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Chiroptical properties of helical polymers do not always align with the sum of the local contributions of their unit cells. This study investigates the discrepancy in optical rotatory strength between local and global structures using a right‐handed helical polyacetylene model. The chirality is examined through density functional theory (DFT) calculations. The analysis reveals that, at higher degrees of polymerization, the contribution of chirality from the helical strand generally surpasses the partial chirality from the local structure. The ratio of local contribution to total contribution is deduced within the framework of crystal orbital theory, and a numerical method using Wannier functions is presented for evaluation. [ABSTRACT FROM AUTHOR]

Electron-phonon coupling (EPC) in bulk materials is an important effect in multifarious physical and chemical phenomena. It is the key to explaining the mechanisms for superconductivity, electronic transport, etc. The EPC matrix describes the coupling of the electronic eigenstates of the studied system under the perturbation of phonons. Although the EPC matrix is closely relevant to many fundamental physicochemical properties, it remains a challenge to calculate the EPC matrix precisely due to the high computational cost. In recent years, Giustino et al. developed the EPW method on open-source ab-initio software Quantum Espresso, which uses Wannier functions (WFs) to calculate EPC matrix. However, due to the limitation of their implementation, it is not possible yet to calculate the EPC matrix under some important computational conditions, e.g., for DFT+U and HSE calculation. Given the importance of these computational conditions (e.g., for transition metal oxides), we have developed our own implementation of EPC matrix calculation based on the domestic ab-initio software PWmat. Our code allows the DFT+U and HSE correction, so we can get a more accurate EPC matrix in the related problems. In this article, we will first review the formulae and elucidate how to calculate the EPC matrix by constructing WFs. Then we will introduce our code along with its workflow on PWmat and present our test results of two classical semiconductor systems AlAs and Si, showing consistency with EPW. Next, the EPC matrix of LiCoO2, a classical cathode material for lithium-ion batteries, is calculated using different exchange correlation (XC) functionals including LDA, PBE, DFT+U and HSE. A comparison is provided for the related EPC matrix. It shows there could be a significant difference for the EPC matrix elements due to the use of different XC functionals. Our implementation thus opens the way for fast calculation of EPC for the important class of materials, like the transition metal oxides. [ABSTRACT FROM AUTHOR]

In this paper, a novel theory of optical activities for helical polymers has been formulated using crystal orbital methods under periodic boundary conditions. The selection rule of the optical transition was determined in the reciprocal space based on the helical angle of the unit cells. The optical rotatory strength was estimated using Wannier functions, which can be chosen to be real localized orbitals. Contrary to conventional exciton models, the structural parameters of helical polymers can be easily reflected in actual calculations of the optical rotatory strength within the crystal orbital framework. The theory was confirmed by evaluating the optical rotatory strength of a right-handed helical polyacetylene. This approach provides a promising method to evaluate the optical activities of helical polymers with itinerant electrons. [ABSTRACT FROM AUTHOR]

Two methods for calculating transport parameters in semiconductor superlattices by applying Green’s functions are compared in the paper. For one of the methods, the Wannier functions method, where computations in the complex space and Wannier functions base are required, the Hamiltonian matrix is small in size and its elements depend solely on the energy. For the real space method, as it operates in the floating point domain and uses the Hamiltonian containing the elements dependent both on energy and position, the Hamiltonian matrix is larger in size. The size makes the method computationally challenging. To find the consequences of choosing one of the methods, a direct comparison between the computations, obtained for both methods with the same input parameters, was undertaken. The differences between the results are shown and explained. Selected simulations allowed us to discuss advantages and disadvantages of both methods. The calculations include transport parameters such as the density of states and the occupation functions, with regard to scattering processes where the self-consistent Born approximation was used, as well as the spatial distribution of electron concentration for two superlattices structures. The numerical results are obtained within the non-equilibrium Green’s functions formalism by solving the Dyson and the Keldysh equations.

