Hybrid Density Functional Theory Functionals Research Articles

A Visual Representation for Accurate Local Basis Set Construction and Optimization: A Case Study of SrTiO3 with Hybrid DFT Functionals

The linear combination of atomic orbitals (LCAO) method is advantageous for calculating important bulk and surface properties of crystals and defects in/on them. Compared to plane wave calculations and contrary to common assumptions, hybrid density functional theory (DFT) functionals are actually less costly and easier to implement in LCAO codes. However, choosing the proper basis set (BS) for the LCAO calculations representing Guassian-type functions is crucial, as the results depend heavily on its quality. In this study, we introduce a new basis set (BS) visual representation, which helps us (1) analyze the collective behavior of individual atoms’ shell exponents (s, p, and d), (2) better compare different BSs, (3) identify atom-type invariant relationships, and (4) suggest a robust method for building a local all-electron BS (denoted as BS1) from scratch for each atom type. To compare our BS1 with the others existing in the literature, we calculate the basic bulk properties of SrTiO3 (STO) in cubic and tetragonal phases using several hybrid DFT functionals (B3LYP, PBE0, and HSE06). After adjusting the exact Hartree–Fock (HF) exchange of PBEx, HSEx, and the state-of-the-art meta-GGA hybrid r2SCANx functionals, we find the r2SCAN15 and HSE27 for BS1, with the amount of exact HF exchange of 0.15 and 0.27, respectively, perform equally well for reproducing several most relevant STO properties. The proposed robust BS construction scheme has the advantage that all parameters of the obtained BS can be reoptimized for each new material, thus increasing the quality of DFT calculation predictions.

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat.

Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at the level of generalized gradient approximation (GGA), which is at the second rung of DFT functionals in terms of accuracy. Hybrid DFT functionals, which form the fourth rung in the accuracy ladder, are not commonly used in AIMD simulations as the computational cost involved is 100 times or higher. To facilitate AIMD simulations with hybrid functionals, we propose here an approach using multiple time stepping with adaptively compressed exchange operator and resonance-free thermostat, that could speed up the calculations by ∼30 times or more for systems with a few hundred of atoms. We demonstrate that by achieving this significant speed up and making the compute time of hybrid functional-based AIMD simulations at par with that of GGA functionals, we are able to study several complex condensed matter systems and model chemical reactions in solution with hybrid functionals that were earlier unthinkable to be performed.

Jahn–Teller distortion in Sr2FeO4: group-theoretical analysis and hybrid DFT calculations

We present theoretical justification for distorted Ruddlesden–Popper (RP) phases of the first-order by using hybrid density functional theory (DFT) calculations and group-theoretical analysis. We, thus, demonstrate the existence of the Jahn–Teller effect around an Fe^{4texttt {+}} ion in Sr_{2}FeO_{4}. On the calculation side, we have established a combination of Wu–Cohen (WC) exchange and Perdew-Wang (PW) correlation in a three-parameter functional WC3PW, giving the most accurate description of Sr_{2}FeO_{4} from the comparison of three hybrid DFT functionals. Self-consistently obtained Hartree–Fock exact exchange of 0.16 demonstrates consistent results with the experimental literature data. Importantly, we explain conditions for co-existing proper and pseudo-Jahn–Teller effects from the crystalline orbitals, symmetry-mode analysis and irreps products. Moreover, phonon frequency calculations support and confirm the results of symmetry-mode analysis. In particular, the symmetry-mode analysis identifies a dominating irreducible representation of the Jahn-Teller mode (X2+) and corresponding space group (SG) of ground state structure (SG Cmce model). Therefore, the usually suggested high-symmetry tetragonal crystal structure (SG I4/mmm model) is higher in energy by 121 meV/f.u. (equivalent to the Jahn-Teller stabilization energy) compared with the distorted low-symmetry structure (SG Cmce model). We also present diffraction patterns for the two crystal symmetries to discuss the differences. Therefore, our results shed light on the existence of low-symmetry RP phases and make possible direct comparisons with future experiments.

