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Linear-Scaling ab-initio Calculations for Large and Complex Systems
Abstract
A brief review of the SIESTA project is presented in the context of
linear-scaling density-functional methods for electronic-structure calculations
and molecular-dynamics simulations of systems with a large number of atoms.
Applications of the method to different systems are reviewed, including carbon
nanotubes, gold nanostructures, adsorbates on silicon surfaces, and nucleic
acids. Also, progress in atomic-orbital bases adapted to linear-scaling
methodology is presented.
... The quenching step is particularly critical to obtain trustable amorphous results. Preliminary results (see Section S2, Supporting Information) indicate that i) the relaxation of volume under constant pressure, ii) the use of a relatively large basis set (in particular, double-ζ plus polarization [DZP] [34] ) during the quenching procedure, and iii) a low quenching rate are necessary steps for the building of realistic GeSe amorphous structures. The details of the quenching-and-melting approach are summarized in Table 3. ...
... The generalized gradient approximation (GGA)-Perdew-Burke-Ernzerhof (PBE) [53] functional was used to describe the exchange-correlation. DRSLL van der Waals correction was used in all calculations. [54] Single-ζ (SZ) basis functions [34] were used for the initial relaxation and finite temperature molecular-dynamics simulation, except in the last AIMD run in which DZP basis functions were used. The basis set was generated with an orbital-confining scheme with a cutoff radius corresponding to the energy shift of 0.001 Ry. [34] Only the Γ-point was used for the Brillouin zone integration. ...
... [54] Single-ζ (SZ) basis functions [34] were used for the initial relaxation and finite temperature molecular-dynamics simulation, except in the last AIMD run in which DZP basis functions were used. The basis set was generated with an orbital-confining scheme with a cutoff radius corresponding to the energy shift of 0.001 Ry. [34] Only the Γ-point was used for the Brillouin zone integration. The convergence criterion for the geometry optimization was set to a maximum force of 0.04 eV Å −1 on each atom. ...
The choice of the ideal material employed in selector devices is a tough task both from the theoretical and experimental side, especially due to the lack of a synergistic approach between techniques able to correlate specific material properties with device characteristics. Using a material‐to‐device multiscale technique, a reliable protocol for an efficient characterization of the active traps in amorphous GeSe chalcogenide is proposed. The resulting trap maps trace back the specific features of materials responsible for the measured findings, and connect them to an atomistic description of the sample. The metrological approach can be straightforwardly extended to other materials and devices, which is very beneficial for an efficient material‐device codesign and the optimization of novel technologies. A metrological materials‐to‐device computational approach that extracts defects characteristics from the experimental device electrical data and connects them to the microscopic properties of the material is proposed. This protocol is applied to amorphous GeSe‐based ovonic threshold switching selectors. This method unveils the role of electrical traps in amorphous materials and connects them to the device electrical characteristics.
... Density functional theory calculations are used by means of the VASP code for the oxides [36,37] and the SIESTA code for metals and oxides [38,39], along with the PBE (Perdew−Burke−Ernzerhof) generalized gradient-corrected approximation [40]. In VASP, the projector augmented wave (PAW) potentials were generated by G. Kresse [41] whereas the PAW method was first suggested and used by Peter Blöchl [42]. ...
... A plane wave basis set is adopted with 400 eV (250 eV) planewave energy cutoff for the oxide cases (for β-TiNbAg cases without oxygen) which includes the valence electrons for all elements along with the 3p and 4p of Ti and Nb semicore orbitals respectively. In SIESTA, core and semicore electrons are replaced by norm-conserving pseudopotentials in the fully nonlocal Kleinman−Bylander form, while the basis set is a linear combination of numerical atomic orbitals (NAOs) constructed from the eigenstates of the atomic pseudopotentials [38,39]. It should be noted that for small organic molecules and metallic atoms on surfaces or tiny clusters, there are dispersion corrections, such as PBE+D3 in the DFT calculations to better describe the long-range interactions providing better adsorption energies and activation barriers [43][44][45]. ...
Coatings with tunable multifunctional features are important for several technological applications. Ti-based materials have been used in diverse applications ranging from metallic diodes in electronic devices up to medical implants. This work uses ab initio calculations to achieve a more fundamental understanding of the structural and electronic properties of β-TiNb and its passive TiO2 film surfaces upon Ag addition, investigating the alterations in the electronic band gap and the stability of the antibacterial coating. We find that Ag’s 4d electrons introduce localized electron states, characterized by bonding features with the favoured Ti first neighbour atoms, approximately −5 eV below the fermi level in both β-TiNb bulk and surface. Ag’s binding energy on β-TiNb(110) depends on the local environment (the lattice site and the type of bonded surface atoms) ranging from −2.70 eV up to −4.21 eV for the adatom on a four-fold Ti site, offering a variety of options for the design of a stable coating or for Ag ion release. In Ti–O terminated anatase and rutile (001) surfaces, surface states are introduced altering the TiO2 band gap. Silver is bonded more strongly, and therefore creates a more stable antibacterial coat on rutile than on anatase. In addition, the Ag coating exhibits enhanced 4d electron states at the highest occupied state on anatase (001),which are extended from −5 eV up to the Fermi level on rutile (001), which might be altered depending on the coat structural features, thus creating systems with tunable electronic band gap that can be used for the design of thin film semiconductors.
... The calculations were performed within the DFT [20,21] as implemented in SIESTA package [22,23] with a basis set of finite-range of numerical atomic orbitals. Calculations have been carried out with the generalized gradient approximation (GGA) functional in the Perdue-Burke-Ernzerhof (PBE) form [24] Troullier-Martins pseudopotentials [25], and a basis set of finite-range numerical pseudo-atomic orbitals for the valence wave functions [26]. ...
... [6,8] As explained previously, the wetting conditions are fully determined by the sign of Ω. The extended studies conducted in this work allow to conclude that, overall, III-V (001) surface energies are lying in the meV/Å 2 range, and that the III-V/Si interfaces are compensated, with energies in the [20][21][22][23][24][25][26][27][28][29][30] meV/Å 2 range. However, in the present study, a nude Si(001) surface was assumed to be representative of the substrate surface before the III-V epitaxy. ...
Here, we quantitatively determine the impact of III-V/Si interface atomic configuration on the wetting properties of the system. Based on a description at the atomic scale using density functional theory, we first show that it is possible to determine the absolute interface energies in heterogeneous materials systems. A large variety of absolute GaP surface energies and GaP/Si interface energies are then computed, confirming the large stability of charge compensated III-V/Si interfaces with an energy as low as 23 meV/\r{A}$^{2}$. While stable compensated III-V/Si interfaces are expected to promote complete wetting conditions, it is found that this can be easily counterbalanced by the substrate initial passivation, which favors partial wetting conditions.
... To conduct the ab initio calculations, we utilized the SIESTA code, grounded in the formalism of Density Functional Theory (DFT) [54][55][56][57] . The optimization of lattice geometry and electronic structure were performed with generalized gradient approximation of Perdew, Burke, and Ernzerhof (GGA-PBE) 58,59 . ...
The boron nitride (BN) analogue of 8-16-4 graphyne, termed SBNyne, is proposed for the first time. Its physical properties were explored using first-principles calculations and classical molecular dynamics (MD) simulations. Thermal stability assessments reveal that SBNyne maintains structural integrity up to 1000 K. We found that SBNyne exhibits a wide indirect bandgap of 4.58 eV using HSE06 and 3.20 eV using PBE. It displays strong optical absorption in the ultraviolet region while remaining transparent in the infrared and visible regions. Additionally, SBNyne exhibits significantly lower thermal conductivity compared to h-BN. Phonon spectrum analysis indicates that out-of-plane phonons predominantly contribute to the vibrational density of states only at very low frequencies, explaining its low thermal conductivity. These findings expand the knowledge of BN-based 2D materials and open new avenues for their design and advanced technological applications.
... Most of the Density Functional Theory (DFT) calculations were performed with the SIESTA code [24], while DMol 3 [25,26] was used specifically to calculate some potential barriers. In particular, the GGA-PBE exchange-correlation functional [27], double-ζ polarized basis sets [28,29], and Troullier-Martins pseudopotentials [30] in fully nonlocal form [31] were employed. The energy cut-off for the real-space grid for numerical integrations was 460 Ry. ...