Chemical bonding in compound semiconductors Be–IV–P2 (IV = C, Si, Ge, Sn) is considered using Wannier functions calculated for all valence states. [ABSTRACT FROM AUTHOR]

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis. [ABSTRACT FROM AUTHOR]

In this paper, the crystal field parameters (CFPs) have been calculated in the framework of the density functional theory using a novel theoretical approach proposed by Pavel Novák et al. and extracting the WANNIER functions from the Bloch eigenstates for the CeCl3 compound. Then, the calculated CFPs have been used in an effective atomic-like Hamiltonian, including the crystal field, 4f-4f correlation and spin-orbit coupling, and the splitted energy levels of Ce3+ ion by crystal field have been derived by diagonalization of the Hamiltonian. A hybridization parameter, , has been used to improve the results. The results are found to be in agreement with the experimental data

Twisted multi-layer heterostructures have been considered a platform for studying highly correlated many-particle systems, hosting the emerging phenomena of correlation physics. Electronic structure calculations of such materials which mainly focused on Twisted Bilayer Graphene (TBG) in the framework of the independent-electron approximation, despite the complexity, accurately match the experimental results around the Fermi level. Here, we present a convenient real space π -bands tight-binding model to calculate the band structure of TBG based on the Wannier interlayer hopping parameters obtained from non-twisted bilayer graphene. Our approach is based on mapping hopping parameters onto the real space TBG interlayer couplings, using Radial Basis Function (RBF) interpolation method. This accurate mapping, naturally, transfers all the symmetries and orbital shape features of the bilayer graphene lattice to the TBG lattice and preserves coupling orientation dependencies in addition to distance dependencies. The importance of this fact is explained by showing the effect of the threefold rotation symmetry of AB ′ interlayer coupling on the flat band of the TBG band structure. In addition, due to real space study, the model gives us a comprehensive and intuitive view of the role of each interlayer orbital coupling in the TBG band structure and the structural variation relative to twisting. • A real space tight-binding model for twisted bilayer graphene (TBG) based on Wannier hopping parameters. • π -band ab-initio tight-binding model of twisted bilayer graphene. • Wannier hopping mapping on twisted bilayer graphene structure using RBF interpolation. • Studying the flat band in the band structure based on sublattice couplings in twisted bilayer graphene. • The effect of the threefold rotation symmetry of AB interlayer coupling on the flat band of the TBG band structure. [ABSTRACT FROM AUTHOR]

Gapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved, either these Wannier functions are exponentially localized, as it happens whenever the Hamiltonian operator is time-reversal symmetric, or they are delocalized in the sense that the expectation value of |x|^2 diverges. In- termediate regimes are forbidden. Following the lesson of our Maestro, to whom this contribution is gratefully dedicated, we find useful to explain this subtle mathematical phenomenon in the simplest possible model, namely the discrete model proposed by Haldane [13]. We include a pedagogical introduction to the model and we explain its Localization Dichotomy by explicit analytical arguments. We then introduce the reader to the more general, model-independent version of the dichotomy proved in [22].

The multi-sublattice magnetism and electronic structure in double-double perovskite compound CaMnCrSbO 6 is explored using density functional theory. The bulk magnetization and neutron diffraction suggest a ferrimagnetic order (TC∼49 K) between between Mn 2+ and Cr 3+ spins. Due to the non-equivalent Mn atoms (labelled as Mn(1) and Mn(2) which have tetrahedral and planar oxygen coordinations, respectively) and the Cr atom in the centre of distorted oxygen octahedron in the unit cell, the exchange interactions are more complex than that expected from a two sublattice magnetic system. The separations between the on-site energies of the d -orbitals of Mn(1), Mn(2) and Cr obtained from Wannier function analysis are in agreement with their expected crystal field splitting. While the DOS obtained from non spin-polarized calculations show a metallic character, starting from Hubbard U  = 0 eV the spin-polarized electronic structure calculations yield a ferrimagnetic insulating ground state. The band gap increases withUeff( U  -  J ), thereby showing a Mott-Hubbard nature of the system. The inclusion of anti-site disorder in the calculations show decrease in band-gap and also reduction in the total magnetic moment. Due to the ∼90 ∘ superexchange, nearest neighbour exchange constants obtained from DFT are an order of magnitude smaller than those reported for various magnetic perovskite and double-perovskite compounds. The Mn(1)-O-Mn(2) (out of plane and in-plane), Mn(1)-O-Cr and Mn(2)-O-Cr superexchange interactions are found to be anti-ferromagnetic, while the Cr-O-O-Cr super-superexchange is found to be ferromagnetic. The Mn(2)-O-Cr superexchange is weaker than the Mn(1)-O-Cr super-exchange, thus effectively resulting in ferrimagnetism. From a simple 3-site Hubbard model, we derived expressions for the antiferromagnetic superexchange strengthJAFMand also for the weaker ferromagneticJFM. The relative strengths ofJAFMfor the various superexchange interactions are in agreement with those obtained from DFT. The expression for Cr-O-O-Cr super-superexchange strength (J~SS), which has been derived considering a 4-site Hubbard model, predicts a ferromagnetic exchange in agreement with DFT. Finally, our mean field calculations reveal that assuming a set of four magnetic sub-lattices for Mn 2+ spins and a single magnetic sublattice for Cr 3+ spins yields a much improved T C , while a simple two magnetic sublattice model yields a much higher T C ., (© 2024 IOP Publishing Ltd.)

