All-electron Density Functional Calculations Research Articles

Carbon-doped anatase titania nanoparticles: similarities and differences with respect to bulk and extended surface models.

C-Doping of titania nanoparticles is analyzed by using all-electron density functional theory-based calculations considering the (TiO2)84 nanoparticle as a realistic representative of nanoparticles in the scalable regime. Several sites are evaluated including substituting oxygen (CO) and titanium (CTi) sites as well as interstitial (Ci) situations. The formation energy of such a doped structure is studied as a function of the oxygen chemical potential (or oxygen partial pressure). Our calculations predict that low partial oxygen pressure favors the formation of C-doped (TiO2)84 NPs at oxygen and interstitial sites. For the former, the most stable situation is for O sites at the inner part of the nanoparticle. Interestingly, the substitution of O by C at facet sites requires formation energies as those reported in previous studies where the bulk anatase and surfaces models were considered. However, C-doping - at other low coordinated sites not presented in extended models - is even more favorable which shows the need to employ more realistic models for nanostructures involved in photocatalytic processes.

Pressure induced structural, electronic and optical properties of wurtzite beryllium monoxide (w-BeO) from first-principle calculations

All-electron density functional calculations of structural, electronic and optical properties of wutrzite beryllium oxide (w-BeO) are carried out at different applied hydrostatic pressure. Calculated lattice constants decrease (a, c), while bulk modulus increases with increasing pressure. Direct fundamental band-gap (Eg) of w-BeO increases with increasing pressure and vice versa and the variation provides first and second order pressure coefficient of band-gap. The calculated volume deformation potential of band-gap of w-BeO is −11.5972 eV. Optical properties of w-BeO at zero and high pressures have been studied in terms of dielectric function ε(ω) and related ancillary optical parameters. Each optical parameter is marginally anisotropic. Calculated components of refractive index at each pressure signify uniaxial characteristics of the w-BeO. Calculated components of static dielectric constant, refractive index and reflectivity decreases, while critical point energy in the spectra of each component of ε2(ω), k(ω), σ(ω) and α(ω) increases with increasing pressure and vice versa. Calculated optical energy-gap (Eopt) of w-BeO increases like Eg with increasing pressure and vice versa. The transmission cutoff energy (ECutoff) is shifted towards the higher energy region with increasing pressure.

Role of opacity at the 9 keV back lighter energy used in measuring the equation of state of boron at pressures up to a Gbar

Many experiments have been conducted at the National Ignition Facility to measure the equation of state Hugoniot of plastic, boron, and diamond at extreme pressures up to a Gbar. The “Gbar” design employs a strong spherically converging shock launched through a solid ball of material using a hohlraum radiation drive. The shock front conditions are characterized using X-ray radiography, typically at energies near 9 keV. In this paper we examine how the opacity of boron at 9 keV changes at high pressures and temperatures. Understanding this is vital to unfolding the density in the shock front as pressures exceed 100 Mbar. We compare opacity calculations from a number of methods including the legacy XSN opacity tables, super transition array (STA), average atom (AVAT), and detailed configuration accounting (DCA) methods. We examine how the changing opacity is correlated with the K-shell occupation calculated using the opacity methods as well as other electronic structure methods such as MECCA, Purgatorio, and an all-electron Kohn-Sham density functional theory calculation that uses optimized all-electron norm-conserving Vanderbilt pseudopotentials (ONCV). We also examine the relative contribution of free-free opacity to the overall opacity, which is dominated by bound-free absorption.

All-electron density functional calculations for electron and nuclear spin interactions in molecules and solids

The interaction between electronic and nuclear spins in the presence of external magnetic fields can be described by a spin Hamiltonian, with parameters obtained from first principles, electronic structure calculations. We describe an approach to compute these parameters, applicable to both molecules and solids, which is based on Density Functional Theory (DFT) and real-space, all-electron calculations using finite elements (FE). We report results for hyperfine tensors, zero field splitting tensors (spin-spin component) and nuclear quadrupole tensors of a series of molecules and of the nitrogen-vacancy center in diamond. We compare our results with those of calculations using Gaussian orbitals and plane-wave basis sets, and we discuss their numerical accuracy. We show that calculations based on FE can be systematically converged with respect to the basis set, thus allowing one to establish reference values for the spin Hamiltonian parameters, at a given level of DFT.

