Two-component Zeroth-order Regular Approximation Research Articles

Relativistic and quantum electrodynamics effects on NMR shielding tensors of TlX (X = H, F, Cl, Br, I, At) molecules.

The results of relativistic calculations of nuclear magnetic resonance shielding tensors (σ) for the thallium monocation (Tl+), thallium hydride (TlH), and thallium halides (TlF, TlCl, TlBr, TlI, and TlAt) are presented as obtained within a four-component polarization propagator formalism and a two-component linear response approach within the zeroth-order regular approximation. In addition to a detailed analysis of relativistic effects performed in this work, some quantum electrodynamical (QED) effects on those nuclear magnetic resonance shieldings and other small contributions are estimated. A strong dependence of σ(Tl) on the bonding partner is found, together with a very weak dependence of QED effects with them. In order to explain the trends observed, the excitation patterns associated with relativistic ee (or paramagnetic-like) and pp (or diamagnetic-like) contributions to σ are analyzed. For this purpose, the electronic spin-free and spin-dependent contributions are separated within the two-component zeroth-order regular approximation, and the influence of spin-orbit coupling on involved molecular orbitals is studied, which allows for a thorough understanding of the underlying mechanisms.

Dynamic and relativistic effects on Pt-Pt indirect spin-spin coupling in aqueous solution studied by abinitio molecular dynamics and two- vs four-component density functional NMR calculations.

Treating 195Pt nuclear magnetic resonance parameters in solution remains a considerable challenge from a quantum chemistry point of view, requiring a high level of theory that simultaneously takes into account the relativistic effects, the dynamic treatment of the solvent-solute system, and the dynamic electron correlation. A combination of Car-Parrinello molecular dynamics (CPMD) and relativistic calculations based on two-component zeroth order regular approximation spin-orbit Kohn-Sham (2c-ZKS) and four-component Dirac-Kohn-Sham (4c-DKS) Hamiltonians is performed to address the solvent effect (water) on the conformational changes and JPtPt1 coupling. A series of bridged PtIII dinuclear complexes [L1-Pt2(NH3)4(Am)2-L2]n+ (Am = α-pyrrolidonate and pivalamidate; L = H2O, Cl-, and Br-) are studied. The computed Pt-Pt coupling is strongly dependent on the conformational dynamics of the complexes, which, in turn, is correlated with the trans influence among axial ligands and with the angle N-C-O from the bridging ligands. The J-coupling is decomposed in terms of dynamic contributions. The decomposition reveals that the vibrational and explicit solvation contributions reduce JPtPt1 of diaquo complexes (L1 = L2 = H2O) in comparison to the static gas-phase magnitude, whereas the implicit solvation and bulk contributions correspond to an increase in JPtPt1 in dihalo (L1 = L2 = X-) and aquahalo (L1 = H2O; L2 = X-) complexes. Relativistic treatment combined with CPMD shows that the 2c-ZKS Hamiltonian performs as well as 4c-DKS for the JPtPt1 coupling.

S2p core level spectroscopy of short chain oligothiophenes.

The Near-Edge X-ray-Absorption Fine-Structure (NEXAFS) and X-ray Photoemission Spectroscopy (XPS) of short-chain oligothiophenes (thiophene, 2,2'-bithiophene, and 2,2':5',2″-terthiophene) in the gas phase have been measured in the sulfur L2,3-edge region. The assignment of the spectral features is based on the relativistic two-component zeroth-order regular approximation time dependent density functional theory approach. The calculations allow us to estimate both the contribution of the spin-orbit splitting and of the molecular-field splitting to the sulfur binding energies and give results in good agreement with the experimental measurements. The deconvolution of the calculated S2p NEXAFS spectra into the two manifolds of excited states converging to the LIII and LII edges facilitates the attribution of the spectral structures. The main S2p NEXAFS features are preserved along the series both as concerns the energy positions and the nature of the transitions. This behaviour suggests that the electronic and geometrical environment of the sulfur atom in the three oligomers is relatively unaffected by the increasing chain length. This trend is also observed in the XPS spectra. The relatively simple structure of S2p NEXAFS spectra along the series reflects the localized nature of the virtual states involved in the core excitation process.

