On the accuracy of one-component pseudopotential spin-orbit calculations

Improvements on current one-component extraction procedures of spin-orbit pseudopotentials are investigated for high accuracy computation of spin-orbit coupling energies. By means of the perturbation-theory formalism we first show that spin-orbit pseudopotentials, extracted at the one-component self-consistent-field level from a reference all-electron Dirac-Coulomb or Dirac-Coulomb-Breit calculation, include valence spin-orbit polarization and relaxation effects. As a consequence the use of these pseudopotentials in uncontracted spin-orbit configuration interaction (CI) with singles from the reference ground-state configuration gives rise to double counting of these spin-orbit effects. Two new methods that avoid such double counting have been investigated. The first, so-called "explicit" method, calculates explicitly, by means of a four-component spin-orbit CI, the double-counted spin-orbit effects and removes them from the pseudopotentials. Due to the nonadditivity of the core and valence spin-orbit effects as well as the so-called "pseudovariational collapse," this method is shown to be cumbersome. In the second "implicit" method the spin-orbit pseudopotential is extracted at the spin-orbit polarized and relaxed level by means of a single-excitation spin-orbit CI calculation. Atomic tests on iodine demonstrate the ability of the latter method to solve the double-counting problem.     

Energy decomposition analysis of metal-metal bonding in [M2X8]2- (X=Cl, br) complexes of 5f (U, Np, Pu), 5d (W, Re, Os), and 4d (Mo, Tc, Ru) elements

The electronic structures of a series of [M2X8]2- (X=Cl, Br) complexes involving 5f (U, Np, Pu), 5d (W, Re, Os), and 4d (Mo, Tc, Ru) elements have been calculated using density functional theory, and an energy decomposition approach has been used to carry out a detailed analysis of the metal-metal interactions. The energy decomposition analysis involves contributions from orbital interactions (mixing of occupied and unoccupied orbitals), electrostatic effects (Coulombic attraction and repulsion), and Pauli repulsion (associated with four-electron two-orbital interactions). As previously observed for Mo, W, and U M2X6 species, the general results suggest that the overall metal-metal interaction is considerably weaker or unfavorable in the actinide systems relative to the d-block analogues, as a consequence of a significantly more destabilizing contribution from the combined Pauli and electrostatic (prerelaxation) effects. Although the orbital-mixing (postrelaxation) contribution to the total bonding energy is predicted to be larger in the actinide complexes, this is not sufficiently strong to compensate for the comparatively greater destabilization originating from the Pauli-plus-electrostatic effects. A generally weak electrostatic contribution accounts for the large prerelaxation destabilization in the f-block systems, and ultimately for the weak or unfavorable nature of metal-metal bonding between the actinide elements. There is a greater variation in the energy decomposition results across the [M2Cl8]2- series for the actinide than for the d-block elements, both in the general behavior and in some particular properties.     

Electron transfer in neptunyl(VI)-neptunyl(V) complexes in solution

The rates and mechanisms of the electron self-exchange between Np(V) and Np(VI) in solution have been studied with quantum chemical methods and compared with previous results for the U(V)-U(VI) pair. Both outer-sphere and inner-sphere mechanisms have been investigated, the former for the aqua ions, the latter for binuclear complexes containing hydroxide, fluoride, and carbonate as bridging ligand. Solvent effects were calculated using the Marcus equation for the outer-sphere reactions and using a nonequilibrium PCM method for the inner-sphere reactions. The nonequilibrium PCM appeared to overestimate the solvent effect for the outer-sphere reactions. The calculated rate constant for the self-exchange reaction NpO2(+)(aq) + NpO2(2+)(aq) right harpoon over left harpoon NpO2(2+)(aq) + NpO2(+)(aq), at 25 degrees C is k = 67 M(-1) s(-1), in fair agreement with the observed rates 0.0063-15 M(-1) s(-1). The differences between the Np(V)-Np(VI) and the U(V)-U(VI) pairs are minor.     

Simple non-empirical calculations of the zero-field splitting in bis(aquo) bis(malonato) nickel(II)

Summary A simple non-empirical method is applied to calculate the splittings of the ground state triplet, caused by the spin-orbit coupling, in bis(aquo) bis(malonato) nickel(II), allowing for a certain geometry variation. The calculations yield splittings on the order of 10–20 cm^–1. The comparison of exact (within model) and second-order perturbation theory calculations indicate that the spin Hamiltonian formalism is valid. The implications of the results for the theory of nuclear spin relaxation in paramagnetic complexes in solution are discussed.     

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.     