Size-Dependent Level Alignment between Rutile and Anatase TiO2 Nanoparticles: Implications for Photocatalysis.

Motivated by the enormous importance of nanoscale TiO2 in a wide range of photocatalytic applications and the ill-understood high activity of the commercial nano-TiO2 photocatalysts, we provide a predictive map of how the anatase-rutile level alignment varies from the smallest nanoparticles (NPs) to the bulk. Specifically, we compute the size dependence of the energies of vacuum-referenced electronic levels in a range of realistically structured rutile and anatase TiO2 NPs employing accurate all-electron density functional calculations. In agreement with most recent work, a staggered type II anatase level alignment is predicted for the bulk phases, which we further find to persist into the regime of large NPs. We predict that other level alignments will emerge when the diameter of the TiO2 NPs is reduced below ∼15 nm. Our results suggest how experiment could test the widely debated importance of the bulk-like type II anatase level alignment for enhanced photoactivity of nano-TiO2.

Mössbauer parameters of Fe-related defects in group-IV semiconductors: First principles calculations

We employ a combination of pseudopotential and all-electron density functional calculations, to relate the structure of defects in supercells to the isomer shifts and quadrupole splittings observed in Mössbauer spectroscopy experiments. The methodology is comprehensively reviewed and applied to the technologically relevant case of iron-related defects in silicon, and to other group-IV hosts to a lesser degree. Investigated defects include interstitial and substitutional iron, iron-boron pairs, iron-vacancy, and iron-divacancy. We find that, in general, agreement between the calculations and Mössbauer data is within a 10% error bar. Nonetheless, we show that the methodology can be used to make accurate assignments, including to separate peaks of similar defects in slightly different environments.

Recent Advances in the Korringa-Kohn-Rostoker Green Function Method

The Korringa-Kohn-Rostoker (KKR) Green function (GF) method is a technique for all-electron full-potential density-functional calculations. Similar to the historical Wigner-Seitz cellular method, the KKR-GF method uses a partitioning of space into atomic Wigner-Seitz cells. However, the numerically demanding wave-function matching at the cell boundaries is avoided by use of an integral equation formalism based on the concept of reference Green functions. The advantage of this formalism will be illustrated by the recent progress made for very large systems with thousands of inequivalent atoms and for very accurate calculations of atomic forces and total energies.

Structural investigation of nanocrystalline graphene grown on (6√3 × 6√3)R30°-reconstructed SiC surfaces by molecular beam epitaxy

Growth of nanocrystalline graphene films on (6√3 × 6√3)R30°-reconstructed SiC surfaces was achieved by molecular beam epitaxy, enabling the investigation of quasi-homoepitaxial growth. The structural quality of the graphene films, which is investigated by Raman spectroscopy, increases with growth time. X-ray photoelectron spectroscopy proves that the SiC surface reconstruction persists throughout the growth process and that the synthesized films consist of sp2-bonded carbon. Interestingly, grazing incidence x-ray diffraction measurements show that the graphene domains possess one single in-plane orientation, are aligned to the substrate, and offer a noticeably contracted lattice parameter of 2.450 Å. We correlate this contraction with theoretically calculated reference values (all-electron density functional calculations based on the van der Waals corrected Perdew–Burke–Ernzerhof functional) for the lattice parameter contraction induced in ideal, free-standing graphene sheets by: substrate-induced buckling, the edges of limited-size flakes and typical point defects (monovacancies, divacancies, Stone–Wales defects).

