Calculations Of spin-Hamiltonian Parameters Research Articles

Investigations on the defect structures for Mn2+ in CdSe nanocrystals and bulk materials and the criterion of occupation for Mn2+ in CdX (X = S, Se, Te) nanocrystals.

The spin Hamiltonian parameters and defect structures are theoretically studied for the substitutional Mn2+ at the core of CdSe nanocrystals and in the bulk materials from the perturbation calculations of spin Hamiltonian parameters for trigonal tetrahedral 3d5 clusters. Both the crystal-field and charge transfer contributions are taken into account in the calculations from the cluster approach. The impurity-ligand bond angles are found to be about 1.84° larger and 0.10° smaller in the CdSe:Mn2+ nanocrystals and bulk materials, respectively, than those (≈109.37°) of the host Cd2+ sites. The quantitative criterion of occupation (at the core or surface) for Mn2+ in CdX (X = S, Se, Te) nanocrystals is presented for the first time based on the inequations of hyperfine structure constants (HSCs). This criterion is well supported by the experimental HSCs data of Mn2+ in CdX nanocrystals. The previous assignments of signals SI as Mn2+ at the core of CdS nanocrystals are renewed as Mn2+ at the surface based on the above criterion. The present studies would be helpful to achieve convenient determination of occupation for Mn2+ impurities in CdX semiconductor nanocrystals by means of spectral (e.g., HSCs) analysis.

DFT Protocol for EPR Prediction of Paramagnetic Cu(II) Complexes and Application to Protein Binding Sites

With the aim to provide a general protocol to interpret electron paramagnetic resonance (EPR) spectra of paramagnetic copper(II) coordination compounds, density functional theory (DFT) calculations of spin Hamiltonian parameters g and A for fourteen Cu(II) complexes with different charges, donor sets, and geometry were carried out using ORCA software. The performance of eleven functionals was tested, and on the basis of the mean absolute percent deviation (MAPD) and standard deviation (SD), the ranking of the functionals for Az is: B3LYP > B3PW91 ~ B3P86 > PBE0 > CAM-B3LYP > TPSSh > BH and HLYP > B2PLYP > MPW1PW91 > ω-B97x-D >> M06; and for gz is: PBE0 > BH and HLYP > B2PLYP > ω-B97x-D > B3PW91~B3LYP~B3P86 > CAM-B3LYP > TPSSh~MPW1PW91 >> M06. With B3LYP the MAPD with respect to A z exp t l is 8.6% with a SD of 4.2%, while with PBE0 the MAPD with respect to g z exp t l is 2.9% with a SD of 1.1%. The results of the validation confirm the fundamental role of the second order spin-orbit contribution to Az. The computational procedure was applied to predict the values of gz and Az of the adducts formed by Cu(II) with albumin and two fragments of prion protein, 106–126 and 180–193.

Unified calculations of spin-Hamiltonian parameters and optical band positions for Ni+ ion in AgGaSe2 crystal

The complete diagonalisation (of energy matrix) method based on the two-spin-orbit-parameter model is applied to unifiedly calculate the spin-Hamiltonian parameters (g factors g//, g⊥ and hyperfine structure constants A//, A⊥) and optical band positions for Ni+ ion in silver gallium selenide (AgGaSe2) crystal. In the model, besides the contribution due to the spin-orbit parameter of central dn ion (i.e., the one-spin-orbit-parameter model in the traditional crystal-field theory), that of ligand ions are taken into account. The calculated results are reasonably consistent with the experimental values. The local structure of Ni+ centre in AgGaSe2 is estimated through the calculation. The complete diagonalisation method based on the one-spin-orbit-parameter model is also applied to calculate these electron paramagnetic resonance and optical data. It is found that although the calculated optical band positions are close to those based on the two-spin-orbit-parameter model and hence to the experimental values, the calculated spin-Hamiltonian parameters (in particular, the g factors) are in disagreement with the experimental values. The latter point is further confirmed from the calculations with the perturbation method. So, for the rational calculations of spin-Hamiltonian parameters of dn clusters with ligand having large spin-orbit parameter, the contributions due to spin-orbit parameters of both the central dn ion and ligand ion should be contained.