Nonadiabatic effects in the photodetachment of ClH2(-)

The photoelectron spectra of the ClH2(-) and ClD2(-) anions have been simulated using a Franck-Condon model involving vertical excitation to the four coupled quasidiabatic potential energy surfaces that correlate with Cl(2P)+H2(1 Sigma g +). A careful analysis of the excitation process is presented. All electrostatic, spin-orbit, and Coriolis couplings in the photodetached ClH2 (ClD2) neutral are included. At a resolution of 1 meV, the resulting spectra are dominated by the bound and resonant states of the Cl...H2 and Cl...D2 van der Waals complexes, along with contributions from the associated continua. Only small differences occur between these spectra and those simulated under the assumption that each of the three electronically adiabatic Cl(2P)+H2 states can be treated separately. In particular, photodetachment to form the Cl*(2P 1/2)H2 complex leads to very low intensity of spectral features associated with Cl(2P 3/2)H2. This clearly implies that, while nonadiabatic effects do have some influence on the bound and resonance state energies of both complexes as shown recently by Garand et al. [Science 319, 72 (2008)], nonadiabatic transitions between the two complexes are extremely rare.     

Harvesting highly electronically excited energy to triplet manifolds: state-dependent intersystem crossing rate in Os(II) and Ag(I) complexes

A series of newly synthesized Os(II) and Ag(I) complexes exhibit remarkable ratiometric changes of intensity for phosphorescence versus fluorescence that are excitation wavelength dependent. This phenomenon is in stark contrast to what is commonly observed in condensed phase photophysics. While the singlet to triplet intersystem crossing (ISC) for the titled complexes is anomalously slow, approaching several hundred picoseconds in the lowest electronic excited state (S(1) → T(1)), higher electronic excitation leads to a much accelerated rate of ISC (10(11)-10(12) s(-1)), which is competitive with internal conversion and/or vibrational relaxation, as commonly observed in heavy transition metal complexes. The mechanism is rationalized by negligible metal d orbital contribution in the S(1) state for the titled complexes. Conversely, significant ligand-to-metal charge transfer character in higher-lying excited states greatly enhances spin-orbit coupling and hence the ISC rate. The net result is to harvest high electronically excited energy toward triplet states, enhancing the phosphorescence.     

Relativistic density functional theory study of dioxoactinide(VI) and -(V) complexation with alaskaphyrin and related Schiff-base macrocyclic ligands

Formation of complexes of alaskaphyrin 1, bi-pyen 2 and bi-tpmd 3 ligands with actinyl ions AnO2(n+), An = U, Np, Pu and n = 1, 2, was studied using density functional theory (DFT) within the scalar relativistic four-component approximation. The alaskaphyrin complexes of the uranyl are predicted to have a bent conformation, in contrast to the experimentally available X-ray data. This deviation is likely due to crystal packing effects. Apart from these conformational differences, calculated geometry parameters and vibrational frequencies are in agreement with the available experimental data. The character of bonding in the complexes is investigated using bond order analysis and extended transition states (ETS) energy decomposition. Metal-to-ligand bonds can be described as primarily ionic although substantial charge transfer is observed as well. Based on ETS analysis, it is shown that steric and/or fit/misfit requirements of actinyl cations to the ligand cavities, among the studied complexes, are the most favorable for the bi-pyen ligand 2, because its flexibility allows for optimal metal-to-donor-atom distances. Planarity of the equatorial coordination sphere of the actinide atom is found to be less important than the ability of a ligand to provide optimal uranium-to-nitrogen bond lengths. Experimental differences in demetalation rates between similar alaskaphyrin, bi-pyen and bi-tpmd uranyl complexes are explained as a result of easier protonation of the Schiff-base nitrogen of the latter. Reduction potentials calculated for the uranium complexes show a good agreement with the experiment, both in relative and in absolute terms.     

Metal-metal bonding in molecular actinide compounds: electronic structure of [M2X8](2-) (M = U, Np, Pu; X = Cl, Br, I) complexes and comparison with d-block analogues

