Ab initio and coupled-perturbed density functional theory estimation of zero-field splittings in MnII transition metal complexes

The paper presents a method comparison for the prediction of zero-field splitting (ZFS) parameters in a series of Mn (II) coordination complexes. The test set consists of Mn (II) complexes that are experimentally well-characterized by X-ray diffraction and high-field electron paramagnetic resonance. Their ZFS parameters have been calculated using density functional theory (DFT) as well as complete active space self-consistent field (CASSCF) methods. It is shown that the recently introduced coupled-perturbed spin-orbit coupling (CP-SOC) approach [ Neese, F. J. Chem. Phys. 2007, 127, 164112 ] together with hybrid-DFT functionals leads to a slope of the correlation line (plot of experimental vs calculated D values) that is essentially unity provided that the direct spin-spin interaction is properly included in the treatment. This is different from our previous DFT study on the same series of complexes where a severe overestimation of the D parameter has been found [ Zein, S. ; Duboc, C. ; Lubitz, W. ; Neese, F. Inorg. Chem. 2008, 47, 134 ]. CASSCF methods have been used to evaluate the ZFS in an "ab initio ligand-field" type treatment. The study demonstrates that a substantial part of the relevant physics is lost in such a treatment since only excitations within the manganese d-manifold are accounted for. Thus, a severe underestimation of the D parameter has been found. Because the CASSCF calculations in combination with quasidegenerate perturbation theory treats the SOC to all orders, we have nevertheless verified that second-order perturbation theory is an adequate approximation in the case of the high-spin d (5) configuration.     

First-principles calculations of zero-field splitting parameters

In this work, an implementation of an approach to calculate the zero-field splitting (ZFS) constants in the framework of ab initio methods such as complete active space self-consistent field, multireference configuration interaction, or spectroscopy oriented configuration interaction is reported. The spin-orbit coupling (SOC) contribution to ZFSs is computed using an accurate multicenter mean-field approximation for the Breit-Pauli Hamiltonian. The SOC parts of ZFS constants are obtained directly after diagonalization of the SOC operator in the basis of a preselected number of roots of the spin-free Hamiltonian. This corresponds to an infinite order treatment of the SOC in terms of perturbation theory. The spin-spin (SS) part is presently estimated in a mean-field fashion and appears to yield results close to the more complete treatments available in the literature. Test calculations for the first- and second-row atoms as well as first-row transition metal atoms and a set of diatomic molecules show accurate results for the SOC part of ZFSs. SS contributions have been found to be relatively small but not negligible (exceeding 1 cm(-1) for oxygen molecule). At least for the systems studied in this work, it is demonstrated that the presented method provides much more accurate estimations for the SOC part of ZFS constants than the emerging density functional theory approaches.     

Spin-spin contributions to the zero-field splitting tensor in organic triplets, carbenes and biradicals-a density functional and ab initio study

An evaluation study for the direct dipolar electron spin-spin (SS) contribution to the zero-field splitting (ZFS) tensor in electron paramagnetic resonance (EPR) spectroscopy is presented. Calculations were performed on a wide variety of organic systems where the SS contribution to the ZFS dominates over the second-order spin-orbit coupling (SOC) contribution. Calculations were performed using (hybrid) density functional theory (DFT), as well as complete active space self-consistent field (CASSCF) wave functions. In the former case, our implementation is an approximation, because we use the two-particle reduced spin-density matrix of the noninteracting reference system. In the latter case, the SS contribution is approximated by a mean-field method which, nevertheless, gives accurate results, compared to the approximation free computation of the SS part in a CASSCF framework. For the case of the triplet dioxygen molecule, it was shown that restricted open-shell density functional theory (RODFT), as well as CASSCF, can provide accurate spin-spin couplings while spin-unrestricted DFT leads to much larger errors. Furthermore, 15 organic radicals, including several 1,3 and 1,5 diradicals, dinitroxide biradicals, and even a chlorophyll a model system, were examined as test cases to demonstrate the accuracy and efficiency of our approach within a DFT framework. Accurate D values with root-mean-square deviations of 0.0035 cm(-1) were obtained. Furthermore, all trends, including those due to substituent effects, were correctly reproduced. In a different set of calculations, the polyacenes benzene, naphthalene, anthracene, and tetracene were studied. Applying DFT, the absolute D values were noticeably underestimated, but it was possible to correctly reproduce the trend to smaller D values with larger size of the systems. Finally, it was demonstrated that our approach is also well-suited for the study of carbenes. The smaller organic radicals of this work were also studied, through the use of CASSCF wave functions. This was a special advantage in the case of the triplet polyacenes, where the CASSCF approach gave better results than the DFT method. In comparing spin-restricted and spin-unrestricted results, it was shown through a natural orbital analysis and comparison to high-level ab initio calculations that even small amounts of spin polarization introduced by the unrestricted calculations lead to large deviations between the unrestricted Kohn-Sham (UKS) and restricted open-shell Kohn-Sham (ROKS) approaches. It is challenging to understand why the ROKS results show much better correlation with the experimental data.     