... All the calculations were performed within DFT [21,22] as implemented in the SIESTA [23,24] package with a basis set of finite-range numerical pseudoatomic orbitals for the valence wave functions [25]. As an exchange-correlation functional, the generalized gradient approximation functional in the Perdew-Burke-Ernzerhof [26] form of the Troullier-Martins pseudopotentials were used [27]. ...
Here, we quantitatively estimate the impact of the inevitable Si surface passivation prior to III-V/Si heteroepitaxy on the surface energy of the Si initial substrate, and explore its consequences for the description of wetting properties. Density functional theory is used to determine absolute surface energies of P- and Ga-passivated Si surfaces and their dependences with the chemical potential. Especially, we show that, while a ≈90meV/Å2 surface energy is usually considered for the nude Si surface, surface passivation by Ga- or P- atoms leads to a strong stabilization of the surface, with a surface energy in the [50–75 meV/Å2] range. The all ab initio analysis of the wetting properties indicate that a complete wetting situation would become possible only if the initial passivated Si surface could be destabilized by at least 15meV/Å2 or if the III-V (001) surface could be stabilized by the same amount.
... However, the calculated band gap with HSE06 [60,61] implemented in the CASTEP code is 2.888 eV at the Γ point. The results are consistent with the results obtained with the PBE and HSE06 using the VASP [62] and SIESTA [63,64] codes. The results of the band gap of the present study are in agreement with the previous reports in the literature [6,[8][9][10]44,65]. ...
... We performed standard Kohn-Sham self-consistent density functional theory calculations within the SIESTA code [30,31]. Core electrons were replaced by norm-conserving pseudopotentials in the fully nonlocal Kleinman-Bylander form and the basis set was a general and flexible linear combination of numerical atomic orbitals constructed from the eigenstates of the atomic pseudopotentials [32]. ...
The protection of implant surfaces from biofilm and corrosion is crucial for osteogenesis and tissue engineering. To this end, an L-glutamine-based green corrosion inhibitor with recently established anticancer properties has been applied onto antibacterial Cu(111) surfaces that usually cover the Ti-based implants. Among several configurations, L-glutamine prefers the parallel to the surface orientation with the carbon chain along the [110] direction having the heteroatoms N and O atoms on top of Cu surface atoms, which is important for the creation of a planar two-dimensioned (2d) stable coating. L-glutamine forms well-localized, directional covalent-like bonded states (below −3 eV) with the Cu surface atoms, using mainly its backbone’s N1 atom that interestingly also shows electron charge occupation in the single-molecule highest occupied state, denoting its ability as an active center. The Mulliken analysis shows charge transfer from the molecule’s N, C and Cu neighboring atoms towards the O atoms revealing the strong bond tendency of L-glutamine and therefore its ability to act as a corrosion inhibitor on the Cu surface. Additional L-glutamine adsorption results in intermolecular covalent bonding between the molecules, proving the ability of this amino acid to form a stable protective 2d organic coating on Cu(111). These results could be used for the design of a multifunctional hybrid (organic–metallic) coating with anticorrosion, anticancer and antibacterial properties suitable for many technological applications.
... First-principles electronic structure calculations were performed using DFT as implemented in the SIESTA software package [52,53]. The van der Waals density functional by Dion et al [54] with the modified exchange correlation by Klimeš et al [55] was used. ...
On-surface synthesis of graphene nanoribbons (GNRs) enables engineering their electronic and magnetic properties, which sensitively depend on their precise bonding structure, morphology and chemical composition. Here, we investigate nitrogen and boron co-doping in order to better understand the effects of simultaneous chemical substitution in sites along the backbone of 7AGNRs. In a comparative analysis with the pristine system, the origin of the impurity bands that nitro-borylated systems exhibit was addresed. In addition to this, we studied the appearance of an electric dipolar moment, the charge transfer mechanism behind it and its dependence on the distance between BN centres. The high defect concentration limit and the dilute limit were investigated, along with various doping schemes with four substitutional doping sites and the possible emergence of magnetism in these systems.
... This study performed a DFT-based calculation implanted in the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) [34,35] with norm-conserving pseudopotentials in the semi-local form [36] to determine the interaction among electrons and ions. The exchange-correlation potential treated in the generalized gradient approximation (GGA) of PBE [37] within doublezeta polarization basis sets was set for all properties calculations. ...
Cubic boron arsenide (c-BAs), a semiconducting material with ultra-high thermal conductivity and carrier mobilities, has been studied using first-principles calculation. This study examined the elastic and optoelectronic properties of c-BAs. The challenge of subphase boron (B) formation in bulk form owing to the volatile nature of arsenic (As) makes it mandatory to calculate its optoelectronic properties, by producing vacancies and antisite defects with BAs (As atom on a B site) and AsB (B atom on an As site). The mechanical properties including bulk (B), shear (G) moduli, and Poison’s ratio of all the systems were studied. It was found that mechanical instability of the structure is observed for the overall vacancy creation, arsenic substitution, and mutual antisite defects. Further, pristine c-BAs showed an indirect bandgap of 1.48 eV. Defect formation reduces the bandgap and shifts the absorption peaks, which improves the overall optoelectronic properties of the host material. In addition, B vacancy formation shows the maximum optical absorption and reflectivity and low energy loss, suggesting its potential applications for optoelectronic devices. The obtained anticipated data from this study is for the optoelectronic and elastic properties of c-BAs, for the device applications in photonics and electronics.
In this paper, the elastic and optoelectronic properties of the pristine and defected c-BAs were systematically investigated using the Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA). The SIESTA program uses pseudopotentials in the norm-conserving nonlocal forms and pseudo-atomic orbital (PAO) basis set with a double-zeta potential (DZP) which are fundamental for calculating the Hamiltonian and overlap matrices in O(N) operations.
... SOC was taken into account through the so-called off-site approach as following the Hemstreet formalism (60). Core electrons were described with Troullier-Martins pseudopotentials (61), while valence wave functions were developed over double-ζ polarized basis set of finite-range numerical pseudoatomic orbitals (62). In all cases, an energy cutoff of 150 rydberg for real-space mesh size was used, and the Brillouin zone was sampled using a 8 × 8 × 2 grid. ...
Hybrid perovskite semiconductor materials are predicted to lock chirality into place and encode asymmetry into their electronic states, while softness of their crystal lattice accommodates lattice strain to maintain high crystal quality with low defect densities, necessary for high luminescence yields. We report photoluminescence quantum efficiencies as high as 39% and degrees of circularly polarized photoluminescence of up to 52%, at room temperature, in the chiral layered hybrid lead-halide perovskites (R/S/Rac)-3BrMBA2PbI4 [3BrMBA = 1-(3-bromphenyl)-ethylamine]. Using transient chiroptical spectroscopy, we explain the excellent photoluminescence yields from suppression of nonradiative loss channels and high rates of radiative recombination. We further find that photoexcitations show polarization lifetimes that exceed the time scales of radiative decays, which rationalize the high degrees of polarized luminescence. Our findings pave the way toward high-performance solution-processed photonic systems for chiroptical applications and chiral-spintronic logic at room temperature.
... † susantag@mtu.edu respect to the system size when bulk insulators are considered [14][15][16][17][18][19], while others exhibit sub-quadratic scaling when used for calculations of low-dimensional materials (i.e., nanostructures) [20][21][22]. Contrary to these specialized approaches, there are only a handful of firstprinciples electronic structure calculation techniques that operate universally across bulk metallic, insulating, and semiconducting systems, while performing more favorably than traditional cubic scaling methods. ...
The ground state electron density - obtainable using Kohn-Sham Density Functional Theory (KS-DFT) simulations - contains a wealth of material information, making its prediction via machine learning (ML) models attractive. However, the computational expense of KS-DFT scales cubically with system size which tends to stymie training data generation, making it difficult to develop quantifiably accurate ML models that are applicable across many scales and system configurations. Here, we address these fundamental challenges using Bayesian neural networks and employ transfer learning to leverage the multi-scale nature of the training data. Our ML models employ descriptors involving simple scalar products, comprehensively sample system configurations through thermalization, and quantify uncertainty in electron density predictions. We show that our models incur significantly lower data generation costs while allowing confident - and when verifiable, accurate - predictions for a wide variety of bulk systems well beyond training, including systems with defects, different alloy compositions, and at unprecedented, multi-million-atom scales.
