattering rates. Acoustic deformation potential and polar optical phonons are considered for electron–phonon scattering, where polar optical phonon scattering is found to be the main factor which determines the mobility of both electrons and holes at room temperature. The calculated phonon-limited electron mobility is found to be 265 cm2V−1s−1, whereas that of holes is found to be 7.6 cm2V−1s−1. We present the mobility as a function of the carrier concentration, which shows the upper mobility limit. The large difference between the mobilities of n-type and p-type SnO2 is a result of the different effective masses between electrons and holes.

Ab initio studies on a highly luminescent and oxygen-sensitive Tb(III) complex with a 1,4,7-triazacyclononane-based tris-aryloxide ligand

The strongly luminescent and highly oxygen-sensitive Tb(III) complex [{(MeMeArO)3tacn}TbIII(THF)] (denoted hereafter as [1Tb THF]) was studied with density functional theory (DFT) and wavefunction-based ab initio electronic structure methods combined with Tb relativistic ab initio pseudopotentials. The optimized geometries as well as the calculated UV–vis absorption spectra at the DFT level agree well with the available experimental data. The calculated vertical S0*/5D4 → S0*/7FJ (ligand/Tb3+ states) emission energies for J = 0–6 at the RSPT2//CASSCF level including spin-orbit corrections are 475, 511, 549, 583, 614, 638, and 644 nm, respectively, and are lower by 15, 36, 39, 39, 39, 35, and 35 nm, respectively, than the corresponding experimental values. The luminescence quenching mechanism of [1Tb THF] in presence of O2 was investigated. RSPT2//CASSCF calculations for [1Tb THF]·O2 indicate that the S0*/7FJ (J = 0–6)/1O2 (1Δg or 1Σ+g) states (ligand/Tb3+/O2 states) are energetically more stable than the emission states S0*/5DJ (J = 0–4)/3O2 (3Σ-g). Therefore, after initial photo excitation of the ligand and subsequent energy transfer to the Tb3+ ion, the energy will be further transferred to O2 leading to the observed luminescence quenching of [1Tb THF] in air. A comparison is made to [1Sm THF]·O2 which shows a significantly smaller luminescence quantum yield and no oxygen quenching.

Modeling of Mg12O11–X (X = B, N, P and S) Nanostructured Materials as Sensors for Melamine (C3H6N6)

This research is focused on the sensor properties of pure and X-decorated ([Formula: see text], N, P and S) magnesium oxide (Mg[Formula: see text]O[Formula: see text]) nanocages for melamine (C3H6N6) molecule detection using density functional theory (DFT) electronic structure approach. Comparative adsorption study was carried out on four distinct computational models of hybrid functionals: [Formula: see text]B97XD, PBE0-D3BJ, M062X-D3BJ and DSDPBEP86 with the double-hybrid (DSDPBEP86), being the superior model at the fifth rung of the Jacobi’s ladder, was used as the reference. The atoms-in-molecule (AIM), alongside with the non-covalent interactions (NCIs) as visual extension had been utilized in the study of weak interactions and to affirm the degree of interactions between the clusters and the toxin. In all cases, this study suggests that the adsorption phenomena are best described as chemisorption due to the negative adsorption enthalpy observed. The mean absolute deviation (MAD) and root mean square deviation (RMSD) statistical approaches suggest the behavior of the possible adsorptions to be ranked as follows: PBE0-D3BJ (first rank), [Formula: see text]B97XD (second rank) and finally, M062X-D3BJ (third rank) with ([Formula: see text], 0.7870 and 0.8402) and ([Formula: see text], 0.8946 and 0.9560), respectively. These results are consistent with those of the topological and the sensing parameters, hence, arriving at a conclusive scientific report that Mg[Formula: see text]O[Formula: see text] and Mg[Formula: see text]PO[Formula: see text] surfaces exhibit relatively better sensing performances for the trapping of melamine (MB).