Spin ground state and magnetic properties of cobalt(II): relativistic DFT calculations guided by EPR measurements of bis(2,4-acetylacetonate)cobalt(II)-based complexes

The spin ground state of the core ion and structure of the bis(2,4-acetylacetonate)cobalt(II) model complex and its synthetic aqua and ethanol derivatives, Co(acac)(2)L(n), (L = EtOH, H(2)O), were examined by means of density functional theory (DFT) calculations supported by electron paramagnetic resonance (EPR) measurements. Geometry optimizations were carried out for low-spin (doublet) and high-spin (quartet) states. For the Co(acac)(2) complex two possible conformations, a square-planar and a tetrahedral one, were taken into account. For all structures relative energies were calculated with both "pure" and hybrid functionals. The calculated data were complemented with the results of the EPR investigations carried out at liquid helium temperature, allowing for definite assignment of the high-spin state for the Co(acac)(2)(EtOH)(2) complex. However, because of the unresolved spectral features, only effective g-values could be assessed, whereas the zero-field splitting parameters (ZFS) were calculated by means of the spin-orbit mean field (SOMF) relativistic DFT method for which direct spin-spin (SS) and spin-orbit coupling (SOC) contributions were quantified.     

Ab initio and DFT studies of the spin-orbit and spin-spin contributions to the zero-field splitting tensors of triplet nitrenes with aryl scaffolds

Spin-orbit and spin-spin contributions to the zero-field splitting (ZFS) tensors (D tensors) of spin-triplet phenyl-, naphthyl-, and anthryl-nitrenes in their ground state are investigated by quantum chemical calculations, focusing on the effects of the ring size and substituted position of nitrene on the D tensor. A hybrid CASSCF/MRMP2 approach to the spin-orbit term of the D tensor (D(SO) tensor), which was recently proposed by us, has shown that the spin-orbit contribution to the entire D value, termed the ZFS parameter or fine-structure constant, is about 10% in all the arylnitrenes under study and less depends on the size and connectivity of the aryl groups. Order of the absolute values for D(SO) can be explained by the perturbation on the energy level and spatial distributions of π-SOMO through the orbital interaction between SOMO of the nitrene moiety and frontier orbitals of the aryl scaffolds. Spin-spin contribution to the D tensor (D(SS) tensor) has been calculated in terms of the McWeeny-Mizuno equation with the DFT/EPR-II spin densities. The D(SS) value calculated with the RO-B3LYP spin density agrees well with the D(Exptl) -D(SO) reference value in phenylnitrene, but agreement with the reference value gradually becomes worse as the D value decreases. Exchange-correlation functional dependence on the D(SS) tensor has been explored with standard 23 exchange-correlation functionals in both RO- and U-DFT methodologies, and the RO-HCTH/407 method gives the best agreement with the D(Exptl) -D(SO) reference value. Significant exchange-correlation functional dependence is observed in spin-delocalized systems such as 9-anthrylnitrene (6). By employing the hybrid CASSCF/MRMP2 approach and the McWeeny-Mizuno equation combined with the RO-HCTH/407/EPR-II//U-HCTH/407/6-31G* spin densities for D(SO) and D(SS), respectively, a quantitative agreement with the experiment is achieved with errors less than 10% in all the arylnitrenes under study. Guidelines to the putative approaches to D(SS) tensor calculations are given.     