... As explained previously, the wetting conditions are fully determined by the sign of . The extended studies conducted in this paper allow us to conclude that, overall, III-V (001) surface energies lie in the [50 − 70] meV/Å 2 range and that the III-V/Si interfaces are compensated, with energies in the [20][21][22][23][24][25][26][27][28][29][30] meV/Å 2 range. However, in this paper, a nude Si(001) surface was assumed to be representative of the substrate surface before the III-V epitaxy. ...
Here, we quantitatively determine the impact of III-V/Si interface atomic configuration on the wetting properties of the system. Based on a description at the atomic scale using density functional theory, we first show that it is possible to determine the absolute interface energies in heterogeneous materials systems. A large variety of absolute GaP surface energies and GaP/Si interface energies are then computed, confirming the large stability of charge-compensated III-V/Si interfaces with an energy as low as 23meV/Å2. While stable compensated III-V/Si interfaces are expected to promote complete wetting conditions, it is found that this can be easily counterbalanced by the substrate initial passivation, which favors partial wetting conditions.
... Norm-conserving Troullier-Martins [41] relativistic pseudopotentials were used to represent the core electrons. The valence electrons were represented by a triple-ζ polarized (TZP) basis set of numerical atomic orbitals with the default energy shift of 0.02 Ry [42]. The electronic Brillouin zone was sampled at the point. ...
We present real-time time-dependent density-functional-theory calculations of the electronic stopping power for negative and positive projectiles (electrons, protons, antiprotons, and muons) moving through liquid water. After correction for finite mass effects, the nonlinear stopping power obtained in this paper is significantly different from the previously known results from semiempirical calculations based on the dielectric response formalism. Linear-nonlinear discrepancies are found both in the maximum value of the stopping power and the Bragg peak's position. Our results indicate the importance of the nonlinear description of electronic processes, particularly, for electron projectiles, which are modeled here as classical point charges. Our findings also confirm the expectation that the quantum nature of the electron projectile should substantially influence the stopping power around the Bragg peak and below.
... III, we use the DFT SIESTA code [17] to create a minimal, qualitative description of the electronic band structure of ZrSiSe. Specifically, that code permits an explicit specification of the number of orbitals employed, as well as of their spatial extent [18]. That freedom allowed us to create minimal basis sets with a single s, p and/or d orbital character, depending on the element at hand. ...
Spin orbit coupling (SOC) breaks energy degeneracies and produces an energy gap on the linear band crossings of ZrSiSe around the Fermi energy. Klemenz \textit{et al.} [{\em Phys. Rev. B} {\bf 101}, 165121 (2020)] suggested that the relevant energy dispersion of this class of materials is two-dimensional, and that it can be obtained by recourse to silicon orbitals only. Crucially, the relevant energy-degenerate crossings are created by a band-folding procedure in that model. Given that band folding is only {\em a choice} for displaying an electronic structure, it does not affect the charge carrier's dynamics {\em per se}. We first show that SOC does not induce a band gap on the zero-energy crossings of that model: such gaps appear elsewhere in the first Brillouin zone. We then develop a minimal, qualitative tight binding model for ZrSiSe that has the proper SOC-induced gap openings and electron symmetries. The model relies on the density-functional-theory (DFT) electronic dispersion obtained with a tool in which electronic states are written in terms of localized atomic orbitals [{\em J. Phys.: Condens. Matter} {\bf 14}, 2745 (2002)]: we remove orbitals gradually, and perform calculations with SOC turned on, to arrive at a minimal set of parameters that include silicon and zirconium atomic orbitals. We are able to determine that the electronic bands due to silicon in previous model lie above the Fermi energy. Our tight binding model with SOC is shown to describe ZrSiSe slabs as well.
... [53,54] The valence electrons were described with a split-valence double-ζ basis set including polarization functions. [55] The energy cutoff of the real space integration mesh was set to 500 Ry. To build the charge density (and, from this, obtain the DFT total energy and atomic forces), the reciprocal space was sampled with the Monkhorst-Pack scheme. ...
Polymorphic phases and collective phenomena—such as charge density waves (CDWs)—in transition metal dichalcogenides (TMDs) dictate the physical and electronic properties of the material. Most TMDs naturally occur in a single given phase, but the fine‐tuning of growth conditions via methods such as molecular beam epitaxy (MBE) allows to unlock otherwise inaccessible polymorphic structures. Exploring and understanding the morphological and electronic properties of new phases of TMDs is an essential step to enable their exploitation in technological applications. Here, scanning tunneling microscopy (STM) is used to map MBE‐grown monolayer (ML) TaTe2. This work reports the first observation of the 1H polymorphic phase, coexisting with the 1T, and demonstrates that their relative coverage can be controlled by adjusting synthesis parameters. Several superperiodic structures, compatible with CDWs, are observed to coexist on the 1T phase. Finally, this work provides theoretical insight on the delicate balance between Te…Te and Ta–Ta interactions that dictates the stability of the different phases. The findings demonstrate that TaTe2 is an ideal platform to investigate competing interactions, and indicate that accurate tuning of growth conditions is key to accessing metastable states in TMDs.
... In this case, the generalized gradient approximation (GGA) was employed for the exchange-correlation potential using the PBE scheme [7]. The valence electrons were treated using a split-valence double-ζ basis set with polarization functions (DZP) [8] whereas the core electrons were represented using the norm-conserving Troullier-Martins pseudo potentials [9]. The accuracy of the results was guaranteed via convergence studies on the mesh-cutoff energy and the number of k-points. ...
How many times you need to change your method description because you were "accused" of plagiarism from text you already published? I will use this preprint to add all the methods I currently used in running the simulations for my research works. Then, I will cite it as needed.
... Calculations were based on standard Kohn-Sham self-consistent density functional theory (DFT) calculations within the SIESTA code (Sánchez-Portal et al., 1997) and the PBE (Perdew-Burke-Ernzerhof) generalized gradient-corrected approximation (Perdew et al., 1996). Core and semicore electrons were replaced by norm-conserving pseudo-potentials in the fully nonlocal Kleinman-Bylander form and the basis set was a linear combination of numerical atomic orbitals (NAOs) constructed from the eigenstates of the atomic pseudopotentials (Artacho et al., 1999;Junquera et al., 2001;Sánchez-Portal et al., 1997;Soler et al., 2002). A double-ζ plus polarization basis set for the all species' valence and semicore states was used. ...
This work aims to investigate the structural, mechanical and electronic properties of four novel β-type (100-x)(Ti–45Nb)-xGa alloys (x = 2, 4, 6, 8 wt%) for implant applications by means of experimental and theoretical (ab initio) methods. All alloys retain the bcc β phase in the solution-treated and quenched state while the lattice parameter decreases with increase in Ga content. This is due to its smaller atomic radius compared to Ti and Nb, in line with the present density functional theory (DFT) calculations. Tensile and microhardness tests indicate a clear strengthening effect with increasing Ga content, with yield strengths in the range 551 ÷ 681 MPa and microhardness in the range 174 ÷ 232 HV0.1, mainly attributed to grain refinement and solid solution strengthening. Ga also positively affects ductility, with a maximum value of tensile strain at fracture of 32%. Non-destructive ultrasonic measurements and DFT calculations reveal that the bulk modulus is unaffected by the Ga presence. This phenomenon might be due to the fact that Ga introduced bonding and anti-bonding electron low energy states which balance the average bond strength among the atoms in the metallic matrix. Nevertheless, the introduction of new Ga–Ti super sp-like bonding orbitals along the [110] and [−110] directions in the Ga neighborhood could explain the increase of the Young's modulus upon Ga addition (73 ÷ 82.5 GPa) that was found experimentally in the present work. Hence, Ga addition to Ti–45Nb leads to a suitable balance between increased strength and low Young's modulus.
... The one-electron Kohn-Sham eigenstates were expanded in a basis of strictly localized numerical atomic orbitals [28,29]. For Mn, both single-ζ and double-ζ -polarized basis sets with the default values to define the range of the orbitals were used. ...
