Relativistic Density Functional Method Research Articles

Actinyls in Expanded Porphyrin: A Relativistic Density-Functional Study

Actinyls AnO2 with An = U, Np, and Pu in an expanded porphyrin, alaskaphyrin (AP), are studied by a relativistic density-functional method. The electronic structures of both AnO2 and AnO2AP are investigated by considering all possible low-lying states. To examine the importance of relativity, nonrelativistic calculations were also performed. For UO2 and NpO2, the ground state is altered by the relativistic effects, but it remains unchanged for PuO2. The nonrelativistic ground states of the AnO2AP complexes are all high spin, where the AP highest occupied molecular orbital, b2g, is singly occupied. At the relativistic level, there are two electrons in b2g. The bonding characteristics in AnO2AP are examined by calculations of the AnO2−AP binding energy and charge distribution on AnO2. Other properties such as ionization potentials and electron affinities are also calculated. The predicted spectroscopic constants for NpO2, PuO2, NpO2AP, and PuO2AP would aid in future spectroscopic studies of these molecules.

Noncollinear and collinear relativistic density-functional program for electric and magnetic properties of molecules

We present the general theory of the collinear and noncollinear description for the magnetic effects within the full relativistic density-functional method. As examples for the implementation in a molecular code with numerical basis functions we present results with an even number of electrons $({\mathrm{Pt}}_{2})$ and with an odd number of active electrons (NiAu). The results are promising.

Relativistic Density Functional Study of the Dinuclear Uranyl Complex [(UO2)2(μ2‐OH)2Cl2(H2O)4] in Its Crystalline Environment

AbstractThe hexavalent dinuclear uranyl dichloride complex [(UO2)2(μ2‐OH)2Cl2(H2O)4] was studied computationally with an all‐electron scalar relativistic density functional method. This suggested hydrolysis product of uranyl in the presence of chlorine ions is one of the few polynuclear uranyl species for which a crystal structure is known. The calculated gas‐phase structure is similar to the experimental crystal geometry; any major deviations are due to hydrogen bonds in the crystal. If the eight strongest hydrogen bonds are included in a model of the complex’s crystalline environment, the calculated structure improves significantly. Based on this model, the hydrogen bond lengths and angles were determined, indicating that they are moderate and strong with an average binding energy of 39 kJ/mol. These computational results corroborate earlier suggestions based on experimental results concerning the location and strength of the hydrogen bonds. In addition, a valuable reference for relativistic quantum chemical methods is provided by the gas‐phase results. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2003)

Theoretical investigation of the apparently irregular behavior of pt-pt nuclear spin-spin coupling constants.

One-bond Pt-Pt nuclear spin-spin coupling constants J(Pt-Pt) for closely related dinuclear Pt complexes can differ by an order of magnitude without any obvious correlation with Pt-Pt distances. As representative examples, the spin-spin couplings of the dinuclear Pt(I) complexes [Pt(2)(CO)(6)](2+) (1) and [Pt(2)(CO)(2)Cl(4)](2-) (2) have been computationally studied with a recently developed relativistic density functional method. The experimental values are (1)J((195)Pt-(195)Pt) = 5250 Hz for 2 but 551 Hz for 1. Many other examples are known in the literature. The experimental trends are well reproduced by the computations and can be explained based on the nature of the ligands that are coordinated to the Pt-Pt fragment. The difference for J(Pt-Pt) of an order of magnitude is caused by a sensitive interplay between the influence of different ligands on the Pt-Pt bond, and relativistic effects on metal-metal and metal-ligand bonds as well as on "atomic orbital contributions" to the nuclear spin-spin coupling constants. The results can be intuitively rationalized with the help of a simple qualitative molecular orbital diagram.

First-principles approach to spin-orbit coupling in dilute magnetic semiconductors

We describe the implementation of a spin-polarized fully relativistic plane wave pseudopotential density functional method. Using the method, we compare the calculated electronic band structures of hypothetical ferromagnetic zinc blende structure MnAs and MnSe within the scalar-relativistic and fully relativistic pseudopotential approximations. We extract the conduction band and valence band exchange constants and extrapolate to the low concentration limit following a simple mean field approximation. Finally we investigate how strongly the exchange constants are affected by the spin-orbit term and provide a computational justification for extracting these constants from scalar-relativistic calculations.