Periodic trends in parity-violating hyperfine coupling constants of open-shell diatomic molecules

Nuclear spin-dependent parity violation effects are predicted with the help of a quasi-relativistic two-component zeroth order regular approximation (ZORA) approach for a series of open-shell diatomic molecules that feature a 2Σ electronic ground state. The particular focus is on scaling behaviour of the parity violating parameter Wa in the effective spin-rotational Hamiltonion with increasing nuclear charge Z of the heavier atom in the diatomic molecule. Previously (Isaev and Berger, 2012) an approximate R(A,Z)Z2 scaling law, with R(A,Z) denoting a relativistic enhancement factor, was confirmed for Wa in the series of valence isoelectronic group II monofluorides and valence isoelectronic group XII monohydrides, that is along columns of the periodic table of the elements. In this work, a pronounced R(A,Z)Zk scaling is predicted for isolobal 2Σ diatomic molecules along rows of the periodic table, with k being approximately 4 and 6 for the fourth and fifth row, respectively, and even larger for the sixth and seventh row. This observation opens up a another dimension in the systematic search of candidate systems for measuring nuclear spin-dependent parity violating interactions in molecules.

The Influence of a Presence of a Heavy Atom on (13)C Shielding Constants in Organomercury Compounds and Halogen Derivatives.

(13)C nuclear magnetic resonance shielding constants have been calculated by means of density functional theory (DFT) for several organomercury compounds and halogen derivatives of aliphatic and aromatic compounds. Relativistic effects have been included through the four-component Dirac-Kohn-Sham (DKS) method, two-component Zeroth Order Regular Approximation (ZORA) DFT, and DFT with scalar effective core potentials (ECPs). The relative shieldings have been analyzed in terms of the position of carbon atoms with respect to the heavy atom and their hybridization. The results have been compared with the experimental values, some newly measured and some found in the literature. The main aim of the calculations has been to evaluate the magnitude of heavy atom effects on the (13)C shielding constants and to check what are the relative contributions of scalar relativistic effects and spin-orbit coupling. Another object has been to compare the DKS and ZORA results and to check how the approximate method of accounting for the heavy-atom-on-light-atom (HALA) relativistic effect by means of scalar effective core potentials on heavy atoms performs in comparison with the more rigorous two- and four-component treatment.

A comparison of two-component and four-component approaches for calculations of spin-spin coupling constants and NMR shielding constants of transition metal cyanides

Relativistic density functional theory (DFT) calculations of nuclear spin-spin coupling constants and shielding constants have been performed for selected transition metal (11th and 12th group of periodic table) and thallium cyanides. The calculations have been carried out using zeroth-order regular approximation (ZORA) Hamiltonian and four-component Dirac-Kohn-Sham (DKS) theory with different nonrelativistic exchange-correlation functionals. Two recent approaches for representing the magnetic balance (MB) between the large and small components of four-component spinors, namely, mDKS-RMB and sMB, have been employed for shielding tensor calculations and their results have been compared. Relativistic effects have also been analysed in terms of scalar and spin-orbit contributions at the two-component level of theory, including discussion of heavy-atom-on-light-atom effects for (1)J(CN), σ(C), and σ(N). The results for molecules containing metals from 4th row of periodic table show that relativistic effects for them are small (especially for spin-spin coupling constants). The biggest effects are observed for the 6th row where nonrelativistic theory reproduces only about 50%-70% of the two-component ZORA results for (1)J(MeC) and about 75% for heavy metal shielding constants. It is important to employ a full Dirac picture for calculations of heavy metal shielding constants, since ZORA reproduces only 75%-90% of the DKS results. Smaller discrepancies between ZORA-DFT and DKS are observed for nuclear spin-spin coupling constants. No significant differences are observed between the results obtained using mDKS-RMB and sMB approaches for magnetic balance in four-component calculations of the shielding constants.

Application of 204mPb Perturbed Angular Correlation of γ-rays Spectroscopy in Coordination Chemistry

(204m)Pb perturbed angular correlation of γ-rays (PAC) spectroscopy has been applied successfully for the first time to detect the nuclear quadrupole interaction in a lead(II) coordination compound in a molecular crystal [tetraphenylarsonium lead(II) isomaleonitriledithiolate ([AsPh(4)](4)[Pb(2)(i-mnt)(4)])]. The recorded parameters from a powder crystalline sample are ν(Q) = 0.178(1) GHz and η = 0.970(7). The electric field gradient (EFG) was determined at the PW91/QZ4P level including relativistic effects using the two-component zeroth-order regular approximation method for both the [Pb(i-mnt)(2)](2-) monomer and the [Pb(2)(i-mnt)(4)](4-) dimer. Only the EFG for the latter compares favorably with the experimental data, indicating that the picture of this complex as a prototypical hemidirected coordination geometry with a stereochemically active lone pair on lead(II) is inadequate. Advantages and limitations of (204m)Pb PAC spectroscopy as a novel technique to elucidate the electronic and molecular structures of lead-containing complexes and biomolecules are presented.

