A simplified relativistic time-dependent density-functional theory formalism for the calculations of excitation energies including spin-orbit coupling effect

In the present work we have proposed an approximate time-dependent density-functional theory (TDDFT) formalism to deal with the influence of spin-orbit coupling effect on the excitation energies for closed-shell systems. In this formalism scalar relativistic TDDFT calculations are first performed to determine the lowest single-group excited states and the spin-orbit coupling operator is applied to these single-group excited states to obtain the excitation energies with spin-orbit coupling effects included. The computational effort of the present method is much smaller than that of the two-component TDDFT formalism and this method can be applied to medium-size systems containing heavy elements. The compositions of the double-group excited states in terms of single-group singlet and triplet excited states are obtained automatically from the calculations. The calculated excitation energies based on the present formalism show that this formalism affords reasonable excitation energies for transitions not involving 5p and 6p orbitals. For transitions involving 5p orbitals, one can still obtain acceptable results for excitations with a small truncation error, while the formalism will fail for transitions involving 6p orbitals, especially 6p1/2 spinors.     

Solvent effects on heavy atom nuclear spin-spin coupling constants: a theoretical study of Hg-C and Pt-P couplings.

The computation of indirect nuclear spin-spin coupling constants, based on the relativistic two-component zeroth order regular approximate Hamiltonian, has been recently implemented by us into the Amsterdam Density Functional program. Applications of the code for the calculation of one-bond metal-ligand couplings of coordinatively unsaturated compounds containing (195)Pt and (199)Hg, including spin-orbit coupling or coordination effects by solvent molecules, show that relativistic density functional calculations are able to reproduce the experimental findings with good accuracy for the systems under investigation. Spin-orbit effects are rather small for these cases, while coordination of the heavy atoms by solvent molecules has a great impact on the calculated couplings. Experimental trends for different solvents are reproduced. An orbital-based analysis of the solvent effect is presented. The scalar relativistic increase of the coupling constants is of the same order of magnitude as the nonrelativistically obtained values, making a relativistic treatment essential for obtaining quantitatively correct results. Solvent effects can be of similar importance.     

High-spin organic molecules with dominant spin-orbit contribution and unprecedentedly large magnetic anisotropy

High-spin organic molecules with dominant spin-orbit contribution to magnetic anisotropy are reported. Quintet 4-azido-3,5-dibromopyridyl-2,6-dinitrene (Q-1), quintet 2-azido-3,5-dibromopyridyl-4,6-dinitrene (Q-2), and septet 3,5-dibromopyridyl-2,4,6-trinitrene (S-1) were generated in solid argon matrices by ultraviolet irradiation of 2,4,6-triazido-3,5-dibromopyridine. The zero-field splitting (ZFS) parameters, derived from electron spin resonance spectra, show unprecedentedly large magnitudes of the parameters D: ∣D(Q1)∣ = 0.289, ∣D(Q2)∣ = 0.373, and ∣D(S1)∣ = 0.297 cm(-1). The experimental ZFS parameters were successfully reproduced by density functional theory calculations, confirming that magnetic anisotropy of high-spin organic molecules can considerably be enhanced by the "heavy atom effect." In bromine-containing high-spin nitrenes, the spin-orbit term is dominant and governs both the magnitude and the sign of magnetic anisotropy. The largest negative value of D among septet trinitrenes is predicted for 1,3,5-trinitrenobenzene bearing three heavy atoms (Br) in positions 2, 4, and 6 of the benzene ring.     

A dual ion-selective electrode detector for the simultaneous detection of bromine- and chlorine- containing compounds in gas chromatography

A dual ion-selective electrode gas chromatographic detector which allows the simultaneous detection of chlorine- and bromine-containing compounds through two-channel operation is described. Components eluted from the g.c. column are hydrogenated, the hydrogen chloride and hydrogen bromide produced being absorbed in a standard solution of halide; the ion concentrations in the resulting solution are monitored by chloride- and bromide-selective electrodes. The dual electrode detector gives two chromatograms simultaneously, one selective for chlorine- and bromine-containing compounds and the other for bromine-containing compounds. The response ratio, i.e., the peak area of the readout from the chloride channel divided by that from the bromide channel for the same compound, gives valuable information. The Cl/Br ratio in an eluted molecule can be determined accurately from the response ratio if a standard reference compound is injected simultaneously.     