Comparative study of relativistic density functional methods applied to actinide species AcO(2)(2+) and AcF(6) for Ac = U, Np.

A two-component relativistic density functional method based on the Douglas-Kroll-Hess transformation has been applied to the actinyls and hexafluorides of U and Np. All-electron scalar relativistic calculations as well as calculations including spin-orbit interaction have been compared to results obtained with a pseudopotential approach. In addition, several exchange-correlation potentials have been applied to examine their performance for the bond lengths and vibrational frequencies of the title compounds. The calculations confirm the well-known accuracy of the LDA approach for geometries and frequencies, which is corroborated for the hexafluorides where gas phase experimental data are available. Comparison with results of accurate wave function based methods provides further confirmation of this finding. Gradient-corrected functionals tend to overestimate bond lengths and underestimate frequencies also for actinide compounds. The results obtained with Stoll-Preuss (small core) effective core potentials agree very well with those of all-electron calculations, while calculations with Hay-Martin large core pseudopotentials are somewhat less accurate. For all molecules and properties considered, spin-orbit effects have been found negligible concomitant with the closed-shell electronic structure of the U(VI) compounds and the open-shell situation of the Np(VI) compounds with a single valence f electron.

Electronic Structures, (d-p)p Conjugation Effects, and Spectroscopic Properties of Polyoxometalates: M6O192- (M=Cr, Mo, W)

The electronic structures and bonding of isopoly oxometalates M6O192- (M= Cr, Mo, W) have been investigated by using ab initio and relativistic density functional methods. We have discussed the role of the central oxygen atom and the (d-p)p conjugation interactions between the metal and bridging oxygen atoms. It is found that there exist 12 three-centered two-electron (d-p-d)p bonds for the three M4(m-O)4 planar rings in M6O192- ions and these hexametalates are considered to have quasi-aromaticity. The (d-p)p conjugation effects play essential role in stabilizing these cluster compounds, and the reduced (d-p)p conjugation effects account for the instability of the isopoly oxochromate ion, Cr6O192-. The vibrational spectra and electronic spectra of M6O192- ions are evaluated and assigned theoretically and the calculated spectra are in fairly good agreement with the measured experimental results.

Hydrogen‐bonding effects on electronic g‐tensors of semiquinone anion radicals: Relativistic density functional investigation

AbstractWe report results of systematic g‐tensor calculations of hydrogen‐bonded complexes of two benchmark semiquinone anion radicals, 1,4‐benzoquinone and tetramethyl‐1,4‐benzoquinone (duroquinone), with water and methanol molecules. The calculations have been carried out with the help of a recently developed g‐tensor module that is based on a relativistic density functional method that takes spin–orbit interaction self‐consistently into account. We demonstrate the applicability of this new computational scheme to describe quantitatively delicate effects of hydrogen bonding on electronic g‐tensor values. Also, we explored general trends of how g‐tensors depend on the structure and stoichiometry of hydrogen‐bonded semiquinone complexes. Complexes exhibiting one hydrogen bond per oxygen atom of the quinones with a linear arrangement of the CO … H moieties were shown to feature g‐shifts induced by these hydrogen bonds that are in close agreement with measured electron paramagnetic resonance data. Based on deviations of calculated and measured g‐components, we classify all other model complexes studied as less probable under the experimental conditions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002

Adsorption of CO on cluster models of platinum (111): A four-component relativistic density-functional approach

We report on results of a theoretical study of the adsorption process of a single carbon oxide molecule on a Platinum (111) surface. A four-component relativistic density functional method was applied to account for a proper description of the strong relativistic effects. A limited number of atoms in the framework of a cluster approach is used to describe the surface. Different adsorption sites are investigated. We found that CO is preferably adsorbed at the top position.

A new implementation of four-component relativistic density functional method for heavy-atom polyatomic systems

A new four-component Dirac–Kohn–Sham (DKS) method is presented. The method provides a computationally efficient way to perform fully relativistic and correlated ground state calculations on heavy-atom molecular systems with reliable accuracy. The DKS routine has been implemented in the four-component Dirac–Hartree–Fock program system REL4D. Two-component generally contracted, kinetically balanced Gaussian-type spinors (GTSs) are used as basis spinors. The one-electron and Coulomb integrals are computed analytically, and exchange-correlation potentials are calculated with a numerical grid-quadrature routine. An approximation scheme is presented to reduce the evaluation time of the two-electron repulsion integrals over full sets of small-component GTSs, (SS|SS). Benchmark calculations for the ground states of the group IB hydrides, MH, and dimers, M2 (M=Cu, Ag, and Au), by the DKS method are presented.