... All first-principles calculations were based on DFT theory as implemented in the SIESTA code [22][23][24]. These calculations were carried out within the scope of the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) [25,26] functional for the exchange-correlation term. ...
... In this work, we utilize the Spanish initiative for electronic simulations with thousands of atoms (SIESTA) code (PSML version) [18,19] to perform all of the DFT calculations. The highly-tested standard normconserving pseudopotentials within the Troullier−Martins scheme [20] provided by the Pseudo Dojo [21] library is used. ...
In this work, first-principles density functional theory (DFT) calculations are used to study the structural, electronic, and optical properties of pristine and Cu-doped TiO2 (112) surface in oxygen-rich environment, and then compare the results to the bulk phase. We find the pristine (112) surface to be chemically and thermodynamically stable, exhibiting indirect band gap value of 2.89 eV. By 5.6% concentration of Cu-doping, the energy gap in the asymmetric spin bands and PDOS reaches a value of 2.00 eV, with induced magnetism. The visible range direct band gap in Cu-doped systems enhances the photo-absorption triggering the threshold value and the inter-band transitions by lowering the intensity of the dielectric constant, reflectance, and refractive index, making them suitable candidates for optoelectronics and photocatalytic applications.
... The SIESTA [40] (Spanish Initiative for Electronic Simulations with Thousands of Atoms) software package was used to perform the DFT calculations [41,42] presented in this work. The Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional [43], within the general gradient approximation (GGA), was used together with optimized double-ζ polarized basis sets [44,45] and norm-conserving Troullier-Martins pseudopotentials [46]. To define the real space grid for numerical integrations, a cut-off energy of 300 Ry was used, which was found to be sufficiently fine to yield converged results. ...
Ultrasensitive chemical sensors based on silicon nanowires (SiNW) are optimal for detection of biological species, since they are fast and non-invasive, their fabrication is compatible with current semiconductor technology, and silicon is a biocompatible material. SiNW-based DNA sensors are well known, but there are few studies regarding the interaction of SiNWs with the single DNA/RNA nucleobases: Guanine (G), Cytosine (C), Adenine (A), Thymine (T), and Uracil (U). This work uses Density Functional Theory to study the interaction between the single nucleobases and SiNWs decorated with Cu, Ag and Au atoms, to determine their potential use as nucleobase detectors or carriers, or even to use nucleobase-functionalized SiNWs as sensing platform for other chemical species. Numerical results show remarkable changes of the nanowire's band gap upon adsorption of nucleobases. Likewise, the adsorption energies of the nucleobases on the functionalized SiNW follow the trend C > G > A > T > U. Cu-functionalized nanowires are suitable for the electrical detection of cytosine, while Au-functionalized nanowires may detect thymine and uracil. On the other hand, large variations of the nanowire work function were found when guanine and adenine are adsorbed on Cu-functionalized nanowires.
... The Spanish Initiative for Electronic Simulations with Thousands of Atoms (SIESTA) [27,28] code is utilized to perform all DFT calculations. The generalized gradient approximation (GGA)-Perdew-Burke-Ernzerhof (PBE) [29] parametrization is used to account for both the electronic exchange and correlation potentials. ...
Pentagonal two-dimensional ternary sheets are an emerging class of materials because of their novel characteristic and wide range of applications. In this work, we use first-principles density functional theory (DFT) calculations to identify a new pentagonal SiPN, p-SiPN, which is geometrically, thermodynamically, dynamically, and mechanically stable, and has promising experimental potential. The new p-SiPN shows an indirect bandgap semiconducting behavior that is highly tunable with applied equ-biaxial strain. It is mechanically isotropic, along the x-y in-plane direction, and is a soft material possessing high elasticity and ultimate strain. In addition, its exceptional anisotropic optical response with strong UV light absorbance, and small reflectivity and electron energy loss make it a potential material for optoelectronics and nanomechanics.
... The TDDFT implementation [49] of the SIESTA code is used [50][51][52][53]. The publicly available open-source version of the program was used as in its master branch, commit 6c3c0249 [54]. ...
The process by which a nuclear projectile is decelerated by the electrons of the condensed matter it traverses is currently being studied by following the explicit dynamics of projectile and electrons from first principles in a simulation box with a sample of the host matter in periodic boundary conditions. The approach has been quite successful for diverse systems even in the strong-coupling regime of maximal dissipation. This technique is here revisited for periodic solids in light of the Floquet theory of stopping, a time-periodic scattering framework characterizing the stationary dynamical solutions for a constant velocity projectile in an infinite solid. The effect of proton projectiles in diamond is studied under that light, using time-dependent density-functional theory in real time. The Floquet quasienergy-conserving stationary scattering regime, characterized by time-periodic properties such as particle density and the time derivative of energy, is obtained for a converged system size of 1000 atoms. The validity of the customary calculation of electronic stopping power from the average slope of the density-functional total energy is discussed. Quasienergy conservation, as well as the implied fundamental approximations, are critically reviewed.
... All the DFT calculations were performed with the SIESTA code [33], within the generalized gradient approximation. In particular the Perdew-Burke-Ernzerhof (PBE) functional was used [34] together with double-ξ polarized basis sets [35,36] and norm-conserving Troullier-Martins pseudopotentials [37]. A 4 × 4 × 1 supercell of 2D SiGe with a vacuum space of 30 Å perpendicular to the nanosheet was employed [25]. ...
In this work, we employed density functional theory calculations to investigate the feasibility of X-decorated (X = Li, Na, K, Mg, Ca, Sc, Ti, and Pd) two-dimensional siligene (2D SiGe) for ammonia (NH3) sensing through variations of its work function. The results indicated that NH3 molecule is physisorbed on pristine 2D SiGe. Moreover, Li, Na, K, Sc, Ti, Pd and Ca atoms are chemisorbed on the 2D SiGe, while Mg is barely adsorbed. Likewise, NH3 tends to be adsorbed on the metal atoms of the decorated 2D SiGe with adsorption energies between −0.13 eV and − 1.47 eV. The changes observed in the work functions of Na-, Mg-, Ca-, Sc-, and Pd-decorated 2D SiGe upon NH3 may allow its detection. Moreover, the results indicate that only the recovery times of 2D SiGe decorate with Na, K, Ca and Pd atoms could allow for their use as reusable sensors of NH3, while 2D SiGe decorated with Li, Mg, Sc and Ti could be used to trap NH3. From the results of work functions and recovery times on metal decorated 2D SiGe, it is concluded that Pd, Ca, and Na-decorated 2D SiGe are the most suitable material for sensing NH3 molecules.
Exploring more high-performance anode materials for sodium-ion batteries (SIBs) can smoothly help to build a more sustainable, cleaner, and reliable energy system. This study systematically investigates the potential of 2D pristine SiCN (p-SiCN) and defective (d-SiCN) substrate as candidate materials for SIBs anodes using first-principles computational method. The computational results reveal that the p-SiCN possesses excellent thermal stability and structural cyclical performance, good conductivity, high theoretical specific capacity (1486 mAh⋅g− 1), low diffusion barrier (0.177 eV), and appropriate open-circuit voltage (0.340 V), which allows the p-SiCN substrate more suitable as a potential anode material for SIBs. Furthermore, by investigating the effects of intentionally designed defects on p-SiCN, it is observed that the adsorption energy and diffusion barrier of the Na atom on the d-SiCN substrate increase. Our work demonstrates that investigating the effect of defects on p-SiCN
can better explore the properties of anode materials, thus further optimizing the battery performances.
For the widespread commercialization of lithium‑sulfur (Lisingle bondS) batteries, the identification of anchoring materials capable of effectively mitigating the shuttle effect is of paramount importance. This study is centered around examining the adsorption characteristics of lithium polysulfides (S8 and Li2Sn, n = 1, 2, 4, 6, 8), as well as investigating the sulfur reduction reaction (SRR), and the decomposition mechanisms of Li2S on the pristine and defective Hd-Graphene monolayers. These investigations were carried out using first-principles calculations. The results reveal that the adsorption energies of polysulfides to the electrolytes (DOL and DME) are lower compared to that on the substrates. The moderate anchoring strength (0.8–2.0 eV) between polysulfides and the monolayer can effectively suppress the shuttle effect. Additionally, the Gibbs free energy barrier for SRR on the substrate is determined to be about 0.68 eV. The dissociation energy barrier of Li2S on Hd-Graphene is about 1.54 eV. Lower energy barriers indicate favorable reaction kinetics, leading to improved discharging and charging efficiency. Based on these findings, Hd-Graphene is predicted to be a promising anchoring material for Lisingle bondS batteries.