Electronic and optical properties of boron-containing GaN alloys: The role of boron atom clustering

Boron (B) containing III-nitride materials, such as wurtzite (wz) (B, Ga)N alloys, have recently attracted significant interest due to their ability to tailor the electronic and optical properties of optoelectronic devices operating in the visible and ultraviolet spectral range. However, the growth of high quality samples is challenging and B atom clustering is often observed in (B, Ga)N alloys. To date, a fundamental understanding of the impact of such clustering on the electronic and optical properties of these alloys is sparse. In this work, we employ density functional theory (DFT) in the framework of the meta-generalized gradient approximation [modified Becke Johnson (mBJ) functional] to provide insight into this question. We use mBJ DFT calculations, benchmarked against state-of-the-art hybrid functional DFT, on (B, Ga)N alloys in the experimentally relevant B content range of up to 7.4%. Our results reveal that B atom clustering can lead to a strong reduction in the bandgap of such an alloy, in contrast to alloy configurations where B atoms are not forming clusters, thus not sharing nitrogen (N) atoms. We find that the reduction in bandgap is linked mainly to carrier localization effects in the valence band, which stem from local strain and polarization field effects. However, our study also reveals that the alloy microstructure of a B atom cluster plays an important role: B atom chains along the wz c axis impact the electronic structure far less strongly when compared to a chain formed within the c-plane. This effect is again linked to local polarization field effects and the orbital character of the involved valence states in wz BN and GaN. Overall, our calculations show that controlling the alloy microstructure of (B, Ga)N alloys is of central importance when it comes to utilizing these systems in future optoelectronic devices with improved efficiencies.

Charge transfer and electronic relaxation effects in the photoemission of EMIM-DCA ionic liquid vapor

Ultraviolet photoelectron spectroscopy (UPS) measurements of EMIM-DCA vapors have been conducted. Density functional theory (DFT), Møller–Plesset perturbation theory (MP2) and many-body perturbation theory calculations (GW) have been used to interpret the experimentally measured spectra. The vapor of ionic liquids normally consists of isolated ion-pairs and the corresponding photoemission spectra should reflect the electronic binding energies of the molecular orbitals. The UPS spectra have revealed that many photolines are shifted when compared to ab initio calculation results. The hybrid DFT functionals, which performed very good in the description of the UPS spectra of many other ionic liquid vapors have shortcomings in the EMIM-DCA case. The MP2 calculation and the quasiparticle GW approach are shown to offer a better description of the experimental UPS spectra. The charge distribution analysis showed that there seems to be a favorable charge transfer from the cation to the anion upon ionization. The new data provides strong support to the argument that in some cases DFT still has difficulties in the modeling of IL ion-pairs.

Defect engineering in ZnIn2X4 (X=S, Se, Te) semiconductors for improved photocatalysis

ZnIn2S4 has emerged as a material of interest for semiconductor-based chalcogenide photocatalysts due to its visible light absorption, chemical and thermal stability, and low cost. However, the photocatalytic activity of ZnIn2S4 is affected by the limited range of visible light absorption and ultrafast recombination of solar light-induced holes and electrons. While previous studies have considered the consequences of metal doping, metal deposition, and vacancy engineering on the photocatalytic activity of ZnIn2S4, a comprehensive understanding of native point defects and how they affect electronic and photocatalytic properties remains elusive. Here, we present a density functional theory (DFT) investigation of defect energetics in ZnIn2X4 (X=S, Se, Te) compounds in both bulk and ultrathin phases. Using both semi-local and hybrid DFT functionals, properties of interest such as the electronic band gap and band edges, optical absorption spectra, and carrier mobilities are first computed for defect-free structures. Although ultrathin ZnIn2S4 shows lower absorption compared to other chalcogenides, it exhibits sufficient overpotential for oxidation and reduction reactions for photocatalytic water splitting. Formation energies of all possible vacancies, self-interstitials, and anti-site substitutional defects are then computed for all structures, as a function of chemical growth conditions, charge state, and Fermi level (EF), which leads to the identification of the lowest energy acceptor and donor type defects and their corresponding shallow or deep level nature. DFT results show that these metal sulfide photocatalysts are prone to ZnIn and InZn anti-site substitutions, which pin the equilibrium EF close to the conduction band edge, indicative of n-type conductivity. While ZnIn does not create deep defect levels in ZnIn2X4, most of the stable native defects do create deep levels, which could adversely affect solar absorption. Finally, we report the influence of defects on the photocatalytic hydrogen evolution reaction (HER) and oxygen evolution reaction (OER) on ultrathin ZnIn2X4. Our results suggest that a metal interstitial defect could substantially boost HER and OER on the surface of ultrathin ZnIn2X4. Overall, this systematic first principles investigation can help drive the experimental design and defect engineering of ZnIn2X4 compounds for a variety of photocatalytic applications.

