Spin-orbit Relativistic Effects Research Articles

Relativistic effects in HgHe and HgXe CCSD(T) ground state potential curves. Low-density viscosity simulations of Hg:Xe mixture

The comparison of coupled cluster with single and double excitations and with perturbative correction of triple excitations [CCSD(T)] ground state potential curves of mercury with rare gases (RG): HgHe and HgXe, at several levels of theory is presented. The scalar relativistic (REL) effects and spin-orbit coupling effects in the ground state potential curves of these weakly bounded dimers are considered. The CCSD(T) ground state potential curves at the level of the Dirac-Coulomb Hamiltonian (DCH) are compared with CCSD(T) curves at the level of 4-component spin-free modified DCH, the scalar 2nd order Douglas-Kroll-Hess (DKH2) and the nonrelativistic (NR-LL) (Lévy-Leblond) Hamiltonian. In addition, London-Drude formula and SCF interaction energy curves are employed in the analysis of different contributions of REL effects in dissociation energies of HgRG and Hg(2) dimers. Moreover, the large anharmonicity of the HgHe ground state potential curve is highlighted. The computationally less demanding scalar DKH2 Hamiltonian is employed to calculate the HgXe, Hg(2) , and Xe(2) all electron CCSD(T) ground state potential curves in highly augmented quadruple zeta basis sets. These potential curves are used to simulate the shear viscosity of mercury, xenon, and mercury-xenon (Hg:Xe) mixture.

Accurate computational thermochemistry from explicitly correlated coupled-cluster theory

Explicitly correlated coupled-cluster theory has developed into a valuable computational tool for the calculation of electronic energies close to the limit of a complete basis set of atomic orbitals. In particular at the level of coupled-cluster theory with single and double excitations (CCSD), the space of double excitations is quickly extended towards a complete basis when Slater-type geminals are added to the wave function expansion. The purpose of the present article is to demonstrate the accuracy and efficiency that can be obtained in computational thermochemistry by a CCSD model that uses such Slater-type geminals. This model is denoted as CCSD(F12), where the acronym F12 highlights the fact that the Slater-type geminals are functions f(r 12) of the interelectronic distances r 12 in the system. The performance of explicitly correlated CCSD(F12) coupled-cluster theory is demonstrated by computing the atomization energies of 73 molecules (containing H, C, N, O, and F) with an estimated root-mean-square deviation from the values compiled in the Active Thermochemical Tables of σ = 0.10 kJ/mol per valence electron. To reach this accuracy, not only the frozen-core CCSD basis-set limit but also high-order excitations (connected triple and quadruple excitations), core–valence correlation effects, anharmonic vibrational zero-point energies, and scalar and spin–orbit relativistic effects must be taken into account.

Relativistic density functional investigation of UX6 (X = F, Cl, Br and I)

The molecular structures and the vibrational frequencies of uranium hexahalides UX6 (X = F, Cl, Br and I) molecules are investigated by using local density approximation (LDA) and generalised gradient approximation (GGA) functions (BP, BLYP and RPBE) in combination with two different relativistic methods (scalar and scalar + spin–orbit relativistic effects). The calculated results show that the differences are trivial between scalar and scalar+spin–orbit relativistic methods. The vibrational frequencies are also compared with existing experimental values, and overall, the RPBE approach gives the smallest error. The bond dissociation energies (BDEs) of UX6 are computed by using the RPBE function, thereby obtaining exact vibrational frequencies. In addition, the calculated magnitudes of the spin–orbit effect on the BDE of UX6 (X = F, Cl, Br, and I) are found to be approximately −0.3198, −0.3218, −0.3609 and −0.4415 eV, respectively.

Inside a Superatom: The M7q (M=Cu, Ag, q=1+, 0, 1−) Case

All-electron relativistic density functional calculations are performed to obtain the electronic structure and nucleus-independent chemical shifts (NICS) of D(5h) pentagonal-bipyramidal (PBP) Cu(7)(q) and Ag(7)(q) (q=1+,0,1-) clusters. Scalar and spin-orbit relativistic effects are taken into account at two levels: the two-component zero-order regular approximation (ZORA) Hamiltonian and fully relativistic four-component calculations via the Dirac equation. These clusters are treated by including the spin-orbit effect in the jellium model, within the double-valued point group (D(5h)*) establishing the symmetry correlations between the molecular and the atomic spinors given by the full rotation group. These clusters show highly spherical aromaticity, which is suggested to increase the hardness of the superatom. Thus, the calculations suggest that the paramagnetic Cu(7) and Ag(7) clusters can be regarded as pseudohalogens.

