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Thermal hybrid exchange-correlation density functional for improving the description of warm dense matter

Finite-temperature density functional theory (FT-DFT) has become a standard tool for first principles calculations of the properties of warm dense matter (WDM) relevant to high-energy density physics (HEDP) applications. In this work we introduce theoretical grounds of thermal hybrid exchange-correlation (XC) functionals within the generalized Mermin-Kohn-Sham scheme for an improved description of WDM. Building on the previously developed KSDT (Karasiev-Sjostrom-Dufty-Trickey) [Karasiev et al., Phys. Rev. Lett. 112, 076403 (2014)] local density approximation (LDA) and the KDT16 (Karasiev-Dufty-Trickey 2016) [Karasiev et al., Phys. Rev. Lett. 120, 076402 (2018)] generalized-gradient approximation (GGA) XC free-energy density functionals, we construct a new thermal hybrid XC functional, referred to here as KDT0. The KDT0 model at low temperature reduces to the popular ground-state PBE0 hybrid due to properties of the used KDT16 density functional approximation. Application to static calculations of electronic band gap and band structure at a wide range of temperatures for various systems of interest to HEDP show that KDT0 provides a significant improvement to the lower LDA and GGA rung XC functionals and to the ground-state PBE0 hybrid.

36 MATERIALS SCIENCE↗

Hyperfine interactions for small systems including transition-metal elements using self-interaction corrected density-functional theory

The interactions between the electronic magnetic moment and the nuclear spin moment, i.e., magnetic hyperfine (HF) interactions, play an important role in understanding electronic properties of magnetic systems and in realizing platforms for quantum information science applications. We investigate the HF interactions for atomic systems and small molecules, including Ti or Mn, by using Fermi–Löwdin orbital (FLO) based self-interaction corrected (SIC) density-functional theory. We calculate the Fermi contact (FC) and spin-dipole terms for the systems within the local density approximation (LDA) in the FLO-SIC method and compare them with the corresponding values without SIC within the LDA and generalized-gradient approximation (GGA), as well as experimental data. For the moderately heavy atomic systems (atomic number Z ≤ 25), we find that the mean absolute error of the FLO-SIC FC term is about 27 MHz (percentage error is 6.4%), while that of the LDA and GGA results is almost double that. Therefore, in this case, the FLO-SIC results are in better agreement with the experimental data. For the non-transition-metal molecules, the FLO-SIC FC term has the mean absolute error of 68 MHz, which is comparable to both the LDA and GGA results without SIC. For the seven transition-metal-based molecules, the FLO-SIC mean absolute error is 59 MHz, whereas the corresponding LDA and GGA errors are 101 and 82 MHz, respectively. Therefore, for the transition-metal-based molecules, the FLO-SIC FC term agrees better with experiment than the LDA and GGA results. We observe that the FC term from the FLO-SIC calculation is not necessarily larger than that from the LDA or GGA for all the considered systems due to the core spin polarization, in contrast to the expectation that SIC would increase the spin density near atomic nuclei, leading to larger FC terms.

Chemistry↗

Comparative Density Functional Theory Study of Magnetic Exchange Couplings in Dinuclear Transition-Metal Complexes

Multicenter transition-metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information-processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular, the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory is the only practical electronic structure method for evaluating the J coupling. Here, we assess the accuracy of different density functional approximations for predicting the magnetic couplings of eight dinuclear transition-metal complexes, including five dimanganese, two dicopper, and one divanadium with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r 2 SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids tested in this work have a tendency to over-correct the error in magnetic coupling parameters from the Perdew–Burke–Ernzerhof (PBE) GGA as seen for manganese complexes. The performance of local hybrid density functionals shows no improvement in terms of bias and is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r 2 SCAN meta-GGAs are found to perform as well as benchmark global hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error or delocalization error.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Oxygen–Chlorine Chemisorption Scaling for Seawater Electrolysis on Transition Metals: The Role of Redox