Fragment-based approach for the efficient calculation of the refractive index of metal-organic frameworks.

Increasing demands on materials in the field of optical applications require novel materials. Metal-organic frameworks (MOFs) are a prominent class of hybrid inorganic-organic materials with a modular layout. This allows the fine-tuning of their optical properties and the tailored design of optical systems. In the present theoretical study, an efficient method to calculate the refractive index (RI) of MOFs is introduced. For this purpose, the MOF is split into disjoint fragments, the linkers and the inorganic building units. The latter are disassembled until metal ions are obtained. The static polarizabilities are calculated individually using molecular density functional theory (DFT). From these, the MOF's RI is calculated. To obtain suitable polarizabilities, an exchange-correlation functional benchmark was performed first. Subsequently, this fragment-based approach was applied to a set of 24 MOFs including Zr-based MOFs and ZIFs. The calculated RI values were compared to the experimental values and validated using HSE06 hybrid functional DFT calculations with periodic boundary conditions. The examination of the MOF set revealed a speed up of the RI calculations by the fragment-based approach of up to 600 times with an estimated maximal deviation from the periodic DFT results below 4%.

PREDICTION OF DIPROPYL SULFONE PROPERTIES BY DENSITY FUNCTIONAL THEORY METHODS: CONFORMATIONAL ANALYSIS AND SIMULATED IR SPECTRUM

In this work, the conformational and vibrational analysis of dipropyl sulfone in its isolated gaseous state with identification of all stable conformers, their energy and degeneracy, relative population determined by Boltzmann distribution, as well as IR spectra have been performed by density functional theory (DFT) methods. Several DFT methods and basis sets were tested. It was demonstrated that the various local and hybrid DFT functionals such as well-known B3LYP, regardless of the size of basis sets, completely fail in the prediction of correct molecular structures, let alone the IR spectra. It was found that only long-range corrected hybrid density functionals, combined with decently sized basis sets are capable to predict correct values of dihedral angles between non-bonded atomic groups: the most important coordinates in conformational analysis. Thus, wB97XD/6-311++G(2df,2pd) method/basis set combination appears to be the best method for the titled system both in terms of geometry and IR spectra prediction. A detailed analysis of the potential energy surface revealed the existence of 28 distinct conformers with various populations at 298 K, which have significant impact in the simulated IR spectra. The linear scaling equation (LSE) fitting methodology was successfully adopted for the calibration of wavenumbers and achievement of the best match between theoretical and experimental absorption regions of functional groups in sulfones. Moreover, in the construction of the simulated IR spectra, the Lorentzian broadening of each calculated mode with different full widths at half maximum was considered to obtain extinction coefficients, thus more realistic ε(ν) dependency, that is directly comparable with experimental spectra. The authenticity of the results obtained have been verified by comparison with existing experimental literature data on sulfones.