Carbon and proton shielding tensors in methyl halides

The series of methyl halides, CH(3)X (X = F, Cl, Br, and I), is prototypic for demonstrating the s.c. normal halogen dependence of light-atom nuclear magnetic resonance shielding constants in the presence of halogen atoms of varying electronegativity. We report a systematic experimental and first-principles theoretical study of the (13)C and (1)H shielding tensors in this series. The experimental shielding constants were obtained from gas-phase NMR experiments and the anisotropies were determined using liquid crystal NMR spectroscopy. After taking into account rovibrational effects and solute-solvent interactions, this provided the currently best experimental estimates for the full shielding tensors. Quantum chemical calculations were carried out at ab initio and density functional theory levels, involving relativistic corrections taken into account at the leading-order Breit-Pauli perturbation level. Anharmonic and harmonic vibrational corrections were performed. The main trends of the shielding constants and anisotropies of the nearby light (13)C and (1)H nuclei as functions of the halogen mass, were confirmed to be mainly due to relativistic spin-orbit effects. For carbon, also the scalar relativistic effects are important for quantitative results. Thermal averaging at 300 K decreases the magnitude of all the parameters but exhibits partial cancellation between the nonrelativistic and smaller relativistic rovibrational averages. For the shielding anisotropy, the relativistic terms add to the negative rovibrational effect. Overall, the current experimental and theoretical results are in excellent agreement for all the shielding parameters, setting a standard for further investigations of normal halogen dependence.

Relativistic Zeroth-Order Regular Approximation Combined with Nonhybrid and Hybrid Density Functional Theory: Performance for NMR Indirect Nuclear Spin-Spin Coupling in Heavy Metal Compounds.

A benchmark study for relativistic density functional calculations of NMR spin-spin coupling constants has been performed. The test set contained 47 complexes with heavy metal atoms (W, Pt, Hg, Tl, Pb) with a total of 88 coupling constants involving one or two heavy metal atoms. One-, two-, three-, and four-bond spin-spin couplings have been computed at different levels of theory (nonhybrid vs hybrid DFT, scalar vs two-component relativistic). The computational model was based on geometries fully optimized at the BP/TZP scalar relativistic zeroth-order regular approximation (ZORA) and the conductor-like screening model (COSMO) to include solvent effects. The NMR computations also employed the continuum solvent model. Computations in the gas phase were performed in order to assess the importance of the solvation model. The relative median deviations between various computational models and experiment were found to range between 13% and 21%, with the highest-level computational model (hybrid density functional computations including scalar plus spin-orbit relativistic effects, the COSMO solvent model, and a Gaussian finite-nucleus model) performing best.

Measurement of Δ 1J( 199Hg, 31P) in [HgPCy 3(OAc) 2] 2 and relativistic ZORA DFT investigations of mercury–phosphorus coupling tensors

Using 31P solid-state NMR spectroscopy, anisotropy in the indirect 199Hg- 31P spin–spin coupling tensor (Δ J) for powdered [HgPCy 3(OAc) 2] 2 ( 1) has been measured as 4700±300 Hz. Zeroth-order regular approximation (ZORA) density functional theory (DFT) calculations, including scalar and spin-orbit relativistic effects, performed on 1 and a series of other related compounds show that Δ J( 199Hg, 31P) arises entirely from the ZORA Fermi-contact–spin-dipolar cross term. The calculations validate assumptions made in the spectral analysis of 1 and in previous determinations of Δ J in powder samples, namely that J is axially symmetric and shares its principal axis system with the direct dipolar coupling tensor ( D). Agreement between experiment and theory for various 199Hg, 31P spin–spin coupling anisotropies is reasonable; however, experimental values of 1 J( 199Hg, 31P) iso are significantly underestimated by the calculations. The most important improvements in the agreement were obtained as a result of including more of the crystal lattice in the model used for the calculations, e.g., a change of 43% was noted for 1 J( 199Hg, 31P) iso in [HgPPh 3(NO 3) 2] 2 depending on whether the two or three nearest nitrate ions are included in the model. Finally, we have written a computer program to simulate the effects of non-axial symmetry in J and of non-coincidence of the J and D on powder NMR spectra. Simulations clearly show that both of these effects have a pronounced impact on the 31P NMR spectrum of 199Hg– 31P spin pairs, suggesting that the effects should be observable experimentally if a suitable compound can be identified.