Spin-orbit relativistic long-range corrected time-dependent density functional theory for investigating spin-forbidden transitions in photochemical reactions

A long-range corrected (LC) time-dependent density functional theory (TDDFT) incorporating relativistic effects with spin-orbit couplings is presented. The relativistic effects are based on the two-component zeroth-order regular approximation Hamiltonian. Before calculating the electronic excitations, we calculated the ionization potentials (IPs) of alkaline metal, alkaline-earth metal, group 12 transition metal, and rare gas atoms as the minus orbital (spinor) energies on the basis of Koopmans' theorem. We found that both long-range exchange and spin-orbit coupling effects are required to obtain Koopmans' IPs, i.e., the orbital (spinor) energies, quantitatively in DFT calculations even for first-row transition metals and systems containing large short-range exchange effects. We then calculated the valence excitations of group 12 transition metal atoms and the Rydberg excitations of rare gas atoms using spin-orbit relativistic LC-TDDFT. We found that the long-range exchange and spin-orbit coupling effects significantly contribute to the electronic spectra of even light atoms if the atoms have low-lying excitations between orbital spinors of quite different electron distributions.

Validation of Relativistic DFT Approaches to the Calculation of NMR Chemical Shifts in Square-Planar Pt(2+) and Au(3+) Complexes.

Recently implemented hybrid density functional methods of calculating nuclear magnetic shielding using the two-component zeroth-order regular approximation approach (J. Phys. Chem. A2009, 113, 11495) have been employed for a series of compounds containing heavy transition-metal atoms. These include Pt(2+), Pd(2+), and Au(3+) organometallics and metal complexes with azines, some of which exhibit interesting biological and catalytic activities. In this study we investigate the effects of geometry, exchange-correlation functional, solvent, and scalar relativistic and spin-orbit corrections on the nuclear magnetic shielding-mainly for (13)C and (15)N atoms connected to a heavy-atom center. Our calculations demonstrate that the B3LYP method using effective core potentials and a cc-pwCVTZ-PP/6-31G** basis set augmented with the polarizable continuum model of the dimethylsulfoxide solvent provides geometries for the complexes in question which are compatible with the experimental NMR results in terms of both the trends and the absolute values of the (13)C shifts. The important role of the exact exchange admixture parameter for hybrid functionals based on B3LYP and PBE0 is investigated systematically for selected Pt(2+) and Au(3+) complexes. The (13)C and (15)N NMR chemical shifts are found to be best reproduced by using a B3LYP or PBE0 approach with 30% and 40-50% exact exchange admixtures for the Pt(2+) and Au(3+) complexes, respectively. The spin-orbit contributions to the (15)N NMR chemical shifts reflect metal-ligand bonding that is much more ionic for the Au(3+) than for the Pt(2+) complex. Finally, an optimized density functional method is applied to a series of transition-metal complexes to estimate the scope and the limitations of the current approach.

Relativistic calculations of aminotroponiminate complexes containing group 15 (P, As, Sb, Bi) elements

Abstract The relativistic electronic structure calculations of N,N′-chelated pnictogenium cations containing aminotroponiminate units, (E = P(1), As(2), Sb(3), Bi(4)), have been investigated employing density functional (DF) methods, including spin–orbit relativistic corrections, via the two-component zeroth order regular approximation (ZORA) Hamiltonian. The role of replacement of the pnictogen atom when going down into the 15 group was discussed on the basis of geometrical parameters, Hirshfield charge analyses, DF reactivity indexes. The degree of electronic delocalization into the five- and seven membered rings was estimated via the electron localization function (ELF) and the nuclear independent chemical shifts (NICS) indexes. Our results show an existence of a lack of systems 2–4 to act as donor ligands for the metal complexation, compared with 1, due to the positive charge over the pnictogen atoms besides the lone-pair orbital of the pnictogen atom which lies at low energies from their corresponding reacting HOMO’s. It is also interesting to note some effects over the aromaticity when going down into the 15 group, i.e., the C5 ring is affected by the change of the pnictogen atom, while the aromaticity on the C7 ring is not affected, as suggested by the analysis of the ELF, NICS and geometrical parameters.

