All-electron Relativistic Calculations Research Articles

Structural, electronic, and optical properties of Pt-based vacancy-ordered double perovskites A2PtX6 (A = K, Rb, Cs; X = Cl, Br, I) in tetragonal P4/mnc polymorph

We study the structural, electronic, and optical properties of the Pt-based vacancy-ordered double perovskites A 2 Pt X 6 ( A = K, Rb, Cs; X = Cl, Br, I) in the tetragonal P 4/ mnc polymorph using the relativistic all-electron calculations based on the density functional theory. It is found that the rotation angles θ of the Pt X 6 octahedra are non-zero for all the compounds. For a given A -site cation, θ increases from Cl to Br to I while for a given halide anion, θ decreases from K to Rb to Cs. As a result, the largest θ is found for K 2 PtI 6 . Taking the three iodides, K 2 PtI 6 , Rb 2 PtI 6 and Cs 2 PtI 6 , as representatives, it is found that K 2 PtI 6 is a direct-band-gap semiconductor and that Rb 2 PtI 6 and Cs 2 PtI 6 are quasi-direct-band-gap semiconductors with the small differences between the indirect and direct band gaps. The band gap in the tetragonal P 4/ mnc polymorph is larger than the corresponding one in the cubic F m 3 ̄ m polymorph. Employing the spectroscopically limited maximum efficiency as a metric for quantifying the photovoltaic performance, K 2 PtI 6 , Rb 2 PtI 6 , and Cs 2 PtI 6 are found to be promising absorber materials for thin-film solar cells. • Pt-based vacancy-ordered double perovskites A 2 Pt X 6 in tetragonal P 4/ mnc polymorph were studied theoretically. • Non-zero rotation angles of Pt X 6 octahedra were found for all the compounds. • The electronic and optical properties of K 2 PtI 6 , Rb 2 PtI 6 , and Cs 2 PtI 6 were examined as representatives.

Theoretical study of structural, electronic, and optical properties of mixed chalcogenide-halide bismuth perovskites CH3NH3BiChI2 (Ch = S, Se, Te)

We investigate the structural, electronic, and optical properties of the mixed chalcogenide-halide bismuth perovskites CH3NH3BiChI2 (Ch = S, Se, Te) using the relativistic all-electron calculations. We use the structural model where the Ch atoms are placed at the apical position in the BiCh2I4 octahedron. It is found that the structures of CH3NH3BiChI2 are contracted in the apical direction and the Bi–Ch bond lengths decrease in the order of Ch = S, Se, and Te. CH3NH3BiChI2 exhibit anisotropic optical properties and show higher absorption coefficients than CH3NH3PbI3. Furthermore, employing the spectroscopically limited maximum efficiency as a metric for quantifying the photovoltaic performance, we find that CH3NH3BiSI2 and CH3NH3BiSeI2 are promising candidates for thin-film solar cells.

Segmented Contracted Error-Consistent Basis Sets of Quadruple-ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations.

Segmented contracted basis sets of quadruple-ζ quality for exact two-component (X2C) calculations are presented for the elements H-Rn. These sets are the all-electron relativistic counterparts of the Karlsruhe "def2" and "dhf" systems of bases, which were designed for Hartree-Fock and density functional treatments and-with a somewhat extended set-also for correlated treatments. The bases were optimized with analytical basis set gradients and the finite nucleus model based on a Gaussian charge distribution at the scalar-relativistic X2C level. Extensions are provided for self-consistent two-component treatments to describe spin-orbit coupling, polarization effects, and nuclear magnetic resonance (NMR) shielding constants. The basis sets were designed to yield comparable errors in atomization energies, orbital energies, dipole moments, and NMR shielding constants all across the periodic table of elements. A test set of more than 360 molecules representing (nearly) all elements in their common oxidation states was utilized for the valence properties, and a test set of more than 250 closed-shell molecules was employed for the NMR shielding constants. The quality of the developed basis sets is compared to other frequently used relativistic all-electron bases.