Density functional and multiconfigurational (ab initio) calculations have been performed on [M(2)X(8)](2-) (X = Cl, Br, I) complexes of 4d (Mo, Tc, Ru), 5d (W, Re, Os), and 5f (U, Np, Pu) metals in order to investigate general trends, similarities and differences in the electronic structure and metal-metal bonding between f-block and d-block elements. Multiple metal-metal bonds consisting of a combination of sigma and pi interactions have been found in all species investigated, with delta-like interactions also occurring in the complexes of Tc, Re, Np, Ru, Os, and Pu. The molecular orbital analysis indicates that these metal-metal interactions possess predominantly d(z2) (sigma), d(xz) and d(yz) (pi), or d(xy) and d(x2-y2) (delta) character in the d-block species, and f(z3) (sigma), f(z2x) and f(z2y) (pi), or f(xyz) and f(z) (delta) character in the actinide systems. In the latter, all three (sigma, pi, delta) types of interaction exhibit bonding character, irrespective of whether the molecular symmetry is D(4h) or D(4d). By contrast, although the nature and properties of the sigma and pi bonds are largely similar for the D(4h) and D(4d) forms of the d-block complexes, the two most relevant metal-metal delta-like orbitals occur as a bonding and antibonding combination in D(4h) symmetry but as a nonbonding level in D(4d) symmetry. Multiconfigurational calculations have been performed on a subset of the actinide complexes, and show that a single electronic configuration plays a dominant role and corresponds to the lowest-energy configuration obtained using density functional theory.     

DFT calculations of 29Si-NMR chemical shifts in Ru(II) silyl complexes: searching for trends and accurate values

The (29)Si chemical shifts in a series of closely related Ru(II) silyl complexes have been calculated by DFT methods and compared to the experimental values. The factors that lead to possible discrepancies between experimental and calculated values have been identified. It is shown that it is necessary to include the spin-orbit coupling associated with the relativistic effects of the heavy atoms for quantitative agreement with observed chemical shifts but trends are reasonably reproduced when the calculations do not include this correction. An NBO analysis of the NMR contributions from the bonds to Si and the Si core shows the greater importance of the former and a fine tuning originating from the latter.     

Electronic structure and molecular properties of the heptacyanorhenate [Re(CN)7]3- and [Re(CN)7]4- complexes

We report scalar relativistic and Dirac scattered wave (DSW) calculations on the heptacyanorhenate [Re(CN)7](3-) and Re(CN)7(4-) complexes. Both the ground and lowest excited states of each complex split by spin-orbit interaction by about 0.3 eV. The calculated molecular electronegativities chi indicate that the open-shell complex is less reactive than the closed-shell complex, in agreement with experimental observations. The calculations indicate that the ground state spin density is highly anisotropic and that spin-orbit effects are responsible for the magnetic anisotropy of the molecular g tensor of the Re(CN)7(3-) complex. The calculated optical electronic transitions for both complexes with a polarizable continuum model using a time-dependent density functional (TDDFT)/B3LYP formalism are in reasonable agreement with those observed in the absorption spectrum.     

Stability constants of Np(V) complexes with fluoride and sulfate at variable temperatures

Summary A solvent extraction method was used to determine the stability constants of Np(V) complexes with fluoride and sulfate in 1.0M NaClO₄ from 25 to 60 °C. The distribution ratio of Np(V) between the organic and aqueous phases was found to decrease as the concentrations of fluoride and sulfate were increased. Stability constants of the 1 : 1 Np(V)-fluoride complexes and the 1 : 1 Np(V)-sulfate and 1 : 2 Np(V)-sulfate complexes, dominant in the aqueous phase under the experimental conditions, were calculated from the effect of [F^-] and [SO₄^2-] on the distribution ratio. The enthalpy and entropy of complexation were calculated from the stability constants at different temperatures by using the Van't Hoff equation.     

Spin-orbit relaxation of Cl(2P1/2) and F(2P1/2) in a gas of H2

The authors present quantum scattering calculations of rate coefficients for the spin-orbit relaxation of F(2P1/2) atoms in a gas of H2 molecules and Cl(2P1/2) atoms in a gas of H2 and D2 molecules. Their calculation of the thermally averaged rate coefficient for the electronic relaxation of chlorine in H2 agrees very well with an experimental measurement at room temperature. It is found that the spin-orbit relaxation of chlorine atoms in collisions with hydrogen molecules in the rotationally excited state j=2 is dominated by the near-resonant electronic-to-rotational energy transfer accompanied by rotational excitation of the molecules. The rate of the spin-orbit relaxation in collisions with D2 molecules increases to a great extent with the rotational excitation of the molecules. They have found that the H2/D2 isotope effect in the relaxation of Cl(2P1/2) is very sensitive to temperature due to the significant role of molecular rotations in the nonadiabatic transitions. Their calculation yields a rate ratio of 10 for the electronic relaxation in H2 and D2 at room temperature, in qualitative agreement with the experimental measurement of the isotope ratio of about 5. The isotope effect becomes less significant at higher temperatures.     