Zeroth order regular approximation approach to parity violating nuclear magnetic resonance shielding tensors

In this paper, a quasirelativistic two-component zeroth order regular approximation (ZORA) density functional theory (DFT) approach to the calculation of parity violating (PV) resonance frequency differences between the nuclear magnetic resonance (NMR) spectra of enantiomers is presented and the systematics of PV NMR shielding constants in C(2)-symmetric dihydrogen dichalcogenides (H(2)X(2) with X=(17)O, (33)S, (77)Se, (125)Te, (209)Po) are investigated. The typical sin(2alpha)-like dependence of the PV NMR frequency splittings on the dihedral angle alpha is observed for the entire series. As for the scaling behavior of the effect with the nuclear charge Z of X, the previously reported Z(2.5+/-0.5) scaling in the nonrelativistic limit is reproduced and a scaling of approximately Z(3) for the paramagnetic and Z(5) for the spin-orbit coupling contribution to the frequency splitting is observed in the relativistic framework. The paramagnetic and spin-orbit coupling contributions are typically of opposite sign for the molecular structures studied herein and the maximum scaling of the total ZORA frequency splitting (i.e., the sum of the two contributions) is Z(3.9) for H(2)Po(2). Thus, an earlier claim for a spin-orbit coupling contribution scaling with up to Z(7) for H(2)Po(2) and the erratic dihedral angle dependence obtained for this compound within a four-component Dirac-Hartree-Fock-Coulomb study is not confirmed at the DFT level. The maximum NMR frequency splitting reported here is of the order of 10 mHz for certain clamped conformations of H(2)Po(2) inside a static magnetic field with magnetic flux density of 11.7 T. Frequency splittings of this size have been estimated to be detectable with present day NMR spectrometers. Thus, a NMR route toward molecular PV appears promising once suitable compounds have been identified.

Two-component relativistic density functional method for computing nonsingular complex linear response of molecules based on the zeroth order regular approximation

We report the implementation of a frequency-dependent two-component relativistic density functional theory method based on the zeroth order regular approximation (ZORA) for computations of complex linear response of molecules including spin-orbit coupling. The implementation is based on Slater-type atomic orbital basis functions and makes extensive use of density fitting techniques. The complex response is obtained by applying damping in the computations. The method is validated by computations of the real and imaginary part of the static and dynamic polarizability of group 12 atoms, of a number of heavy-atom diatomic molecules, of a range of two- and three-dimensional gold clusters, and of group 8 oxides and metallocenes. Simulated spectra--a plot of extinction coefficient as a function of frequency--obtained from the isotropic imaginary polarizability are compared to broadened spectra obtained from two-component ZORA excitation energies and oscillator strengths.

Relativistic Effects on the Topology of the Electron Density.

The topological analysis of electron densities obtained either from X-ray diffraction experiments or from quantum chemical calculations provides detailed insight into the electronic structure of atoms and molecules. Of particular interest is the study of compounds containing (heavy) transition-metal elements, which is still a challenge for experiment as well as from a quantum-chemical point of view. Accurate calculations need to take relativistic effects into account explicitly. Regarding the valence electron density distribution, these effects are often only included indirectly through relativistic effective core potentials. But as different variants of relativistic Hamiltonians have been developed all-electron calculations of heavy elements in combination with various electronic structure methods are feasible. Yet, there exists no systematic study of the topology of the total electron density distribution calculated in different relativistic approximations. In this work we therefore compare relativistic Hamiltonians with respect to their effect on the electron density in terms of a topological analysis. The Hamiltonians chosen are the four-component Dirac-Coulomb, the quasi-relativistic two-component zeroth-order regular approximation, and the scalar-relativistic Douglas-Kroll-Hess operators.

Spin−Orbit Relativistic Time-Dependent Density Functional Calculations of the Metal and Ligand Pre-Edge XAS Intensities of Organotitanium Complexes: TiCl4, Ti(η5-C5H5)Cl3, and Ti(η5-C5H5)2Cl2

Time-dependent density functional theory (TDDFT) coupled to the relativistic two-component zeroth-order regular approximation, both available in the last version of the ADF package, have been successfully used to simulate X-ray absorption spectra of TiCl4, Ti(eta5-C5H5)Cl3, and Ti(eta5-C5H5)2Cl2 in terms of their oscillator strength distributions. Besides allowing a first principle assignment of Ti 1s, Cl 1s, and Ti 2p (L2,3 edges) core excitation spectra, theoretical outcomes provide a rationale for deviations from the expected L3/L2 branching ratio.

