Spin–Orbit Contributions in High‐Spin Nitrenes/Carbenes: A Hybrid CASSCF/MRMP2 Study of Zero‐Field Splitting Tensors

Zero‐field splitting (ZFS) tensors ( D tensors) of organic high‐spin oligonitrenes/oligocarbenes up to spin‐septet are quantitatively determined on the basis of quantum chemical calculations. The spin–orbit contributions, D ^SO tensors are calculated in terms of a hybrid CASSCF/MRMP2 approach, which was recently proposed by us. The spin–spin counterparts, D ^SS tensors are computed based on McWeeny–Mizuno’s equation in conjunction with the RODFT spin densities. The present calculations show that more than 10 % of ZFS arises from spin–orbit interactions in the high‐spin nitrenes under study. Contributions of spin‐bearing site–site interactions are estimated with the aid of a semi‐empirical model for the D tensors and found to be ca. 5 % of the D ^SO tensor. The analysis of intermediate states reveal that the largest contributions to the calculated D ^SO tensors are attributed to intra‐site spin flip excitations and delocalized π and π* orbitals play an important role in the inter‐site spin–orbit interactions.     

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.     

Computational studies of electron paramagnetic resonance parameters for paramagnetic molybdenum complexes. 1. Method validation on small and medium-sized systems

A variety of density functional methods have been evaluated in the computation of electronic g-tensors and molybdenum hyperfine couplings for systems ranging from the Mo atom through MoIIIN, [MoVOCl4]-, and [MoVOF5]2- to two larger MoV complexes MoXLCl2 (X=O, S; L=tris(3,5-dimethylpyrazolyl)hydroborate anion). In particular, the influence of the molybdenum basis set and of various exchange-correlation functionals with variable admixtures of Hartree-Fock exchange on the computed EPR parameters have been evaluated in detail. Careful basis-set studies have provided a moderate-sized 12s6p5d all-electron basis on molybdenum that gives hyperfine tensors in excellent agreement with much larger basis sets and that will be useful for calculations on larger systems. The best agreement with experimental data for both hyperfine and g-tensors is obtained with hybrid functionals containing approximately 30-40% Hartree-Fock exchange. Only for MoSLCl2 does increasing spin contamination with increasing exact-exchange admixture restrict the achievable computational accuracy. In all cases, spin-orbit corrections to the hyperfine tensors are sizable and have to be included in accurate calculations. Scalar relativistic effects enhance the isotropic Mo hyperfine coupling by approximately 15-20%. Two-component g-tensor calculations with variational inclusion of spin-orbit coupling show that the Deltag parallel components in [MoVOCl4]- and [MoVOF5]2- depend on higher-order spin-orbit contributions and are thus described insufficiently by the usual second-order perturbation approaches. Computed orientations of g- and hyperfine tensors relative to each other and to the molecular framework for the MoXLCl2 complexes provide good agreement between theory and single-crystal electron paramagnetic resonance experiments. In these cases, the hyperfine tensor orientations are influenced only slightly by spin-orbit effects.     

Calculation of the zero-field splitting tensor on the basis of hybrid density functional and Hartree-Fock theory

The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>12. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to approximately 0.5 in previous treatments.     

Relativistic spin-orbit effects on hyperfine coupling tensors by density-functional theory

A second-order perturbation theory treatment of spin-orbit corrections to hyperfine coupling tensors has been implemented within a density-functional framework. The method uses the all-electron atomic mean-field approximation and/or spin-orbit pseudopotentials in incorporating one- and two-electron spin-orbit interaction within a first-principles framework. Validation of the approach on a set of main-group radicals and transition metal complexes indicates good agreement between all-electron and pseudopotential results for hyperfine coupling constants of the lighter nuclei in the system, except for cases in which scalar relativistic effects become important. The nonrelativistic Fermi contact part of the isotropic hyperfine coupling constants is not always accurately reproduced by the exchange-correlation functionals employed, particularly for the triplet and pi-type doublet radicals in the present work. For this reason, ab initio coupled-cluster singles and doubles with perturbative triples results for the first-order contributions have been combined in the validation calculations with the density-functional results for the second-order spin-orbit contributions. In the cases where spin-orbit corrections are of significant magnitude relative to the nonrelativistic first-order terms, they improve the agreement with experiment. Antisymmetric contributions to the hyperfine tensor arise from the spin-orbit contributions and are discussed for the IO2 radical, whereas rovibrational effects have been evaluated for RhC, NBr, and NI.     

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.     