Theoretical study of frequency and temperature dependence of dipole-quadrupole polarizability of P4 and adamantane

The frequency and temperature dependence of dipole-quadrupole polarizability of tetrahedral P4 and adamantane molecules have been studied using first-principle all-electron density functional theory calculation. The recently developed time-dependent auxiliary density functional theory is extended for the calculation of dynamic dipole-quadrupole polarizabilities. Temperature effects are incorporated by Born–Oppenheimer molecular dynamics (BOMD) simulations recorded up to 100ps. The dynamic dipole-quadrupole polarizabilities are calculated along these trajectories. The frequency and temperature effects can be significant for the accurate calculation of dipole-quadrupole polarizability. We have also identified the main reason for the observed discrepancy between experiment and theory in the case of adamantane.

Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments: Test calculations for Au, AuF, and Snn cluster (n ⩽ 20)

The response of the electronic wavefunction to an external electric or magnetic field is widely considered to be a typical valence property and should, therefore, be adequately described by accurately adjusted pseudopotentials, especially if a small-core definition is used within this approximation. In this paper we show for atomic Au and Au(+), as well as for the molecule AuF and tin clusters, that in contrast to the case of the static electric dipole polarizability or the electric dipole moment, core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation. This error increases with increasing size of the core chosen. For tin clusters, which are of interest in ongoing molecular beam experiments currently carried out by the Darmstadt group, the diamagnetic and paramagnetic isotropic components of the magnetizability tensor almost cancel out and large-core pseudopotentials do not even predict the correct sign for this property due to erroneous results in both the diamagnetic and (more importantly) the paramagnetic terms. Hence, all-electron calculations or pseudopotentials with very small cores are required to adequately predict magnetizabilities for atoms, molecules and the solid state, making it computationally more difficult to obtain this quantity for future investigations in heavy atom containing molecules or clusters. We also demonstrate for this property that all-electron density functional calculations are quite robust and give results close to wavefunction based methods for the atoms and molecules studied here.

One-dimensional uranium–organic coordination polymers: crystal and electronic structures of uranyl-diacetohydroxamate

The structure of the uranyl-diacetohydroxamate compound, UO(2)(C(2)NO(2)H(4))(2), was elucidated using a combination of single crystal X-ray diffraction measurements and all-electron scalar relativistic density functional calculations. This polymeric compound crystallizes in the C2/c space group (IT No. 15; a = 12.8386(13) Å, b = 7.5661(7) Å, c = 8.9299(9) Å, β = 103.185(2) °; Z = 4), with main-chain repeating units featuring a bidentate structure analogous to that frequently found for d-block as well as lanthanide metal ions. Density functional analysis reveals that this compound is a semiconductor, with a direct band gap of 1.1 eV.

Continuously tunable band gap in GaN/AlN (0001) superlattices via built-in electric field

Based on all-electron density-functional theory calculations using the generalized gradient approximation, we demonstrate the continuous tunability of the band gap and strength of the built-in electric field in GaN/AlN (0001) superlattices by control of the thickness of both the well (GaN) and barrier (AlN) regions. The effects of strain for these quantities are also studied. Calculations taking into account the self-interaction correction exhibit the same dependence on thickness. The calculated electric field strength values are in good agreement with recent experiments. Spontaneous polarization dominates the contribution to the electric field and the strain-induced piezoelectric polarization is estimated to contribute only about 5--10%.

