Scalar Relativistic Approximation Research Articles

Reexamination of the ground-state Born-Oppenheimer Yb2 potential

The precision of the photoassociation spectroscopy of Yb dimer in degenerate gases is enough to improve the constraints on the new short-range gravity-like forces if the theoretical knowledge of the Born-Oppenheimer interatomic potential and non-Born-Oppenheimer interactions is refined [M. Borkowski et al. Sci. Rep. A {\bf 9}, 14807 (2019)]. The ground-state interaction potential of ytterbium dimer is investigated at the eXact 2-component core-correlated CCSD(T) level of {\it ab initio} theory in the complete basis set limit with extensive augmentation by diffuse functions. For the small basis set the comparison is made with the four-component relativistic finite-nuclei CCSD(T) calculations to identify the contraction of the dimer bond length as the main unrecoverable consequence of the scalar-relativistic approximation. Empirical constraint on the number of bound vibrational energy levels of the $^{174}$Yb$_2$ dimer is accounted for by representing the global {\it ab initio}-based Born-Oppenheimer potential with the model semianalytical function containing the scale and shift parameters. The results support the previous evaluation of the Yb dimer potentials from the photoassociation spectroscopy data and provide an accurate and flexible reference for future refinement of the constraints on the short-range gravity-like forces by ultracold atomic spectroscopy.

Optimization of atomic density-fitting basis functions for molecular two-electron integral approximations.

A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the product densities, modeling their contribution to the exchange and second-order correlation energy, and a simple weighted error measure is minimized. Generally contracted Gaussian auxiliary basis sets are optimized to match the wavefunction basis sets [D. N. Laikov, Theor. Chem. Acc. 138, 40 (2019)] for all 102 elements in a scalar-relativistic approximation [D. N. Laikov, J. Chem. Phys. 150, 061103 (2019)].

Electron energy loss spectroscopy of bulk gold with ultrasoft pseudopotentials and the Liouville-Lanczos method

The implementation of ultrasoft pseudopotentials into time-dependent density-functional perturbation theory is detailed for both the Sternheimer approach and the Liouville-Lanczos (LL) method, and equations are presented in the scalar relativistic approximation for periodic solids with finite momentum transfer q. The LL method is applied to calculations of the electron energy loss (EEL) spectrum of face-centered cubic bulk Au both at vanishing and finite q. Our study reveals the richness of the physics underlying the various contributions to the density fluctuation in gold. In particular, our calculations suggest the existence in gold of two quasi-separate 5d and 6s electron gasses, each one oscillating with its own frequency at resp. 5.1 eV and 10.2 eV. We find that the contribution near 2.2 eV comes from 5d to 6s interband transitions modified by the intraband contribution to the real part of the dielectric function, which we call a mixed excitation.

Two-dimensional square lattice polonium stabilized by the spin\u2013orbit coupling

Polonium is known as the only simple metal that has the simple cubic (SC) lattice in three dimension. There is a debate about whether the stabilized SC structure is attributed to the scalar relativistic effect or the spin–orbit coupling (SOC). Here, we study another phase, two-dimensional (2D) polonium (poloniumene), by performing density-functional theory calculations. We show that the 2D polonium has the square lattice structure as its ground state and demonstrate that the SOC (beyond the scalar relativistic approximation) suppresses the Peierls instability and is necessary to obtain no imaginary phonon frequencies over the Brillouin zone.