Cluster-embedding method to simulate large cluster and surface problems

In order to describe processes which are localized on a surface or inside the bulk of a solid, molecular calculations of an inner cluster may be adequate as long as the effect of the outer environment is taken into account via an embedding-method. Using a relativistic density functional method for the self-consistent cluster calculation we have developed a new cluster-embedding scheme here. As an example we have studied the adsorption of Al on an Al(100) surface and we get significant agreement with different methods. This indicates that this embedding-method is reliable enough to simulate an unlimited solid.

M-shell satellite structure of W X-ray emission lines

The M-shell satellite structure of W X-ray emission lines excited by electron bombardment is investigated by a high resolution single crystal spectrometer, and the obtained structure is further compared with calculated transition energies obtained by the Relativistic Density Functional method. The transition hole states situated in the N- and O-shells—due to Coster–Kronig transitions—correspond to the parts of the spectra situated in the close neighbourhood of the diagram transition (0.7–4.4 eV).

Tungsten Atoms and Clusters Adsorbed on the MgO(001) Surface: A Density Functional Study

Adsorption of tungsten clusters Wn (n = 1−4) on the ideal MgO(001) surface has been studied computationally using a scalar relativistic density functional method and a gradient-corrected exchange-correlation functional. Structure and energetic features of the adsorption complexes Wn/MgO(001) have been analyzed. The oxide surface was represented by cluster models embedded in a large array of point charges (PCs). To reduce the artificial polarization of oxygen anions in the immediate vicinity of positive PCs, the cations at the cluster boundaries were treated as Mg2+ ions at either all-electron or pseudopotential (PP) level. Compared to the all-electron + PC embedding, the significantly more economic PP + PC approach is demonstrated to impose cluster model boundary conditions appropriate to the ionic oxide MgO. The cluster size dependence of the adsorption properties is found weak. Like other transition metal clusters considered previously, tungsten species favor adsorption sites in the proximity of oxygen centers of MgO(001). Rather small calculated adsorption-induced deformations of the tungsten clusters manifest notably stronger W−W bonds compared to W−O bonds between metal and substrate. The tetrahedron shape of W4, most stable in the gas phase, is calculated to be energetically preferred also in the adsorbed state, in particular over a square-planar adsorbate. This finding is at variance with a model of two-dimensional W4 clusters on MgO(001) derived from a recent high-resolution electron microscopy investigation (Tanaka, N., et al. Surf. Rev. Lett. 1998, 5, 723). The configuration of W3 with two W atoms located close to two nearest-neighbor oxygen ions is favored over that where two W atoms are close to next-nearest-neighbor substrate anions. In both cases, the adsorbed W3 cluster tilts considerably from an upright orientation.

Zirconium microclusters: molecular-dynamics simulations and density functional calculations

Structural stability and energetics of zirconium microclusters Zr n ( n=3–13) have been investigated by molecular-dynamics simulations and density functional calculations. A semi-empirical modelpotential energy function has been parametrized for the zirconium element by using the dimer interaction potential energy profile of Zr 2, which is calculated by the relativistic density functional method. Stable structures of the microclusters for n=3–13 have been determined by a molecular-dynamics simulation. Relativistic density functional calculations have been performed for n=3–7. It has been found that zirconium microclusters prefer to form three-dimensional compact structures.

Total Energy Calculations of RfCl4 and Homologues in the Framework of Relativistic Density Functional Theory

Calculations of total and binding energies of group IV tetrachlorides MCl4 (M = Ti, Zr, Hf, and element 104, Rf) were performed using the four-component fully relativistic density functional method. The calculations show the binding energies to be in good agreement with thermochemical dissociation energies obtained via the Born−Haber cycle. The method therefore demonstrates a predictive power which is important for further applications in the area of the heavy element compounds.