A systematic density functional study of the zero-field splitting in Mn(II) coordination compounds

This work presents a detailed evaluation of the performance of density functional theory (DFT) for the prediction of zero-field splittings (ZFSs) in Mn(II) coordination complexes. Eighteen experimentally well characterized four-, five-, and six-coordinate complexes of the general formula [Mn(L)nL'2] with L' = Cl, Br, I, NCS, or N3 (L = an oligodentate ligand) are considered. Several DFT-based approaches for the prediction of the ZFSs are compared. For the estimation of the spin-orbit coupling (SOC) part of the ZFS, it was found that the Pederson-Khanna (PK) approach is more successful than the previously proposed quasi-restricted orbitals (QRO)-based method. In either case, accounting for the spin-spin (SS) interaction either with or without the inclusion of the spin-polarization effects improves the results. This argues for the physical necessity of accounting for this important contribution to the ZFS. On average, the SS contribution represents approximately 30% of the axial D parameters. In addition to the SS part, the SOC contributions of d-d spin flip (alphabeta) and ligand-to-metal charge transfer excited states (betabeta) were found to dominate the SOC part of the D parameter; the observed near cancellation between the alphaalpha and betaalpha parts is discussed in the framework of the PK model. The calculations systematically (correlation coefficient approximately 0.99) overestimate the experimental D values by approximately 60%. Comparison of the signs of calculated and measured D values shows that the signs of the calculated axial ZFS parameters are unreliable once E/D > 0.2. Finally, we find that the calculated D and E/D values are highly sensitive to small structural changes. It is observed that the use of theoretically optimized geometries leads to a significant deterioration of the theoretical predictions relative to the experimental geometries derived from X-ray diffraction. The standard deviation of the theoretical predictions for the D values almost doubles from approximately 0.1 to approximately 0.2 cm-1 upon using quantum chemically optimized structures. We do not find any noticeable improvement in considering basis sets larger than standard double- (SVP) or triple-zeta (TZVP) basis sets or using functionals other than the BP functional.     

A combined experimental and quantum chemistry study of selenium chemical shift tensors

A comprehensive investigation of selenium chemical shift tensors is presented. Experimentally determined chemical shift tensors were obtained from solid-state 77Se NMR spectra for several organic, organometallic, or inorganic selenium-containing compounds. The first reported indirect spin-spin coupling between selenium and chlorine is observed for Ph(2)SeCl(2) where 1J(77Se,35Cl)iso is 110 Hz. Selenium magnetic shielding tensors were calculated for all of the molecules investigated using zeroth-order regular approximation density functional theory, ZORA DFT. The computations provide the orientations of the chemical shift tensors, as well as a test of the theory for calculating the magnetic shielding interaction for heavier elements. The ZORA DFT calculations were performed with nonrelativistic, scalar relativistic, and scalar with spin-orbit relativistic levels of theory. Relativistic contributions to the magnetic shielding tensor were found to be significant for (NH4)2WSe4 and of less importance for organoselenium, organophosphine selenide, and inorganic selenium compounds containing lighter elements.     

Theoretical determination of the zero-field splitting in copper acetate monohydrate

The zero-field splitting of the copper acetate monohydrate complex is studied using wave function based calculations. The anisotropy parameters extracted from highly correlated methods are in excellent agreement with the most accurate experimental results; in particular, the negative sign of the axial anisotropy parameter D is reproduced. During several decades, the interpretation of experimental data based on an analytical expression derived from perturbation theory led to a positive D-value. Although the validity of this expression is confirmed, it is explained that the incorrect attribution of a positive D is related to the assumption of an antiferromagnetic coupling between excited states. We have found in the present work that this coupling is actually ferromagnetic. The analysis of the various contributions to the anisotropy parameters shows that both spin-spin and spin-orbit couplings participate in the magnetic anisotropy of this complex. Although the anisotropy arising from the spin-spin coupling is essentially independent of the level of calculation, the zero-field-splitting parameters resulting from the spin-orbit coupling are strongly sensitive to the effects of dynamic correlation. This works provides important new insights into the physical origin of the zero-field-splitting parameters in copper dimers.     

Theoretical analysis of the spin Hamiltonian parameters in Co(II)S4 complexes, using density functional theory and correlated ab initio methods