We present a first-principles theoretical study of the atomistic footprints in the valence Electron Energy Loss Spectroscopy (EELS) of nanometer-size metallic particles. Charge density maps of excited plasmons and EEL...
The parameters of molecular hydrogen adsorption on a tetraoxa[8]circulene monolayer were studied using the density functional theory with dispersion interaction corrections (semi-empirical and analytical). The calculations were carried out using two different approaches to the system wave function representation: atomic-like orbital basis set and plane wave basis. Utilizing a less computationally expensive pseudo-atomic basis, it is possible to obtain results for molecular hydrogen adsorption consistent with values calculated with plane waves if the atomic-like basis is optimized and basis set superposition error is corrected for both hydrogen binding energy and geometrical characteristics. Otherwise, the H2 binding energy will be overestimated by 4–6 times (sometimes even more, by 20); and the hydrogen–monolayer distance will be underestimated by 10–20%. The obtained optimized parameters of the pseudo-atomic basis set can be used for further study of the modified forms of the tetraoxa[8]circulene monolayer. Moreover, our calculations showed that the hydrogen binding to a pristine tetraoxa[8]circulene monolayer is predominantly van der Waals with an energy of 60–90 meV, which is several times less than the desired range of 200–600 meV. To achieve such values, it will be necessary to modify the surface of the monolayer, creating more active sorption cites, for example, by decorating it with metals or applying structural defects.
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Herein are reported the synthesis, in-depth structural description and conducting properties of various salts of the symmetric bis-vinylenedithio-tetrathiafulvalene (BVDT-TTF) and dissymmetric ethylene-vinylenedithio-tetrathiafulvalene (EVT-TTF). Compared to the omnipresent bis-ethylenedithio-tetrathiafulvalene (BEDT-TTF) these two closely related and easily synthesizable organic donors have been reported ca. 200 times less in the literature. Four new structures of organic conductors are herein investigated and analysed through a battery of techniques, including X-ray analysis on single-crystals, conductivity measurements, Raman spectroscopy and band structure calculations. All materials exhibit semiconducting behaviours with conductivities in the 10⁻³ to 10⁻¹ S cm⁻¹ range at RT and ambient pressure. The impact of the structural or electronic disorder on the conductivity and dimensionality of the salts is examined.
DFT modeling of hydrogen sorption on graphene and C2N monolayers using the SIESTA and VASP packages demonstrates the need for optimizing the pseudo-atomic orbital basis set and calculating the counterpoise correction to the basis set superposition error for H2 binding energy. The use of pseudo-atomic orbitals reduces the H2-monolayer distance by 10%, relative to plane wave data. The optimized pseudo-atomic orbital parameters for a C2N monolayer can be used to further investigate this material.
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Searching for good anchoring materials that can suppress the shuttle effect is critical to large-scale commercialization of lithium-sulfur (Li-S) batteries. In this work, the adsorption behavior of lithium polysulfides (LiPSs, such as S8 and Li2Sn, n = 1, 2, 4, 6, and 8), the sulfur reduction reaction (SRR), the decomposition processes of Li2S and the diffusion behavior of Li atoms on intrinsic and doped 2D biphenylene (BIP) are systematically investigated by employing the first-principles calculation method. Calculations show that the adsorption energies of LiPSs on the electrolyte (DOL and DME) are smaller than those on the intrinsic/B doped BIP. The moderate anchoring strength (0.8-2.0 eV) between LiPSs and the BIP can effectively suppress the shuttle effect. Moreover, the Gibbs free energy barrier for SRR is 0.72/0.64 eV on intrinsic/B doped BIP. The dissociation energy barrier of Li2S on intrinsic/B doped BIP is 1.35 eV, while the diffusion energy barrier of Li atoms on intrinsic/B doped BIP is 0.18 eV/0.30 eV. Lower energy barriers are conducive to enhancing the discharging and charging efficiency. Therefore, intrinsic and B doped BIP are predicted as good anchoring materials for Li-S batteries.
Harnessing a bis(selenomethyl)tetrathiafulvalene (TTF) derivative as a donor, conducting charge transfer (CT) salts are realized thanks to original packing structures supported by chalcogen bonding (ChB) interactions. Specifically, co-crystallization of EDT-TTF(SeMe)2...
Carbon allotropes have contributed to all aspects of people's lives throughout human history. As emerging carbon-based low-dimensional materials, graphyne family members (GYF), represented by graphdiyne, have a wide range potential applications due to their superior physical and chemical properties. In particular, graphdiyne (GDY), as the leader of the graphyne family, has been practically applied to various research fields since it was first successfully synthesized. GYF have a large surface area, both sp and sp2 hybridization, and a certain band gap, which was considered to originate from the overlap of carbon 2pz orbitals and the inhomogeneous π-bonds of carbon atoms in different hybridization forms. These properties mean GYF-based materials still have many potential applications to be developed, especially in energy storage and catalytic utilization. Since most of the GYF have yet to be synthesized and applications of successfully synthesized GYF have not been developed for a long time, theoretical results in various application fields should be shared to experimentalists to attract more intentions. In this Review, we summarized and discussed the synthesis, structural properties, and applications of GYF-based materials from the theoretical insights, hoping to provide different viewpoints and comments.
Density functional theory (DFT) has become one of the most popular and successful methods for determining the microscopic properties of matter. In particular, its low computational cost makes it an excellent method for ab-initio calculations. The successes and failures of the theory crucially depend on the accuracy of the approximations for the exchange-correlation (xc) functionals. However, some quantities are not accessible with original DFT and therefore one needs to extend the framework. In this thesis, we study equilibrium properties and propose methodological developments on the steady-state transport problem within DFT. We apply our general results for model Hamiltonians, a perfect scenario with full control of the interactions to explore the structural properties of the xc functionals which, in the case of strong correlations, are governed by steps at integer occupation.
The thesis is divided in two parts. Part I explores the multi-orbital situation at equilibrium and low temperatures. From an analysis of stability diagrams, we find that the functionals of a double quantum dot in a thermal bath subject to generic density-density interactions and Hund’s rule coupling can be decomposed into four basic potentials based on the single orbital problem. In addition, we generalize this decomposition for an arbitrary number of interacting dots subject to inter- and intra-Coulomb repulsion. We also study the properties of the xc functionals for a strongly correlated double quantum dot asymmetrically coupled to the electrodes, where abrupt population inversions occur between the two dots.
Part II deals with the non-equilibrium transport problem. We extend the steady- state DFT framework to arbitrary thermal gradients between the electrodes, finding a general, exact expression for the Seebeck coefficient which is successfully applied for the single impurity Anderson model in the Kondo regime. Furthermore, we construct a general and formally exact density functional theory formalism which gives access not only to the correct density and electrical current, but also to the heat current of the interacting system in the steady-state. The linear response regime of this new framework is presented and gives access to all the transport coefficients in terms of quantities of the theory. We further apply the theory to the Anderson model and parametrize the xc functionals from a reverse engineering procedure in the Coulomb Blockade regime. Finally, using our theory in a three-terminal setup with one of the terminals only weakly connected, a general expression for the
non-equilibrium spectral function at arbitrary temperature is derived and applied for an Anderson impurity at finite bias voltage, capturing the splitting of the Kondo resonance as predicted by numerically exact many-body approaches.