• The examined hydrogen transfer does not involve stable intermediates. • The electron transfer results in a loss of electron density from the π orbital. • The SI error is responsible for underestimation of the reaction timescales. Understanding the basic chemistry between highly reactive free radicals and dopamine is an important step in characterizing the antioxidative activity of catecholamine neurotransmitters. In this work, we simulated the reactions between dopamine and hydroxyl, peroxyl and methoxy radicals in aqueous solution by employing first principle molecular dynamics based on density functional theory and the BLYP functional. The simulations provide mechanistic insight into the reaction mechanisms but underestimate reaction timescales. The failure of the BLYP functional to address the formal hydrogen atom transfer barriers between dopamine and free radicals is attributed to the self-interaction error. [ABSTRACT FROM AUTHOR]

Highlights • A capped (5,5) carbon nanotube has been analysed by the linear-scaling DFT code ONETEP. • The charge distribution varies very little with external fields, showing screening. • The calculation reports details of individual Kohn-Sham orbitals. • The highest occupied orbital and its distribution change with applied field. • The work function is part of an energy change from the cores, due to many-electron effects. Abstract The apex region of a capped (5,5) carbon nanotube (CNT) has been modelled with the DFT package ONETEP, using boundary conditions provided by a classical calculation with a conducting surface in place of the CNT. Results from the DFT solution include the Fermi level and the physical distribution and energies of individual orbitals for the CNT tip. Application of an external electric field changes the orbital number of the highest occupied molecular orbital (HOMO) and consequently changes its distribution on the CNT. [ABSTRACT FROM AUTHOR]

We study properties of an infinite system of discrete nonlinear Schrödinger equations that is equivalent to a coupled Schrödinger-elliptic differential equation with periodic coefficients. The differential equation was derived as a model for laser beam propagation in optical waveguide arrays in a nematic liquid crystal substrate and can be relevant to related systems with nonlocal nonlinearities. The infinite system is obtained by expanding the relevant physical quantities in a Wannier function basis associated to a periodic Schrödinger operator appearing in the problem. We show that the model can describe stable beams, and we estimate the optical power at different length scales. The main result of the paper is the Hamiltonian structure of the infinite system, assuming that the Wannier functions are real. We also give an explicit construction of real Wannier functions, and examine translation invariance properties of the linear part of the system in the Wannier basis.

The recent discovery of superconductivity in infinite-layer Sr-doped NdNiO 2 grown on SrTiO 3 (001) provides a new platform to explore the conducting mechanism of unconventional superconductors. However, the electronic structure of infinite-layer nickelates remains controversial. In this paper, we systematically compare the structural and electronic properties of NdNiO 2 films grown on SrTiO 3 and LaAlO 3 substrates using first-principles calculations. Our results show that the lattice reconstruction accompanied by electronic reconstruction occurs in nickelate films on both substrates. Although both heterostructures (HSs) are conducting at the interface, the SrTiO 3 -based HS shows distinct atomic displacement in the interfacial TiO 2 layer and significant electron accumulation deep into three SrTiO 3 layers below the interface, while the LaAlO 3 -based HS shows negligible atomic displacement and electron localization in the interfacial AlO 2 layer, reflecting the impact of polarity mismatch on the electronic structure. Further, Wannier function calculations reveal that the interface stress has no obvious effect on the splitting energy and hopping integral between Ni 3 d and Nd-layer orbitals. Although the hybridization between Ni 3 d x 2 - y 2 and Nd 5 d orbitals is tiny, the hybridization between the Ni 3 d x 2 - y 2 orbital and an itinerant interstitial s (IIS) orbital is significantly strong in both cases, suggesting that the IIS orbital may play a critical role in the superconductivity of nickelates.

In this work, density functional calculations and Boltzmann semiclassical theory of transport are used to investigate structural, electronic, and thermoelectric properties of AgSbSe2 crystal. According to the published experimental measurements, five more likely structures of this compound are considered and their structural and electronic properties are calculated and compared together. Then, thermoelectric properties (electrical conductivity, electronic contribution to the thermal conductivity, power factor, and Seebeck coefficient) of three more stable structures are investigated in the constant relaxation time approximation. Finally, the calculated temperature dependence of Seebeck coefficient is compared with the corresponding experimental measurements of others.