Speciation of Np(V) uptake by Opalinus Clay using synchrotron microbeam techniques

Synchrotron-based X-ray absorption spectroscopy has been used to determine the chemical speciation of Np sorbed on Opalinus Clay (OPA, Mont Terri, Switzerland), a natural argillaceous rock revealing a micro-scale heterogeneity. Different sorption and diffusion samples with Np(V) were prepared for spatially resolved molecular-level investigations. Thin sections of OPA contacted with Np(V) solution under aerobic and anaerobic conditions as well as a diffusion sample were analysed spatially resolved. Micro-X-ray fluorescence (μ-XRF) mapping has been used to determine the elemental distributions of Np, Fe and Ca. Regions of high Np concentration were subsequently investigated by micro-X-ray absorption fine structure spectroscopy to determine the oxidation state of Np. Further, micro-X-ray diffraction (μ-XRD) was employed to gain knowledge about reactive crystalline mineral phases in the vicinity of Np enrichments. One thin section was also analysed by electron microprobe to determine the elemental distributions of the lighter elements (especially Si and Al), which represent the main elements of OPA. The results show that in most samples, Np spots with considerable amounts of Np(IV) could be found even when the experiments were carried out in air. In some cases, almost pure Np(IV) L(III)-edge X-ray absorption near-edge structure spectra were recorded. In the case of the anaerobic sample, the μ-XRF mapping showed a clear correlation between Np and Fe, indicating that the reduction of Np(V) is caused by an iron(II)-containing mineral which could be identified by μ-XRD as pyrite. These spatially resolved investigations were complemented by extended X-ray absorption fine structure measurements of powder samples from batch experiments under aerobic and anaerobic conditions to determine the structural parameters of the near-neighbour environment of sorbed Np.     

The role of the bridging group in exchange coupling in dinuclear homo- and heterometallic Ni(ii) and Co(ii) complexes with oxalate, oxamidate and dithiooxamidate bridges

Six homodinuclear and two heteronuclear complexes Tp(Np)Co-C(2)O(4)-CoTp(Np) (1), Tp(Np)Co-C(2)O(4)-NiTp(Cy) (2), Tp(Cy)Ni-C(2)O(4)-NiTp(Cy) (3), Tp(Np)Co-C(2)O(2)(NH)(2)-CoTp(Np) (4), Tp(Cy)Ni-C(2)O(2)(NH)(2)-NiTp(Cy) (5), Tp(Np)Co-C(2)S(2)(NH)(2)-CoTp(Np) (6), Tp(Np)Co-C(2)S(2)(NH)(2)-NiTp(Cy) (7), Tp(Cy)Ni-C(2)S(2)(NH)(2)-NiTp(Cy) (8) (Tp(Np) = tris(3-neopentylpyrazolyl)borate, Tp(Cy) = tris(3-cyclohexylpyrazolyl)borate), were synthesized and characterized by mass spectrometry, electronic spectroscopy and X-ray crystallography. These compounds possess similar molecular structures, with the metal ions linked by bridging oxalate (1-3), oxamidate (4 and 5) or dithiooxamidate (6-8) ions. The heteronuclear nature of compounds 2 and 7 was additionally confirmed by high-resolution mass spectrometry. The magnetic properties of the Co(2+) complexes were modelled taking into account zero-field splitting of this ion, yielding D-values for Co(2+) in the range -17(1) to -50(1) cm(-1). All the metal ion pairs in compounds 1-8 are antiferromagnetically-coupled, with J values between -10.0(1) and -45.0(2) cm(-1) (via the exchange Hamiltonian ?(ex.) = -2J?(1)?(2)) and |J| increasing in the order oxalate < oxamidate < dithiooxamidate. This tendency can be attributed to greater M-S bond covalency compared to M-N or M-O bonds (M = Co(2+) and Ni(2+)). It was found that this antiferromagnetic coupling of Co(2+) and Ni(2+) ions through oxalate is more efficient for these tris(pyrazolyl)borate complexes than for similar oxalate-bridged systems with neutral aliphatic amine ligands.     