Uniaxial negative thermal expansion and band renormalization in monolayer Td−MoTe2 at low temperature

The temperature-induced structure variation and its effect on physical properties is pivotal in material preparation for devices application. Motivated by surface scanning tunnel microscope (STM) measurement of ${T}_{d}\ensuremath{-}{\mathrm{MoTe}}_{2}$ single crystal at low temperature, temperature dependent electronic structure, lattice dynamics, and topological properties are explored to understand the microscopic origin of the observed anisotropic negative thermal expansion and abnormal STM images below 70 K. Remarkably, we find that the nonequivalent Te atoms in ${T}_{d}\ensuremath{-}{\mathrm{MoTe}}_{2}$ have qualitatively different contributions to both phonon spectra and electronic structures. The in-plane longitudinal acoustic mode and the ${\mathrm{Te}}_{(2)}$ atoms are found to play an important role in uniaxial negative thermal expansion and the temperature dependent electronic phase transition, respectively. Interestingly, under the scalar relativistic approximation, a band renormalization occurs, accompanied by a Dirac phase transition from type II to type I, upon cooling below 70 K. Introducing spin-orbit coupling induces a temperature dependent semimetal--semiconductor transition. Our results explain the experimental phenomena very well: abnormal surface STM image below 70 K does not originate from the displacement of the Te atoms but the band renormalization owing to strong electron-lattice coupling.

Theoretical Study of the Mechanism of Propionic Acid Deoxygenation on the Palladium Surface

Using the DFT–PBE method in the scalar relativistic approximation, the mechanisms of the two main pathways of propionic acid deoxygenation on the rough and flat (111) palladium surfaces have been studied. According to the calculations, in the decarboxylation mechanism on rough and flat surfaces, the formation of the following intermediates is preferable: C2H5COO, C2H4COO, and C2H4. For the second deoxygenation pathway via decarbonylation reactions, the mechanisms on different surfaces of palladium differ. Thus, on a rough surface, the most likely steps are C2H5COOH → C2H5CO → C2H5 → C2H4, and on the Pd(111) surface the most likely steps are C2H5COOH → C2H4COOH → C2H4CO → C2H4. The coordination unsaturation of palladium atoms contributes to a decrease in the activation barriers of the reaction by 8–13 kcal/mol. Thus, the flat surface of palladium particles is less active in the deoxygenation of carboxylic acids. The type of palladium surface insignificantly affects the selectivity of deoxygenation. On a rough surface, the decarbonylation rate is slightly higher than the rate of decarboxylation. On the Pd(111) surface, the rate of decarboxylation is higher. The difference in the activation barriers of these pathways of deoxygenation is small (0.7 kcal/mol).

Atomic basis functions for molecular electronic structure calculations

Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of higher quality. Following our earlier work [Chem. Phys. Lett. 416, 116 (2005)] where general correlation-consistent basis sets are defined, for any atom, as solutions of purely atomic functional minimization problems, and which are shown to work well for chemical bonding in molecules, we take a further step here and define a new kind of atomic polarization functionals, the minimization of which yields additional sets of diffuse functions that help to calculate better molecular electron affinities, polarizabilities, and intermolecular dispersion interactions. Analytical representations by generally-contracted Gaussian functions of up to microhartree numerical accuracy grades are developed for atoms Hydrogen through Nobelium within the four-component Dirac-Coulomb theory and its scalar-relativistic approximation, and also for Hydrogen through Krypton in the two-component nonrelativistic case. The convergence of correlation energy with the basis set size is studied, and complete-basis-set extrapolation formulas are developed.

Absence of the Rashba Splitting of Au(111) Surface Bands

The electronic structure of Au(111) films is studied by means of relativistic DFT calculations. It is found that the twinning of the surface bands, observed in photoemission experiment, does not necessarily correspond to the spin-splitting of the surface states caused by the break of the inversion symmetry at the surface. The twinning of the bands of clean Au(111) films can be obtained within nonrelativistic or scalar-relativistic approximation, so that it is not a result of spin-orbit coupling. However, the spin-orbit coupling does not lead to the spin-splitting of the surface bands. This result is explained by Kramers’ degeneracy, which means that the existence of a surface itself does not destroy the inversion symmetry of the system. The inversion symmetry of the Au(111) film can be broken, for example, by means of adsorption, and a hydrogen monolayer deposited on one face of the film indeed leads to the appearance of the spin-splitting of the bands.