Electronic spectrum of UO22+ and [UO2Cl4]2− calculated with time-dependent density functional theory

The electronic spectra of UO(2) (2+) and [UO(2)Cl(4)](2-) are calculated with a recently proposed relativistic time-dependent density functional theory method based on the two-component zeroth-order regular approximation for the inclusion of spin-orbit coupling and a noncollinear exchange-correlation functional. All excitations out of the bonding sigma(u) (+) orbital into the nonbonding delta(u) or phi(u) orbitals for UO(2) (2+) and the corresponding excitations for [UO(2)Cl(4)](2-) are considered. Scalar relativistic vertical excitation energies are compared to values from previous calculations with the CASPT2 method. Two-component adiabatic excitation energies, U-O equilibrium distances, and symmetric stretching frequencies are compared to CASPT2 and combined configuration-interaction and spin-orbit coupling results, as well as to experimental data. The composition of the excited states in terms of the spin-orbit free states is analyzed. The results point to a significant effect of the chlorine ligands on the electronic spectrum, thereby confirming the CASPT2 results: The excitation energies are shifted and a different luminescent state is found.

Electroweak interactions in chiral molecules: two-component density functional theory study of vibrational frequency shifts in polyhalomethanes

In this paper, a two-component density functional theory study of parity violation-induced vibrational frequency shifts in chiral polyhalomethanes is reported and the prospects to detect in these compounds, for the first time, signals of parity violation in molecular systems are discussed. The recent synthesis of enantiomerically enriched CHClFI has renewed interest in examining electroweak corrections for this class of compounds. Utilizing a (quasi-relativistic) two-component zeroth-order regular approximation approach to molecular parity violation, together with density functional theory, the parity violation-induced relative vibrational frequency splittings Δ νpv/ν between the C–F stretching fundamental of polyhalomethane enantiomers are computed. The relative splitting in CHClFI is raised compared with CHBrClF, for which upper bounds were determined experimentally. To facilitate measurement, molecules possessing more pronounced relative splittings are desirable. Therefore, the chiral methane derivative CHAtFI is considered, which exhibits a significantly larger electroweak contribution that induces a vibrational frequency splitting on the order of the experimental resolution previously reported for CHBrClF. Employing compounds containing heavy nuclei such as astatine may thus be necessary with present detection methods.

Theoretical study of the electronic spectra of square-planar platinum (II) complexes based on the two-component relativistic time-dependent density-functional theory

In the present work the electronic spectra of [PtCl(4)](2-), [PtBr(4)](2-), and [Pt(CN)(4)](2-) are studied with a recently proposed relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. The contribution to the double group excited states in terms of singlet and triplet single group excited states is estimated through the inner product of the transition density matrix obtained from two-component and scalar relativistic TDDFT calculations to better understand the double group excited states. Spin-orbital coupling effects are found to be very important in order to simulate the electronic spectra of these complexes. The results show that the two-component TDDFT formalism can afford excitation energies with high accuracy for the transition-metal systems studied here when use is made of a proper XC potential.

The calculation of excitation energies based on the relativistic two-component zeroth-order regular approximation and time-dependent density-functional with full use of symmetry

In the present work, we propose a relativistic time-dependent density-functional theory (TDDFT) based on the two-component zeroth-order regular approximation and a noncollinear exchange-correlation (XC) functional. This two-component TDDFT formalism has the correct nonrelativistic limit and affords the correct threefold degeneracy of triplet excitations. The relativistic TDDFT formalism is implemented into the AMSTERDAM DENSITY FUNCTIONAL program package for closed-shell systems with full use of double-group symmetry to reduce the computational effort and facilitate the assignments. The performance of the formalism is tested on some closed-shell atoms, ions, and a few diatomic molecules containing heavy elements. The results show that the fine structure of the excited states for most atoms and ions studied here can be accurately accounted for with a proper XC potential. For the excitation energies of the molecules studied here, the present formalism shows promise and the error encountered is comparable to that of nonrelativistic TDDFT calculations on light elements.

The ZORA formalism applied to the Dirac-Fock equation

The zeroth-order regular approximation (ZORA), a two component approximation to the Dirac equation that was earlier formulated and tested within the framework of density functional theory, is generalized to a treatment based on the Dirac-Fock equation. The performance of the ZORA equation and an improvement known as scaled ZORA is investigated, in particular with respect to orbital energies and various radial expectation values in the case of the xenon and radon atoms. The results of the simple ZORA approximation are shown to be quite close to the full Dirac-Fock method, except in the deep core region where the scaled version of the method is needed. It is found that a further approximation in which the density is calculated from the two-component ZORA orbitals alone gives satisfactory results, which is an important result from a practical point of view since in this way one can avoid calculating any two-electron integrals involving small-component basis functions.