Theoretical study of structural, electronic, and optical properties of ternary metal sulfides MBiS2 (M = Ag, Na)

We study the structural, electronic, and optical properties of MBiS2 (M = Ag, Na) using the relativistic all-electron calculations. We find that for both M = Ag and Na, the and superstructures are the lowest-energy superstructures. and MBiS2 are indirect band-gap semiconductors with the differences between the indirect and direct band gaps, Δ, of about 0.5 and 0.1 eV for M = Ag and Na, respectively. and MBiS2 exhibit high absorption coefficients of the order of 105 cm−1. Employing the spectroscopically limited maximum efficiency as a metric for quantifying the photovoltaic performance, it is found that the power conversion efficiency in the thick-film limit for M = Na is 32% because of its small Δ while that for M = Ag is 15% because of its large Δ.

Theoretical study on electronic and optical properties of mixed valence perovskite Cs2Au2X6 (X = Cl, Br, I)

We study the electronic and optical properties of the mixed valence perovskite Cs2Au2X6 (X = Cl, Br, I) using the fully relativistic all-electron calculations. We find that Cs2Au2X6 exhibits indirect fundamental band gaps although the differences between the indirect and direct band gaps are small. For the electric field of light perpendicular to the tetragonal c axis, Cs2Au2Br6 and Cs2Au2I6 exhibit the maximum absorption coefficient of about 20 × 104 cm−1 around the photon energy of 2 eV, which is considerably larger than that of CH3NH3PbI3. For the electric field of light parallel to the tetragonal c axis, the absorption coefficient of Cs2Au2I6 is comparable to that of CH3NH3PbI3 in the main part of the solar spectrum. Furthermore, we estimate the photovoltaic performance of Cs2Au2X6 employing the spectroscopically limited maximum efficiency as a metric and discuss its dependence on the film thicknes in detail.

Reliable and computationally affordable prediction of the energy gap of (TiO2)n (10 ≤ n ≤ 563) nanoparticles from density functional theory.

The optical gap (Ogap) of a set of (TiO2)n nanoclusters and nanoparticles with n = 10-563 and different morphologies such as spherical, octahedral, lamellar, or tubular finite structures is investigated based on a relativistic all-electron description along with a numerical atomic centered orbital basis set. Two different functionals are used, PBE and PBEx, the former corresponds to a standard implementation of the generalized gradient approximation (GGA) and the latter to a hybrid functional with 12.5% of Fock exchange which reproduces the band gap of bulk TiO2 anatase and rutile. It is shown that the inclusion of exchange Fock in the PBE functional promotes a systematic energy gap opening of 1.25 eV relative to the PBE values. Remarkably, a linear correlation is found between PBEx and PBE Ogap calculated values with concomitant similar correlations for the HOMO and LUMO orbital energies. However, it appears that PBEx induces a larger downshift on the HOMO orbital than the upshift observed on the LUMO one. The fact that the PBEx hybrid functional was shown to reproduce the experimental energy gaps of stoichiometric and reduced TiO2 bulk phases leads to a suitable and practical way to successfully estimate Ogap of TiO2 nanoparticles containing up to thousands of atoms with PBEx precision from computationally affordable PBE calculations.

Methanol molecule adsorption on small platinum-doped gold clusters

An all-electron relativistic calculation on Au n PtCH3OH (n = 1–12) clusters had been performed using density functional theory with the generalized gradient approximation at the Perdew–Wang91 (PW91) level. The CH3OH molecule prefers to be adsorbed on Pt atom in Au n Pt (n = 1–5, 9) clusters and the complexes formed by bonding CH3OH at the on-top site with one gold atom are the lowest energy geometries for other Au n PtCH3OH clusters. The introduction of impure Pt strengthens the adsorption toward the CH3OH molecule then promotes the reactivity enhancement of the CH3OH molecule. An odd-even alteration of electronic structure stability for Au n PtCH3OH (n = 1–12) clusters can be observed clearly.

Segmented Contracted Error-Consistent Basis Sets of Double- and Triple-ζ Valence Quality for One- and Two-Component Relativistic All-Electron Calculations.