DFT Modeling of Mechanism of Hydrogenation of Phenylacetylene into Styrene on a Pd(111) Surface

A quantum chemical study of the possible routes of the phenylacetylene (PA) hydrogenation to styrene on a Pd(111) surface is carried out by the DFT-PBE method in the scalar-relativistic approximation. It is shown that the routes associated with the formation of the Ph–C–CH2 or Ph–CH–CH intermediates at the first stage have similar values of the turnover frequency (156 and 48 h–1, respectively). The route associated with the 1,2-hydride transfer in the adsorbed PA molecule is improbable due to the formation of a thermodynamically stable intermediate, Ph–CH–C. The interaction of the Ph group in the adsorbed PA molecule with the metal surface leads to the nonselective hydrogenation of the PA.

Quantum chemical study of H2 adsorption on Pd21 cluster

Modeling of the interaction of an H2 molecule with the surface of the Pd21 cluster in different spin states was performed using the DFT/PBE scalar relativistic approximation. The spin multiplicity of the system significantly affects the mechanism of adsorption, its parameters, and migration of hydrogen atoms. The H atoms can migrate over the cluster surface with low barriers (1.6 kcal mol–1). The complex with C 2v symmetry, wherein the H atoms occupy adjacent fcc sites, is the most energetically stable.

Quantum chemical modeling of phenylacetylene and styrene adsorption over Pd21 cluster

The adsorption interaction of phenylacetylene and styrene molecules with the Pd21 cluster was modeled in terms of the scalar relativistic approximation of the density functional theory (DFT/PBE). Various types of adsorption complexes were described, and their structural and energy characteristics were analyzed. The adsorption of phenylacetylene over Pd21 both in the presence and in the absence of pre-adsorbed hydrogen is thermodynamically more preferable.

Adsorption of carbon oxide on tetrahedral bimetallic gold–copper clusters

The interaction between carbon oxide and [Au20–nCun]q clusters (n = 0, 1, 19, 20 and q = 0, ±1) is studied by means of DFT/PBE in the scalar relativistic approximation. To establish the composition and structure of an adsorption site, isomers of bimetallic Au19Cu and AuCu19 particles with different positions of the heteroatom at an apex, edge, and face of the tetrahedral framework are considered. The optimized structures are used as the basis to determine the electronic properties of clusters (average bond energy per atom, difference of energies between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), ionization potential, electron affinity energy). The calculated parameters shrink as the copper content in clusters grows. Among the uncharged models, the highest CO adsorption energy is typical of Au19Cu, the heteroatom of which lies at a cluster’s apex. The CO adsorption energy for cationic and anionic clusters grows in comparison to neutral clusters.

Elimination of the linearization error and improved basis-set convergence within the FLAPW method

We analyze in detail the error that arises from the linearization in linearized augmented-plane-wave (LAPW) basis functions around predetermined energies El and show that it can lead to undesirable dependences of the calculated results on method-inherent parameters such as energy parameters El and muffin-tin sphere radii. To overcome these dependences, we evaluate approaches that eliminate the linearization error systematically by adding local orbitals (LOs) to the basis set. We consider two kinds of LOs: (i) constructed from solutions ul(r,E) to the scalar-relativistic approximation of the radial Dirac equation with E>El and (ii) constructed from second energy derivatives ∂2ul(r,E)/∂E2 at E=El. We find that the latter eliminates the error most efficiently and yields the density functional answer to many electronic and materials properties with very high precision. Finally, we demonstrate that the so constructed LAPW +LO basis shows a more favorable convergence behavior than the conventional LAPW basis due to a better decoupling of muffin-tin and interstitial regions, similarly to the related APW +lo approach, which, however, requires an extra set of LOs to reach the same total energy.