To clarify what controls species oxidation selectivity in seawater electrolysis, density functional theory (DFT) is used to identify chemisorption enthalpy trends and scaling relations for the simplest relevant adsorbates (O, Cl, and H) on relevant surfaces of 3d transition metals, as well as Pd and Pt, in face-centered-cubic and, if different, their ground-state crystal structures. Approximations are tested for electron exchange-correlation (XC) and van der Waals interactions to assess their ability to reproduce experimental adsorption enthalpies of H and O on Pt(111). The vdW-uncorrected generalized gradient approximation to XC of Perdew, Burke, and Ernzerhof (PBE) agrees most closely with experiments. Using DFT-PBE thereafter, it is determined that the O chemisorption enthalpy on this wide range of transition-metal surfaces is proportional to the sum of first and second atomic ionization energies, akin to a Born–Haber cycle for a redox reaction, indicating that metal redox activity controls O chemisorption strength. Then it is shown that the O and Cl chemisorption enthalpies are strongly correlated, suggesting that the transition metals considered will oxidize unselectively water and Cl – . This strong correlation appears also for crystal reduction potentials of binary oxides and chlorides, indicating a fundamental challenge for future seawater electrode materials design.

08 HYDROGEN↗

Understanding the chemical bonding of ground and excited states of HfO and HfB with correlated wavefunction theory and density functional approximations

Knowledge of the chemical bonding of HfO and HfB ground and low-lying electronic states provides essential insights into a range of catalysts and materials that contain Hf–O or Hf–B moieties. Here, we carry out high-level multi-reference configuration interaction theory and coupled cluster quantum chemical calculations on these systems. We compute full potential energy curves, excitation energies, ionization energies, electronic configurations, and spectroscopic parameters with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We also investigate equilibrium chemical bonding patterns and effects of correlating core electrons on property predictions. Differences in the ground state electron configuration of HfB(X 4 Σ - ) and HfO(X 1 Σ + ) lead to a significantly stronger bond in HfO than HfB, as judged by both dissociation energies and equilibrium bond distances. We extend our analysis to the chemical bonding patterns of the isovalent HfX (X = O, S, Se, Te, and Po) series and observe similar trends. We also note a linear trend between the decreasing value of the dissociation energy (D e ) from HfO to HfPo and the singlet–triplet energy gap (ΔE S–T ) of the molecule. Finally, we compare these benchmark results to those obtained using density functional theory (DFT) with 23 exchange–correlation functionals spanning multiple rungs of “Jacob’s ladder.” When comparing DFT errors to coupled cluster reference values on dissociation energies, excitation energies, and ionization energies of HfB and HfO, we observe semi-local generalized gradient approximations to significantly outperform more complex and high-cost functionals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling Liquid Water by Climbing up Jacob’s Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn–Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric–isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Density functional based methods for light harvesting molecules

The goal of the proposal was to computationally study the photoinduced charge transfer excited states of organic molecules. The systems of interest are the large organic supramolecules that have potential for photovoltaic applications. The simulation of the charge transfer excited states in large supramolecular assemblies require quantum mechanical methods that can be applied to systems with hundreds of atoms. Through this project we have implemented a perturbative delta-self-consistent field method that can easily describe the charge transfer excited states with regular density functionals without range separation. The cost of the calculations of an excited state is similar to that of the ground state. The method also allows for calculation of the energy gradients of the excited state. The developed method was applied to study a number of different supramolecular systems containing hundreds of atoms with excellent agreement with experiment. The absorption characteristics and the influence of density functional approximations were also examined. These led to several studies on the variety of organic electron donor and acceptor molecules. Apart from these developments through this project we also improved the code capabilities by implementing new meta-GGA functionals. This was a major step since the code is purely density functional and earlier the functional capabilities were limited only to generalized gradient approximations. A total of 23 peer-reviewed publications in top chemical physics journals resulted from this grant.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations?