Highly conducting, mixed-valence, multi-component nickel bis(diselenolene) salts were obtained by electrocrystallization of the monoanionic species [Ni(Me-thiazds)2]-1 (Me-thiazds: N-methyl-1,3-thiazoline-2-thione-4,5-diselenolate), with 1:2 and 1:3 stoichiometries depending of the counter ion used (Et4N+ and nBu4N+ vs Ph4P+, respectively). This behavior strongly differs from that of the corresponding monoanionic dithiolene complexes whose oxidation afforded the single component neutral species. This provides additional rare examples of mixed-valence conducting salts of nickel diselenolene complexes, only known in two examples with the dsit (1,3-dithiole-2-thione-4,5-diselenolate) and dsise (1,3-dithiole-2-selone-4,5-diselenolate) ligands. The mixed-valence salts form highly dimerized or trimerized bi- and trimetallic units, rarely seen with such nickel complexes. Transport measurements under a high pressure (up to 10 GPa) and band structure calculations confirm the semiconducting character of [Ph4P][Ni(Me-thiazds)2]3 and the quasi metallic character of [Et4N][Ni(Me-thiazds)2]2 and [NBu4]x[Ni(Me-thiazds)2]2 salts (0 < x < 1).
Designing an anchoring layer on the sulfur electrode has been considered one of the effective approaches to promoting the real application of room-temperature sodium-sulfur (RT-Na-S) batteries. In this work, based on the first-principles calculation method, the potential of pristine and doped borophosphene (BP) as anchoring materials for Na-S batteries has been investigated. The calculated adsorption energies of sodium polysulfides (NaPSs) adsorbed on pristine and doped substrates are higher than those of NaPSs adsorbed with the electrolytes (DOL&DME), indicating that the shuttle effect could be well alleviated. Meanwhile, the projected density of states (PDOS) suggests that the metallic characteristics of the adsorption systems are still well preserved, which is in favor of improving the electronic conductivity. More importantly, excellent electrocatalytic properties of the substrates are exhibited by reducing the catalytic decomposition energy barriers of Na2S, in which 0.27/0.79/1.02 eV is found on the pristine/N-doped/C-doped BP, indicating that the electrochemical processes could be improved smoothly. Therefore, it could be expected that pristine and doped BP are excellent anchoring materials for sodium-sulfur batteries.
The unique spin texture of quantum states in topological materials underpins many proposed spintronic applications. However, realizations of such great potential are stymied by perturbations, such as temperature and local fields imposed by impurities and defects, that can render a promising quantum state uncontrollable. Here, we report room-temperature observation of interaction between Rashba states and topological surface states, which manifests unique spin textures controllable by layer thickness of thin films. Specifically, we combine scanning tunneling microscopy/spectroscopy with the first-principles theoretical calculation to find the robust Rashba states coexisting with topological surface states along the surface steps with characteristic spin textures in momentum space. The Rashba edge states can be switched off by reducing the thickness of a topological insulator Bi2Se3 to bolster their interaction with the hybridized topological surface states. The study unveils a manipulating mechanism of the spin textures at room temperature, reinforcing the necessity of thin film technology in controlling quantum states.
Novel coordination polymers embedding electroactive moieties present a high interest in the development of porous conducting materials. While tetrathiafulvalene (TTF) based metal‐organic frameworks were reported to yield through‐space conducting frameworks, the use of S‐enriched scaffolds remains elusive in this field. Herein is reported the employment of bis(vinylenedithio)‐tetrathiafulvalene (BVDT‐TTF) functionalized with pyridine coordinating moieties in coordination polymers. Its combination with various transition metals yielded four isostructural networks, whose conductivity increased upon chemical oxidation with iodine. The oxidation was confirmed in a single‐crystal to single‐crystal X‐ray diffraction experiment for the Cd(II) coordination polymer. Raman spectroscopy measurements and DFT calculations confirmed the oxidation state of the bulk materials, and band structure calculations assessed the ground state as an electronically localized antiferromagnetic state, while the conduction occurs in a 2D manner. These results are shedding light to comprehend how to improve through‐space conductivity thanks to sulfur enriched ligands.
The lowest energy structures of Aun ( n = 38, 55, 75) nanoclusters are obtained by unconstrained dynamical and genetic-symbiotic optimization methods, using a Gupta n-body potential. A set of amorphous structures, nearly degenerate in energy, are found as the most stable configurations. Some crystalline or quasicrystalline isomers are also minima of the cluster potential energy surface with similar energy. First principles calculations using density functional theory confirm these results and give different electronic properties for the ordered and disordered gold cluster isomers.
We have examined theoretically the spontaneous thinning process of tip-suspended nanowires, and subsequently studied the structure and stability of the monatomic gold wires recently observed by transmission electron microscopy. The methods used include thermodynamics, classical many-body force simulations, local density and generalized gradient electronic structure calculations as well as ab initio simulations including the two tips. The wire thinning is well explained in terms of a thermodynamic tip suction driving migration of surface atoms from the wire to the tips. For the same reason the monatomic wire becomes progressively stretched. Surprisingly, however, all calculations so far indicate that the stretched monatomic gold wire should be unstable against breaking, contrary to the apparent experimental stability. The possible reasons for this stability are discussed.
We develop a plane-wave pseudopotential scheme for noncollinear magnetic structures, based on a generalized local spin-density theory in which the direction of the magnetization is a continuous variable of position. We allow the atomic and magnetic structures to relax simultaneously and self-consistently. Application to small Fe clusters yields noncollinear magnetic structures for Fe3 and Fe5. The components of the magnetization density vary smoothly with position. The spin direction undergoes sizable changes only in the regions of small charge and spin density between the atoms and is generally uniform in the magnetic regions of the atoms.
We describe a method for performing electronic-structure calculations of
the total energy and interatomic forces which scales linearly with
system size. An energy functional is introduced which possesses a global
minimum for which (1) electronic wave functions are orthonormal and (2)
the correct electronic ground-state energy is obtained. Linear scaling
is then obtained by introducing a spatially truncated Wannier-like
representation for the electronic states. The effects of this
representation are studied in detail. Molecular-dynamics simulations
using an orthogonal tight-binding basis and ab initio local-orbital
density-functional methods are presented. We study both Car-Parrinello
and conjugate-gradient molecular-dynamics schemes and discuss practical
methods for dynamical simulation. A detailed connection between our
method and the density matrix approach of Daw [Phys. Rev. B 47, 10 895
(1993)] and Li, Nunes, and Vanderbilt, [Phys. Rev. B 47, 10 891 (1993)]
is also provided.
An energy functional for orbital-based O(N) calculations is proposed, which depends on a number of nonorthogonal, localized orbitals larger than the number of occupied states in the system, and on a parameter, the electronic chemical potential, determining the number of electrons. We show that the minimization of the functional with respect to overlapping localized orbitals can be performed so as to attain directly the ground-state energy, without being trapped at local minima. The present approach overcomes the multiple-minima problem present within the original formulation of orbital-based O(N) methods; it therefore makes it possible to perform O(N) calculations for an arbitrary system, without including any information about the system bonding properties in the construction of the input wave functions. Furthermore, while retaining the same computational cost as the original approach, our formulation allows one to improve the variational estimate of the ground-state energy, and the energy conservation during a molecular dynamics run. Several numerical examples for surfaces, bulk systems, and clusters are presented and discussed.