Charge transfer in cold Yb++Rb collisions

Charge-transfer cold Yb$^+$ + Rb collision dynamics is investigated theoretically using high-level {\it ab initio} potential energy curves, dipole moment functions and nonadiabatic coupling matrix elements. Within the scalar-relativistic approximation, the radiative transitions from the entrance $A^1\Sigma^+$ to the ground $X^1\Sigma^+$ state are found to be the only efficient charge-transfer pathway. The spin-orbit coupling does not open other efficient pathways, but alters the potential energy curves and the transition dipole moment for the $A-X$ pair of states. The radiative, as well as the nonradiative, charge-transfer cross sections calculated within the $10^{-3}-10$ cm$^{-1}$ collision energy range exhibit all features of the Langevin ion-atom collision regime, including a rich structure associated with centrifugal barrier tunneling (orbiting) resonances. Theoretical rate coefficients for two Yb isotopes agree well with those measured by immersing Yb$^+$ ion in an ultracold Rb ensemble in a hybrid trap. Possible origins of discrepancy in the product distributions and relations to previously studied similar processes are discussed.

Two-Component Relativistic Calculations of Electric-Field Gradients Using Exact Decoupling Methods: Spin-orbit and Picture-Change Effects.

Electric field gradients (EFGs) for heavy nuclei in diatomic molecules (hydrogen halides and group-13 iodides), uranyl (UO22+), and a uranyl carbonate complex, were computed with different formally exactly (or nearly exactly) decoupled two-component relativistic Hamiltonians: the “exact two-component” (X2C) method, the Barysz–Sadlej–Snijders (BSS) approach, and up to 35th order in the Douglas–Kroll–Hess (DKH) expansion, utilizing a new implementation in the open-source NWChem quantum chemistry package. Results from two-component Hartree–Fock and density functional theory (DFT) calculations at the scalar relativistic approximation as well as including spin–orbit coupling are reported. Picture-change corrected EFGs obtained with X2C, BSS, and high-order DKH are shown to be numerically equivalent. Effects from spin–orbit coupling on the EFGs tend to be moderate but should not be excluded for reliable predictions. Picture-change effects on the EFG of a heavy atom can be as large as the correct picture-change ...

Compton profiles and electronic properties of Nd

We report the Compton profile (CP) measurement of Nd using a 20 Ci 137Cs Compton spectrometer. To interpret our experimental Compton data, we have also computed the CPs using the spin-polarized relativistic Korringa–Kohn–Rostoker (SPR-KKR) method and the linear combination of atomic orbitals method. To check the role of spin–orbit coupling in KKR calculations, we have also computed the CPs within the scalar relativistic approximation. It is seen that the CPs calculated using relativistic KKR calculations are in better agreement with the present experiment than scalar relativistic KKR calculations and the generalized gradient approximation (GGA) within the pseudopotential density functional theory and the recently developed second-order GGA. Using the SPR-KKR method, we have also computed the energy bands along with total and partial density of states of Nd.

Transition metal impurity effect on charge and spin density in iron: Ab initio calculations and comparison with Mössbauer data

Density functional theory was applied to study influence of the isolated impurity located on the regular site of the α-Fe crystal on the charge and spin density (hyperfine interactions) on the iron nucleus. Calculations were performed using both pseudopotential and the full potential methods. The scalar relativistic approximation was applied. Perturbations of the charge and spin density on iron were calculated for all d impurities soluble in iron and additionally for Ga impurity. It was found that impurities have measurable effect on the iron charge and spin density up to the second or third coordination shell depending on the impurity. Hyperfine parameters of iron adjacent to the impurity are affected by two intermixed physical mechanisms, i.e., the volume mismatch due to the impurity and electron band mixing caused by the electronic configuration of the impurity outer shells. Some correlations between ab initio calculations and Mössbauer experimental results are discussed. A table is provided with the parameters allowing calculate Mössbauer spectrum of the binary iron alloy with d impurity or Ga. On the other hand, provided parameters allow extraction from the Mössbauer data information about impurity concentration and eventual order.