A systematic Density Functional Theory (DFT) and multiconfigurational ab initio computational analysis of the Spin Hamiltonian (SH) parameters of tetracoordinate S = 3/2 Co((II))S(4)-containing complexes has been performed. The complexes under study bear either arylthiolato, ArS(-), or dithioimidodiphosphinato, [R(2)P(S)NP(S)R'(2)](-) ligands. These complexes were chosen because accurate structural and spectroscopic data are available, including extensive Electron Paramagnetic Resonance (EPR)/Electron Nuclear Double Resonance (ENDOR) studies. For comparison purposes, the [Co(PPh(3))(2)Cl(2)] complex, which was thoroughly studied in the past by High-Field and Frequency EPR and Variable Temperature, Variable Field Magnetic Circular Dichroism (MCD) spectroscopies, was included in the studied set. The magnitude of the computed axial zero-field splitting parameter D (ZFS), of the Co((II))S(4) systems, was found to be within ~10% of the experimental values, provided that the property calculation is taken beyond the accuracy obtained with a second-order treatment of the spin-orbit coupling interaction. This is achieved by quasi degenerate perturbation theory (QDPT), in conjunction with complete active space configuration interaction (CAS-CI). The accuracy was increased upon recovering dynamic correlation with multiconfigurational ab initio methods. Specifically, spectroscopy oriented configuration interaction (SORCI), and difference dedicated configuration interaction (DDCI) were employed for the calculation of the D-tensor. The sign and magnitude of parameter D was analyzed in the framework of Ligand Field Theory, to reveal the differences in the electronic structures of the investigated Co((II))S(4) systems. For the axial complexes, accurate effective g'-tensors were obtained in the QDPT studies. These provide a diagnostic tool for the adopted ground state configuration (±3/2 or ±1/2) and are hence indicative of the sign of D. On the other hand, for the rhombic complexes, the determination of the sign of D required the SH parameters to be derived along suitably constructed symmetry interconversion pathways. This procedure, which introduces a dynamic perspective into the theoretical investigation, helped to shed some light on unresolved issues of the corresponding experimental studies. The metal hyperfine and ligand super-hyperfine A-tensors of the C(2) [Co{(SPPh(2))(SP(i)Pr(2))N}(2)] complex were estimated by DFT calculations. The theoretical data were shown to be in good agreement with the available experimental data. Decomposition of the metal A-tensor into individual contributions revealed that, despite the large ZFS, the observed significant anisotropy should be largely attributed to spin-dipolar contributions. The analysis of both, metal and ligand A-tensors, is consistent with a highly covalent character of the Co-S bonds.     

Matrix isolation ESR spectroscopy and quantum chemical calculations on 5-methylhexa-1,2,4-triene-1,3-diyl, a highly delocalized triplet "hybrid" carbene

The ESR spectrum of 5-methylhexa-1,2,4-triene-1,3-diyl (1) was recorded in an argon matrix at 15 K. The derived zero-field splitting (ZFS) parameters (D = 0.5054 ± 0.0006 cm(-1) and E = 0.0045 ± 0.0002 cm(-1)) fall between those determined previously for propargylene (2) and vinylcarbene (3). DFT and ab initio (CAS and MRCI) quantum-chemical calculations of the ZFS parameters of 1, 2, and 3 were performed. These calculations indicate that multireference methods are needed to successfully predict ZFS parameters of delocalized carbenes/biradicals such as 1-3. The calculated singly occupied MOs and spin density distributions show that the spin is more delocalized in 1 than in 2 and 3, indicating that 1 is a "hybrid" of the constituent ethynyl- and vinylcarbenes, 2 and 3, respectively. The dominant contribution to the D-value in 1 and 2 is found to result from spin-spin interactions on the C atoms of the propylidene moiety, which is strongly affected by spin polarization. Accurate values for the D-parameter are also predicted for other types of delocalized triplet carbenes such as HC(5)H and HCCN.     

High-spin organic molecules with dominant spin-orbit contribution and unprecedentedly large magnetic anisotropy

High-spin organic molecules with dominant spin-orbit contribution to magnetic anisotropy are reported. Quintet 4-azido-3,5-dibromopyridyl-2,6-dinitrene (Q-1), quintet 2-azido-3,5-dibromopyridyl-4,6-dinitrene (Q-2), and septet 3,5-dibromopyridyl-2,4,6-trinitrene (S-1) were generated in solid argon matrices by ultraviolet irradiation of 2,4,6-triazido-3,5-dibromopyridine. The zero-field splitting (ZFS) parameters, derived from electron spin resonance spectra, show unprecedentedly large magnitudes of the parameters D: ∣D(Q1)∣ = 0.289, ∣D(Q2)∣ = 0.373, and ∣D(S1)∣ = 0.297 cm(-1). The experimental ZFS parameters were successfully reproduced by density functional theory calculations, confirming that magnetic anisotropy of high-spin organic molecules can considerably be enhanced by the "heavy atom effect." In bromine-containing high-spin nitrenes, the spin-orbit term is dominant and governs both the magnitude and the sign of magnetic anisotropy. The largest negative value of D among septet trinitrenes is predicted for 1,3,5-trinitrenobenzene bearing three heavy atoms (Br) in positions 2, 4, and 6 of the benzene ring.     