Excitons and light-emission in semiconducting MoSi2X4 two-dimensional materials

Semiconducting two-dimensional materials with chemical formula MoSi2X4 (X = N, P, or As) are studied by means of atomistic ground- and excited-state first-principles simulations. Full-fledged quasi-particle bandstructures within the G0W0 approach substantially correct the electronic bandgaps previously obtained with hybrid-functional density functional theory and highlight the absence of lateral valleys close in energy to the conduction band minimum. By solving the Bethe–Salpeter equation, we show that the optical properties are dominated by strongly bound excitons with the absorbance and maximum short-circuit current densities of MoSi2P4 and MoSi2As4 comparable to those of transition metal dichalcogenides. Due to the presence of the outer SiX layers, the exciton binding energies are smaller than those generally found for transition metal dichalcogenides. Long radiative lifetimes of bright excitons, over 10 ns at room temperature for MoSi2As4, and the absence of band-nesting are very promising for application in efficient ultra-thin optoelectronic devices.

Wide-range IR spectra of diarylethene derivatives and their simulation using the density functional theory

Diarylethenes (DAEs), promising photochromic molecular switches, undergo pericyclic reactions upon ultraviolet or visible light illumination. For this reason, most studies on DAEs employ UV–vis spectroscopies. However, also their infrared (IR) spectra are valuable, in particular, for understanding the vibrational dynamics which accompanies the relevant photoreactions. An accurate assignment of IR bands to molecular modes can be achieved through a comparison between experimental and computed theoretical spectra. Even though more sophisticated computational methods are available, the density functional theory (DFT) is usually employed for this task, because of its modest cost and versatility. Here, we have tested the ability of several DFT functionals to reproduce the wide-range, 400–3200 cm−1, IR spectra of open and closed isomers of four representative DAE molecules. We find that global and range-separated, corrected for anharmonicity by scaling factors, hybrid DFT functionals are able to reproduce the IR spectra of DAEs, however, instead of the popular B3LYP functional we propose the use of the dispersion-corrected PBE0 functional. The paper also proposes a semi-automatic method of band assignment.

Pathway of in situ polymerization of 1,3-dioxolane in LiPF6 electrolyte on Li metal anode

Although the lithium metal battery has been considered to be one of the most promising candidates to facilitate high-density energy storage, the practical applications of lithium metal anodes are significantly hindered by its high reactivity. Electrolytes based on 1,3-dioxolane (DOL) have been demonstrated to be one of the most effective electrolytes that can suppress side reactions, but the underlying mechanism is still far from clear. In this work, we carried out multi-scale simulations that combine density functional theory (DFT) and reactive force field (ReaxFF) to investigate the initial reactions of 1.0 M LiPF6 salt in DOL with Li metal anode. Our simulation results reveal that PF6− anions can either fully decompose via reduction reaction when they directly in contact with Li anode or convert to PF5 when they stay in bulk. While the decomposition products (F− and Px−) contribute to the formation of the inorganic part of the solid electrolyte interphase (SEI), the latter PF5 can serve as an initiator of the polymerization of DOL. Such polymerization of the electrolyte provides an unexpected protective effect that resembles the polymer electrolyte but is formed in situ. The most kinetically favorable polymerization pathway is then distinguished from hybrid functional DFT calculations, which confirms that PF5 plays an important role in activating the DOL ring for further polymerization. The insights revealed from this work should be of help to expedite the rational design of electrolytes that provide protective SEI to stabilize Li anode.

Accurate binding energies of ammonia clusters and benchmarking of hybrid DFT functionals

Investigation of the ammonia clusters has received much less attention in comparison to water clusters and methanol clusters. Although some studies have been reported on the structures and energetics of the ammonia clusters, no highly accurate ab-initio energetic study has been reported for the ammonia clusters. In this work, we have computed accurate binding energies of ten different isomers of small ammonia clusters at MP2/CBS, DLPNO-MP2/CBS, DLPNO-CCSD(T)/CBS and CCSD(T)/CBS levels of theory. The results show that the DLPNO-MP2/CBS binding energies excellently reproduce the MP2/CBS binding energies. The maximum deviation and the mean absolute deviation between these two sets of data are evaluated to be 0.17 cal and 0.09 cal, respectively. The same differences have been found between DLPNO-CCSD(T)/CBS and CCSD(T)/CBS levels of theory. In addition, we have used the calculated accurate binding energies as benchmark for ten functionals of the density functional theory (DFT). It comes out that the functional PW6B95D3 has the smallest mean absolute deviation. Thus, the functional PW6B95D3 is recommended for further affordable and accurate investigations of medium and large sized ammonia clusters.