Shortening the screening process towards high-performance 2D-MOF NRR electrocatalysts with [formula omitted] as the descriptor of N2 activation capability

Developing efficient and light pollution electrocatalytic nitrogen reduction reaction (NRR) method for dinitrogen (N2) fixation is a very important and challenging issue in the field of energy and environment. However, the existing multiple-step screening methods for NRR electrocatalysts are inefficient, and it is urgent to search for suitable descriptor to shorten screening process. Herein, by density functional theory (DFT) calculation, the structures, electronic structures and NRR activity of TM3C24X12 (TM-X MOF, TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, and Mo, X = NH, and S) are investigated, and a descriptor relevant to magnetism Δ(μB_TM-μB_X) is proposed. An “inverted-volcano” relationship between Δ(μB_TM-μB_X) and ΔGN2→NNH reflects direct relevancy between the descriptor and N2 activation capability, leading the way to the two-step screening method. Mo-S MOF is predicted to be the best among catalysts prefer end-on N2 adsorption according to the descriptor, which is verified via a modified three-step screening method, showing that Mo-S MOF has a low limiting potential of −0.41 V and a satisfying activation energy of 0.85 eV in the determining step. The descriptor provides new thoughts for revealing the activity mechanism of 2D-MOF catalysts shortening the screening steps, and finding high-performance catalysts.

Synthesis and characterization of a novel colorimetric and fluorometric probe “Turn-on” for the detection of Cu2+ of derivatives rhodamine

A new Rhodamine-based “Turn On” fluorescent probe (E)- 3′,6′-bis(diethylamino)-2-((2,5-dimethoxybenzylidene)amino)spiro[isoindoline-1,9′-xanthen]-3-one (WGB) was synthesized. Results show that WGB is selective for Cu2+ cations, forming a WGB-Cu2+ complex in a 2:1 stoichiometry, confirmed through density functional theory (DFT) electronic structure calculations and reactive molecular dynamics (MD) simulations. Theoretical calculations agreed with the experimental data. The detection limit of WGB-Cu+2 complex is 6.76 × 10-8 M. Preliminary studies employing epifluorescence microscopy demonstrate that Cu2+ can be imaged in neuroblastoma SH-SY5Y cells treated with WGB.

The role of crystal packing on the optical response of trialkyltetrelethynyl acenes.

The electronic and optical responses of an organic semiconductor (OSC) are dictated by the chemistries of the molecular or polymer building blocks and how these chromophores pack in the solid state. Understanding the physicochemical nature of these responses is not only critical for determining the OSC performance for a particular application, but the UV/visible optical response may also be of potential use to determine aspects of the molecular-scale solid-state packing for crystal polymorphs or thin-film morphologies that are difficult to determine otherwise. To probe these relationships, we report the quantum-chemical investigation of a series of trialkyltetrelethynyl acenes (tetrel = silicon or germanium) that adopt the brickwork, slip-stack, or herringbone (HB) packing configurations; the π-conjugated backbones considered here are pentacene and anthradithiophene. For comparison, HB-packed (unsubstituted) pentacene is also included. Density functional theory and G0W0 (single-shot Green's function G and/or screened Coulomb function W) electronic band structures, G0W0-Bethe-Salpeter equation-derived optical spectra, polarized ϵ2 spectra, and distributions of both singlet and triplet exciton wave functions are reported. Configurational disorder is also considered. Furthermore, we evaluate the probability of singlet fission in these materials through energy conservation relationships.