Origin of the zero-field splitting in mononuclear octahedral dihalide MnII complexes: an investigation by multifrequency high-field electron paramagnetic resonance and density functional theory

The synthesis, structural characterization, and electronic properties of a new series of high-spin six-coordinate dihalide mononuclear MnII complexes [Mn(tpa)X2] (tpa=tris-2-picolylamine; X=I (1), Br (2), and Cl (3)) are reported. The analysis of the crystallographic data shows that in all investigated complexes the manganese ion lies in the center of a distorted octahedron with a cis configuration of the halides imposed by the tpa ligand. By a multifrequency high-field electron paramagnetic resonance investigation (95-285 GHz), the electronic properties of 1-3 were determined (DI=-0.600, DBr=-0.360, DCl=+0.115 cm-1), revealing the important effect of (i) the nature of the halide and (ii) the configuration (cis/trans) of the two halides on the magnitude of D. The spin Hamiltonian parameters obtained by density functional theory calculations initiated from the crystal structure of 1-3 are in reasonable agreement with the experimental values. The absolute value of D is consistently overestimated, but the sign and the trend over the chemical series is well reproduced. Theoretical models (cis- and trans-[Mn(NH3)4X2], X=I, Br, Cl and F) have been used to investigate the different contributions to D and also to understand the origin of the experimentally observed changes in D within the series reported here. This study reveals that the spin-spin coupling contributions to the D tensor are non-negligible for the lighter halides (F, Cl) but become insignificant for the heavier halides (I, Br). The four different types of excitations involved in the spin-orbit coupling (SOC) part of the D tensor contribute with comparable magnitudes and opposing signs. The general trend observed for halide MnII complexes (DI>DBr>DCl) can be explained by the fact that the halide SOC dominates the D value in these systems with a major contribution arising from interference between metal- and halide-SOC contributions, which are proportional to the product of the SOC constants of Mn and X.     

Spin-spin and spin-orbit interactions in nanographene fragments: a quantum chemistry approach

The relativistic behavior of graphene structures, starting from the fundamental building blocks--the poly-aromatic hydrocarbons (PAHs) along with other PAH nanographenes--is studied to quantify any associated intrinsic magnetism in the triplet (T) state and subsequently in the ground singlet (S) state with account of possible S-T mixture induced by spin-orbit coupling (SOC). We employ a first principle quantum chemical-based approach and density functional theory (DFT) for a systematic treatment of the spin-Hamiltonian by considering both the spin-orbit and spin-spin interactions as dependent on different numbers of benzene rings. We assess these relativistic spin-coupling phenomena in terms of splitting parameters which cause magnetic anisotropy in absence of external perturbations. Possible routes for changes in the couplings in terms of doping and defects are also simulated and discussed. Accounting for the artificial character of the broken-symmetry solutions for strong spin polarization of the so-called "singlet open-shell" ground state in zigzag graphene nanoribbons predicted by spin-unrestricted DFT approaches, we interpolate results from more sophisticated methods for the S-T gaps and spin-orbit coupling (SOC) integrals and find that these spin interactions become weak as function of size and increasing decoupling of electrons at the edges. This leads to reduced electron spin-spin interaction and hence almost negligible intrinsic magnetism in the carbon-based PAHs and carbon nanographene fragments. Our results are in agreement with the fact that direct experimental evidence of edge magnetism in pristine graphene has been reported so far. We support the notion that magnetism in graphene only can be ascribed to structural defects or impurities.     

Theoretical investigations of zero-field splitting of excited states for 3d3 ions in trigonal crystal fields

By taking into account slight interactions, i.e. spin-spin, spin-other-orbit and orbit-orbit interactions, in addition to spin-orbit interaction, the zero-field splitting of ground state and low excited states and g factors of ZnGa2O4:Cr3+ crystal have been interpreted systematically. And the contributions to zero-field splitting arising from slight magnetic interaction and trigonal crystal field are investigated. It is found that there exist combined mechanism between magnetic interactions and trigonal crystal field.     