Heats of Formation of the H1,2OmSn (m, n = 0−3) Molecules from Electronic Structure Calculations

Atomization energies at 0 K and heats of formation at 0 and 298 K are predicted from high level ab initio electronic structure calculations using the coupled cluster CCSD(T) method with augmented correlation-consistent basis sets extrapolated to the complete basis set (CBS) limit for the H(1,2)O(m)S(n) (m, n = 0-3) compounds, as well as various radicals involved in different bond breaking processes. To achieve near chemical accuracy (+/-1.0 kcal/mol), additional corrections were added to the CBS binding energies based on the frozen core CCSD(T) energies including corrections for core-valence, scalar relativistic, and first-order atomic spin-orbit effects. Geometries were optimized up through the CCSD(T)/aV(T+d)Z level. Vibrational zero point energies were computed at the MP2/aV(T+d)Z level. The calculated heats of formation are in excellent agreement with the available experimental data and allow the prediction of adiabatic bond dissociation energies (BDEs) to within +/-1.0 kcal/mol. The decomposition mechanisms were largely determined by a preference to maintain a strong S=O bond in the dissociated products as opposed to O=O and S=S bonds, exactly matching the ordering of the BDEs in the diatomics. For the H(2)X(2) and H(2)X(3) systems, as well as the HX(3) radicals, the energetically favorable decomposition pathway leads to the formation of XH radicals and breaking the X-X bond as opposed to breaking the X-H bond. For the HX(2) radicals, however, the more thermodynamically favorable pathway leads to a breaking of the H-X bond and forming X(2) molecules.

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.

Spin–orbit effects on the aromaticity of the Re 3Cl 9 and Re 3Br 9 clusters

Here, we report density functional calculations of the electronic structure and nuclear independent chemical shift (NICS) values of the Re 3Cl 9 and Re 3Br 9 clusters including scalar and spin–orbit relativistic effects (ADF + ZORA + SO). Our calculations have shown that both the clusters exhibit aromaticity and that spin–orbit effects decreases aromaticity due to the fact that the 5d 3/2 spinors are mostly occupied and are more contracted than the scalar 5d orbitals.

Computational NMR Spectroscopy of Organoarsenicals and the Natural Polyarsenic Compound Arsenicin A

The (1)H and (13)C NMR chemical shifts and coupling constants of a series of organoarsenic compounds were calculated with DFT methods and compared with available experimental spectra. We show that non-relativistic methods successfully model the NMR spectra of these molecules; relativistic spin-orbit effects are small but appreciable for (13)C shifts, and their inclusion is beneficial. Application of the same methods of calculation to the intriguing natural polyarsenic compound arsenicin A allowed several viable alternative structures to be ruled out and thereby confirmed the previously suggested adamantane-like structure of arsenicin A. These results not only reinforce the known predictive power of DFT NMR calculations, but also open the way for the investigation of other naturally occurring molecules with unusual structures outside the scope of empirical methods.

Accurate ab initio computation of thermochemical data for C 3H x[formula omitted] species

We have computed the atomization energies of nineteen C 3H x molecules and radicals using explicitly-correlated coupled-cluster theory including corrections for core–core and core–valence correlation, scalar and spin–orbit relativistic effects, and anharmonic vibrational zero-point energies. Equilibrium geometries were obtained at the coupled-cluster level [CCSD(T) model] in a correlation-consistent polarized core–valence quadruple-zeta basis set, using a spin-restricted Hartree–Fock reference wave function, and including all electrons in the correlation treatment. Applied to a set of selected CH x and C 2H x systems, our approach yields highly accurate atomization energies with a mean absolute deviation of 1.4 kJ/mol and a maximum deviation of 4.2 kJ/mol (for dicarbon) from the Active Thermochemical Tables (ATcT) values. The explicitly-correlated coupled-cluster approach provides energies near the basis-set limit of the CCSD(T) model, which is the coupled-cluster model with single and double excitations (CCSD) augmented with a perturbative correction for triple excitations (T). To obtain even more accurate atomization energies than those presented here, it would be required to include full triple excitations (CCSDT) and corrections for excitations beyond triples, as for instance done in the CCSDT(Q) model, which includes a perturbative correction for quadruple excitations (Q).