Insights into the aftereffects phenomenon in solids based on DFT and time-differential perturbed γ−γ angular correlation studies in 111In (→ 111Cd) -doped tin oxides

Recently, a model based on a combined ab initio/time-differential perturbed $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ angular correlation (TDPAC) study in the $^{111}\mathrm{In}(\ensuremath{\rightarrow}^{111}\mathrm{Cd})$-doped ${\mathrm{SnO}}_{2}$ semiconductor was proposed to enlighten the origin of the dynamic hyperfine interactions (HFIs) observed in oxides after the electron-capture (EC) decay of the probe nucleus of the $^{111}\mathrm{In}$ parent. It was demonstrated that both the EC as well as the acceptor level introduced by the Cd impurity can contribute to the variation of the electric-field gradient (EFG) at the Cd site (responsible for this phenomenon) due to charge fluctuations of the electronic holes created [Darriba et al., J. Phys. Chem. C 122, 17423 (2018)]. To disentangle both effects, we performed here TDPAC reversible experiments in $^{111}\mathrm{In}(\ensuremath{\rightarrow}^{111}\mathrm{Cd})$-doped SnO in the temperature range 20--900 K and a complete electronic structure density functional theory study of the Cd-doped SnO system as a function of the charge state $(q)$ of the impurity. The isovalent $^{111}\mathrm{Cd}$ probe impurity in this isocationic oxide was selected to demonstrate that the acceptor character of the probe is not a necessary condition to observe this electronic phenomenon when the EC is already present. A majority fraction of probes sensed a time-dependent HFI (HFI1) for all temperatures, and the unexpected minority always sensed a static interaction (HFI2). Comparing results from these experiments, the ab initio calculations of the EFG tensor and defect formation energies, HFI1 and HFI2, were assigned to $^{111}\mathrm{Cd}$ probes localized at substitutional Sn sites free of defects [with the valence band (VB) completely filled, $q=0$] and with an electronic hole trapped $(q=1+)$, respectively. In addition, we show that the systems with charge state between these values have very similar formation energies at the top of the VB and different predicted EFGs, giving support from first principles to the existence of random fluctuations between different EFGs, necessary in the construction of the on-off perturbation factor used. We demonstrate that all the probes fill their electronic holes before the TDPAC time window except the outermost one, giving a quantification of the number of electronic holes involved in the production of the dynamic effect, only one in SnO. The probes related to HFI2 reach their stable electronic configuration $(q=1+)$ before the emission of the first \ensuremath{\gamma} ray $({\ensuremath{\gamma}}_{1})$ of the \ensuremath{\gamma}-\ensuremath{\gamma} cascade, while those related to HFI1 fill the last hole after the emission of ${\ensuremath{\gamma}}_{1}$, producing the dynamic interaction. Enlighted by these results and reviewing TDPAC experiments from the literature using probes with different nuclear decay characteristics, we concluded that, in the absence of EC decay of the probe nucleus of the parent, any probe impurity introducing acceptor or donor states (in semiconductors and insulators) whose ionization changes the EFG should observe a time-dependent HFI provided the lifetime of the nuclear levels that feed the ${\ensuremath{\gamma}}_{1}$ level and this level itself is shorter than the lifetime of the recovery process (i.e., the lifetime of the electronic holes or the ionized donor electrons).

The Lanthanide Contraction Is a Variable.

Upon examination of the bond distances of the recently reported series of [Ln(SST)3(THF)2] [Ln = lanthanides, SST = tris(trimethylsilyl)siloxide (OSi(SiMe3)3), and THF = tetrahydrofuran] compounds, it was found that over the Ln-series (La through Lu), the Ln-O(THF) bond changed by 0.257 Å, whereas the Ln-O(SST) bond varied by 0.164 Å. Examination of all similarly ligated Ln-O(THF) (Ln = La vs Lu) structures available in the Cambridge Structural Database (CSD) revealed that this previously unreported, increased Ln-contraction is pervasive. Further evaluations showed that this enhanced Ln-contraction also occurs for pyridine (py) in the [Ln(SST)3(py)2] family as well as the average Ln-N(py) (La vs Lu) structure distances recovered from the CSD. Additional ligands, such as halides (Cl and I) were found to display this enhanced Ln-contraction, while other species (i.e., cyclopentadienide, alkoxide, SST, and dimethyl sulfoxide) yielded a "normal" Ln-contraction (La-L vs Lu-L). Gas-phase electronic structure density functional theory calculations were carried out to evaluate the molecular orbital influence on the Ln-contraction between Ln-O(SST) and Ln-O(THF). The calculated [Ln(SST)3(THF)2] structures were found to demonstrate the same capricious Ln-contraction. Based on these studies, one can say that the variability of the Ln-contraction noted in the [Ln(SST)3(THF)2] experimental data is due to the different bonding types, ion-ion for the Ln-SST bond versus ion-dipole for the Ln-THF bond.