Herein, we examine the effect of removing self-interaction error (SIE) on the calculation of molecular polarizabilities in the local spin density (LSDA) and generalized gradient approximations (GGA). To this end, we utilize a database of 132 molecules taken from a recent benchmark study [Hait and Head-Gordon, Phys. Chem. Chem. Phys. , 2018, 20 , 19800] to assess the influence of SIE on polarizabilities by comparing results with accurate reference data. Our results confirm that the general overestimation of molecular polarizabilities by these density functional approximations can be attributed to SIE. However, removing SIE using the Perdew–Zunger self-interaction-correction (PZ-SIC) method, implemented using the Fermi–Löwdin Orbital SIC approach, leads to an underestimation of molecular polarizabilities, showing that PZ-SIC overcorrects when combined with LSDA or GGA. Application of a recently proposed locally scaled SIC [Zope, et al., J. Chem. Phys. , 2019, 151 , 214108] is found to provide more accurate polarizabilities. We attribute this to the ability of the local scaling scheme to selectively correct for SIE in the regions of space where the correction is needed most.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Delocalization error poisons the density-functional many-body expansion

The many-body expansion is a fragment-based approach to large-scale quantum chemistry that partitions a single monolithic calculation into manageable subsystems. This technique is increasingly being used as a basis for fitting classical force fields to electronic structure data, especially for water and aqueous ions, and for machine learning. Here, we show that the many-body expansion based on semilocal density functional theory affords wild oscillations and runaway error accumulation for ion–water interactions, typified by F − (H 2 O) N with N ≳ 15. We attribute these oscillations to self-interaction error in the density-functional approximation. The effect is minor or negligible in small water clusters, explaining why it has not been noticed previously, but grows to catastrophic proportion in clusters that are only moderately larger. This behavior can be counteracted with hybrid functionals but only if the fraction of exact exchange is ≳50%, whereas modern meta-generalized gradient approximations including ωB97X-V, SCAN, and SCAN0 are insufficient to eliminate divergent behavior. Other mitigation strategies including counterpoise correction, density correction (i.e., exchange–correlation functionals evaluated atop Hartree–Fock densities), and dielectric continuum boundary conditions do little to curtail the problematic oscillations. In contrast, energy-based screening to cull unimportant subsystems can successfully forestall divergent behavior. These results suggest that extreme caution is warranted when the many-body expansion is combined with density functional theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quasiparticle self-consistent GW band structures and phase transitions of LiAlO 2 in tetrahedrally and octahedrally coordinated structures

In this work, a first-principles computational study is presented of various phases of LiAlO 2 . The relative total energies and equations of state of the α, β, and γ phases are determined after structural relaxation of each phase. The β and γ tetrahedral phases are found to be very close in energy and lattice volume with the γ phase having the lowest energy. The octahedral α phase is a high-pressure phase and the transition pressure from the γ and β phases to α is determined to be about 1 GPa. The electronic band structures of each phase at their own equilibrium volume are determined using the quasiparticle self-consistent (QS) GW method as well as using the 0.8 Σ approach in which the QS GW self-energy is reduced by a factor of 0.8 to correct for the underscreening of W in QS GW. The effective masses of the band edges and the nature of the band gaps are presented. The lowest energy γ phase is found to have a pseudodirect gap of 7.69 eV. The gap is direct at Γ but corresponds to a dipole forbidden transition. The imaginary part of the dielectric function and the absorption coefficient are calculated in the long-wavelength limit and the random phase approximation, without local field or electron-hole interaction effects for each phase, and their anisotropies are discussed. Si doping on the Al site is investigated as a possible n-type dopant in γ-LiAlO 2 using a 128-atom supercell corresponding to 3.125% Si on the Al sublattice in the generalized gradient approximation and a smaller 16-atom cell with 25% Si in the QS GW approximation. The Si is found to significantly perturb the conduction band and lower the gap but a clearly separated deep donor defect level is not found. However, the donor binding energy is still expected to be relatively deep, on the order of a few tenths eV in the hydrogenic effective mass approximation.

