Zeroth-order Regular Approximation Research Articles

Spin–Spin Coupling Constants Transmitted through IrH⋅⋅⋅HN Dihydrogen Bonds

Relativity matters: Calculations of NMR shielding tensors and spin-spin coupling constants transmitted through Ir-H...H-N dihydrogen bonds are presented. The picture shows one of the simplified models employed. It is shown that the spin-orbit relativistic effects influence the NMR shielding constants far more than the spin-spin coupling constants.We present calculations of NMR shielding tensors and spin-spin coupling constants transmitted through Ir-H...H-N dihydrogen bonds. For this purpose, three six-coordinated complexes of iridium have been selected as models of heavy metal complexes and their NMR properties have been calculated within the DFT-ZORA (density functional theory zeroth-order regular approximation) methodology. The influence of intramolecular interactions between hydrogen atoms from IrH(3) and NH(2) groups (including both single dihydrogen bonding and bifurcated hydrogen bonding) on the NMR properties is discussed and the results are compared with the experimental observations. In complexes where dihydrogen bonding occurs, the calculated value of "through-space" (1h)J(H(a)H(b)) is in the range 1.6-7.9 Hz [depending on the model, but with R(H(a)-H(b))<2.0 A], while the experimental values are 2-5 Hz for similar H(a)--H(b) distances. The (2h)J(NH) coupling is also sizeable, ranging from approximately -5.1 Hz for dihydrogen bonds of 2 A up to -7.1 Hz for very short (1.6 A) dihydrogen bonds, and should therefore be experimentally accessible when using (15)N-labelled compounds. The dihydrogen-bond transmitted spin-spin coupling constants (1h)J(HH) and (2h)J(NH) and the shielding tensor of the H(a) atom are the most sensitive probes of the H(a)-H(b) distance, which potentially makes them attractive tools to determine the structure of molecules. The main conclusions are qualitatively similar to those drawn from nonrelativistic calculations in small inorganic complexes, and the spin-orbit relativistic effects influence the NMR shielding constants far more than the spin-spin coupling constants.

Magnetic anisotropy from density functional calculations. Comparison of different approaches: Mn12O12 acetate as a test case

Magnetic anisotropy is the capability of a system in a triplet or higher spin state to store magnetic information. Although the source of the magnetic anisotropy is the zero-field splitting of the ground state of the system, there is a difference between these two quantities that has to be fully rationalized before one makes comparisons. This is especially important for small spins such as triplets, where the magnetic anisotropy energy is only half of the zero-field splitting. Density functional calculations of magnetic anisotropy energies correspond to a high-field limit where the spins are aligned by the external magnetic field. Data are presented for the well-studied molecular magnet Mn(12)O(12) acetate. Both perturbative and self-consistent treatments, different quasirelativistic Hamiltonians (zeroth order regular approximation, Douglas-Kroll, effective core potentials) and exchange-correlation functionals are compared. It is shown that some effects usually considered minor, such as the inclusion of the exchange-correlation potential in the effective one-particle spin-orbit operator, lead to sizable differences when computing magnetic anisotropy energies. Higher-order contributions, that is, the difference between self-consistent and perturbative results, increase the magnetic anisotropy energy somewhat but do not introduce sizeable quartic terms or an in-plane anisotropy. In numerical experiments, on can switch off and on spin-orbit coupling at individual atomic sites. This procedure yields single-site contributions to the overall magnetic anisotropy energy that could be used as parameters in phenomenological spin Hamiltonians. If ferrimagnetic systems are treated with broken symmetry density functional methods where the Kohn-Sham reference function is not a spin eigenfunction, corrections are needed which depend on the size of the exchange couplings in the system and must therefore be evaluated case by case.

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.

Revisiting HgCl 2: A solution- and solid-state 199Hg NMR and ZORA–DFT computational study

The 199Hg chemical-shift tensor of solid HgCl 2 was determined from spectra of polycrystalline materials, using static and magic-angle spinning (MAS) techniques at multiple spinning frequencies and field strengths. The chemical-shift tensor of solid HgCl 2 is axially symmetric ( η = 0) within experimental error. The 199Hg chemical-shift anisotropy (CSA) of HgCl 2 in a frozen solution in dimethylsulfoxide (DMSO) is significantly smaller than that of the solid, implying that the local electronic structure in the solid is different from that of the material in solution. The experimental chemical-shift results (solution and solid state) are compared with those predicted by density functional theory (DFT) calculations using the zeroth-order regular approximation (ZORA) to account for relativistic effects. 199Hg spin–lattice relaxation of HgCl 2 dissolved in DMSO is dominated by a CSA mechanism, but a second contribution to relaxation arises from ligand exchange. Relaxation in the solid state is independent of temperature, suggesting relaxation by paramagnetic impurities or defects.