Dynamical Mean Field Studies of Infinite Layer Nickelates: Physics Results and Methodological Implications

This article summarizes recent work on the many-body (beyond density functional theory) electronic structure of layered rare-earth nickelates, both in the context of the materials themselves and in comparison to the high-temperature superconducting (high-Tc) layered copper-oxide compounds. It aims to outline the current state of our understanding of layered nickelates and to show how the analysis of these fascinating materials can shed light on fundamental questions in modern electronic structure theory. A prime focus is determining how the interacting physics defined over a wide energy range can be estimated and “downfolded” into a low energy theory that would describe the relevant degrees of freedom on the ∼0.5 eV scale and that could be solved to determine superconducting and spin and charge density wave phase boundaries, temperature dependent resistivities, and dynamical susceptibilities.

On the conformational equilibria between isobutyl halide (CH3)2CH–CH2X (X=Cl, Br and I) rotational isomers: A combined ultrasonic relaxation spectroscopic and computational study

In this study, ultrasonic relaxation spectroscopy and molecular orbital calculations have been used to investigate the rotational-isomeric equilibria in isobutyl halide (CH3)2CH–CH2X (X = Cl, Br and I) liquids as a function of frequency and temperature under isobaric conditions. The sound absorption in the a/f2 representation appeared to deviate from straight line with frequency in the MHz region revealing a single Debye-type relaxation process, which is attributed to thermal relaxation of a rotational isomeric equilibrium for all isobutyl halide systems. From the temperature dependence of the relaxation parameters, the associated thermodynamic parameters and the respective volume changes were estimated for each liquid and discussed in view of the outcome of density functional theory electronic structure calculations. The activation enthalpy was found to be strongly dependent on the ionic radius of the halide. Furthermore, the lower energy state of all isobutyl halide systems is two-fold degenerate. The experimental results indicate that a shear viscosity relaxation is questionable in the frequency region covered in this work. The observed-to-classical absorption ratio α/αcl and the volume-to-shear viscosity ratio nV/ns have been evaluated and used as a measure to monitor the strength of the intermolecular bonding. The values and the strong temperature dependence of these ratios are typical of a relaxation process associated to rotational isomers equilibrium. The results have been discussed in the context of inter- and intra-molecular interactions.

Ferromagnetic helical nodal line and Kane-Mele spin-orbit coupling in kagome metal Fe3Sn2

The two-dimensional kagome lattice hosts Dirac fermions at its Brillouin zone corners K and K', analogous to the honeycomb lattice. In the density functional theory electronic structure of ferromagnetic kagome metal Fe$_3$Sn$_2$, without spin-orbit coupling we identify two energetically split helical nodal lines winding along $z$ in the vicinity of K and K' resulting from the trigonal stacking of the kagome layers. We find that hopping across A-A stacking introduces a layer splitting in energy while that across A-B stacking controls the momentum space amplitude of the helical nodal lines. The effect of spin-orbit coupling is found to resemble that of a Kane-Mele term, where the nodal lines can either be fully gapped to quasi-two-dimensional massive Dirac fermions, or remain gapless at discrete Weyl points depending on the ferromagnetic moment orientation. Aside from numerically establishing Fe$_3$Sn$_2$ as a model Dirac kagome metal, our results provide insights into materials design of topological phases from the lattice point of view, where paradigmatic low dimensional lattice models often find realizations in crystalline materials with three-dimensional stacking.