36 MATERIALS SCIENCE↗

A flexible and scalable scheme for mixing computed formation energies from different levels of theory

Abstract Computational materials discovery efforts are enabled by large databases of properties derived from high-throughput density functional theory (DFT), which now contain millions of calculations at the generalized gradient approximation (GGA) level of theory. It is now feasible to carry out high-throughput calculations using more accurate methods, such as meta-GGA DFT; however recomputing an entire database with a higher-fidelity method would not effectively leverage the enormous investment of computational resources embodied in existing (GGA) calculations. Instead, we propose here a general procedure by which higher-fidelity, low-coverage calculations (e.g., meta-GGA calculations for selected chemical systems) can be combined with lower-fidelity, high-coverage calculations (e.g., an existing database of GGA calculations) in a robust and scalable manner. We then use legacy PBE(+ U ) GGA calculations and new r 2 SCAN meta-GGA calculations from the Materials Project database to demonstrate that our scheme improves solid and aqueous phase stability predictions, and discuss practical considerations for its implementation.

36 MATERIALS SCIENCE↗

Structural and dynamic properties of solvated hydroxide and hydronium ions in water from ab initio modeling

Predicting the asymmetric structure and dynamics of solvated hydroxide and hydronium in water from ab initio molecular dynamics (AIMD) has been a challenging task. The difficulty mainly comes from a lack of accurate and efficient exchange–correlation functional in elucidating the amphiphilic nature and the ubiquitous proton transfer behaviors of the two ions. By adopting the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation functional in AIMD simulations, we systematically examine the amphiphilic properties, the solvation structures, the electronic structures, and the dynamic properties of the two water ions. In particular, we compare these results to those predicted by the PBE0-TS functional, which is an accurate yet computationally more expensive exchange–correlation functional. We demonstrate that the general-purpose SCAN functional provides a reliable choice for describing the two water ions. Specifically, in the SCAN picture of water ions, the appearance of the fourth and fifth hydrogen bonds near hydroxide stabilizes the pot-like shape solvation structure and suppresses the structural diffusion, while the hydronium stably donates three hydrogen bonds to its neighbors. We apply a detailed analysis of the proton transfer mechanism of the two ions and find the two ions exhibit substantially different proton transfer patterns. In conclusion, our AIMD simulations indicate that hydroxide diffuses more slowly than hydronium in water, which is consistent with the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Temperature dependence of nuclear quantum effects on liquid water via artificial neural network model based on SCAN meta-GGA functional

We investigate the temperature dependence of nuclear quantum effects (NQEs) on structural and dynamic properties of liquid water by training a neural network force field using first-principles molecular dynamics (FPMD) based on the strongly constrained and appropriately normed meta-generalized gradient approximation exchange-correlation approximation. The FPMD simulation based on density functional theory has become a powerful computational approach for studying a wide range of condensed phase systems. However, its large computational cost makes it difficult to incorporate NQEs in the simulation and investigate temperature dependence of various properties. To circumvent this difficulty, we use an artificial neural network model and employ the thermostatted ring polymer MD approach for studying the temperature dependence of NQEs on various properties. The NQEs generally bring the radial distribution functions closer to the experimental measurements. Translational diffusivity and rotational dynamics of water molecules are both slowed down by the NQEs. The competing inter-molecular and intra-molecular quantum effects on hydrogen bonds, as discussed by Habershon, Markland, and Manolopoulos [J. Chem. Phys. 131(2), 024501 (2019)], can explain the observed temperature dependence of the NQEs on the dynamical properties in our simulation.

Yao, Yi (ORCID:0000000299576979)↗

Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction

The Perdew–Zunger self-interaction correction (PZ-SIC) improves the performance of density functional approximations for the properties that involve significant self-interaction error (SIE), as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by local scaling self-interaction correction (LSIC) of the PZ-SIC to the local spin density approximation (LSDA). Here, we propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of the atomic number Z in the asymptotic expansion of the exchange–correlation (xc) energy for atoms. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator z σ , which distinguishes one-electron regions from many-electron regions. LSIC+ applied to the LSDA works better for many equilibrium properties than LSDA-LSIC and the Perdew, Burke, and Ernzerhof generalized gradient approximation (GGA), and almost close to the strongly constrained and appropriately normed (SCAN) meta-GGA. LSDA-LSIC and LSDA-LSIC+, however, fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bond, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. To make a locally scaled down SIC to functionals beyond the LSDA requires a gauge transformation of the functional’s energy density. Here, the resulting SCAN-sdSIC, evaluated on SCAN-SIC total and localized orbital densities, leads to an acceptable description of many equilibrium properties including the dissociation energies of weak bonds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Self-consistent implementation of locally scaled self-interaction-correction method

