Corrigendum

Theoretical calculations of g-tensor components for the spin–orbit quartet, which arises as the ground state in three-coordinate d⁹ complexes and low-spin d⁷ complexes of D_3h symmetry, have been made on the assumption that the spin–orbit interaction is commensurable with the electron-vibrational interaction. The calculations were carried out within the framework of crystal field theory using representations of the hole formalism. The analytical expressions for g-tensor components were obtained limited to first-order terms. It was shown that the account of the electron–vibrational interaction in the excited quartet only provides three-axial anisotropy for the g-tensor. It was shown that the g-tensor rotates in the plane of the three-coordinate structure with consensual motion of the atoms. The resulting expressions for the g-factor components are in good agreement with experimental data. Being universal for a wide range of contributions of the vibronic and spin–orbit interactions, these expressions essentially fill the gap in studying structures of coordination compounds.     

Theoretical study of diaquamalonatozinc(II) single crystal for applications in non-linear optical devices

The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM) with the microscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. g-tensor and D-tensor, has been determined by using the ORCA program package developed by F Neese et al. The unrestricted Kohn–Sham orbitals-based Pederson–Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin–orbit tensor (\(D^{\mathrm{SO}})\) of the axial ZFS parameter D. The effects of spin–spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin–spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson–Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn–Sham-based natural orbital with Pederson–Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of \(\hbox {Mn}^{2+}\) ion in the host matrix.     

Split-shell molecular orbital calculations on the diatomic alkali metal molecules

Absolute g-tensor calculations for planar hydrocarbon and for non-planar phenyl substituted hydrocarbon radicals are reported. The relevant interactions determining g are discussed. Calculations are performed on the basis of a second-order perturbation expansion. The electronic wavefunctions are obtained from a simplified version of Hoffmann's extended Hückel model (SEH), where all valence electrons are taken into account explicitly. For planar systems the observed linear dependence of g on the energy of the half filled π orbital is well reproduced. A qualitative analysis of this dependence, making restrictive assumptions about the σ electrons, was given earlier by Stone. The calculations for non-planar model systems reproduce the g-factor anomalies which are observed for highly twisted phenyl substituted hydrocarbon radicals. The results show the necessity of direct π-σ mixing and are consistent with recent investigations of the proton hyperfine couplings in such systems.     

An analysis of the conditions for an isotropic g-tensor in high-spin d5 systems

An analysis of the conditions for an isotropic g-tensor in high-spin d⁵ systems results in six cases: four cases yield an isotropic g-factor of 30/7 and two cases an isotropic g-factor of 10/3. The relationships between the spin-hamiltonian parameters needed to satisfy the six cases are given.     

A coupled cluster study of the magnetisability,rotational g-tensor and quadrupole moment of NF3, PF3 and AsF3

ABSTRACT

A coupled-cluster investigation of magnetic and electric properties of NF₃, PF₃ and AsF₃ provides for a comparison with recent experimental data. For PF₃, achieving reliable values for the magnetisability and rotational g-tensor of PF₃ has been particularly challenging. We report the most accurate calculations to date for PF₃; for the vibrationally corrected anisotropic magnetisability, our extrapolated CCSD(T)/CBS value of ?0.290 a.u is within the uncertainty limits of the most recent experimental value of ?0.286 ± 0.042 a.u. For the rotational g-tensor of PF₃, agreement between theory and experiment for the g_⊥ component is excellent (deviation of less than 0.0006 a.u.). However, the g_|| component remains problematic even though our vibrationally corrected CCSD(T)/CBS value of ?0.0387 a.u is in closer agreement with the recently revised experimental value of ?0.0470 ± 0.0020 a.u. than the original value of ?0.0815 ± 0.0020 a.u. The origin of the remaining discrepancy remains unclear. Dipole and quadrupole moments have also been investigated.     

Singularities in conduction electron spin resonance line-width and g-shift anisotropy — application to silver

It is shown theoretically that at very large ωτ (e.g. numerical calculations for silver show that ωτ must be ? 100) singularities in the CESR line width and g-shift anisotropy exist and can be interpreted to give information about the g-tensor and about many body effects.     

The symmetry properties and collinearity of the magnetogyric,hyperfine splitting and magnetic susceptibility tensors

The symmetry properties of g and A cannot be elicited using invariance properties, due to their special nature, and are found using the properties of a Kramers doublet. It is shown that the collinearity of g and A depends on the molecule having at least C ₂ with σ _v or C ₂′ symmetry elements. The symmetry properties of x are found from those of g. The conditions for collinearity of the tensors and the consequences of non-collinearity are discussed, with examples.     