Theoretical studies of the spin-Hamiltonian parameters for the rhombic Mo5+ tetrahedral centres in ZrSiO4 crystal from a two-mechanism model

The high-order perturbation formulas of spin-Hamiltonian parameters (g factors gi and hyperfine structure constants Ai, i = x, y, z) based on the two-mechanism model for d1 ions in rhombic tetrahedral clusters with the ground state are derived in this paper. In the model, besides the contributions to spin-Hamiltonian parameters due to the crystal-field (CF) mechanism in the widely applied CF theory, those due to the charge-transfer (CT) mechanism are taken into account. From these formulas, the six spin-Hamiltonian parameters gi and Ai for the rhombic Mo5+ tetrahedral centres in ZrSiO4 crystal are calculated with four adjustable parameters. The calculated results are in reasonable agreement with the experimental values. The calculations show that for the exact and complete calculations of spin-Hamiltonian parameters of the high valence state dn ions in crystals, the contributions due to CT mechanism should not be neglected. Some information on the defect structure of Mo5+ impurity centres in ZrSiO4 crystal is also acquired from the calculations. The results are discussed.

Unified calculations of the optical band positions and spin-Hamiltonian parameters for V2+ ions in CdCl2 crystal

The eight optical spectral band positions and three spin-Hamiltonian parameters (g factors g//, g⊥ and zero-field splitting D) of V2+ ions in trigonal CdCl2 crystal are calculated together from the complete diagonalisation (of energy matrix) method (CDM) based on the two-spin-orbit-parameter model (also called the cluster approach). In the model, differing from the usual one-spin-orbit-parameter model in the conventional crystal-field theory (where only the contribution to spin-Hamiltonian parameters due to the spin-orbit parameter of central dn ion is considered), both the contributions from the spin-orbit parameter of central dn ion and that of ligand ions are taken into account. The calculated results show reasonable agreement with the experimental values. The local lattice relaxation in the vicinity of V2+ ion due to the introduction of V2+ impurity is acquired from the calculations. The calculations of spin-Hamiltonian parameters from the CDM based on the one-spin-orbit-parameter and those from the perturbation theory method based on the two-spin-orbit-parameter model are also made for comparison. The results are discussed.

Studies of the spin-Hamiltonian parameters and defect structures for the trigonal Mo 3+ centers in Y 3Al 5O 12 and Lu 3Al 5O 12 crystals

The complete diagonalization (of energy matrix) method (CDM) and the perturbation theory method (PTM) are applied to calculate the spin-Hamiltonian (SH) parameters (electron paramagnetic resonance g factors g //, g ⊥ and zero-field splitting D) of the trigonal Mo 3+ centers in Y 3Al 5O 12 and Lu 3Al 5O 12 crystals. Both methods are based on the cluster approach in which the covalence effect due to the admixture between the d orbitals of central d n ion and p orbitals of ligands is considered. The g factors calculated by both methods are close to each other and agree with the experimental values. However, the calculated zero-field splittings D from PTM for both crystals are about 84% those from CDM. The reasons that the CDM is preferable to the PTM in the calculations of SH parameters are discussed. The angular distortions of Mo 3+ centers in both garnet crystals are predicted.

Investigation of the optical spectra and spin-Hamiltonian parameters for the rhombic Cu2+ center in β-Ca3(PO4)2

The four optical band positions and six spin-Hamiltonian parameters (the g factors gi and the hyperfine structure constants Ai, i=x, y, z) for the rhombic Cu2+ center in β-Ca3(PO4)2 are calculated by two theoretical methods: the complete diagonalization (of energy matrix) method and the perturbation theory method (PTM). Both methods are based on the cluster approach, in which the covalence due to admixture of ligands to the central metal ion is considered. The calculated results of the two methods are close to each other and agree with the experimental values. This suggests that both methods are effective in explaining the optical and electron paramagnetic resonance data for d9 ions in crystals. The calculations also show that although the admixture of |dz2⟩ to the ground state wave function is small, it should not be neglected in calculations of spin-Hamiltonian parameters. So, in PTM, the high-order perturbation formulae of spin-Hamiltonian parameters based on the cluster approach for d9 ion in rhombic symmetry should be derived by taking into account the admixture of the |dz2⟩ state to the |dx2−y2⟩ ground state.

