Effective Spin-orbit Operator Research Articles

Toward a fast evaluation of g-tensor of Cu containing systems: A DFT parametrized approach

DFT has been applied to evaluate electron paramagnetic resonance (EPR) g-tensor components of copper containing systems using an effective Spin–Orbit operator relying on the use of effective nuclear charges (Zeff). In particular, an optimal Zeff value was obtained for the copper atom by fitting the results obtained for a series of twenty copper bioinorganic complexes to the data obtained, at the same level of theory, using more refined approaches to evaluate Spin–Orbit Coupling terms. We showed that spin–orbit effects can be well approximated using the Zeff method giving reliable g-tensor values at low computational cost for large molecular compounds.

Entwicklung und Implementierung zweikomponentiger Hartree-Fock- und Dichtefunktionalmethoden

In the present work a selfconsistent treatment of the spin-orbit interaction is developed in the program system TURBOMOLE implemented and adopted. The underlying formalism deals with two-component Hartree-Fock- and density functional methods including the 'resolution-of-the-identity'-approximation for the Coulomb- and exchange operators. The spin-orbit interaction is included via effective core potentials for the heavier p-elements and at the all-electron level with the effective spin-orbit operator AMFI for the lighter elements. It was discovered that the selfconsistent treatment of the spin-orbit interaction with effective core potentials has special requirements on the basis sets especially on the flexibility of the inner shells. With additions to the existing basis sets the basis set error for the two-component treatment is similar to the one-component approach. The enhanced basis sets have the same quality for one- and two-component calculations. The focus of the applications was on clusters of the heavy main group elements thallium, lead, bismuth and polonium. The inclusion of the spin-orbit interaction gives a realistic estimation of the cohesive energy of the small and medium-sized clusters and highly symmetric structures which show at the one-component level Jahn-Teller distortions to be often preferred. The implemented two-component procedure on the Hartree-Fock-level or by application of hybrid density functionals can be applied for middle-sized systems with comparably large basis sets. The efficiency of the two-component DFT approach with pure density functionals is demonstrated for nanoparticles (ca. 2000 basis functions).

Vibrational assignment and Franck–Condon analysis of the mass-analyzed threshold ionization (MATI) spectrum of CH2ClI: The effect of strong spin-orbit interaction

Detailed analysis of the one-photon mass-analyzed threshold ionization (MATI) spectrum of CH(2)ClI is presented. This includes the determination of the ionization energy of CH(2)ClI, complete vibrational assignments, and quantum-chemical calculations at the spin-orbit density-functional-theory (SODFT) level with various basis sets. Relativistic effective core potentials with effective spin-orbit operators can be used in SODFT calculations to treat the spin-orbit term on an equal footing with other relativistic effects and electron correlations. The comparison of calculated and experimental vibrational frequencies indicate that the spin-orbit effects are essential for the reasonable description of the CH(2)ClI(+) cation. Geometrical parameters and thus the molecular shape of the cation are greatly influenced by the spin-orbit effects even for the ground state. Calculated geometrical parameters deviate substantially for different basis sets or effective core potentials. In an effort to derive the exact geometrical parameters for this cation, SODFT geometries were further improved utilizing Franck-Condon fit of the MATI spectral pattern. This empirical fitting produced the well-converged set of geometrical parameters that are quite insensitive to the choice of SODFT calculations. The C-I bond length and the Cl-C-I bond angle show large deviations among different SODFT calculations, but the empirical spectral fitting yields 2.191 +/- 0.003 Angstroms for the C-I bond length and 107.09 +/- 0.09 degrees for the Cl-C-I angle. Those fitted geometrical parameters along with the experimental vibrational frequencies could serve as a useful reference in calibrating relativistic quantum-chemical methods for radicals.

Spin-Orbit Density Functional Theory Calculations for TlAt with Relativistic Effective Core Potentials

Bond lengths, harmonic vibrational frequencies and dissociation energies of TlAt are calculated at ab initio molecular orbital and density functional theory using effective spin-orbit operator and relativistic effective core potentials. Spin-orbit effects estimated from density functional theory are in good agreement with those from ab initio calculations, implying that density functional theory with effective core potentials can be an efficient and reliable methods for spin-orbit interactions.

Comparative electronic structure of a lanthanide and actinide diatomic oxide: Nd versus U

Using a modified version of the Alchemy electronic structure code and relativistic pseudopotentials, the electronic structure of the ground and low lying excited states of UO, NdO, and NdO+ have been calculated at the Hartree—Fock (HF) and multiconfiguration self-consistent field (MCSCF) levels of theory. Including results from an earlier study of UO+ this provides the information for a comparative analysis of a lanthanide and an actinide diatomic oxide. UO and NdO are both described formally as M+2O−2 and the cations as M+3O−2, but the HF and MCSCF calculations show that these systems are considerably less ionic due to large charge back-transfer in the π orbitals. The electronic states putatively arise from the ligand field (oxygen anion) perturbed f4, sf3, df3, sdf2, or s2f2 states of M+2 and f3, sf2 or df2 states of M+3. Molecular orbital results show a substantial stabilization of the sf3 or s2f2 configurations relative to the f4 or df3 configurations that are the even or odd parity ground states in the M+2 free ion. The compact f and d orbitals are more destabilized by the anion field than the diffuse s orbital. The ground states of the neutral species are dominated by orbitals arising from the M+2sf3 term, and all the potential energy curves arising from this configuration are similar, which allows an estimate of the vibrational frequencies for UO and NdO of 862 cm−1 and 836 cm−1, respectively. For NdO+ and UO+ the excitation energies for the Ω states were calculated with a valence configuration interaction method using ab initio effective spin—orbit operators to couple the molecular orbital configurations. The results for NdO+ are very comparable with the results for UO+, and show the vibrational and electronic states to be interleaved.