Influence of hydrogen bonds on the electronicg-tensor and13C-hyperfine tensors of13C-labeled ubiquinones — EPR and ENDOR study

Selectively^l3C-labeled ubiquinone anion radicals in protic and aprotic solvents are investigated by EPR and ENDOR spectroscopy, yielding information about the effect of hydrogen bonds on the electronicg-tensor and the carbonyl carbon¹³C-hf tensors. Formation of the hydrogen bonds alter theg-tensor significantly to lower values and increases theA _zz , component of the^l3C-hf tensor. Both effects can be explained by electrostatic interactions between the positively charged hydrogen and the electrons at the carbonyl oxygen leading to a redistribution of charge and π-spin density. Two different hydrogen bonds were obtained for UQ ₀ ^? which are in agreement with the results of DFT (density functional theory) calculations.     

A study of liquid 3He in the Brueckner-Goldstone formalism

The two- and three-body correlation energies in liquid ³He are calculated within the framework of Brueckner-Goldstone theory. Various approximations taken from nuclear matter calculations and used in previous liquid helium studies are examined and improved upon.The dependence of the g-matrix elements on the center of mass momentum of the interacting particles and the question of the self-consistency of the hole spectrum are treated more systematically and extensively than before.The contribution to the three-body energy of relative partial wave interactions with nonzero relative angular momentum is studied in some detail for the first time.     

EPR properties of Au atoms adsorbed on various sites of the MgO(1 0 0) surface from relativistic DFT calculations

Using all electron fully relativistic DFT calculations we have computed the EPR properties of Au atoms bound to various sites of the MgO surface. Changes in g-tensor and hyperfine coupling constants provide a way to identify the gold adsorption site and to map the surface morphology by comparison of measured and calculated EPR spectra. We found a strong reduction of the isotropic hyperfine coupling constant, a_iso(Au), for adsorbed gold compared to the free atom; this reduction, which is about 45% for terrace sites, is more pronounced when Au interacts with low-coordinated sites like steps, edges and corners where it is about 60%. The reduction of a_iso(Au) is accompanied by a corresponding increase of the superhyperfine interaction with the surface oxygen sites, as measured by a_iso(¹⁷O). Large anisotropies in the g-tensor are computed for all sites.     

New massively parallel linear-response coupled-cluster module in ACES III: application to static polarisabilities of closed-shell molecules and oligomers and of open-shell radicals

ABSTRACT

Stemming from our implementation of parallel coupled-cluster (CC) capabilities for electron spin resonance properties [J. Chem. Phys. 139, 174103 (2013)], we present a new massively parallel linear response CC module within ACES III. Unlike alternative parallel CC modules, this general purpose module evaluates any type of first- and second-order CC properties of both closed- and open-shell molecules employing restricted, unrestricted and restricted-open-shell Hartree–Fock (HF) references. We demonstrate the accuracy and usefulness of this module through the calculation of static polarisabilities of large molecules. Closed-shell calculations are performed at the following levels: second-order many-body perturbation theory [MBPT(2)], CC with single- and double-excitations (CCSD), coupled-perturbed HF and density functional theory (DFT), and open-shell calculations at the unrestricted CCSD (UCSSD) one. Applications involve eight closed-shell organic-chemistry molecules (Set I), the first four members of the closed-shell thiophene oligomer series (Set II), and five open-shell radicals (Set III). In Set I, all calculated average polarisabilities agree reasonably well with experimental data. In Set II, all calculated average polarisabilities vs. the number of monomers show comparable values and saturation patterns and demonstrate that experimental polarisabilities may be inaccurate. In Set III, UCCSD perpendicular polarisabilities show a reasonable agreement with previous UCCSD(T) and restricted-open-shell-MBPT(2) values.     

Relaxation studies in magnetic resonance spectroscopy

The electron spin and nuclear spin relaxation in liquid solution arising from the electron-nuclear interaction is determined for the general case when the g-tensor may be anisotropic and the nine hyperfine interaction tensor components may be all different. The theoretical expressions are used in an attempt to interpret the relaxation times T ₁ and T ₂ for the various nuclei in the complex ruthenium acetylacetonate.     

E.S.R. of sulphur-substituted purines and nucleosides; carbon-centred radicals in mercaptopurine crystals at 77 K

Single crystals of the sulphur-containing DNA-base analogue 6-methylmercaptopurine (6MeMP) and its riboside 6-methylmercaptopurine riboside (6MeMPR) have been prepared and irradiated by 4·0 MeV electrons at 77 K. Electron spin resonance techniques have been used to study the radiation-induced radicals at 77 K. The primary carbon-centred radical, common to both molecules, has been identified as a species formed by hydrogen atom abstraction from the methyl group. The principal values of the two α-proton hyperfine coupling tensors and the g-tensors were almost the same for both molecules and for 6MeMPR were: α1, -28·8, -17·9 and -6·4 G; α2, -28·2, -15·7 and -9·8 G; and g, 2·0063, 2·0024 and 2·0018. These data indicate a spin density of 0·77 on the methyl carbon atom. Molecular orbitals determined from CNDO/2 methods were used in calculations of the directions and magnitude of the g-tensor principal values. Comparison of these calculated values and experimental data suggests that contribution of spin density in d-orbitals on the sulphur atom is important in describing the g-tensor. Methyl H-abstraction radicals trapped in pairs were also detected in 6MeMP and the data are consistent with an effective interspin distance of 4·67 Å.     