Interpretation of indirect nuclear spin-spin coupling tensors for polyatomic xenon fluorides and group 17 fluorides: results from relativistic density-functional calculations

Significant improvements have been made recently in the calculation of NMR indirect nuclear spin-spin coupling tensors (J). In particular, the relativistic zeroth-order regular approximation density-functional theory (ZORA-DFT) approach holds great promise for the calculation of spin-spin coupling constants for a variety of chemical systems containing heavy nuclei. In the present work, the ZORA-DFT method is applied to the calculation of the complete reduced coupling tensors, K, for a range of chlorine-, bromine-, iodine-, and xenon-containing species: K(Cl,F) for ClF(2)(+), ClF(3), ClF(4)(+), ClF(5), ClF(6)(-), and ClF(6)(+); K(Br,F) for BrF(3), BrF(6)(-), and BrF(6)(+); K(I,F) for IF(4)(+) and IF(6)(+); K(Xe,F) for XeF(+), XeF(2), XeF(3)(+), XeF(4), XeF(5)(-), XeF(5)(+), and XeF(7)(+). These species represent a wide variety of geometrical bonding arrangements. Agreement between the calculated coupling constants and available experimental data is excellent, and the absolute sign of the coupling constants is provided. It is shown that (1)K(iso) may be positive or negative even within the same molecule, e.g., K(Cl,F)(iso) may be of either sign, depending on the local environment. Periodic trends in (1)K(iso) for isovalent and isostructural molecules are evident. The spin-spin coupling anisotropies, Delta K, and the orientations of the K tensors are also determined. The success of the calculations is a direct result of employing reliable geometries and considering both scalar and spin-orbit relativistic effects. The dependence of K(Cl,F)(iso) and K(Xe,F)(iso) on the local molecular and electronic structure is discussed in terms of the paramagnetic spin-orbit (PSO) and combined Fermi-contact spin-dipolar (FC+SD) coupling mechanisms. The PSO term depends strongly on the number of valence shell electron lone pairs on the central heavy atom, and the FC+SD contribution increases with the Cl[bond]F or Xe[bond]F bond length for a given series of compounds. This interpretation allows for the successful rationalization of the existing experimental data.     

A new method to generate spin-orbit coupled potential energy surfaces: effective relativistic coupling by asymptotic representation

A new method has been developed to generate fully coupled potential energy surfaces including derivative and spin-orbit coupling. The method is based on an asymptotic (atomic) representation of the molecular fine structure states and a corresponding diabatization. The effective relativistic coupling is described by a constant spin-orbit coupling matrix and the geometry dependence of the coupling is accounted for by the diabatization. This approach is very efficient, particularly for certain systems containing a very heavy atom, and yields consistent results throughout nuclear configuration space. A first application to a diatomic system is presented as proof of principle and is compared to accurate ab initio calculations. However, the method is widely applicable to general polyatomic systems in full dimensionality, containing several relativistic atoms and treating higher order relativistic couplings as well.     

PtF6(2-) dianion and its detachment spectrum: a fully relativistic study

In this work we calculate the photoelectron spectrum of the PtF(6)2- dianion by application of the third-order Dirac-Hartree-Fock one-particle propagator technique. Relativistic effects and electron correlation are hereby treated on a consistent theoretical basis which is mandatory for systems containing heavy elements. A PtF6(2-) gas phase photoelectron spectrum is not yet available and our calculations therefore have predictive character. As it is characteristic for dianionic systems a strong dependence on basis set size and molecular geometry is observed. In contrast to the already calculated PtCl(6)2- photoelectron spectrum no valence orbital inversion due to strong interplay of spin-orbit coupling and electron correlation is observed. Furthermore an unusually strong spin-orbit splitting was found for the sigma-type subvalence 1t1u molecular spinor despite its very small platinum p population. The double ionization threshold is strongly lowered by relativistic effects now enabling an interatomic Coulombic decay process after ionization from the sigma-bonding orbitals. The results stress the importance of spin-orbit coupling for the understanding of the spectral structure which cannot be reproduced by a scalar-relativistic treatment only.     