Scalar Relativistic Computations of Nuclear Magnetic Shielding and g-Shifts with the Zeroth-Order Regular Approximation and Range-Separated Hybrid Density Functionals.

Density functional theory (DFT) calculations of NMR chemical shifts and molecular g tensors with Gaussian-type orbitals are implemented via second-order energy derivatives within the scalar relativistic zeroth order regular approximation (ZORA) framework. Nonhybrid functionals, standard (global) hybrids, and range-separated (Coulomb-attenuated, long-range corrected) hybrid functionals are tested. Origin invariance of the results is ensured by use of gauge-including atomic orbital (GIAO) basis functions. The new implementation in the NWChem quantum chemistry package is verified by calculations of nuclear shielding constants for the heavy atoms in HX (X = F, Cl, Br, I, At) and H2X (X = O, S, Se, Te, Po) and (125)Te chemical shifts in a number of tellurium compounds. The basis set and functional dependence of g-shifts is investigated for 14 radicals with light and heavy atoms. The problem of accurately predicting (19)F NMR shielding in UF6-nCln, n = 1-6, is revisited. The results are sensitive to approximations in the density functionals, indicating a delicate balance of DFT self-interaction vs correlation. For the uranium halides, the range-separated functionals are not clearly superior to global hybrids.

Homoatomic Stella Quadrangula [Tl8]6−in Cs18Tl8O6, Interplay of Spin−Orbit Coupling, and Jahn−Teller Distortion

Cs(18)Tl(8)O(6) was synthesized reacting the binary compounds CsTl and Cs(2)O. According to single crystal X-ray analysis, the title compound crystallizes as a novel structure type in the cubic space group I23 and is diamagnetic. The electronic structure of the extended solid and of excised Cs(6)Tl(8) clusters has been examined by relativistic density functional calculations including spin-orbit coupling. Cs(18)Tl(8)O(6) comprises a clusteranion [Tl(8)](6-) in the shape of a tetrahedral star. An isoelectronic cluster was found previously in Cs(8)Tl(8)O, however, with the shape of a parallelepiped. Both clusteranions can be derived from a homocubane unit by displacive distortions. It has been shown by quantum mechanical analyses that the closed-shell electronic structure of the parallelepiped is the result of a Jahn-Teller distortion, while in contrast the tetrahedral star in Cs(18)Tl(8)O(6) would still exhibit an open-shell degenerate HOMO within a scalar relativistic approximation. Only if spin-orbit coupling is considered, a closed-shell electronic system is obtained in accordance with the diamagnetic behavior of Cs(18)Tl(8)O(6).

Application of scalar-relativistic DFT approach for calculation of structural and electronic properties of mercaptobenzothiazolyl lanthanide complexes with luminescent activity

The geometry and electronic structure of thiolate complexes of rare earth metals Ln(SR) 3(thf) 2, HSR = 2-mercapto-benzothiazole and Ln = Y, La, Ce, Sm, Eu, Tb, Gd, Er, Tm, in ground and first excited states were studied using nonempirical density functional PBE approach to focus the problem of theoretical description of their luminescent properties. It was found that a scalar-relativistic approximation with four-component basis set of triple-polarized quality allows to describe well the coordination of ligands. Nonrelativistic calculations with the extended basis set of the same quality and explicit treatment of f-shell electrons using SBK pseudopotential, which takes into account inner shell relativistic effects, lead to strong overestimation of Ln–S bond lengths up to 0.5 Ǻ. Meridional arrangement of SR ligands was found to be more favorable than facial one in accordance with experiment. The first excited state in all complexes correspond to π–π∗ excitation of ligand shell for exception of Sm and Eu complexes with LMCT type excited state. The difference in energy of LMCT states for Sm and Eu complexes and the difference of the geometry distortion in the excited state for Tb and Tm complexes allows qualitatively explain the strong difference in yield of luminescence of metal ions in these cases. Calculated optical properties of the complex studied are in good correspondence with the available experimental data.