Multifidelity Statistical Machine Learning for Molecular Crystal Structure Prediction.

The prediction of crystal structures from first-principles requires highly accurate energies for large numbers of putative crystal structures. High accuracy of solid state density functional theory (DFT) calculations is often required, but hundreds or more structures can be present in the low energy region of interest, so that the associated computational costs are prohibitive. Here, we apply statistical machine learning to predict expensive hybrid functional DFT (PBE0) calculations using a multifidelity approach to re-evaluate the energies of crystal structures predicted with an inexpensive force field. The method uses an autoregressive Gaussian process, making use of less expensive GGA DFT (PBE) calculations to bridge the gap between the force field and PBE0 energies. The method is benchmarked on the crystal structure landscapes of three small, hydrogen-bonded organic molecules and shown to produce accurate predictions of energies and crystal structure ranking using small numbers of the most expensive calculations; the PBE0 energies can be predicted with errors of less than 1 kJ mol-1 with between 4.2 and 6.8% of the cost of the full calculations. As the model that we have developed is probabilistic, we discuss how the uncertainties in predicted energies impact the assessment of the energetic ranking of crystal structures.

Benchmark studies on protonated benzene (BZH+) and water (Wn, n = 1–6) clusters: a comparison of hybrid DFT with MP2/CBS and CCSD(T)/CBS methods

The selection of a suitable density functional theory (DFT) method is critical to study the interfacial interactions between the protonated species and water clusters at the carbon surface. The interfacial interactions are crucial for the stability of complexes with the support of various kinds of noncovalent interactions. To model this environment, we consider excess proton with benzene [i.e., protonated benzene (BZH+)] and water clusters using high-level electronic structure calculations. These clusters were stabilized by different kinds of noncovalent interactions at the interface. Modeling these clusters is challenging as high-level electronic structure calculations are expensive, whereas less expensive DFT-based methods are inconsistent. Thus, in the present study, we have chosen various hybrid DFT functionals (such as B3LYP, PBE0, M05-2X, M06-2X, and M11) to study the geometries, energetics, and the importance of interfacial interactions. Furthermore, these methods performance is validated by using MP2/CBS and CCSD(T)/CBS approaches. It is found that the selected functionals are reliable to predict the structure, but the energetics of these clusters are varied. Also, each one of these methods has its own advantage in certain aspects. Scrutiny of result reveals that hybrid GGA (PBE0) and hybrid meta-GGA (M11) functionals are more consistent for the structure and stability with the benchmark obtained from MP2/CBS and CCSD(T)/CBS approaches. Besides, our benchmark report states that the selected DFT method can be suitable for the following individual interactions; (1) PBE0 suited for O–H+···O, O–H+···π and C–H+···O interactions, (2) M05-2X more suited for O–H···π, C–H···O, and (3) B3LYP method highly favor for the O–H+···O interactions (i.e., proton transfer). Overall, PBE0/aVTZ method has an excellent correlation with MP2/CBS and CCSD(T)/CBS methods based on our analysis using the mean signed error and correlation coefficient (r) analyses.