Symmetry exploitation in closed-shell coupled-cluster theory with spin-orbit coupling

In the present work, we report exploitation of spatial symmetry in calculations of ground state energy and analytic first derivatives of closed-shell molecules based on our previously developed coupled-cluster (CC) approach with spin-orbit coupling. Both time-reversal symmetry and spatial symmetry for D(2h) and its subgroups are exploited in the implementation. The symmetry of a certain spin case for the amplitude, intermediate, or density matrix is determined by the symmetry of the corresponding spin functions and the direct product decomposition method is employed in computations involving these quantities. The reduction in computational effort achieved through the use of spatial symmetry is larger than the order of the molecular single point group. Symmetry exploitation renders application of the CC approaches with spin-orbit coupling to larger closed-shell molecules containing heavy elements with high accuracy.     

External heavy atom effect on radiative spin-forbidden transitions

A general model for the external heavy atom effect on radiative transitions within the framework of the dynamic coupling model is proposed. The two different mechanisms are considered, the spin-orbit coupling mechanism and the polarizability mechanism. The question of whether the polarizability of the heavy atom perturber determines the magnitudes of the effect is discussed.     

The Role of Spin-Orbit Coupling and Symmetry in Oxadi-pi-methane Rearrangements and Some Related Photochemical Reactions

The spin-orbit coupling components in the effective one-electron Hamiltonian operator, with the inclusion of symmetry, have been used to formulate mechanisms of spin inversion in triplet reactions for the radiationless decay of triplet complexes to singlet ground state products. This has been applied to investigate the photochemical behavior of oxadi-pi-methane rearrangement in beta,gamma-unsaturated carbonyl cyclic and acyclic systems. It is found that the 1,2-acyl-migrated endo isomer is the most favorable product due to its larger spin-orbit coupling expression as well as better initial overlaps (owing to the less atomic motion). Other related photorearrangements of some molecular systems, such as azadi-pi-methane rearrangement, 4-aryl-substituted cyclopentenones, spirocyclic beta,gamma,delta,epsilon-unsaturated ketones, and heavy atom effect, have also been investigated.     

Two-component relativistic methods for the heaviest elements

Different generalized Douglas-Kroll transformed Hamiltonians (DKn, n=1, 2,...,5) proposed recently by Hess et al. are investigated with respect to their performance in calculations of the spin-orbit splittings. The results are compared with those obtained in the exact infinite-order two-component (IOTC) formalism which is fully equivalent to the four-component Dirac approach. This is a comprehensive investigation of the ability of approximate DKn methods to correctly predict the spin-orbit splittings. On comparing the DKn results with the IOTC (Dirac) data one finds that the calculated spin-orbit splittings are systematically improved with the increasing order of the DK approximation. However, even the highest-order approximate two-component DK5 scheme shows certain deficiencies with respect to the treatment of the spin-orbit coupling terms in very heavy systems. The meaning of the removal of the spin-dependent terms in the so-called spin-free (scalar) relativistic methods for many-electron systems is discussed and a computational investigation of the performance of the spin-free DKn and IOTC methods for many-electron Hamiltonians is carried out. It is argued that the spin-free IOTC rather than the Dirac-Coulomb results give the appropriate reference for other spin-free schemes which are based on approximate two-component Hamiltonians. This is illustrated by calculations of spin-free DKn and IOTC total energies, r(-1) expectation values, ionization potentials, and electron affinities of heavy atomic systems.     

Recent advances and perspectives in four-component Dirac-Kohn-Sham calculations

We review recent theoretical and computational advances in the full relativistic four-component Dirac-Kohn-Sham (DKS) approach and its application to the calculation of the electronic structure of chemical systems containing many heavy atoms. We describe our implementation of an all-electron DKS approach based on the use of G-spinor basis sets, Hermite Gaussian functions, state-of-the-art density-fitting techniques and memory distributed parallelism. This approach has enormously extended the applicability of the DKS method, including for example large clusters of heavy atoms, and opens the way for future key developments. We examine the current limitations and future possible applications of the DKS approach, including the implementation of four-current density functionals and real-time propagation schemes. This would make possible to describe molecules in strong fields, accurately accounting for relativistic kinematic effects and spin-orbit coupling.     