Theoretical calculations of the spin-Hamiltonian parameters from a two-mechanism model for Cr5+ ions in MVO3 (M = Li, Na, K, Rb) crystals

The spin-Hamiltonian parameters (g factors g //, g ⊥ and hyperfine structure constants A //, A ⊥) of the approximately-tetragonal Cr5+ centers in MVO3 (M = Li, Na, K, Rb) crystals are calculated from the complete high-order perturbation formulas for d1 ions in tetragonal symmetry with the ground state . These formulas are based on a two-mechanism model, in which not only the contribution to spin-Hamiltonian parameters from the crystal-field (CF) mechanism concerning CF excitations, but also that from the charge-transfer (CT) mechanism concerning CT excitations (which is neglected in the widely-used CF theory) are included. The calculated results are in reasonable agreement with the experimental values and the signs of hyperfine structure constants are suggested. The calculations show that for a high valence state dn ion (e.g. Cr5+) in crystals, the exact calculation of spin-Hamiltonian parameters should take the contributions due to both CF and CT mechanisms into account.

Theoretical calculations of spin-Hamiltonian parameters and defect structures for Cu2+ in trigonally-distorted tetrahedral sites of ZnO and GaN crystals

The spin-Hamiltonian (SH) parameters (g factors g //, g ⊥ and hyperfine structure constants 63 A //, 63 A ⊥, 65 A //, 65 A ⊥) for Cu2+ ions in the trigonally-distorted tetrahedral sites of ZnO and GaN crystals are calculated from a complete diagonalization (of energy matrix) method (CDM) based on a two spin-orbit parameter model for d 9 ions in trigonal symmetry. In the method, the Zeeman and hyperfine interaction terms are added to the Hamiltonian in the conventional CDM. The calculated results are in good agreement with the experimental values. The calculated SH parameters are also compared with those using the traditional diagonalization method or perturbation method only within the 2 T 2 term. It appears that, for exact calculations of SH parameters of d 9 ions in trigonal tetrahedral clusters in crystals, the present CDM is preferable to the traditional diagonalization method or perturbation method within the 2 T 2 term. The local structures of Cu2+ centers (which differ from the corresponding structure in the host crystal) in ZnO : Cu2+ and GaN : Cu2+ are obtained from the calculations. The results are discussed.

Angular overlap calculations of the spin Hamiltonian parameters of transition metal ions in low symmetry environments. High spin iron(II), iron(III) and manganese(III)

A non-perturbative method is presented for the calculation of spin Hamiltonian parameters of d″ ions, 1 ≤ n ≤ 9. In its present form, it allows the calculation of the linear Zeeman and the second- and fourth-order zero-field spin Hamiltonian parameters. Symmetry restraints can easily be applied but application to non-symmetric molecules with determination of all 20 spin Hamiltonian parameters does not present particular difficulties. The model is based on a direct comparison of the spin Hamiltonian energies with the ligand field energies including spin-orbit coupling and Zeeman interaction of all-order perturbation. The model is applied to compute the spectromagnetic parameters of high spin iron(III), high spin iron(II) and high spin manganese(III) model chromophores.

The calculation of spin-Hamiltonian parameters via the cluster approach: New results for some quasi-one-dimensional magnetic materials (abstract)

The cluster approach to magnetic susceptibility (CAMS) has been used to determine the spin-Hamiltonian parameters for the quasi-one-dimensional next-nearest-neighbor chain compounds Cu(HzH)Cl3(J1=−4.84, J2=−5.66), Cu(amp)Cl2 (J1=−3.79, J2=−3.24), and Cu(Me3en)Br2 (J1=−3.45, J2=−3.06). We will explain the magnetic behavior of these compounds in terms of various structural parameters. Specifically, the discussion will focus on the possibility of predicting the magnitude and nature of the exchange coupling based on the geometry of the bridge, as well as the onset of phase transitions based on the extended structures.