A study based on ab initio calculations is presented on the estructural, elastic, and vibrational properties of single-wall carbon nanotubes with different radii and chiralities. We use SIESTA, an implementation of pseudopotential-density-functional theory which allows calculations on systems with a large number of atoms per cell. Different quantities like bond distances, Young moduli, Poisson ratio and the frequencies of different phonon branches are monitored versus tube radius. The validity of expectations based on graphite is explored down to small radii, where some deviations appear related to the curvature effects. For the phonon spectra, the results are compared with the predictions of the simple zone-folding approximation. Except for the known defficiencies of this approximation in the low-frequency vibrational regions, it offers quite accurate results, even for relatively small radii. Comment: 13 pages, 7 figures, submitted to Phys. Rev. B (11 Nov. 98)
The continuing miniaturization of microelectronics raises the prospect of nanometre-scale devices with mechanical and electrical properties that are qualitatively different from those at larger dimensions. The investigation of these properties, and particularly the increasing influence of quantum effects on electron transport, has therefore attracted much interest. Quantum properties of the conductance can be observed when `breaking' a metallic contact: as two metal electrodes in contact with each other are slowly retracted, the contact area undergoes structural rearrangements until it consists in its final stages of only a few bridging atoms. Just before the abrubt transition to tunneling occurs, the electrical conductance through a monovalent metal contact is always close to a value of 2e^2/h, where e is the charge on an electron and h is Plack's constant. This value corresponds to one quantum unit of conductance, thus indicating that the `neck' of the contact consists of a single atom. In contrast to previous observations of only single-atom necks, here we describe the breaking of atomic-scale gold contacts, which leads to the formation of gold chains one atom thick and at least four atoms long. Once we start to pull out a chain, the conductance never exceeds 2e^2/h, confirming that it acts as a one-dimensional quantized nanowire. Given their high stability and the ability to support ballistic electron transport, these structures seem well suited for the investigation of atomic-scale electronics. Comment: 5 pages, 3 figures
The projection of the eigenfunctions obtained in standard plane-wave first-principle calculations is used for analyzing atomic-orbital basis sets. The "spilling" defining the error in such a projection allows the evaluation of the quality of an atomic-orbital basis set for a given system and its systematic variational optimization. The same projection allows obtaining the band structure and the Hamiltonian matrix elements in the previously optimized atomic basis. The spilling is shown to correlate with the mean square error in the energy bands, indicating that the basis optimization via spilling minimization is qualitatively equivalent to the energy-minimization scheme, but involves a much smaller computational effort. The spilling minimization also allows the optimization of bases for uses different than total-energy calculations, like the description of the band gap in semiconductors. The method is applied to the characterization of finite-range pseudo-atomic orbitals {[}O. F. Sankey and D. J. Niklewski, Phys. Rev. B {\bf 40}, 3979 (1989){]} in comparison to infinite-range pseudo-atomic and Slater-type orbitals. The bases are evaluated and optimized for several zincblende semiconductors and for aluminum. The quality of the finite-range orbitals is found to be perfectly comparable to the others with the advantage of a limited range of interacions. A simple scheme is proposed to expand the basis without increasing the range. It is found that a double-$z$ basis substantially improves the basis performance on diamond, whereas $d$-polarization is required for Si and Al for similar results. Finally, the projection allows the chemical analysis of the plane-wave results via population analysis on the previously optimized atomic basis. Comment: 11 pages, RevTeX, plus 13 uuencoded, compressed, tared figures
A fully ab initio tight-binding formalism, based on that of Sankey and Niklewski [O. F. Sankey and D. J. Niklewski, Phys. Rev. B 40, 3979 (1989)] is presented. Several modifications are proposed. In particular the question of basis sets and the effect of self-consistency have been given attention. It is found that double numeric basis sets give well-converged results, and that charge transfer need only be considered in the extreme case of bonding between atoms of widely differing electronegativities. Geometries are well described by the spherical atomic charge approximation. To obtain the maximum computational efficiency the number of lookup tables has been reduced to a minimum through the use of separable pseudopotentials and a many-center expansion for the exchange-correlation terms. This method is applied to the study of the effect of the temporary attachment of an electron to a hydrocarbon molecule and a fluorocarbon molecule.
A new method for generating and using first-principles pseudopotentials is developed to treat explicitly the nonlinear exchange and correlation interaction between the core and the valence charge densities. Compared to existing potentials, the new scheme leads to significant improvement in the transferability of the potential. In particular, the spin-polarized configurations are well described with a single potential. The need for separate spin-up and spin-down ionic pesudopotentials is, thus, eliminated. The method can easily be implemented with minimal increase in computational effort. Results for both atoms and solids are demonstrated.
As the scale of microelectronic engineering continues to shrink, interest has focused on the nature of electron transport through essentially one-dimensional nanometre-scale channels such as quantum wires1 and carbon nanotubes2,3. Quantum point contacts (QPCs) are structures (generally metallic) in which a 'neck' of atoms just a few atomic diameters wide (that is, comparable to the conduction electrons' Fermi wavelength) bridges two electrical contacts. They can be prepared by contacting a metal surface witha scanning tunnelling microscope (STM)4, 5, 6, 7 and by other methods8, 9, 10, 11, 12, and typically display a conductance quantized in steps of 2e2/h(13 k-1)13,14, where e is the electron charge and h is Planck's constant. Here we report conductance measurements on metal QPCs prepared with an STM that we can simultaneously image using an ultrahigh-vacuum electron microscope, which allows direct observation of the relation between electron transport and structure. We observe strands of gold atoms that are about one nanometre long and one single chain of gold atoms suspended between the electrodes. We can thus verify that the conductance of a single strand of atoms is 2e2/h and that the conductance of a double strand is twice as large, showing that equipartition holds for electron transport in these quantum systems.
We present a method for selfconsistent Density Functional Theory calculations in which the effort required is proportional to the size of the system, thus allowing the aplication to problems with a very large size. The method is based on the LCAO approximation, and uses a mixed approach to obtain the Hamiltonian integrals between atomic orbitals with Order-N effort. We show the performance and the convergence properties of the method in several silicon and carbon systems, and in a DNA periodic chain.
The theoretical scanning-tunneling-spectroscopy image catalog of quantized molecular orbitals of finite armchair carbon nanotubes deposited on a gold (111) surface is presented. Just four different three-dimensional standing-wave (SW) patterns are obtained for electrons close to the Fermi level. The experimental observations of a SW modulation of 0.74 nm and peak pairing in line scans are understood in sight of our results. We show that SW patterns can be explained in terms of the simple Hückel model, but the associated energies, relevant to spectroscopic and transport measurements, are very sensitive to different effects beyond that model including the relaxed geometry, the electronic self-consistency in the finite tubes, and the interaction with the substrate.
We discuss the problem of searching for the electronic ground state in linear-scaling DFT techniques, with particular attention to the pseudopotential scheme embodied in the CONQUEST code. An important source of difficulty in the ground-state search is ill conditioning associated with the different dependence of the total energy on wavefunction variations at different length scales. We recall how this ‘length-scale ill conditioning’ is handled by preconditioning in conventional plane-wave methods, and we show that analogous preconditioning schemes can be derived in the linear-scaling framework. We present the results of practical tests which show that the proposed preconditioning gives a substantial speed-up in convergence to the ground state.
We consider a localised spherical-wave basis set suitable for O(N) total-energy pseudopotential calculations. The basis set is conveniently truncated using a single parameter, the kinetic energy cutoff used with the plane-wave basis. We present analytic results for the overlap integrals between any two basis functions centred on different sites, as well as for the kinetic energy matrix-elements which can therefore be evaluated accurately in real-space. A method for analytically performing the projection of the basis states onto angular-momentum states required for the use of nonlocal pseudopotentials is also presented.
Methods exhibiting linear scaling with respect to the size of the system, the so-called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms that take advantage of the decay properties of the density matrix. In this article the physical decay properties of the density matrix will first be studied for both metals and insulators. Several strategies for constructing O(N) algorithms will then be presented and critically examined. Some issues that are relevant only for self-consistent O(N) methods, such as the calculation of the Hartree potential and mixing issues, will also be discussed. Finally some typical applications of O(N) methods are briefly described. [S0034-6861(99)00104-X] CONTENTS I. Introduction 1085 II. Locality in Quantum Mechanics 1086 III. Basic Strategies for O(N) Scaling 1093 A. The Fermi operator expansion 1094 1. The Chebyshev Fermi operator expansion 1094 2. The rational Fermi operator expansion 1097 B. The Fermi operator projection method 1098 C. The divide-and-conquer method 1099 D. The density-matrix minimization approach 1100 E. The orbital minimization approach 1103 F. The optimal basis density-matrix minimization method 1105 IV.
We have implemented a linear scaling, fully self-consistent density-functional method for performing first-principles calculations on systems with a large number of atoms, using standard norm-conserving pseudopotentials and flexible linear combinations of atomic orbitals (LCAO) basis sets. Exchange and correlation are treated within the local-spin-density or gradient-corrected approximations. The basis functions and the electron density are projected on a real-space grid in order to calculate the Hartree and exchange–correlation potentials and matrix elements. We substitute the customary diagonalization procedure by the minimization of a modified energy functional, which gives orthogonal wave functions and the same energy and density as the Kohn–Sham energy functional, without the need of an explicit orthogonalization. The additional restriction to a finite range for the electron wave functions allows the computational effort (time and memory) to increase only linearly with the size of the system. Forces and stresses are also calculated efficiently and accurately, allowing structural relaxation and molecular dynamics simulations. We present test calculations beginning with small molecules and ending with a piece of DNA. Using double-z, polarized bases, geometries within 1% of experiments are obtained. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 453–461, 1997
This article describes recent technical developments that have made the total-energy pseudopotential the most powerful ab initio quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in as many scientific disciplines as possible.