Density-functional calculations of relativistic spin-orbit effects on nuclear magnetic shielding in paramagnetic molecules

Terms arising from the relativistic spin-orbit effect on both hyperfine and Zeeman interactions are introduced to density-functional theory calculation of nuclear magnetic shielding in paramagnetic molecules. The theory is a generalization of the former nonrelativistic formulation for doublet systems and is consistent to O(alpha4), the fourth power of the fine structure constant, for the spin-orbit terms. The new temperature-dependent terms arise from the deviation of the electronic g tensor from the free-electron g value as well as spin-orbit corrections to hyperfine coupling tensor A, the latter introduced in the present work. In particular, the new contributions include a redefined isotropic pseudocontact contribution that consists of effects due to both the g tensor and spin-orbit corrections to hyperfine coupling. The implementation of the spin-orbit terms makes use of all-electron atomic mean-field operators and/or spin-orbit pseudopotentials. Sample results are given for group-9 metallocenes and a nitroxide radical. The new O(alpha4) corrections are found significant for the metallocene systems while they obtain small values for the nitroxide radical. For the isotropic shifts, none of the three beyond-leading-order hyperfine contributions are negligible.     

Trace element speciation using solid phase microextraction

An initial review of research targeting applications of solid phase microextraction for organometallic speciation, published in 2001, encompassed literature from the early days of solid phase microextraction up to June 2000. In this article, the reader will find a compilation and discussion of relevant literature published from June 2000 to December 2004. Because of the maturity of the technique, only a brief overview of the measurement principles is presented. The major thrust of the article highlights applications of solid phase microextraction to the fields of elemental and organometallic analyses. In contrast to the earlier review, applications related to the determination of phosphorus-, sulfur-, bromine-, chlorine- and iodine-containing compounds have also been included for those cases where the target of the determination is the element or a specific molecule containing the element for which atomic spectroscopy has been advocated as a detection technique. Additionally, other microextraction techniques are also considered, including stirbar sorptive extraction and single droplet microextraction.     

The effect of Lewis bases on the (13)c NMR of iodoalkynes.

In Lewis-basic solvents, alkynyl carbons bonded to iodine have chemical shifts approximately 12-15 ppm higher in frequency than the corresponding shifts in CDCl3. We offer computational evidence that this solvent effect comes directly from polarization of the iodoalkyne triple bond. Hartree-Fock and Density Functional Theory calculations reproduce the change in chemical shift for a gas-phase complex between the iodoalkyne and dimethyl sulfoxide as Lewis base. The amount of spin-orbit coupling from the adjacent iodine does not change appreciably in the complex, according to the calculations.     

Freezing halide ion solutions and the release of interhalogens to the atmosphere

The effect of freezing on a variety of acidified and neutral, nitrite ion and halide-containing mixtures has been investigated using UV/vis spectroscopy. Several trihalide ions were formed and monitored, including I(2)Cl(-), I(2)Br(-), ICl(2)(-) and IBr(2)(-). A mechanism to explain the observations is given in terms of steps involving INO and the nitroacidium ion, [H(2)ONO](+). The transformation of sea salt components to specific trihalide ions by freezing represents a potentially important process in a polar atmospheric context. This is because the dichloro- and dibromo-trihalide ions can release chlorine- and bromine-containing gases, which are key intermediates in ozone destruction.     

Understanding the extraordinary deshielding of 129Xe in a permetallated cryptophane by relativistic DFT

Shift change: Relativistic ZORA DFT calculations highlight the various factors (solvent effect, spin-orbit coupling, number and type of metal centres) responsible of the extraordinarily large deshielding of xenon encapsulated in a metallated cryptophane (see figure).     

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.     

Time-dependent four-component relativistic density functional theory for excitation energies

Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.