The so-called improper blue-shifting (BS) Hydrogen bond, characterising some small complexes, is theoretically investigated by first-principles calculations based on the Density Functional Theory. We compute structural, energetic, electronic and electrostatic properties not only of complexes with linear Hydrogen bonds but also of systems with multiple intermolecular contacts leading to the formation of ‘bifurcated’ or even ‘trifurcated’ Hydrogen bonds. In particular, Hydrogen bonds are characterised in terms of differential electron densities distributions and profiles, and of the shifts of the centres of Maximally localised Wannier Functions. The information from the latter quantities can be conveyed into simple geometric bonding parameters that are helpful in characterising the interatomic bonds. The effect of including dispersion corrections for describing BS Hydrogen bonds is also investigated. Our detailed comparison of the properties of systems with BS Hydrogen bonds to those of others, where more conventional red-shifting Hydrogen bonds are formed, supports the view that there is no fundamental difference between the two kinds of bonds. [ABSTRACT FROM AUTHOR]

The advent of graphene and related 2-D materials has attracted the interest of the electron device research community in the past 14 years. The possibility to boost the transistor performance and the prospects to build novel device concepts with 2-D materials and their heterostructures has awakened a strong experimental interest that requires continuous support from modeling. In this paper, we review the state of the art in the simulation of electron devices based on 2-D materials. We outline the main methods to model the electronic bandstructure and to study electron transport, classifying them in terms of accuracy and computational cost. We briefly discuss, how they can be combined in a multiscale approach to provide a quantitative understanding of the mechanisms determining the operation of electron devices, and we examine the application of these methods to different families of 2-D materials. Finally, we shortly analyze the main open challenges of modeling 2-D-based electron devices. [ABSTRACT FROM AUTHOR]

The Wannier localization problem in quantum physics is mathematically analogous to finding a localized representation of a subspace corresponding to a nonlinear eigenvalue problem. While Wannier localization is well understood for insulating materials with isolated eigenvalues, less is known for metallic systems with entangled eigenvalues. Currently, the most widely used method for treating systems with entangled eigenvalues is to first obtain a reduced subspace (often referred to as disentanglement) and then to solve the Wannier localization problem by treating the reduced subspace as an isolated system. This is a multiobjective nonconvex optimization procedure, and its solution can depend sensitively on the initial guess. We propose a new method to solve the Wannier localization problem, avoiding the explicit use of an optimization procedure. Our method is robust and efficient, relies on few tunable parameters, and provides a unified framework for addressing problems with isolated and entangled eigenvalues. [ABSTRACT FROM AUTHOR]

We provide a constructive proof of exponentially localized Wannier functions and related Bloch frames in 1- and 2-dimensional time-reversal symmetric (TRS) topological insulators. The construction is formulated in terms of periodic TRS families of projectors (corresponding, in applications, to the eigenprojectors on an arbitrary number of relevant energy bands), and is thus model-independent. The possibility to enforce also a TRS constraint on the frame is investigated. This leads to a topological obstruction in dimension 2, related to topological phases. We review several proposals for indices that distinguish these topological phases, including the ones by Fu-Kane [16], Prodan [33], Graf-Porta [24] and Fiorenza-Monaco-Panati [27]. We show that all these formulations are equivalent. In particular, this allows to prove a geometric formula for the invariant of 2-dimensional TRS topological insulators, originally indicated in [16], which expresses it in terms of the Berry connection and the Berry curvature. [ABSTRACT FROM AUTHOR]

It is shown that the standard sp n hybrid orbitals are orthogonal orbitals that minimize the total quadratic spread. This is done in a concise way that may improve the understanding of hybrid orbitals. The fact that maximally localized Wannier functions of crystalline materials may resemble hybrid orbitals is discussed.