A simple way has been discovered to put model pseudopotentials, V(r→)=lm|YlmVl(r)×Ylm|, into a form which reduces the number of integrals of V(r→) required for an energyband calculation from mn(n+1)2 to mn for each l in the sum (where n is the number of plane waves used in the expansion and m the number of points in the Brillouin zone at which the calculation is performed). The new form may be chosen to improve the accuracy of the pseudopotential when used in other chemical environments.
An efficient implementation of the Gaussian very fast multipole method (GvFMM) for periodic systems (pGvFMM) is presented. Relevant details of our algorithm are discussed and linear scaling properties with unit cell size demonstrated on benchmarks using minimum and double-zeta bases on solid NaCl, (5,5) and (10,10) carbon nanotubes containing up to 960 atoms in the unit cell.
We introduce the continuous fast multipole method (CFMM), a generalization of the fast multipole method for calculating Coulomb interaction of point charges. The CFMM calculates Coulomb interactions between charge distributions, represented by continuous functions, in work scaling linearly with their number for constant density systems. Model calculations suggest that for errors in the potential of 10−10, the CFMM becomes faster than direct evaluation for less than 10000 Gaussian charge distributions. Using the CFMM to form the J matrix in ab initio density functional and Hartree-Fock calculations shows that a two-three times speedup is attainable for the linear alkanes C10H22-C20H42.
During the last few years, there has been an intense effort in the development of the so-called Order-N methods to solve the electronic-structure problem, for which the numerical efforts scale only linearly with the size of the system. The combination of these algorithms with total energy schemes has expanded our capability of performing electronic-structure based molecular dynamics (MD) simulations for systems of unprecedented size. In general, Order-N methods yield approximate solutions, based on physically motivated approximations. The central idea is, in most cases, the concept of localization (or the dependence of the relevant physical quantities on only the local environment). Therefore, the Tight-Binding (TB) formulation (or, more generally, the use of some kind of localized basis set), either from first principles or in an empirical form, is a natural framework to develop and apply Order-N schemes. In this paper we analyze the main ideas involved in these methods and their different implementations. We will focus on schemes to compute total energies and forces, therefore suited for MD simulations, and also on approaches to study the spectral properties like the density of states and eigenvalue information. These two classes of methods provided valuable complementary information and are often based on very similar assumptions and formalisms.
A density functional theory-based algorithm for periodic and non-periodic ab initio calculations is presented. This scheme uses pseudopotentials in order to integrate out the core electrons from the problem. The valence pseudo-wavefunctions are expanded in Gaussian-type orbitals and the density is represented in a plane wave auxiliary basis. The Gaussian basis functions make it possible to use the efficient analytical integration schemes and screening algorithms of quantum chemistry. Novel recursion relations are developed for the calculation of the matrix elements of the density-dependent Kohn-Sham self-consistent potential. At the same time the use of a plane wave basis for the electron density permits efficient calculation of the Hartree energy using fast Fourier transforms, thus circumventing one of the major bottlenecks of standard Gaussian based calculations. Furthermore, this algorithm avoids the fitting procedures that go along with intermediate basis sets for the charge density. The performance and accuracy of this new scheme are discussed and selected examples are given.
We present a simple procedure to generate first-principles norm-conserving pseudopotentials, which are designed to be smooth and therefore save computational resources when used with a plane-wave basis. We found that these pseudopotentials are extremely efficient for the cases where the plane-wave expansion has a slow convergence, in particular, for systems containing first-row elements, transition metals, and rare-earth elements. The wide applicability of the pseudopotentials are exemplified with plane-wave calculations for copper, zinc blende, diamond, alpha-quartz, rutile, and cerium.
A parallel implementation of linear-scaling first-principles total-energy calculations is presented. The theoretical basis is density functional theory (DFT) and the pseudopotential approximation. The linear-scaling method is the one due to the present authors, but the parallelisation techniques are also relevant to other linear-scaling DFT methods. The theoretical and computational framework of the linear-scaling method is summarised, in order to identify the main classes of computer operation required. For each class of operation, the issues involved in distributing tasks and data between processors are discussed and a solution is proposed. Practical tests of the proposed implementation on a Cray T3D are presented, and it is shown that the scaling with respect to both the number of atoms and the number of processors is excellent for systems containing up to over 6 000 atoms.
An algorithm for first-principles electronic-structure calculations having a computational cost that scales linearly with the system size is presented. Our method exploits the real-space localization of the density matrix, and in this respect it is related to the technique of Li, Nunes, and Vanderbilt. The density matrix is expressed in terms of localized support functions, and a matrix of variational parameters Lαβ having a finite spatial range. The total energy is minimized with respect to both the support functions and the Lαβ parameters. The method is variational and becomes exact as the ranges of the support functions and the L matrix are increased. We have tested the method on crystalline silicon systems containing up to 216 atoms, and we discuss some of these results.
A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density-functional theory in which the ground-state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes, and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated.
We present a method to perform fully self-consistent density-functional calculations that scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis functions. The sparse Hamiltonian and overlap matrices are calculated with an O(N) effort. The long-range self-consistent potential and its matrix elements are computed in a real-space grid. The other matrix elements are directly calculated and tabulated as a function of the interatomic distances. The computation of the total energy and atomic forces is also done in O(N) operations using truncated, Wannier-like localized functions to describe the occupied states, and a band-energy functional which is iteratively minimized with no orthogonality constraints. We illustrate the method with several examples, including carbon and silicon supercells with up to 1000 Si atoms and supercells of beta-C3N4. We apply the method to solve the existing controversy about the faceting of large icosahedral fullerenes by performing dynamical simulations on C60, C240, and C540.
The temperature dependence of surface-induced atomic layering in liquid gallium has been investigated with x-ray reflectivity. The prominent layering peak at qz=2.4 Å-1 decreases dramatically upon heating from 22 to 170 °C, but its width stays, unexpectedly, unchanged. The decrease is traced to the temperature dependence of capillary-wave induced surface roughness. The constant width indicates a temperature-independent layering decay length. The measured layering amplitudes are found to be significantly underestimated by existing theory and molecular simulations.
A new, approximate method has been developed for computing total energies and forces for a variety of applications including molecular-dynamics simulations of covalent materials. The method is tight-binding-like and is founded on density-functional theory within the pseudopotential scheme. Slightly excited pseudo-atomic-orbitals are used to derive the tight-binding Hamiltonian matrix in real space. The method is used to find the electronic states and total energies for a variety of crystalline phases of Si and the Si{sub 2} molecule. Excellent agreement is found with experiment and other first-principles methods. As simple applications of the method, we perform a molecular-dynamics simulated-annealing study of the Si{sub 3} molecule to determine the ground-state configuration, and a molecular-dynamics simulation of the spectral density function of the Si{sub 2} molecule at high and low excitation levels.
A widely applicable ``nearsightedness'' principle is first discussed as the physical basis for the existence of computational methods scaling linearly with the number of atoms. This principle applies to the one particle density matrix n\(r,r'\) but not to individual eigenfunctions. A variational principle for n\(r,r'\) is derived in which, by the use of a penalty functional P[n\(r,r'\)], the (difficult) idempotency of n\(r,r'\) need not be assured in advance but is automatically achieved. The method applies to both insulators and metals.
Generalized gradient approximations (GGA{close_quote}s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. {copyright} {ital 1996 The American Physical Society.}
In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is represented in terms of an array of `blip functions'' on the points of a grid. We analyze the relation between blip-function basis sets and the plane-wave basis used in standard pseudopotential methods, derive criteria for the approximate equivalence of the two, and describe practical tests of these criteria. Techniques are presented for using blip-function basis sets in linear-scaling calculations, and numerical tests of these techniques are reported for Si crystal using both local and non-local pseudopotentials. We find rapid convergence of the total energy to the values given by standard plane-wave calculations as the radius of the linear-scaling localized orbitals is increased. Comment: revtex file, with two encapsulated postscript figures, uses epsf.sty, submitted to Phys. Rev. B
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