A radical mechanism for C–H bond cross-coupling and N2activation catalysed by β-diketiminate iron complexes

Density functional theory calculations and electronic structure analyses reveal a radical mechanism with spin-crossovers for C–H bond cross-coupling and N2activation catalysed by β-diketiminate iron complexes.

Evolution of atomic and electronic structures of Cun (n = 2–10) clusters supported on anatase TiO2(1 0 1) surface

Based on extensive structural search and density functional theory (DFT) calculations, the atomic and electronic structures of of Cun (n = 2–10) clusters supported on anatase TiO2(101) surface (denoted as Cun/A(101)) are systematically studied. The atomic structures exhibit obvious hereditary feature, i.e. most of the low-energy structures of larger clusters can be obtained by adding additional Cu atoms onto those of smaller clusters. Small sized clusters (n ≤ 6) prefer to quasi planar structures while large sized clusters (n > 6) prefer to complex three-dimensional structures. The thermodynamic stabilities of the supported Cun clusters are investigated by calculating the binding energies, second order energy difference, adsorption energies and nucleation energies. It is found that Cu3/A(101), Cu5/A(101), and Cu8/A(101) are particularly stable and Cu3, Cu5 and Cu9 clusters would be stabilized by the substrate mostly. All these Cun clusters can introduce in-gap states and reduce the band gaps according to the calculated density of states. Supported Cun clusters play the role of electron donor, resulting in partial oxidation state Cuδ+ and zero valence state Cu0.

Effect of Point Defects on Electronic Structure of Monolayer GeS.

Using density functional theory calculations, atomic and electronic structure of defects in monolayer GeS were investigated by focusing on the effects of vacancies and substitutional atoms. We chose group IV or chalcogen elements as substitutional ones, which substitute for Ge or S in GeS. It was found that the bandgap of GeS with substitutional atoms is close to that of pristine GeS, while the bandgap of GeS with Ge or S vacancies was smaller than that of pristine GeS. In terms of formation energy, monolayer GeS with Ge vacancies is more stable than that with S vacancies, and notably GeS with Ge substituted with Sn is most favorable within the range of chemical potential considered. Defects affect the piezoelectric properties depending on vacancies or substitutional atoms. Especially, GeS with substitutional atoms has almost the same piezoelectric stress coefficients as pristine GeS while having lower piezoelectric strain coefficients but still much higher than other 2D materials. It is therefore concluded that Sn can effectively heal Ge vacancy in GeS, keeping high piezoelectric strain coefficients.

Deformation potential extraction and computationally efficient mobility calculations in silicon from first principles

We present a first-principles framework to extract deformation potentials in Silicon based on density-functional theory (DFT) and density-functional perturbation theory (DFPT). We compute the electronic band structures, phonon dispersion relations, and electron-phonon matrix elements to extract deformation potentials for acoustic and optical phonons for all possible processes. The matrix elements clearly show the separation between intra- and inter-valley scattering in the conduction band, and quantify the strength of the scattering events in the degenerate bands of the valence band. We then use an advanced numerical Boltzmann transport equation (BTE) simulator that couples DFT electronic structures and energy/momentum-dependent scattering rates to compute the transport properties for electrons and holes. By incorporating ionized impurity scattering as well, we calculate the n-type and p-type mobility versus carrier density and make comparisons to experiments, indicating excellent agreement. The fact that the method we present uses well-established theoretical tools and requires the extraction of only a limited number of matrix elements, makes it generally computationally very attractive, especially for semiconductors with a large unit cell and lower symmetry.

First-principles theory for Schottky barrier physics

We develop a first-principles theory for Schottky barrier physics. The Poisson equation is solved completely self-consistently with the electrostatic charge density and outside the normal density functional theory (DFT) electronic structure iteration loop, allowing computation of a Schottky barrier entirely from DFT involving thousands of atomic layers in the semiconductor. The induced charge in the bulk consists of conduction and valence band charges from doping and band bending, as well as charge from the evanescent states in the gap of the semiconductor. The Schottky barrier height is determined when the induced charge density and the induced electrostatic potential reach self-consistency.