Segmented contracted Gaussian basis sets optimized at the one-electron exact two-component (X2C) level - including a finite size model for the nucleus - are presented for elements up to Rn. These basis sets are counterparts for relativistic all-electron calculations to the Karlsruhe "def2" basis sets for nonrelativistic (H-Kr) or effective core potential based (Rb-Rn) treatments. For maximum consistency, the bases presented here were obtained from the latter by modification and reoptimization. Additionally we present extensions for self-consistent two-component calculations, required for the splitting of inner shells by spin-orbit coupling, and auxiliary basis sets for fitting the Coulomb part of the Fock matrix. Emphasis was put both on the accuracy of energies of atomic orbitals and on the accuracy of molecular properties. A large set of more than 300 molecules representing (nearly) all elements in their common oxidation states was used to assess the quality of the bases all across the periodic table.

Ab initio calculation on the low-lying excited states of [formula omitted] cation including spin–orbit coupling

Ab initio all-electron relativistic calculations of the low-lying excited states of Si2+ have been performed at MRCI+Q/AVQZ level. The calculated electronic states, including 12 doublet and 12 quartet Λ–S states, are correlated to the dissociation limit of Si(3Pg)+Si+(2Pu). Spin–orbit interaction is taken into account via the state interaction approach with the full Breit-Pauli Hamiltonian, which causes the entire 24 Λ–S states to split into 54Ω states. This is the first time that spin–orbit coupling (SOC) calculation has been performed on Si2+. The obtained potential energy curves (PECs) of Λ–S and Ω states are respectively depicted with the aid of the avoided crossing rule between the same symmetry. The spectroscopic constants of the bound Λ–S and Ω states are determined, and excellent agreements with the latest theoretical results are achieved.

Solution Structure of Ln(III) Complexes with Macrocyclic Ligands Through Theoretical Evaluation of 1H NMR Contact Shifts

Herein, we present a new approach that combines DFT calculations and the analysis of Tb(III)-induced (1)H NMR shifts to quantitatively and accurately account for the contact contribution to the paramagnetic shift in Ln(III) complexes. Geometry optimizations of different Gd(III) complexes with macrocyclic ligands were carried out using the hybrid meta-GGA TPSSh functional and a 46 + 4f(7) effective core potential (ECP) for Gd. The complexes investigated include [Ln(Me-DODPA)](+) (H(2)Me-DODPA = 6,6'-((4,10-dimethyl-1,4,7,10-tetraazacyclododecane-1,7-diyl)bis(methylene))dipicolinic acid, [Ln(DOTA)(H(2)O)](-) (H(4)DOTA = 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetate), [Ln(DOTAM)(H(2)O)](3+) (DOTAM = 1,4,7,10- tetrakis[(carbamoyl)methyl]-1,4,7,10-tetraazacyclododecane), and related systems containing pyridyl units (Ln = Gd, Tb). Subsequent all-electron relativistic calculations based on the DKH2 approximation, or small-core ECP calculations, were used to compute the (1)H hyperfine coupling constants (HFCCs) at the ligand nuclei (A(iso) values). The calculated A(iso) values provided direct access to contact contributions to the (1)H NMR shifts of the corresponding Tb(III) complexes under the assumption that Gd and Tb complexes with a given ligand present similar HFCCs. These contact shifts were used to obtain the pseudocontact shifts, which encode structural information as they depend on the position of the nucleus with respect to the lanthanide ion. An excellent agreement was observed between the experimental and calculated pseudocontact shifts using the DFT-optimized geometries as structural models of the complexes in solution, which demonstrates that the computational approach used provides (i) good structural models for the complexes, (ii) accurate HFCCs at the ligand nuclei. The methodology presented in this work can be classified in the context of model-dependent methods, as it relies on the use of a specific molecular structure obtained from DFT calculations. Our results show that spin polarization effects dominate the (1)H A(iso) values. The X-ray crystal structures of [Ln(Me-DODPA)](PF(6))·2H(2)O (Ln = Eu or Lu) are also reported.