Hg + Br → Hg Br recombination and collision-induced dissociation dynamics

A global potential energy surface has been constructed for the system HgBr+Ar-->Hg+Br+Ar to determine temperature dependent rate constants for the collision-induced dissociation (CID) and recombination of Hg and Br atoms. The surface was decomposed using a many-body expansion. Accurate two-body potentials for HgBr, HgAr, and ArBr were calculated using coupled cluster theory with single and double excitations and a perturbative treatment of triple excitations [CCSD(T)], as well as the multireference averaged coupled pair functional method. Correlation consistent basis sets were used to extrapolate to the complete basis set limit and corrections were included to account for scalar and spin-orbit relativistic effects, core-valence correlation, and the Lamb shift. The three-body potential was computed with the CCSD(T) method and triple-zeta quality basis sets. Quasiclassical trajectories using the final analytical potential surface were directly carried out on the CID of HgBr by Ar for a large sampling of initial rotational, vibrational, and collision energies. The recombination rate of Hg and Br atoms is a likely first step in mercury depletion events that have been observed in the Arctic troposphere during polar sunrise. The effective second order rate constant for this process was determined in this work from the calculated CID rate as a function of temperature using the principle of detailed balance, which resulted in k(T) = 1.2 x 10(-12) cm(3) molecule(-1) s(-1) at 260 K and 1 bar pressure.

Orbital Order inZnV2O4

In view of recent controversy regarding the orbital order in the frustrated spinel ZnV2O4, we analyze the orbital and magnetic groundstate of this system within an ab initio density functional theory approach. While LDA+U calculations in the presence of a cooperative Jahn-Teller distortion stabilize an A-type staggered orbital order, the consideration of relativistic spin-orbit effects unquenches the orbital moment and leads to a uniform orbital order with a net magnetic moment close to the experimental one. Our results show that ab initio calculations are able to resolve the existing discrepancies in previous theories and that it is the spin-orbit coupling alongwith electronic correlations which play a significant role in determining the orbital structure in these materials.

Corrections and parametrization of semiempirical large unit cell method for covalent semiconductors

Self-consistent Hartree-Fock within the framework of large unit cell (LUC) formalism using complete and intermediate neglect of differential overlap (INDO) is used to simulate electronic band structure of covalent crystalline semiconductors. Correlation corrections are added via second-order Moller-Plesset perturbation method. Other corrections such as relativistic spin-orbit effects on the band gap and zero-point energy are also included. Cohesive energy, band gap, valence-band width, and hybridization orbitals are obtained from band calculations. Bulk modulus, charge distribution, and x-ray form factors are also calculated. These calculations are directed toward large scale or defected systems. Results show that the effects of some of these corrections are indispensable to obtain a clear view of semiempirical parameters used to fit band structure of covalent semiconductors. Correlation and INDO corrections removed some electronic cloud from the bonding region to the spherical region around the atom. Correlation corrections with its long time and limited improvements are not advised for large scale calculations. Solid parameters are compared with those of molecules and free atoms to understand the rules of parametrization in solids. Resemblance with size-dependent nanocluster properties is established for present calculations such as the decrease of band gap with increasing size of LUC. The major difference of the present calculations from previous nanocluster calculations is the use of the same element atom of the cluster to cap surface dangling bonds.

Theoretical investigation on H1 and C13 NMR chemical shifts of small alkanes and chloroalkanes