Importance of out-of-state spin-orbit coupling for slow magnetic relaxation in mononuclear Fe(II) complexes

Two mononuclear high-spin Fe(II) complexes with trigonal planar ([Fe(II)(N(TMS)(2))(2)(PCy(3))] (1) and distorted tetrahedral ([Fe(II)(N(TMS)(2))(2)(depe)] (2) geometries are reported (TMS = SiMe(3), Cy = cyclohexyl, depe = 1,2-bis(diethylphosphino)ethane). The magnetic properties of 1 and 2 reveal the profound effect of out-of-state spin-orbit coupling (SOC) on slow magnetic relaxation. Complex 1 exhibits slow relaxation of the magnetization under an applied optimal dc field of 600 Oe due to the presence of low-lying electronic excited states that mix with the ground electronic state. This mixing re-introduces orbital angular momentum into the electronic ground state via SOC, and 1 thus behaves as a field-induced single-molecule magnet. In complex 2, the lowest-energy excited states have higher energy due to the ligand field of the distorted tetrahedral geometry. This higher energy gap minimizes out-of-state SOC mixing and zero-field splitting, thus precluding slow relaxation of the magnetization for 2.     

Theoretical investigation of electronic structures and excitation energies of hexaphyrin and its group 11 transition metal (III) complexes

Density functional theory is carried out to study hexaphyrin and its bis-metal and mixed bis-metal (M = Cu³⁺, Ag³⁺, and Au³⁺) complexes. The electronic structures and bonding situations of them are studied by using natural bond orbital approach and the topological analysis of the electron localization function. Electronic spectra are investigated by using time-dependent density functional theory. The introduction of group 11 transition metals leads to red shifts in the spectra of these metal complexes with respect to that of hexaphyrin. Moreover, it is noteworthy that the spectra of copper contained complexes are mainly derived from combination of ligand-to-metal charge transfer and ligand-to-ligand charge transfer transitions. In addition, the relativistic time-dependent density functional theory with spin-orbit coupling calculations indicate that the effects of spin-orbit coupling on the excitation energies are so small that it is safe enough to neglect spin-orbit coupling for these systems.     

The mechanism of the reduction of [AnO2]2+ (An = U, Np, Pu) in aqueous solution, and by Fe(II) containing proteins and mineral surfaces, probed by DFT calculations

The fate of actinyl species in the environment is closely linked to oxidation state, since the reduction of An(VI) to An(IV) greatly decreases their mobility due to the precipitation of the relatively insoluble An(IV) species. Here we study the mechanism of the reduction of [AnO(2)](2+) (An = U, Np, Pu) both in aqueous solution and by Fe(II) containing proteins and mineral surfaces, using density functional theory calculations. We find a disproportionation mechanism involving a An(V)-An(V) cation-cation complex, and we have investigated how these complexes are formed in the different environments. We find that the behaviour of U and Pu complexes are similar, but the reduction of Np(V) to Np(IV) would seems to be more difficult, in line with the experimental finding that Np(V) is generally more stable than U(V) or Pu(V). Although the models we have used are somewhat idealised, our calculations suggest that there are strong similarities between the biotic and abiotic reduction pathways.     

On the paucity of molecular actinide complexes with unsupported metal-metal bonds: a comparative investigation of the electronic structure and metal-metal bonding in U2X6 (X = Cl, F, OH, NH2, CH3) complexes and d-block analogues

Density functional calculations have been performed on M2X6 complexes (where M = U, W, and Mo and X = Cl, F, OH, NH2, and CH3) to investigate general aspects of their electronic structures and explore the similarities and differences in metal-metal bonding between f-block and d-block elements. A detailed analysis of the metal-metal interactions has been conducted using molecular orbital theory and energy decomposition methods. Multiple (sigma and pi) bonding is predicted for all species investigated, with predominant f-f and d-d metal orbital character, respectively, for U and W or Mo complexes. The energy decomposition analysis involves contributions from orbital interactions (mixing of occupied and unoccupied orbitals), electrostatic effects (Coulombic attraction and repulsion), and Pauli repulsion (associated with four-electron two-orbital interactions). The general results suggest that the overall metal-metal interaction is stronger in the Mo and W species, relative to the U analogues, as a consequence of a significantly less destabilizing contribution from the combined Pauli and electrostatic ("pre-relaxation") effects. Although the orbital-mixing ("post-relaxation") contribution to the total bonding energy is predicted to have a larger magnitude in the U complexes, this is not sufficiently strong to compensate for the comparatively greater destabilization that originates from the Pauli-plus-electrostatic effects. Of the pre-relaxation terms, the Pauli repulsion is comparable in analogous U and d-block compounds, contrary to the electrostatic term, which is (much) less favorable in the U systems than in the W and Mo systems. This generally weak electrostatic stabilization accounts for the large pre-relaxation destabilization in the U complexes and, ultimately, for the relative weakness of the U-U bonds. The origin of the small electrostatic term in the U compounds is traced primarily to MX(3) fragment overlap effects.