A comparison of two-component and four-component approaches for calculations of spin-spin coupling constants and NMR shielding constants of transition metal cyanides

Relativistic density functional theory (DFT) calculations of nuclear spin-spin coupling constants and shielding constants have been performed for selected transition metal (11th and 12th group of periodic table) and thallium cyanides. The calculations have been carried out using zeroth-order regular approximation (ZORA) Hamiltonian and four-component Dirac-Kohn-Sham (DKS) theory with different nonrelativistic exchange-correlation functionals. Two recent approaches for representing the magnetic balance (MB) between the large and small components of four-component spinors, namely, mDKS-RMB and sMB, have been employed for shielding tensor calculations and their results have been compared. Relativistic effects have also been analysed in terms of scalar and spin-orbit contributions at the two-component level of theory, including discussion of heavy-atom-on-light-atom effects for (1)J(CN), σ(C), and σ(N). The results for molecules containing metals from 4th row of periodic table show that relativistic effects for them are small (especially for spin-spin coupling constants). The biggest effects are observed for the 6th row where nonrelativistic theory reproduces only about 50%-70% of the two-component ZORA results for (1)J(MeC) and about 75% for heavy metal shielding constants. It is important to employ a full Dirac picture for calculations of heavy metal shielding constants, since ZORA reproduces only 75%-90% of the DKS results. Smaller discrepancies between ZORA-DFT and DKS are observed for nuclear spin-spin coupling constants. No significant differences are observed between the results obtained using mDKS-RMB and sMB approaches for magnetic balance in four-component calculations of the shielding constants.     

Investigations of zero-field splitting (ZFS) and local distortion parameters of ZnAl2S4:Mn2+ by theoretical analysis

Fourth-order perturbation formula on the basis of the dominant spin-orbit coupling mechanism is employed to investigate the local environment around Mn2+ centers in ZnAl2S4 single crystals. The zero-field splitting (ZFS) parameter D is calculated for the Mn2+ ions at the Al3+ site with local symmetry D3d using the different orbital reduction factors. Both the contributions of the lattice distortions to the crystal-field (CF) parameters and the D are examined by means of different cases. The comparison between the calculated results in this study and the previous experimental and theoretical values reveals a good agreement and reasonable distortion parameters for Mn2+ ions at Al3+ sites.     

Syntheses, X-ray structures, solid state high-field electron paramagnetic resonance, and density-functional theory investigations on chloro and aqua Mn(II) mononuclear complexes with amino-pyridine pentadentate ligands

The two pentadentate amino-pyridine ligands L5(2) and L5(3) (L5(2) and L5(3) stand for the N-methyl-N,N',N'-tris(2-pyridylmethyl)ethane-1,2-diamine and the N-methyl-N,N',N'-tris(2-pyridylmethyl)propane-1,3-diamine, respectively) were used to synthesize four mononuclear Mn(II) complexes, namely [(L5(2))MnCl](PF6) (1(PF6)), [(L5(3))MnCl](PF6) (2(PF6)), [(L5(2))Mn(OH2)](BPh4)2 (3(BPh4)2), and [(L5(3))Mn(OH2)](BPh4)2 (4(BPh4)2). The X-ray diffraction studies revealed different configurations for the ligand L5(n) (n = 2, 3) depending on the sixth exogenous ligand and/or the counterion. Solid state high-field electron paramagnetic resonance spectra were recorded on complexes 1-4 as on previously described mononuclear Mn(II) systems with tetra- or hexadentate amino-pyridine ligands. Positive and negative axial zero-field splitting (ZFS) parameters D were determined whose absolute values ranged from 0.090 to 0.180 cm(-1). Density-functional theory calculations were performed unraveling that, in contrast with chloro systems, the spin-spin and spin-orbit coupling contributions to the D-parameter are comparable for mixed N,O-coordination sphere complexes.     

Zero-field splittings and local tilting angles tauMn2+ for Mn2+ in ZnGeP2 and CdGeP2 crystals

The electron paramagnetic resonance (EPR) zero-field splittings (ZFSs) D of Mn2+ in ZnGeP2 and CdGeP2 crystals are calculated from both the microscopic spin-orbit coupling mechanism and the empirical superposition model. From the calculations, the ZFS D of ZnGeP2:Mn2+ is reasonably explained by using the local tilting angle tauMn2+ (rather than the corresponding angle tauZn2+ in the host crystal) and the local tilting angle tauMn2+ (which has not been reported) in CdGeP2:Mn2+ is estimated. The intrinsic ZFS parameter b2(R0) approximately -0.052(6)cm(-1) (with R0 approximately 2.43 angstroms) is suggested for Mn2+-P(3-) combination by using the local tilting angles tauMn2+. The value is quite unlike that (approximately 0.4(2)cm(-1)) obtained in the previous paper by combining the crystallographic data of host crystals with the ZFSs for Mn2+ ions in crystals. The reasonableness of these results is discussed.