Electronic structure and molecular properties of binuclear group VII pentalene metal carbonyl complexes [C 8H 6{M(CO 3)} 2] (M = Mn, Tc, Re, Bh): A relativistic density functional theory study

Homobimetallic systems where the metals are linked through a pentalenediide ligand, of the type anti-[Pn{M(CO) 3} 2] (Pn = pentalenediide), which include transition metals of the group VII with M = 25Mn ( 1), 43Tc ( 2), 73Re ( 3) and 107Bh ( 4), and the syn-[Pn{M(CO) 3} 2] isomer with M = 25Mn ( s1), 43Tc ( s2), 73Re ( s3) and 107Bh ( s4), were studied with relativistic all-electron density functional (DFT) calculations, including spin-orbit (SO) coupling via the two components ZORA Hamiltonian. The electronic structure was studied in detail in the four systems. Broken symmetry calculations were performed for all the paramagnetic systems to verify their mixed-valence character. The infrared (IR) spectra were obtained at the scalar relativistic regime and the UV–Vis was obtained by time-dependent spin-orbit DFT and compared against the experimental data available (only for 1 and 3). The relative binding energy calculations predict that the not yet reported s1, 2, s2, 4 and s4 complexes may be synthesized. Their optical and vibrational properties are described here. Due to the relativistic indirect effect acting on metal d orbitals there is an increased overlap between the nd and 2π∗ empty carbonyl orbitals, and hence the backbonding effect increases from 1/ s1 to 4/ s4. The calculated spin-dependent properties of the anionic complexes reveals that the isotropic g tensor decreases down the group, showing that the quenching of the total angular momentum of the unpaired electron increases along the group.

Martensitic transformation path of NiTi

We present the structural evolution mechanism during the NiTi martensitic transformation and show the origins of this behavior in electronic and phononic anomalies. By employing highly precise all-electron density-functional theory calculations, we establish a barrierless transformation path for equiatomic NiTi consisting of a basal shear composed of bilayer $⟨100⟩{011}$ stacking faults to the B2 phase followed by another basal shear which causes a relaxation of the structure's monoclinic angle and results in the $\text{B}1{9}^{\ensuremath{'}}$ phase. This path is traced to evolving Fermi-surface nesting regions, which drive the structural transformation between the austenitic and martensitic phases.

Lowest-energy structures and photoelectron spectra of In nP n ( n = 1–12) clusters from density functional theory

Lowest-energy structures of In n P n ( n = 1–12) clusters have been determined from a number of structural isomers using all-electron density functional calculations. The In–P alternating hollow cage-like structures emerge at n = 7. Size-dependent cluster properties such as binding energy, HOMO–LUMO gaps, electron affinities, and photoelectron spectra have been computed and discussed. The simulated electron affinities and photoelectron spectra agree reasonably with experiments. With exceptionally low electron affinity and large HOMO–LUMO gap, In 3P 3 was identified as a magic-numbered cluster of relatively higher stability, in agreement with experimental observations.

A new magic titanium-doped gold cluster and orientation dependent cluster-cluster interaction

The stability and structures of titanium-doped gold clusters Au(n)Ti (n=2-16) are studied by the relativistic all-electron density-functional calculations. The most stable structures for Au(n)Ti clusters with n=2-7 are found to be planar. A structural transition of Au(n)Ti clusters from two-dimensional to three-dimensional geometry occurs at n=8, while the Au(n)Ti (n=12-16) prefer a gold cage structure with Ti atom locating at the center. Binding energy and second-order energy differences indicate that the Au(14)Ti has a significantly higher stability than its neighbors. A high ionization potential, low electron affinity, and large energy gap being the typical characters of a magic cluster are found for the Au(14)Ti. For cluster-cluster interaction between magic transition-metal-doped gold clusters, calculations were performed for cluster dimers, in which the clusters have an icosahedral or nonicosahedral structure. It is concluded that both electronic shell effect and relative orientation of clusters are responsible for the cluster-cluster interaction.

Structures of MAu16− (M=Ag, Li, Na, and K): How far is the endohedral doping?

The structural and electronic properties of MAu16 (-) (M=Ag, Li, Na, and K) have been studied by the scalar relativistic all-electron density-functional calculations, in which particular attention is paid to the stability of the endohedral Au16 (-) cage doped by different dopant atoms. It is found that only the smaller atoms, such as Cu, Li, and Na, can be stably encapsulated in the Au16 (-) cage, while the addition of the larger Ag or K atom prefers to locate in the surface or outside of the cage, which is inconsistent with the previous hypothesis that the Au16 (-) cage could act as a container to hold an arbitrary heterometal atom. The stable endohedral Li@Au16 (-) and Na@Au16 (-) have a large energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital gap, indicating that they are chemically stable and may be used as potential building blocks for designing cluster-assembled materials.