77Se NMR Spectroscopic, DFT MO, and VBT Investigations of the Reversible Dissociation of Solid (Se6I2)[AsF6]2·2SO2in Liquid SO2to Solutions Containing 1,4-Se6I22+in Equilibrium with Sen2+(n= 4, 8, 10) and Seven Binary Selenium Iodine Cations: Preliminary Evidence for 1,1,4,4-Se4Br42+andcyclo-Se7Br+

The composition of a complex equilibrium mixture formed upon dissolution of (Se(6)I(2))[AsF(6)](2).2SO(2) in SO(2)(l) was studied by (77)Se NMR spectroscopy at -70 degrees C with both natural-abundance and enriched (77)Se-isotope samples (enrichment 92%). Both the natural-abundance and enriched NMR spectra showed the presence of previously known cations 1,4-Se(6)I(2)(2+), SeI(3)(+), 1,1,4,4-Se(4)I(4)(2+), Se(10)(2+), Se(8)(2+), and Se(4)(2+). The structure and bonding in 1,4-Se(6)I(2)(2+) and 1,1,4,4-Se(4)I(4)(2+) were explored using DFT calculations. It was shown that the observed Se-Se bond alternation and presence of thermodynamically stable 4ppi-4ppi Se-Se and 4ppi-5ppi Se-I bonds arise from positive charge delocalization from the formally positively charged tricoordinate Se(+). The (77)Se chemical shifts for cations were calculated using the relativistic zeroth-order regular approximation (ZORA). In addition, calculations adding a small number of explicit solvent molecules and an implicit conductor-like screening model were conducted to include the effect that solvent has on the chemical shifts. The calculations yielded reasonable agreement with experimental chemical shifts, and inclusion of solvent effects was shown to improve the agreement over vacuum values. The (77)Se NMR spectrum of the equilibrium solution showed 22 additional resonances. These were assigned on the basis of (77)Se-(77)Se correlation spectroscopy, selective irradiation experiments, and spectral simulation. By combining this information with the trends in the chemical shifts, with iodine, selenium, and charge balances, as well as with ZORA chemical shift predictions, these resonances were assigned to acyclic 1,1,2-Se(2)I(3)(+), 1,1,6,6-Se(6)I(4)(2+), and 1,1,6-Se(6)I(3)(+), as well as to cyclic Se(7)I(+) and (4-Se(7)I)(2)I(3+). A preliminary natural-abundance (77)Se NMR study of the soluble products of the reaction of (Se(4))[AsF(6)](2) and bromine in liquid SO(2) included resonances attributable to 1,1,4,4-Se(4)Br(4)(2+)(.) These assignments are supported by the agreement of the observed and calculated (77)Se chemical shifts. Resonances attributable to cyclic Se(7)Br(+) were also observed. The thermal stability of (Se(6)I(2))[AsF(6)](2).2SO(2)(s) was consistent with estimates of thermodynamic values obtained using volume-based thermodynamics (VBT) and the first application of the thermodynamic solvate difference rule for nonaqueous solvates. (Se(6)I(2))[AsF(6)](2).2SO(2)(s) is the first example of a SO(2) solvate for which the nonsolvated parent salt, (Se(6)I(2))[AsF(6)](2)(s), is not thermodynamically stable, disproportionating to Se(4)I(4)(AsF(6))(2)(s) and Se(8)(AsF(6))(2)(s) (DeltaG degrees for the disproportion reaction is estimated to be -17 +/- 15 kJ mol(-1) at 298 K from VBT theory).

All-electron CI calculations of 3d transition-metalL2,3 XANES using zeroth-order regular approximation for relativistic effects

X-ray-absorption near-edge structures (XANES) at 3d transition-metal (TM)L2,3 edges are computed using the all-electron configuration interaction (CI) method. Slaterdeterminants for the CI calculations are composed of molecular orbitals obtained bydensity functional theory (DFT) calculations of model clusters. Relativistic effects aretaken into account by the zeroth-order regular approximation (ZORA) usingtwo-component wavefunctions. The theoretical spectra are found to be strongly dependenton the quality of the one-electron basis functions. On the other hand, a different choice ofthe exchange–correlation functionals for the DFT calculations does not exhibit visiblechanges in the spectral shape. Fine details of multiplet structures in the experimental TML2,3 XANES of MnO, FeO and CoO are well reproduced by the present calculations when theone-electron basis functions are properly selected. This is consistent with ourprevious report showing good agreement between theoretical and experimental TML2,3 XANES when four-component relativistic wavefunctions were used.