Collecting all intermediates with an optimal scaling for the generalised-active-space coupled-cluster method with application to SbH

ABSTRACT

A string-based coupled-cluster method of general excitation rank, with optimal scaling and easy collection of all possible intermediates, which accounts for special relativity within the four-component framework is presented. The easy identification and collection of intermediates is achieved by extending the excitation-class formalism and introducing a contraction order for the operator indices. Initially, all possible contractions between the Hamiltonian and the intermediates with the cluster operator are found, stored and used for driving the algorithm, thereby defining an algorithm which allows for very complex state-selective, multi-reference, coupled-cluster calculations. The algorithm for solving the coupled-cluster equations can be used in both relativistic as well as non-relativistic calculations by appropriate restrictions in the excitation-class formalism. The capabilities of the new method are demonstrated in the application to the electronic ground state of the SbH molecule. In these calculations simulated multi-reference expansions with double, triple and quadruple excitations into the external space as well as the regular coupled-cluster hierarchy up to full quadruples excitations are compared.     

The effects of vibration-rotation on the quadrupole moment,rotational g-factor and spin-rotation parameters of the water molecule

Ab initio SCF surfaces for the quadrupole moment, rotational g-factor and spin-rotation parameters of the water molecule have been obtained from the magnetizability and nuclear shielding surfaces. Values of these properties in low vibration-rotation states of the more important isotopomers are presented.

Vibrational averaging (with an accurate empirical force field) brings calculated values to within 1 per cent of experimental values for the quadrupole moment components and 3 per cent for the g-tensor components. Substantial vibrational effects on the proton, deuteron and ¹⁷O spin-rotation parameters are predicted but the calculated values differ significantly from experiment. This is attributed to inadequacy of the SCF calculation of paramagnetic shielding.     

Transient EPR at 240 GHz of the excited triplet state of free-base tetra-phenyl porphyrin

The electron paramagnetic resonance (EPR) spectrum measured at 240 GHz of the lowest excited triplet state of the free-base tetra-phenyl porphyrin (H₂-TPP) molecule is presented. The high frequency that is employed allows for the full resolution of theg-anisotropy (2.00354(2), 2.00272(15), and 2.00194(5) forx, y, andz zero-field axes respectively), and the obtained values are compared to those of other porphyrin-based systems. These results are one of the first addressing theg-anisotropy in the photoexcited state of porphyrins. The usefulness of high-field transient EPR in elucidating not only the principal values of theg-tensor but also the orientation of theg-tensor principal axes with respect to those of the zero-field splitting tensor in porphyrin disordered systems is also discussed.     

Many-body diagrammatic treatment of electronicg-tensor

The many-body diagrammatic theory of electronicg-tensor components taking into account also the correlation effects is elaborated. The resulting perturbation expressions are used for calculation ofg-tensor components of some small open shell systems within the INDO semiempirical method.     

Calculation of kinetic energy terms for the vibrational Hamiltonian: Application to large-amplitude vibrations using one-, two-, and three-dimensional models

One-, two-, and three-dimensional models involving large-amplitude vibrations have been used to calculate kinetic energy terms. Principle G matrix elements as well as cross terms in the kinetic energy were determined. Calculations were done on models involving the ring-puckering and PH inversion vibrations for 3-phospholene and the ring-puckering, ring deformation, and SiH₂ in-phase rocking vibrations for 1,3-disilacyclobutane. Kinetic energy expansions for g₄₄ and g₄₅ type terms were determined. Calculations show a coordinate dependence of the principle G matrix elements as well as of the g₄₅ terms. The vectorial models used in these calculations make it possible to treat vibrations in a one-, two-, or three-dimensional model separate from the other vibrations without carrying out a coordinate transformation, which would be necessary for the Wilson GF high- or low-frequency separation.     

Density functional theory for dielectric properties of warm dense matter

ABSTRACT

Density functional theory (DFT) is applied for the calculation of the dielectric function (DF), reflectivity, conductivity, plasma frequency and effective free electron density of warm dense matter (WDM). Shock-compressed xenon plasma and warm dense hydrogen are considered. The longitudinal expression in the long wavelength limit is applied for the calculation of the imaginary part of the DF. The real part of the DF is calculated by means of the Kramers–Kronig transformation. Sum rule within the framework of the DFT is used for determination of the plasma frequency and effective free electron density. Corrections to the reflectivity are considered, which allow for the finite width of the transient layer (wave front) at the WDM border.