Using density functional theory (DFT) with the B3LYP, PBE, and PBE0 exchange-correlation functionals as well as the Moller-Plesset second-order perturbation theory (MP2) combined with a series of rather extended basis sets, 1H and 13C chemical shifts of small alkanes and chloroalkanes (with different numbers of chlorine atoms on specific positions) have been simulated and compared to experimental data. For the 1H chemical shifts, theory tends to reproduce experiment within the limits of the experimental errors. In the case of 13C chemical shift, the differences between theory and experiment increase monotonically with the number of chlorine atoms and exhibit a deviation from additivity. This behavior is related to the saturation of the experimental 13C chemical shifts with the number of chlorine atoms, whereas the evolution is mostly linear at both DFT and MP2 levels of approximation. This difference has been traced back to the relativistic spin-orbit coupling effects, which are exalted as a result of the enhancement of the s character of the C atom when increasing the number of linked Cl atoms. Thus, it was demonstrated that not only electron correlation but also relativistic effects have to be considered for estimating the 13C chemical shifts when several Cl atoms are directly attached to the C atom. Linear (theory/experiment) regressions have then been performed for the different types of C atoms, i.e., bearing one, two, and three Cl atoms, with excellent correlation coefficients. The linear correlation relationships so obtained can then serve to predict and facilitate the interpretation of the nuclear magnetic resonance spectra of more complex compounds. Furthermore, by investigating the basis set effects, the correlation between the chemical shifts calculated using the 6-311 + G(2d,p) basis set and the more extended 6-311 + G(2df,p) and aug-cc-pvtz basis sets is excellent, demonstrating that the choice of the 6-311 + G(2d,p) basis set for calculating the 1H and 13C chemical shifts is relevant.

What is the best theoretical method to study molybdenum dithiolene complexes?

The reaction sequence of sulfoxide reduction by molybdenum complexes containing two enedithiolate and one oxide ligand is used to evaluate different density functional methods. Relative energies are computed for several stationary points: a pentacoordinate reduced complex, its adducts with water and with the sulfoxide substrate, the transition state for oxygen atom transfer to the metal center, a van der Waals complex of the reduced sulfide with the molybdenum oxo complex and the isolated oxo complex itself. Root mean square deviations from CCSD results or values extrapolated (depending on the size of the ligands used) serve to assess the quality of various popular and promising modern DFT methods available in Gaussian03 (in combination with the SDD basis set augmented by additional polarization functions) and ADF2005 (TZP basis set). B3LYP, B1B95, B97-1 and B98 form the group of best functionals provided by Gaussian according to our criteria. PBE1PBE, B1LYP, MPW1PW91 and B97-2 have increasingly larger deviations but describe the considered reaction sequence qualitatively correct. The reaction profiles produced by HCTH147, BP86, HCTH407, BLYP, G96LYP and especially by OLYP, HCTH93, BH and H and VSXC have severe flaws. These functionals are not recommended for the treatment of oxygen atom transfer reactions involving transition metals. DFT functionals used with ADF derived energies for the BP/TZP density. The relative energies show larger RMS, which can be slightly reduced by inclusion of ZORA scalar relativistic effects and in the case of hybrid functionals further by ZORA spin-orbit relativistic effects. Geometries obtained with BP/TZP produce RMS deviations comparable to the best methods identified when relative energies are derived from single point energies computed by one of these methods.

The correlation consistent composite approach (ccCA): An alternative to the Gaussian-n methods

An alternative to the Gaussian-n (G1, G2, and G3) composite methods of computing molecular energies is proposed and is named the "correlation consistent composite approach" (ccCA, ccCA-CBS-1, ccCA-CBS-2). This approach uses the correlation consistent polarized valence (cc-pVXZ) basis sets. The G2-1 test set of 48 enthalpies of formation (DeltaHf), 38 adiabatic ionization potentials (IPs), 25 adiabatic electron affinities (EAs), and 8 adiabatic proton affinities (PAs) are computed using this approach, as well as the DeltaHf values of 30 more systems. Equilibrium molecular geometries and vibrational frequencies are obtained using B3LYP density functional theory. When applying the ccCA-CBS method with the cc-pVXZ series of basis sets augmented with diffuse functions, mean absolute deviations within the G2-1 test set compared to experiment are 1.33 kcal mol(-1) for DeltaHf,0.81 kcal mol(-1) for IPs, 1.02 kcal mol(-1) for EAs, and 1.51 kcal mol(-1) for PAs, without including the "high-level correction" (HLC) contained in the original Gn methods. Whereas the HLC originated in the Gaussian-1 method as an isogyric correction, it evolved into a fitted parameter that minimized the error of the composite methods, eliminating its physical meaning. Recomputing the G1 and G3 enthalpies of formation without the HLC reveals a systematic trend where most DeltaHf values are significantly higher than experimental values. By extrapolating electronic energies to the complete basis set (CBS) limit and adding G3-like corrections for the core-valence and infinite-order electron correlation effects, ccCA-CBS-2 often underestimates the experimental DeltaHf, especially for larger systems. This is desired as inclusion of relativistic and atomic spin-orbit effects subsequently improves theoretical DeltaHf values to give a 0.81 kcal mol(-1) mean absolute deviation with ccCA-CBS-2. The ccCA-CBS method is a viable "black box" method that can be used on systems with at least 10-15 heavy atoms.