Competition between Jahn-Teller effect and spin-orbit coupling in Td Au20 ±γ, γ = 1,2,3

In this work we explored the competition between spin-orbit and Jahn-Teller effects as decisive influences in the ground states of the Td Au20 ±γ (γ=1,2,3). All our electronic calculations were based in the relativistic density functional theory in the zeroth-order regular approximation (ZORA) to the Dirac equation. Calculations were done in both versions of ZORA: scalar relativistic and full-relativistic including the spin-orbit interaction. We concluded that for the Au20 -3 ion is necessary to use a full-relativistic theory in order to predict a symmetry-lowering from tetrahedral. We predict a trigonal C3v isomeric form for this trianion due to a Jahn-Teller distortion of its parent Td. For the rest of ions we found a tendency to conserve their pristine tetrahedral configurations. In these cases we found one of both possibilities: a quenching of the vibronic interaction by spin-orbit coupling or simply a weak Jahn-Teller effect which is not enough to distort appreciably the cluster.

Gaussian Basis Set and Planewave Relativistic Spin−Orbit Methods in NWChem

Relativistic spin-orbit density functional theory (DFT) methods have been implemented in the molecular Gaussian DFT and pseudopotential planewave DFT modules of the NWChem electronic-structure program. The Gaussian basis set implementation is based upon the zeroth-order regular approximation (ZORA) while the planewave implementation uses spin-orbit pseudopotentials that are directly generated from the atomic Dirac-Kohn-Sham wave functions or atomic ZORA-Kohn-Sham wave functions. Compared to solving the full Dirac equation these methods are computationally efficient but robust enough for a realistic description of relativistic effects such as spin-orbit splitting, molecular orbital hybridization, and core effects. Both methods have been applied to a variety of small molecules, including I2, IF, HI, Br2, Bi2, AuH, and Au2, using various exchange-correlation functionals. Our results are in good agreement with experiment and previously reported calculations.

Density functional studies on the exchange interaction of a dinuclear Gd(iii)–Cu(ii) complex: method assessment, magnetic coupling mechanism and magneto-structural correlations

Density functional calculations have been performed on a [Gd(iii)Cu(ii)] complex [L(1)CuGd(O(2)CCF(3))(3)(C(2)H(5)OH)(2)] () (where L(1) is N,N'-bis(3-ethoxy-salicylidene)-1,2-diamino-2-methylpropanato) with an aim of assessing a suitable functional within the DFT formalism to understand the mechanism of magnetic coupling and also to develop magneto-structural correlations. Encouraging results have been obtained in our studies where the application of B3LYP on the crystal structure of yields a ferromagnetic J value of -5.8 cm(-1) which is in excellent agreement with the experimental value of -4.42 cm(-1) (H = JS(Gd).S(Cu)). After testing varieties of functional for the method assessment we recommend the use of B3LYP with a combination of an effective core potential basis set. For all electron basis sets the relativistic effects should be incorporated either via the Douglas-Kroll-Hess (DKH) or zeroth-order regular approximation (ZORA) methods. A breakdown approach has been adopted where the calculations on several model complexes of have been performed. Their wave functions have been analysed thereafter (MO and NBO analysis) in order to gain some insight into the coupling mechanism. The results suggest, unambiguously, that the empty Gd(iii) 5d orbitals have a prominent role on the magnetic coupling. These 5d orbitals gain partial occupancy via Cu(ii) charge transfer as well as from the Gd(iii) 4f orbitals. A competing 4f-3d interaction associated with the symmetry of the complex has also been observed. The general mechanism hence incorporates both contributions and sets forth rather a prevailing mechanism for the 3d-4f coupling. The magneto-structural correlations reveal that there is no unique parameter which the J values are strongly correlated with, but an exponential relation to the J value found for the O-Cu-O-Gd dihedral angle parameter is the most credible correlation.