A theoretical study of gas-phase and solid-state Hg(CF 3) 2

Gas-phase and solid-state Hg(CF 3) 2 have been studied using a relativistic density-functional method. The crystalline environment was simulated by a cut-off-type Madelung potential. Bond lengths, dissociation energies, force constants, and enthalpy of sublimation are calculated. The influence of the crystal field (CF) on the molecular properties is well reproduced by the CF model. The intermolecular bonding in the crystal structure is examined and is revealed to be dominated by electrostatic effects. The relatively high enthalpy of sublimation evaluated for the crystal compound (Δ H sub=18.7 kcal) accounts for its relatively high melting points. A hypothetical crystal Hg(CH 3) 2 is shown to have a small Δ H sub (3 kcal mol −1), which explains why no solid-state Hg(CH 3) 2 exists. Ionization potentials for all the valence MOs of the gas-phase Hg(CF 3) 2 are predicted.

Energetics and structural stability of lanthanum microclusters

The energetics and the structural stability of lanthanum microclusters (La n ) have been investigated by performing relativistic density functional calculations and molecular dynamics (MD) simulations. An empirical potential energy function has been parameterised for a lanthanum element by using the dimer interaction potential energy profile of La 2, which is calculated by relativistic density functional method. Stable structures of the microclusters for n=3–13 have been determined by MD simulation and electronic structures have been calculated by relativistic density functional method. MD simulations have also been performed for spherical clusters with sizes n=19–157.

Stability of lutetium microclusters: Molecular-dynamics simulations

Structural stability and energetics of lutetium microclusters ${\mathrm{Lu}}_{n}(n=3\ensuremath{-}147)$ have been investigated by molecular-dynamics simulations. An empirical model potential energy function has been parametrized for the lutetium element by using the dimer interaction potential energy profile of ${\mathrm{Lu}}_{2}$, which is calculated by the relativistic density functional method. Stable structures of the microclusters for $n=3\ensuremath{-}13$ have been determined by a molecular-dynamics simulation. It has been found that lutetium microclusters prefer to form three-dimensional compact structures. Molecular-dynamics simulations have also been performed for spherical lutetium clusters generated from hcp crystal structure with sizes $n=33\ensuremath{-}147$.

Molecular-Dynamics Simulations of Uranium Microclusters

Structural stability and energetics of uranium microclusters, U n ( n =3–13, 27–137), have been investigated by molecular-dynamics simulations. An empirical model potential energy function has been parameterised for the uranium element by using the dimer interaction potential energy profile of U 2 , which is calculated by relativistic density functional method. Stable structures of the microclusters for n =3–13 have been determined by molecular–dynamics simulation. It has been found that uranium microclusters prefer to form three–dimensional compact structures. Molecular–dynamics simulations have also been performed for spherical uranium clusters with sizes n =27–137.

Relativistic all-electron density functional calculations

The current status of relativistic density functional theory is reviewed. For most applications relevant to chemistry, relativistic corrections to the electron interaction and radiative corrections are not important, and the (four-component) Dirac–Kohn–Sham model can be viewed as a reference. More approximate (two-component) schemes are much more popular not only because of the lower computational effort, but also because, in chemistry, one is only interested in the electronic states of a system, and the two-component methods in one way or another project out the positronic states. It is even possible to arrive at one-component relativistic methods if one can neglect spin-orbit coupling, which is often done for closed-shell compounds containing heavy atoms. Various such schemes are available today, based on first-order perturbation theory or even including higher order corrections, based on the Douglas–Kroll–Hess transformation, or on the so-called regular approximation. In recent years, analytical geometry gradients have been implemented for all these methods, the gradient for the zeroth-order regular approximation (ZORA) being presented in this work for the first time. The availability of such geometry gradients is quite important for the applicability of these methods to “real chemistry”; that is, polyatomic molecules. Results of relativistic density functional methods are collected for some benchmark molecules. Then some results for various tungsten pentacarbonyl phosphines, platinum tricarbonyl phosphines, and molybdenum dinitrogen phosphine carbonyls, as obtained with first-order relativistic density functional calculations by means of direct perturbation theory (DPT), are presented. In another application, the force field of molybdenum, tungsten, and uranium hexafluoride in the metal–fluorine stretch region is calculated at both the DPT and ZORA levels. First-order relativistic calculations are reasonable for second- and third-row transition metal compounds (mainly 4d and 5d electrons involved in bonding), whereas, for uranium and gold compounds (mainly 5f, 6d, and 6s electrons involved), higher order relativistic corrections must be considered. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 51–62, 1999