Scalable properties of metal clusters: A comparative study of modern exchange-correlation functionals

The performance of eight generalized gradient approximation exchange-correlation (xc) functionals is assessed by a series of scalar relativistic all-electron calculations on octahedral palladium model clusters Pd(n) with n = 13, 19, 38, 55, 79, 147 and the analogous clusters Au(n) (for n up through 79). For these model systems, we determined the cohesive energies and average bond lengths of the optimized octahedral structures. We extrapolate these values to the bulk limits and compare with the corresponding experimental values. While the well-established functionals BP, PBE, and PW91 are the most accurate at predicting energies, the more recent forms PBEsol, VMTsol, and VT{84}sol significantly improve the accuracy of geometries. The observed trends are largely similar for both Pd and Au. In the same spirit, we also studied the scalability of the ionization potentials and electron affinities of the Pd clusters, and extrapolated those quantities to estimates of the work function. Overall, the xc functionals can be classified into four distinct groups according to the accuracy of the computed parameters. These results allow a judicious selection of xc approximations for treating transition metal clusters.

Accurate relativistic energy-consistent pseudopotentials for the superheavy elements 111 to 118 including quantum electrodynamic effects

Energy-consistent two-component semi-local pseudopotentials for the superheavy elements with atomic numbers 111-118 have been adjusted to fully relativistic multi-configuration Dirac-Hartree-Fock calculations based on the Dirac-Coulomb Hamiltonian, including perturbative corrections for the frequency-dependent Breit interaction in the Coulomb gauge and lowest-order quantum electrodynamic effects. The pseudopotential core includes 92 electrons corresponding to the configuration [Xe]4f(14)5d(10)5f(14). The parameters for the elements 111-118 were fitted by two-component multi-configuration Hartree-Fock calculations in the intermediate coupling scheme to the total energies of 267 up to 797 J levels arising from 31 up to 62 nonrelativistic configurations, including also anionic and highly ionized states, with mean absolute errors clearly below 0.02 eV for averages corresponding to nonrelativistic configurations. Primitive basis sets for one- and two-component pseudopotential calculations have been optimized for the ground and excited states and exhibit finite basis set errors with respect to the finite-difference Hartree-Fock limit below 0.01 and 0.02 eV, respectively. General contraction schemes have been applied to obtain valence basis sets of polarized valence double- to quadruple-zeta quality. Results of atomic test calculations in the intermediate coupling scheme at the Fock-space coupled-cluster level are in good agreement with those of corresponding fully relativistic all-electron calculations based on the Dirac-Coulomb-Breit Hamiltonian. The results demonstrate besides the well-known need of a relativistic treatment at the Dirac-Coulomb level also the necessity to include higher-order corrections for the superheavy elements.

Performance of Effective Core Potentials for Density Functional Calculations on 3d Transition Metals.

The performance of popular Hartree-Fock-based effective core potentials in Hartree-Fock and density functional calculations of 3d transition metals has been evaluated by basis-set convergence studies for ten cases: the equilibrium bond dissociation energy (De) for dissociation of ground-state Ti2 to ground and excited atoms, the ground-state dissociation energies of FeO, Cu2, ScH, TiH, Sc2, Fe2, and TiV(+), and the first excitation energy (Ex) of Ti atom. Each case is studied with 11 or 13 density functionals. For comparison, the accuracy of the all-electron def2-TZVP basis set is tested with both relativistic and nonrelativistic treatments. Convergence and accuracy are assessed by comparing to relativistic all-electron calculations with a nearly complete relativistic basis set (NCBS-DK, which denotes the cc-pV5Z-DK basis set for 3d metals and hydrogen and the ma-cc-pV5Z-DK basis set for oxygen) and to nonrelativistic all-electron calculations with a nearly complete nonrelativistic basis set (NCBS-NR, which denotes the cc-pV5Z basis set for 3d metals and hydrogen and the ma-cc-pV5Z basis set for oxygen). As compared to NCBS-DK results, all ECP calculations perform worse than def2-TZVP all-electron relativistic calculations when averaged over all 130 data (13 functionals and ten test cases). The compact effective potential (CEP) relativistic effective core potential (RECP) combined with a valence basis set developed for the many-electron Dirac-Fock (MDF10) RECP performs best in effective core potential calculations and has an average basis-set incompleteness error of 3.7 kcal/mol, which is much larger than that (0.9 kcal/mol) of def2-TZVP relativistic all-electron results. Hence, the def2-TZVP relativistic all-electron calculations are recommended for accurate DFT calculations on 3d transition metals. In addition to our general findings, we observed that all kinds of density functionals do not show the same trends. For example, when ECPs are used with hybrid functionals, which sometimes are not recommended for calculations of transition metal systems, they are found to perform better at achieving the basis-set limit than when used with local functionals and meta-GGA functionals. The most successful combination of RECP and basis set has a basis-set incompleteness error of 1.7-2.4 kcal/mol for hybrid generalized gradient approximations, which is smaller than that of nonrelativistic NCBS calculations (whose average basis-set incompleteness error for hybrid functionals is 2.7-2.9 kcal/mol). The average basis-set incompleteness error in Hartree-Fock calculations is 1.0-4.4 kcal/mol for five of the ECP basis sets but is 5.8-10.8 kcal/mol for six others.