DFT Analysis of g and 13C Hyperfine Coupling Tensors for Model NiI(CO)nLm (n = 1−4, L = H2O, OH−) Complexes Epitomizing Surface Nickel(I) Carbonyls

Relativistic calculations within the spin-orbit mean-field (SOMF) approximation, the zero-order regular approximation (ZORA), and the scalar relativistic method based on the Pauli Hamiltonian were performed for the prediction and interpretation of the electronic g tensor and (13)C hyperfine tensor for a set of model polycarbonyl nickel(I) complexes with aqua or hydroxy coligands. They exhibit extensive similarities with heterogeneous [Ni(I)(CO)(n)]-surface complexes produced upon adsorption of carbon monoxide on Ni(I) ions grafted on silica or inside the zeolite channels. Benchmark calculations showing the influence of the exchange-correlation functional on the g tensor were carried out for well-defined nickel(I) complexes of known structure. On this basis, the SOMF-B3LYP scheme was chosen for calculations of the g tensor, and the obtained results were in satisfactory agreement with literature EPR data found for the [Ni(I)(CO)(n)]/SiO(2) system. The calculated g and A((13)C) tensors allowed polycarbonyl complexes of various stereochemistries to be distinguished. The nature of the Deltag(ii) shifts was assessed in terms of the molecular orbital contributions due to the magnetic-field-induced couplings and their structure sensitivity. The noncoincidence of g and (13)C hyperfine principal axes and their orientation with respect to the molecular framework was also examined. The ability of DFT calculations to follow consistently variations of the EPR parameters induced by stereochemical changes around the Ni(I) center provides an invaluable reference for the interpretation of experimental results.

Two-component relativistic hybrid density functional computations of nuclear spin-spin coupling tensors using Slater-type basis sets and density-fitting techniques

Computations of indirect nuclear spin-spin coupling constants using two-component relativistic density functional theory with a hybrid functional are reported. The program implementation makes use of a Slater-type orbital expansion of the molecular orbitals and the zeroth-order regular approximation for the treatment of relativistic effects. Exact exchange terms in the Kohn-Sham response kernel were computed using a fitting procedure. Computations with the PBE0 hybrid functional were carried out for heavy-atom-ligand-one-bond couplings in PbH(4), Pb(CH(3))(2)H(2), Pb(CH(3))(3)H, three platinum complexes, the interhalogen diatomics such as ClF, ClBr, ClI, BrF, BrI, IF, and the series Tl-X with X=F, Cl, Br, I. The hybrid functional computations performed very well. In particular, for the isotropic coupling and the coupling anisotropy of Tl-X, the PBE0 hybrid functional yielded considerably improved agreement with experiment.

Prediction of 207Pb NMR parameters for the solid ionic lead(II) halides using the relativistic ZORA-DFT formalism: Comparison with the lead-containing molecular systems

Density functional calculations of 207Pb NMR shielding in PbX 2 (X=F, Br, Cl and I) anionic fragments suggest that in solid PbX 2, the observed variation of chemical shift with halide is dominated by the paramagnetic contribution to the chemical shielding, with a lesser effect by the spin–orbit contribution. The calculations include relativistic effects at the level of the zero-order regular approximation (ZORA). The present observation contrasts with previous calculations for the molecular system, PbX 4, in which the spin–orbit contribution has been shown to be the major factor in the variation of the NMR chemical shift.

Theoretical study on the photoabsorption of [formula omitted] (M = V, Nb and Ta)

The valence photoabsorption spectra of the series of the monoanionic closed shell icosahedral clusters M Au 12 - with M = V, Nb and Ta have been calculated with the time-dependent density functional theory (TDDFT), employing the zero-order regular approximation (ZORA) at both scalar relativistic and spin–orbit coupling levels. The calculated photoabsorption spectra show interesting variations according to the nature of the encapsulated metal atom. Spin–orbit coupling plays an important role in these systems. The comparison with the neutral isoelectronic clusters WAu 12 and MoAu 12 suggests a curious relationship along the diagonal of the periodic table.

A relativistic density functional study of gaseous uranium tetrahalides

The molecular structures and vibrational frequencies of gaseous UX4 (X = F, Cl, Br and I) molecules have been investigated using generalized gradient approximation (GGA) functions (BP, BLYP, PBE and RPBE) with triple-zeta polarized (TZP) basis set. Scalar relativistic effects are introduced via the zeroth-order regular approximation (ZORA) approach to the Dirac equation in the present study. Of the methods examined here the RPBE has the best performance in terms of the errors compared with experiment and reference for the vibrational frequencies. The bond dissociation energies (BDE) for U–X bonds in the UX4 were obtained using the RPBE method, and are in good agreement with experimental values. In addition, satisfactory calculated entropies of UX4 have also been obtained at temperatures ranging from 600 to 1200 K in 50 steps using the same method.

Stable Geometric and Electronic Structures of Gold-Coated Nanoparticles M@Au12 (M = 5d Transition Metals, from Hf to Hg): Ih or Oh?