Electronic structure and static dipole polarizability of C60@C240

The electronic structure of C60@C240 and its first-order response to a static electric field is studied by an all-electron density functional theory calculation using large polarized Gaussian basis sets. Our results show that the outer C240 shell almost completely shields the inner C60 as inferred from the practically identical values of dipole polarizability of the C60@C240 onion (449 Å3) and that of the isolated C240 fullerene (441 Å3). The C60@C240 is thus a near-perfect Faraday cage.

Relativistic density functional study of FCC americium and the (111) surface

Full-potential all-electron density-functional calculations with mixed basis augmented plane wave plus local orbital--linearized-augmented plane wave have been carried out to investigate the electronic and geometric properties of bulk FCC Am and quantum size effects in the surface energies and the work functions of the (111) ultrathin films up to seven layers at six levels of approximations, namely, non-spin-polarized--no-spin-orbit coupling, non-spin-polarized--spin-orbit coupling, spin-polarized--no-spin-orbit coupling, spin-polarized--spin-orbit coupling, antiferromagnetic--no-spin-orbit coupling, and antiferromagnetic--spin-orbit (AFM-SO) coupling. The antiferromagnetic state including spin-orbit coupling is found to be the ground state of FCC Am with the $5f$ electrons primarily localized. Our calculations show that both spin-polarization and spin-orbit coupling effects play important roles in determining the equilibrium lattice constant, the bulk modulus, as well as the localized feature of $5f$ electrons for FCC Am. Our calculated equilibrium lattice constant of $9.21\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ and a bulk modulus of $25.64\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ at the AFM-SO level are in good agreement with the experimental values of $9.26\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.}$ and $29.4\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, respectively. For the films, surface energy rapidly converges and the semi-infinite surface energy is predicted to be $0.81\phantom{\rule{0.3em}{0ex}}\mathrm{J}∕{\mathrm{m}}^{2}$ at the ground state. The work function of the FCC Am(111) surface at the AFM-SO ground state is predicted to be $3.06\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, and the work function shows some oscillations when the number of layers is less than five, while it becomes relatively stable when the number of layers is greater than five. This suggests that a five-layer film may be required for any future adsorption investigation that requires, for example, an accurate prediction of one-electron properties and adsorbate-induced work function shift.

Trends in adsorption of noble gases He, Ne, Ar, Kr, and Xe onPd(111)(3×3)R30°: All-electron density-functional calculations

It was recently found from ab initio investigations [J. L. F. Da Silva et al., Phys. Rev. Lett. 90, 066104 (2003)] that polarization effects and the site dependence of the Pauli repulsion largely dictate the nature of the interaction and the site preference of Xe adatoms on close-packed metal surfaces. It is unclear if the same interaction mechanism occurs for all rare-gas atoms adsorbed on such surfaces. To address this question, we perform all-electron density-functional theory calculations with the local-density approximation (LDA) and generalized gradient approximations (GGA) for [He, Ne, Ar, Kr, and $\mathrm{Xe}]∕\mathrm{Pd}(111)$ in the $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})R30\ifmmode^\circ\else\textdegree\fi{}$ structure. Our results confirm that polarization effects of the rare-gas adatoms and Pd atoms in the topmost surface layer, together with the site-dependent Pauli repulsion, largely determine the interaction between rare-gas atoms and the Pd(111) surface. Similar to the earlier ab initio study, the on-top site preference is obtained by the LDA for all rare-gas adatoms, while the GGA functionals yield the on-top site preference for Xe, Kr, and He adatoms, but the fcc site for Ne and Ar.