We perform a detailed analysis of the valence band splitting (VBS) effect on the absorption spectra of monoclinic Cu2(Sn,Ge,Si)S3 combining theory and experiment. We calculate the imaginary part of the dielectric function for all three compounds using hybrid functionals and maximally localized Wannier functions in remarkably dense k -meshes to ensure an accurate description of the low energy spectral regime. We find that the VBS will affect the absorption spectra of these materials leading to multiple absorption onsets. Our experimental spectra on Cu2(Sn,Ge)S3, analysed using both Tauc plots and inflection points, verify this prediction. A good agreement between theory and experiment in terms of VBS values is recorded. (© 2016 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Tight-binding models for ultracold atoms in optical lattices can be properly defined by using the concept of maximally localized Wannier functions for composite bands. The basic principles of this approach are reviewed here, along with different applications to lattice potentials with two minima per unit cell, in one and two spatial dimensions. Two independent methods for computing the tight-binding coefficients-one ab initio, based on the maximally localized Wannier functions, the other through analytic expressions in terms of the energy spectrum-are considered. In the one dimensional case, where the tight-binding coefficients can be obtained by designing a specific gauge transformation, we consider both the case of quasi resonance between the two lowest bands, and that between s and p orbitals. In the latter case, the role of the Wannier functions in the derivation of an effective Dirac equation is also reviewed. Then, we consider the case of a two dimensional honeycomb potential, with particular emphasis on the Haldane model, its phase diagram, and the breakdown of the Peierls substitution. Tunable honeycomb lattices, characterized by movable Dirac points, are also considered. Finally, general considerations for dealing with the interaction terms are presented. [ABSTRACT FROM AUTHOR]

Exponentially localized Wannier functions of cumulene are calculated from the Bloch functions obtained through a tight-binding approach. Numerical results and discussions are given for the and bands. In the latter case, the single-band Wannier functions are similar to the orbitals of a diatomic molecule, while the two-band Wannier functions resemble hybrid atomic orbitals. Contour plot of an sp-like Wannier function of cumulene. [ABSTRACT FROM AUTHOR]

We extend the method of Silvestrelli [P. L. Silvestrelli, J. Chem. Phys. 139, 054106 (2013)] to approximate long-range van der Waals interactions at the density functional level of theory to periodic systems. The eventual approach is based on a combination of maximally localized Wannier functions with the quantum harmonic oscillator-model. Applying this scheme to study London dispersion forces between graphene and water layers, we find that collective many-body effects beyond simple pair-wise additive interactions are essential to accurately describe van der Waals forces. [ABSTRACT FROM AUTHOR]

The paper presents the group theory of optimally-localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all of the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into optimally-localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M or to a subgroup of G or M. In this context, the paper considers usual, as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors (Ekkehard Krüger) in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the optimally-localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly-correlated localized electrons makes clear predictions of whether or not the system can possess superconducting or magnetic eigenstates. [ABSTRACT FROM AUTHOR]

The electronic properties of a group of oxides with important technological applications were studied performing ab initio calculations. Al 2 O 3 is an important ceramic and catalyst, suitable insulator for electronic applications and nano scale access memory. SiO 2 is important from both geological and materials science point of view. Pure and doped ZnO structures have direct industrial applications in lasers, sensors, and infra-red and luminescence sensitive devices. A Full Potential Linearized Augmented Plane Waves (FP-LAPW) method within the Density Functional Theory (DFT) formalism was applied to study electronic properties of these oxides and different post-processing tasks as contour plots of electronic charge density, projected densities of states, band structure, Bader's method and Maximally Localized Wannier Functions were used to analyse the electronic charge transfer and bonding properties of the systems. The positions of these Wannier functions, shown in histograms and 3D plots, opened the possibility to calculate the bonding ionicity trend of materials. We report X-ray spectra obtained from self consistent ab initio calculations. K and L 2,3 edges were calculated including the fractional electronic core-hole and double core-hole providing similar features as in the reported experimental X-ray absorption near edge structure (XANES). • The electronic properties of a group of oxides Al2O3,SiO2 and ZnO, with important technological applications were studied performing ab initio calculations. • Bader's method and Maximally Localized Wannier.Functions were used to analyse the electronic charge transfer and bonding properties of the systems. • The positions of these Wannier functions open the possibility to calculate the bonding ionicity trend of these materials. • Ab initio XANES and XES were compared to experiments and XANES was calculated using fractional single and double core hole. • Structural parameters are obtained with PBE potential. • The oxides band gaps were calculated using different potentials. [ABSTRACT FROM AUTHOR]

We investigate the asymptotic decrease of the Wannier functions for the valence and conduction band of graphene, both in the monolayer and the multilayer case. Since the decrease of the Wannier functions is characterised by the structure of the Bloch eigenspaces around the Dirac points, we introduce a geometric invariant of the family of eigenspaces, baptised eigenspace vorticity. We compare it with the pseudospin winding number. For every value $$n \in \mathbb {Z}$$ of the eigenspace vorticity, we exhibit a canonical model for the local topology of the eigenspaces. With the help of these canonical models, we show that the single band Wannier function $$w$$ satisfies $$|w(x)| \le {\mathrm {const}} \cdot |x|^{-2}$$ as $$|x| \rightarrow \infty $$ , both in monolayer and bilayer graphene. [ABSTRACT FROM AUTHOR]