Ab initio investigation of potential energy curves of the 23 electronic states of IBr correlating to neutral2P atoms

Potential energy surfaces for all Born-Oppenheimer electronic states of IBr molecule correlating to the neutral (2)P ((2)P(3/2) and (2)P(1/2)) iodine and bromine are calculated for the first time. Electric dipole and polarizability curves (static and transition) are also determined. Calculations include scalar and spin-orbit relativistic effects within all-electron Douglas-Kroll two-component Hamiltonian. Electron correlation is treated with quasi-degenerate multi-reference second-order perturbation theory. Seven adiabatic electronic states (X (1)Sigma(+), A'(3)Pi(2), A (3)Pi(1), 1 (3)Pi(0-), B (3)Pi(0+), B'(3)Sigma, and 2 (3)Pi(0+)) exhibit significant covalent bonding, and can support vibrational states. Calculated spectroscopic parameters agree with experiment to better than 1000 cm(-1) (T(e)), 10 cm(-1) (omega(e)), and 0.05 Angstrom (r(e)). A new 1 (3)Pi(0-) state correlating to ground-state atoms is predicted at T(e) approximately 14 000 cm(-1), omega(e) approximately 80 cm(-1), and r(e) approximately 3.0 Angstrom. The second new state (2 (3)Pi(0+)) correlates to excited iodine atom, with T(e) approximately 20 000 cm(-1), omega(e) approximately 115 cm(-1), and r(e) approximately 3.3 Angstrom. Non-adiabatic coupling parameters are calculated for the four avoided crossings, which arise due to electronic spin-orbit interaction. Estimated parameters of the B (3)Pi(0+)/B'(3)Sigma crossing (R(c) approximately 3.32 Angstrom; V approximately 120 cm(-1)) agree with experimental values. The previously unsuspected 2 (3)Pi(0-)/1 (1)Sigma(-) crossing of two repulsive surfaces provides a new collisional deactivation channel for Br* atoms at relative velocities above 1000 m s(-1). Several repulsive states (including 1 (1)Pi(1) and 2 (3)Pi(1)) intersect the B/B' system near the avoided crossing point, and may affect dynamics of IBr in strong laser fields.

An Investigation of Lanthanum Coordination Compounds by Using Solid‐State 139La NMR Spectroscopy and Relativistic Density Functional Theory

Lanthanum-139 NMR spectra of stationary samples of several solid La(III) coordination compounds have been obtained at applied magnetic fields of 11.75 and 17.60 T. The breadth and shape of the 139La NMR spectra of the central transition are dominated by the interaction between the 139La nuclear quadrupole moment and the electric field gradient (EFG) at that nucleus; however, the influence of chemical-shift anisotropy on the NMR spectra is non-negligible for the majority of the compounds investigated. Analysis of the experimental NMR spectra reveals that the 139La quadrupolar coupling constants (C(Q)) range from 10.0 to 35.6 MHz, the spans of the chemical-shift tensor (Omega) range from 50 to 260 ppm, and the isotropic chemical shifts (delta(iso)) range from -80 to 178 ppm. In general, there is a correlation between the magnitudes of C(Q) and Omega, and delta(iso) is shown to depend on the La coordination number. Magnetic-shielding tensors, calculated by using relativistic zeroth-order regular approximation density functional theory (ZORA-DFT) and incorporating scalar only or scalar plus spin-orbit relativistic effects, qualitatively reproduce the experimental chemical-shift tensors. In general, the inclusion of spin-orbit coupling yields results that are in better agreement with those from the experiment. The magnetic-shielding calculations and experimentally determined Euler angles can be used to predict the orientation of the chemical-shift and EFG tensors in the molecular frame. This study demonstrates that solid-state 139La NMR spectroscopy is a useful characterization method and can provide insight into the molecular structure of lanthanum coordination compounds.