Low-lying states of Tl2 calculated by the configuration interaction methods based upon relativistic effective core potentials and two-component spinors

We have modified a Dirac–Fock program package, MOLFDIR [L. Visscher et al., Comput. Phys. Commun. 81, 120 (1994)], to perform two-component molecular spinor calculations based upon the relativistic effective core potentials (REPs) incorporating effective spin–orbit operators. The modified MOLFDIR can be used to perform two-component REP calculations instead of four-component all-electron calculations at various levels of theory including the configuration interaction (CI) level. As a test case for the multireference CI methods, the low-lying states of Tl2 are calculated with the two-component CI method and the more conventional spin–orbit CI method. Results indicate that the two-component method has some advantages in describing the ground state of Tl2 while excited states are similarly described by both methods.

Low-lying 0 + states of bismuth hydride

Test calculations for BiH 0 + ground and excited states using a CI configuration selection procedure, including the effective spin-orbit operator in the selection process (intermediate coupling CI), are compared with previous work in which the spin-orbit operator was included only in a final CI over λ− s selected configurations. While the lowest states are well described by the latter procedure, our results show an error in previous work in an upper state due to the failure to detect a charge transfer avoided crossing in their final intermediate coupling CI.

Electronic structures of thorium and protactinium halide clusters of [ThX 8] 4− type

The electronic structures of ThX 4:Pa 4+ (X ≡ Cl, Br) doped crystals are obtained through MS-Xα computation of ThX 8 4− and PaX 8 4− cluster models. The incidence of the Watson sphere charge on the Rydberg-like Pa 6d MOs is discussed. The use of an effective spin-orbit operator gives f-f and f-d optical transition diagrams which, in addition to the theoretical XPS spectrum, agree quite well with the experimental data obtained from optical measurements on single crystals and doped materials at 4.2 K.

An a b i n i t i o study of low-lying 5f→5f excitations in PuF6

The excited electronic states of PuF6 below 3 eV arise from 5f→5f transitions. These states have been investigated using ab initio wave functions based on a relativistic effective core potential (RECP) for plutonium and nonrelativistic ECP for the fluorines and double-zeta quality basis sets. The effects of electron correlation were included by configuration interaction, and the effects of spin-orbit coupling were included by diagonalizing the correlated wave function over an effective spin-orbit operator. The only previous calculations on PuF6 that include both the effects of configuration interaction (CI) and of spin-orbit (SO) coupling are the semiempirical ligand field calculations of Kugel et al. The agreement between the present work and that of Kugel et al. is truly remarkable, with the average difference in excitation energies being less than 0.03 eV for the nine lowest transitions. Both sets of results are in general agreement with recent gas-phase and matrix spectroscopic studies of PuF6.

A b i n i t i o effective spin-orbit operators for use in atomic and molecular structure calculations. Results for CH, OH, SiH, CO+, CO, and SiO

A b initio effective spin-orbit operators, based on relativistic effective core potentials, are used to determine the spin-orbit coupling constants for CH(X 2Πr), OH(X 2Πi), SiH(X 2Πr), CO+(A 2Πi), CO(a 3Πr), and SiO(b 2Πr). In comparison with experimental and ab initio values all electron values are very favorable.

AB initio effective spin—orbit operators for use in atomic and molecular structure calculations. Results for carbon and silicon

Ab initio effective spin-orbit operators for carbon and silicon are derived from relativistic effective core potentials based on Dirac—Fock wavefunctions. Transferability of these operators to electronic states other than the one used in the original derivation is treated by calculating spin—orbit splittings of various neutral and ionic atomic states.

Theoretical treatment of the spin–orbit coupling in the rare gas oxides NeO, ArO, KrO, and XeO

A b initio configuration-interaction calculations have been carried out on the six electronic states of RgO (Rg=Ne, Ar, Kr, and Xe) arising from the Rg(1S)+O(3P, 1D, 1S) separated atom limits similar to the calculations of Dunning and Hay [J. Chem. Phys. 66, 3767 (1977)]. The degree of charge transfer and, hence, the extent to which the interactions are attractive is observed to be sensitive to the method of configuration selection. The off-diagonal spin–orbit coupling matrix elements 〈3Π‖Hso‖1Σ+〉 and 〈3Σ−‖Hso‖1Σ+〉 were calculated for the lowest 3Π, 3Σ−, and 1Σ+ states of RgO as a function of internuclear distance using the configuration-interaction wave functions and the full microscopic spin–orbit Hamiltonian. All one- and two-electron integrals were included. These results are compared in detail with the spin–orbit matrix elements of Cohen, Wadt, and Hay [J. Chem. Phys. 71, 2955 (1979)] computed using equivalent wave functions and an effective spin–orbit operator composed only of one-electron, one-center terms. The good agreement between the results strongly supports the use of an effective spin–orbit operator of this type. The success of their model results from the fact that electron interaction effects can be adequately accounted for by a single adjustable parameter that can be determined from the atomic fine structure. Apparently for the RgO molecules, the numerical results are a more sensitive test of the wave functions (particularly to the extent of charge transfer) than to the exact evaluation of all terms in the full spin–orbit operator. In fact, for the heaviest system considered, XeO, the effective operator approach actually appears to be superior to the ab initio treatment.