Accuracy of Effective Core Potentials and Basis Sets for Density Functional Calculations, Including Relativistic Effects, As Illustrated by Calculations on Arsenic Compounds.

For molecules containing the fourth-period element arsenic, we test (i, ii) the accuracy of all-electron (AE) basis sets from the def2-xZVP and ma-xZVP series (where xZ is S, TZ, or QZ), (iii) the accuracy of the 6-311G series of AE basis sets with additional polarization and diffuse functions, and (iv) the performance of effective core potentials (ECPs). The first set of tests involves basis-set convergence studies with eleven density functionals for five cases: equilibrium dissociation energy (De) of As2, vertical ionization potential (VIP) of As2, IP of As, acid dissociation of H3AsO4, and De of FeAs. A second set of tests involves the same kinds of basis-set convergence studies for the VIP and De values of As3 and As4 clusters. Both relativistic and nonrelativistic calculations are considered, including in each case both AE calculations and calculations with ECPs. Convergence and accuracy are assessed by comparing to relativistic AE calculations with the cc-pV5Z-DK or ma-cc-pV5Z-DK basis and to nonrelativistic AE calculations with the cc-pV5Z or ma-cc-pV5Z basis. The primary objective of this study is to evaluate the abilities of ECPs with both their recommended basis sets and other basis sets to reproduce the results of all-electron relativistic calculations. The performance of the def2 and ma series basis sets is consistent with their sizes, and quadruple-ζ basis sets are the best. The def2-TZVP basis set performs better than most of the 6-311G series basis sets, which are the most commonly used basis sets in the previous studies of arsenic compounds. However, relativistic def2-TZVP calculations are not recommended. The large-core ECPs, which are the only available ECPs for arsenic in the popular Gaussian program, have average errors of 9-12 kcal/mol for the arsenic systems studied; therefore, these ECPs are not recommended. The triple-ζ small-core relativistic ECP (RECP) basis set cc-pVTZ-PP is found to have performance better than that of the def2-TZVP basis set, and it is highly recommended for arsenic-containing systems. The double-ζ RECP basis set ma-sc-SVP is recommended for large arsenic systems for which the def2-TZVP and cc-pVTZ-PP basis sets are unaffordable, if a basis-set error of ∼2 kcal/mol can be tolerated.

Crystal and electronic structure of LaPdSn and RE3Pd 4Sn 6 ( RE = La, Ce)

The stannide LaPdSn has been synthesized by arc-melting and the structure has been refined from X-ray single crystal diffractometer data: TiNiSi type, Pnma, a = 763.8(1), b = 473.47(7), c = 799.4(1) pm, wR2 = 0.0417, 548 F 2 values, 20 variables. The electronic structures of LaPdSn, La 3Pd 4Sn 6 and Ce 3Pd 4Sn 6 (own type) were investigated through scalar relativistic all-electron calculations within the DFT framework. The three stannides show a weakly metallic behavior with itinerant states crossing the Fermi level. The chemical bonding strength is such that Pd–Sn > La(Ce)–Sn > La(Ce)–Pd with a relevant feature of significant Sn–Sn bonding in La 3Pd 4Sn 6, in agreement with the interatomic distances in the [PdSn], respectively [Pd 4Sn 6] polyanions. Spin polarized calculations on Ce 3Pd 4Sn 6 show spin polarization on all three crystallographically independent cerium sites, leading to ferrimagnetism.