The geometric and electronic structures of 5d transition metal “impurities” Hf to Hg encapsulated in icosahedral and cuboctahedral Au12 cages have been investigated theoretically. The best density functional results of the small molecules Au2, AuH, AuCl, and AuCu were obtained for the geometric structures with Xα, and for the electronic energies of those frozen structures with VBP. The same procedure was then applied to the clusters. At the zeroth order regular relativistic approximation ZORA, both at the spin-averaged scalar and at the spin−orbit-split spinor levels, the cuboctahedral clusters tend to be more stable than their icosahedral isomers, except for W@Au12. The neutral clusters have electronic closed shells only for Ih and Oh W@Au12 and for Oh Hg@Au12. The embedding energy of M into Au12 is less attractive for the later transition metal atoms M.

All-Electron Scalar Relativistic Basis Sets for Third-Row Transition Metal Atoms.

A family of segmented all-electron relativistically contracted (SARC) basis sets for the elements Hf-Hg is constructed for use in conjunction with the Douglas-Kroll-Hess (DKH) and zeroth-order regular approximation (ZORA) scalar relativistic Hamiltonians. The SARC basis sets are loosely contracted and thus offer computational advantages compared to generally contracted relativistic basis sets, while their sufficiently small size allows them to be used in place of effective core potentials (ECPs) for routine studies of molecules. Practical assessments of the SARC basis sets in DFT calculations of atomic (ionization energies) as well as molecular properties (geometries and bond dissociation energies for MHn complexes) confirm that the basis sets yield accurate and reliable results, providing a balanced description of core and valence electron densities. CCSD(T) calculations on a series of gold diatomic compounds also demonstrate the applicability of the basis sets to correlated methods. The SARC basis sets will be of most utility in calculating molecular properties for which the core electrons cannot be neglected, such as studies of electron paramagnetic resonance, Mössbauer and X-ray absorption spectra, and topological analysis of electron densities.

The luminescent [Mo 6X 8(NCS) 6] 2− (X = Cl, Br, I) clusters?: A computational study based on time-dependent density functional theory including spin–orbit and solvent-polarity effects

Relativistic time-dependent density functional (TDDFT) calculations including spin–orbit interactions via the zero order regular approximation (ZORA) and solvent effects were carried out on the [Mo 6X 8(NCS) 6] 2− cluster. These calculations indicate that the lowest energy electronic transitions of the LMCT type are similar to those observed in the strongly luminescent 24 electron hexanuclear rhenium chalcogenide clusters. The absorption maximum in all the solvents tends to shift to longer wavelengths as the face-capping halide ligand becomes heavier. Thus our calculations predict that the [Mo 6X 8(NCS) 6] 2− clusters could be luminescent showing an intensity dependence with respect to both, the nature of the face-capping ligand and the solvent polarity.

Quadrupole coupling constants and isomeric Mössbauer shifts for halogen-containing gold, platinum, niobium, tantalum and antimony compounds

We have analyzed by means of Density functional theory calculations the nuclear quadrupole coupling constants of a range of gold, antimony, platinum, niobium and tantalum compounds. The geometrical parameters and halogen nuclear quadrupole coupling constants obtained by these calculations substantially corresponded to the data of microwave and nuclear quadrupole resonance spectroscopy. An analysis of the quality of the calculations that employ pseudo-potentials and all-electron basis sets for the halogen compounds was carried out. The zero order regular approximation (ZORA) method is shown to be a viable alternative for the calculation of halogen coupling constants in molecules. In addition, the ZORA model, in contrast to the pseudo-potential model, leads to realistic values of all metal nuclear quadrupole coupling constants. From Klopman’s approach, it follows that the relationship between the electrostatic bonding and covalent depends on the nature of the central atom. The results on Mossbauer chemical shifts are also in a good agreement with the coordination number of the central atom.

Photoinduced bond cleavage in CH3ReO3: excited state dynamics

The rhenium–methyl bond cleavage in CH3ReO3 has been investigated by means of quantum chemical calculations of the one-D potential energy surfaces (PES) associated to the low-lying singlet and triplet excited states of the molecule. The quantum dynamics is studied by wave packet propagations on the b1A1 absorbing state coupled non-adiabatically to the low-lying a1E state. The spin–orbit states and spin–orbit couplings are evaluated according to the zeroth-order regular approximation (ZORA). The spin–orbit coupling between the a1E state and the a3A1 dissociative state controls the radical formation ˙CH3 + ˙ReO3, which occurs in 400 fs.

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.