Recently proposed local self-interaction correction (LSIC) method is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange–correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew–Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn–Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional and barrier heights of the BH6 database better than some of the most widely used hybrid functionals. The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). Furthermore, this work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Symmetry Breaking with the SCAN Density Functional Describes Strong Correlation in the Singlet Carbon Dimer

The SCAN (strongly constrained and appropriately normed) meta-generalized gradient approximation (meta-GGA), which satisfies all 17 exact constraints that a meta-GGA can satisfy, accurately describes equilibrium bonds that are normally correlated. With symmetry breaking, it also accurately describes some sd equilibrium bonds that are strongly correlated. While sp equilibrium bonds are nearly always normally correlated, the C 2 singlet ground state is known from correlated wave function theory to be a rare case of strong correlation in an sp equilibrium bond. Earlier work that calculated atomization energies of the molecular sequence B 2 , C 2 , O 2 , and F 2 in the local spin density approximation (LSDA), the Perdew–Burke–Ernzerhof (PBE) GGA, and the SCAN meta-GGA, without symmetry breaking in the molecule, found that only SCAN was accurate enough to reveal an anomalous under-binding for C 2 . Here, this work shows that spin symmetry breaking in singlet C 2 , which involves the appearance of net up- and down-spin densities on opposite sides (not ends) of the bond, corrects that underbinding, with a small SCAN atomization-energy error more like that of the other three molecules, suggesting that symmetry breaking with an advanced density functional might reliably describe strong correlation. This article also discusses some general aspects of symmetry breaking and the insights into strong correlation that symmetry breaking can bring. The normally correlated low-lying triplet excited state has the right vertical excitation energy in SCAN but not in LSDA or PBE, where the triplet is a false ground state. Fractional occupation numbers are found only for the symmetry-unbroken singlet and only in LSDA and PBE GGA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

HfNb_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys hafnium-niobium (Hf-Nb). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements Hf and Nb. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect BCC lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,029 randomized atomic structures over 31 chemical compositions. Further methodological and structural information is contained in the dataset README.txt file.

36 MATERIALS SCIENCE↗

VZr_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution binary alloys vanadium-zirconium (V-Zr). The electronic structures of alloys have been calculated using Vienna Ab initio Simulation Package (VASP). Within this package the DFT approach is used to reduce many-body Schrodinger equation to set of single particle Kohn-Sham (KS) equations. The generalized electronic exchange-correlation functional is described by generalized gradient approximation with the Perdew-Burke-Ernzerhof parametrization. The electron-ion interactions is described by pseudopotentials developed within the plane-wave basis projector augmented-wave (PAW) approach \cite{PAW}. These pseudopotentials are available at the VASP portal (http://cms.mpi.univie.ac.at/vasp/). Our calculations have been run with the pseudopotentials treating s and p semi-core states as valence in case for the elements V and Zr. The electronic densities and potentials are expanded over plane-waves with energy cutoff of 350 eV. 2x2x2 k-mesh and normal precision were used. The alloys were modeled by supercell containing 128 randomly distributed atoms. At initial step the atoms occupy perfect bcc lattice cites. This initial structure was optimized until energy changes less than 1e-6 eV, while forces acting on atoms don't exceed 1e-2 eV/angstrom. The electron-ion interaction is described by PAW pseudopotentials. The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 4. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 3,100 randomized atomic structures over 31 chemical compositions.

36 MATERIALS SCIENCE↗