All-electron relativistic calculations on hydrogen atom adsorption onto small copper clusters

An all-electron scalar relativistic calculation on Cu n H (n = 1–13) clusters has been performed by using density functional theory with the generalized gradient approximation at the PW91 level. Our results reveal that the hydrogen atom prefers to occupy the two fold coordination site for Cu n H (n = 2, 4–6, 8, 10–13) clusters, the single fold coordination site for Cu n H (n = 1, 3, 7) and the three fold coordination site for Cu9H cluster. For all Cu n H clusters, only the Cu11 structure in Cu11H is distorted obviously. After adsorption, the Cu–Cu bond is strengthened and the Cu–H bond of odd-numbered Cu n H clusters is relatively stronger than that of adjacent even-numbered Cu n H clusters. The Cu–Cu bond-length and Cu–H bond-length for all Cu n H clusters of our work are significantly shorter than those of previous work. This discrepancy can be explained in terms of the scalar relativistic effect. The most favorable adsorption between small copper clusters and hydrogen atom takes place in the case that hydrogen atom is adsorbed onto an odd-numbered pure Cu n cluster and becomes Cu n H cluster with even number of valence electrons. The odd–even alteration of magnetic moments is observed in Cu n H clusters and may provide the material with tunable code capacity of “0” and “1” by adsorbing a hydrogen atom onto odd- or even-numbered copper clusters.

All-electron relativistic calculation on Au5X (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn) clusters

All-electron scalar relativistic calculations on Au5X (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn) clusters have been performed by using density functional theory with the generalized gradient approximation. Our calculation results indicate that all the lowest energy geometries of Au5X clusters have planar structures; the doped X atoms prefer to occupy the fourfold coordination site. Except Au5Fe, Au5Co and Au5Zn, for other clusters including pure Au6 cluster, the HOMO are delocalized obviously with a contribution from all atoms in the cluster. On the contrary, the electron localization in Au5Zn is very strong resulting in the least stability of this cluster. Au5Cu cluster with six delocalized electrons being defined as magic number for two-dimensional system has the largest VIP and deepest HOMO energy level. With the substitution Au for X atoms, the metallicity of all Au5X clusters is reinforced.

Electronic band structure of [formula omitted] from first principles

Band theoretical results are presented on calcium uranate, CaUO 4 , based on computations within the density functional theory. From pseudo-potential calculations the equation of state is obtained with equilibrium lattice properties in agreement with experiment. For isotropic volume change the bulk modulus amounts to 180 GPa but a much higher value is found for anisotropic compression along the hexagonal c-axis. This is assigned to the short U–O distances in linear uranyl polycation. Scalar relativistic all-electron calculations point to a semiconductor with ~ 3 eV band gap. From density of states, chemical bonding and electron localization function ELF, oxygen is found to behave both as ionic and covalent in the coordination sphere of uranium. The results provide an illustration of the peculiar role of uranyl cation UO 2 2 + according to its chemical environment.

New model core potentials for gold

Four model core potentials (MCPs) for gold were developed using results from the third-order Douglas-Kroll-Hess relativistic all-electron calculations. The MCPs were developed with four different valence spaces, ranging from the 5p, 5d, and 6s orbitals to 5s, 4f, 5p, 5d, and 6s orbitals. The new MCPs were applied in the calculations of atomic properties and potential energy curves of AuH and Au(2). Results indicate that the 4f orbital may be excluded but the 5s orbital must be included in the valence space because of the importance of 5s-6s electron correlation. The model core potential that has the valence space comprising the 5s, 5p, 5d, and 6s orbitals is considered to be the most accurate and efficient of these new potentials.

First-principles study of single-crystal uranium mono- and dinitride

We report all-electron relativistic calculations of the electronic and thermodynamic properties of perfect stoichiometric UN and UN 2 single crystals using the spin-polarized density functional theory. The calculated lattice parameters and interatomic distances of the relaxed unit cells are in very good agreement with recent extended X-ray absorption fine structure (EXAFS) and X-ray diffraction (XRD) data. Densities of states and molecular orbitals show the importance of d–f hybridization and p-orbital contributions in the valence band of UN and UN 2, respectively, while f-orbital character dominates the conduction band of both compounds. The heat capacity of UN derived from the present calculations reproduces calorimetric data within 4% up to 1000 K.