Multiband k·p model and fitting scheme for ab initio based electronic structure parameters for wurtzite GaAs

We develop a 16-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model for the description of wurtzite GaAs, together with a scheme to determine electronic structure parameters for multiband $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ models. Our approach uses low-discrepancy sequences to fit $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ band structures beyond the eight-band scheme to most recent ab initio data, obtained within the framework for hybrid-functional density functional theory with a screened-exchange hybrid functional. We report structural parameters, elastic constants, band structures along high-symmetry lines, and deformation potentials at the $\mathrm{\ensuremath{\Gamma}}$ point. Based on this, we compute the bulk electronic properties ($\mathrm{\ensuremath{\Gamma}}$ point energies, effective masses, Luttinger-like parameters, and optical matrix parameters) for a ten-band and a sixteen-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model for wurtzite GaAs. Our fitting scheme can assign priorities to both selected bands and $\mathbf{k}$ points that are of particular interest for specific applications. Finally, ellipticity conditions can be taken into account within our fitting scheme in order to make the resulting parameter sets robust against spurious solutions.

A New Route for Dioxygen Activation Uncovered from Quantum Mechanics Investigations of X‐Ray‐Diffraction‐Captured Intermediates of the Ferroxidase Reaction of Ferritins from Gram‐Negative Bacteria

AbstractFollowing the recent reassessment from X‐ray‐diffraction‐caught short‐path uptake to wide permeation of the S20A mutant Escherichia coli ferritin by ferrous ions, what happens when dioxygen gets to the diiron system is investigated. It is shown that the previously X‐ray‐caught situation of an unbound‐dioxygen diferrous state actually is an ephemeral state that changes into a P‐type peroxodiferric state, while a water molecule moves to bridge the two ferric ions, in what appears to be a remarkable redox process. All this stems from density functional theory (DFT)‐based quantum mechanics‐molecular mechanics and broken symmetry (BS) calculations that are extended to X‐ray‐diffraction‐caught oxodiferric and I‐type peroxodiferric systems from other subunits of the same crystal structure, validating them while determining antiferromagnetic coupling with all such diiron systems except the oxodiferric one. The latter converged, on BS, to ferromagnetic coupling under a wide variety of hybrid DFT functionals and basis sets. The trend of the Heisenberg J coupling reflects and substantiates the structures of the diiron core.

Defect states in monolayer hexagonal BN: A comparative DFT and DFT-1/2 study

Hexagonal boron nitride (h-BN) acts like a semiconductor vacuum to point defects enabling stable and controllable spin states at room temperature which qualifies them for quantum technological applications. To characterize their properties first-principles techniques constitute indispensable tools. The currently established paradigm for such solid-state electronic structure calculations is the density functional theory (DFT). Recently its variant, so-called DFT-1/2 method was introduced with the promise of accurate band gaps without a computational overhead with respect to ordinary DFT. Here, for the monolayer h-BN we contrast DFT and DFT-1/2 results for carbon substitutional impurities (CB, CN), boron and nitrogen single vacancies (VB, VN), divacancy, and Stone-Wales defects. Comparisons with more sophisticated, yet computationally costly techniques namely, hybrid functional DFT and the GW are also made, where available. From the standpoint of defect states embedded in the band gap region we demonstrate a clear advantage of DFT-1/2 in revealing the localized states otherwise buried within either the valence or conduction band continuum due to well-known gap underestimation syndrome of the standard DFT implementations. Thus, DFT-1/2 can serve for the rapid screening of candidate defect systems before more demanding considerations.

Space charge control of point defect spin states in AlN

One barrier to developing quantum information systems based on impurity point defects is that the desirable spin states of the defects are often unstable for Fermi levels obtained at increased impurity concentrations. The space charge induced band bending near the interface of Si/Mg aluminum nitride (AlN) homojunction is investigated computationally as a method to control the concentration, spin state, and position of such point defects. This is done by solving Poisson's equation with the charge density described by a grand canonical defect chemistry model informed by hybrid-functional density functional theory (DFT) calculations. Previous experimental works have found unintentional carbon and oxygen impurities pervade AlN homojunctions. First principles calculations have predicted the neutral complex between an aluminum vacancy and oxygen impurity on a neighboring nitrogen site (vAl-1ON)0 has a spin triplet configuration, which is stable in a region when the Fermi level is below midgap. From defect equilibrium simulations considering 602 possible defects, vAl-1ON was found to be unstable on the Mg-doped side of the homojunction and isolated oxygen impurities are preferred. On the Si-doped side, vAl-1ON forms but as (vAl-1ON)–2, not (vAl-1ON)0. This makes vAl-1ON a prototypical test case for the proposed strategy. Simulations of the Si/Mg:AlN homojunction showed (vAl-1ON)0 is stabilized within 6 nm of the interface in the Si-doped portion. This result indicates space charge induced band bending enables control over the concentration, spin state, and position of point defects, which is critical to realizing point defect based quantum information systems.

Structure of Electronically Reduced N-Donor Bidentate Ligands and Their Heteroleptic Four-Coordinate Zinc Complexes: A Survey of Density Functional Theory Results.

The role of Hartree-Fock exchange in describing the structural changes occurring upon reduction of bipyridine-based ligands and their complexes is investigated within the framework of density functional theory (DFT) calculations. A set of four free ligands in their neutral and radical anionic forms, and two of their zinc complexes in their dicationic and monocationic radical forms, is used to compare a large panel of pure, conventional, and long-range corrected hybrid DFT functionals; coupled cluster single and double calculations are used alongside experimental results as benchmarks. Particular attention has been devoted to the magnitude of the change, upon reduction, of the Δ-parameter, which measures the difference between the Cpy-Cpy and the C-N bond lengths in bipyridine ligand and is known to experimentally correlate with the charge of the ligands. Our results indicate that the structural changes significantly depend on the amount of exact exchange included in the functional. A progressive evolution is observed for the free ligands, whereas two distinct sets of results are obtained for the complexes. Functionals with a small degree of HF exchange, e.g., B3LYP, do not adequately describe geometric changes for the considered species, and, quite surprisingly, the same holds for the CC2 method. The best agreement to experimental and CCSD values is obtained with functionals that include a significant but not excessive part of exact exchange, e.g., CAM-B3LYP, M06-2X, and ωB97X-D. The calculated localization of the added electron after reduction, which depends on the self-interaction error, is used to rationalize these outcomes. Static correlation is also shown to play a role in the accurate description of the electronic structure.

Efficient ab initio analysis of quantum confinement and band structure effects in ultra-scaled Si1−xGex gate-all-around and fin field-effect transistors for sub-10 nm technology nodes

This paper analyzes the sub-10 nm ultra-scaled Si1−xGex fin field-effect transistor (FinFET) and gate-all-around transistor (GAAFET), based on an improved method by combining Slater partial occupation and ab initio density functional theory (DFT). Compared to the existing generalized gradient approximation (GGA) DFT, which is computationally efficient but inaccurate, and the established hybrid functional DFT, which is accurate but computationally demanding, the proposed method achieves both hybrid functional-like high accuracy and GGA-like high computational efficiency concurrently. By using this improved methodology, batch simulations are performed to investigate the size- and composition-dependent quantum confinement and band structure effects in the Si1−xGex FinFET and GAAFET. It is shown that the quantum confinement in ultra-scaled FinFET and GAAFET significantly increases the bandgap of Si1−xGex channel in the sub-10 nm scale. It is quantitatively demonstrated that, due to its two-dimensional quantum confinement, the ultra-scaled GAAFET has larger confinement-induced bandgap increase, lower direct source-drain quantum tunneling, lower off-state transmission and low-bias conductance, and smaller drain-induced barrier lowering, compared to the FinFET which is confined only in one-dimension. These differences jointly indicate that the ultra-scaled GAAFET could offer better device performance than the ultra-scaled FinFET. It is quantitatively shown that, by reducing the Ge composition of the Si1−xGex channel in ultra-scaled FinFET and GAAFET, the bandgap and the threshold gate voltage can be significantly increased; and the transmission coefficients, the low-bias conductance, and the source-drain current can be significantly reduced. These trends can be utilized to optimize device performance by tuning Ge composition in different technology nodes.