三角对称晶场中 4 A2(3d3 )态离子EPR参量的SS和SOO机制

A CDM/ EPR program has been developed using Visual Basic 6. 0. The spin-spin（SS）and spin-otherorbit（SOO）interactions omitted in published works have also been included in the Hamiltonian. The CDM/EPR program can study not only the EPR parameters but also the CF energy levels and wavefunctions for 4A2 （3d3）states ions in crystals. Utilizing the CDM/ EPR program,the EPR parameters and fine spectra for Ruby and Emerald have been investigated. The theoretical results are in good agreement with the experimental findings. The contributions to the EPR parameters and fine spectra arising from SS and SOO interactions have been studied. The investigation shows:① The EPR parameters are mainly induced by SO coupling interaction;② The contribution to the zerofield-splitting（ZFS）arising from SS interaction is appreciable and cannot be omitted,whereas the contributions to the ZFS parameter D arising from SOO interaction are smaller;③ The contribution to the Zeeman g-factors and spectra arising from SS and SOO interactions is slight.     

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.     

Performance of multi-configurational calculations for a 1,4-bis(phenylethynyl)benzene derivative conjugated molecule.

The theoretical challenge of finding a single method that quantitatively reproduces both the experimental low-lying excitation energies and the torsional barrier of a prototypical conjugated molecule, which could act as a molecular wire, has been addressed here. The results indicate that this goal can be reasonably achieved when multi-reference perturbation theory up to second order (MRMP2) based on a complete active space self-consistent field (CASSCF) wave function using large active spaces is used. The results obtained were also used to compare with less expensive Kohn-Sham (KS) density functional theory (DFT) calculations when applied to these properties. The results obtained with BLYP and B3LYP exchange-correlation functionals indicate that quantitative agreement with all the experimental data cannot be obtained with this methodology, with a clear dependence on the exchange-correlation form selected. We thus encourage a careful testing of pure and hybrid density functionals whenever KS DFT is used for the rational design of conjugated materials for charge conduits.     

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.     

First-principle computation of zero-field splittings: application to a high valent Fe(IV)-oxo model of nonheme iron proteins

We report the computational implementation of a combined spin-density-functional theory and perturbation theory (SDFT-PT) methodology for the accurate calculation of zero-field splittings (ZFS) in complexes of the most diverse nature including metal centers in proteins. We have applied the SDFT-PT methodology to study the cation of the recently synthesized complex [Fe(IV)(O)-(TMC)(NCCH(3))](OTf)(2), [J. Rohde et al., Science 299, 1037 (2003)] which is an important structural and functional analog of high-valent intermediates in catalytic cycles of nonheme iron enzymes. The calculated value (D(Theory)=28.67 cm(-1)) is in excellent agreement with the unusually large ZFS reported by experiment (D(Exp)=29+/-3 cm(-1)). The principal component D(zz) of the ZFS tensor is oriented along the Fe(IV)=oxo bond indicating that the oxo ligand dominates the electronic structure of the complex.     

Comparative density-functional study of the electron paramagnetic resonance parameters of amavadin

Electronic g tensors and hyperfine coupling tensors have been calculated for amavadin, an unusual eight-coordinate vanadium(IV) complex isolated from Amanita muscaria mushrooms. Different density-functional methods have been compared, ranging from local via gradient-corrected to hybrid functionals with a variable Hartree-Fock exchange admixture. For both electron paramagnetic resonance (EPR) properties, hybrid functionals with an appreciable exact-exchange admixture provide the closest agreement with experimental data. Second-order spin-orbit corrections provide non-negligible contributions to the 51V hyperfine tensor. The orientation of g and A tensors relative to each other also depends on spin-orbit corrections to the A tensor. A rationalization for the close resemblance of the EPR parameters of amavadin to those of the structurally rather different vanadyl complexes is provided, based on the nature of the relevant frontier orbitals.     

The electronic spectrum of AgCl2: ab initio benchmark versus density-functional theory calculations on the lowest ligand-field states including spin-orbit effects

The X 2pi(g), 2sigma(g)+, and 2delta(g) states of AgCl2 have been studied through benchmark ab initio complete active space self-consistent field plus second-order complete active space multireference Moller-Plesset algorithm (CASSCF+CASPT2) and complete active space self-consistent field plus averaged coupled pair functional (CASSCF+ACPF) and density-functional theory (DFT) calculations using especially developed basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges, and spin densities. The spin-orbit (SO) effects were included through the effective Hamiltonian formalism using the LambdaSSigma ACPF energies as diagonal elements. At the ACPF level, the ground state is 2pi(g) in contradiction with ligand-field theory, SCF, and large CASSCF; the adiabatic excitation energies for the 2sigma(g)+ and 2delta(g) states are 1640 and 18,230 cm(-1), respectively. The inclusion of the SO effects leads to a pure omega = 32(2pi(g)) ground state, a omega = 12 (66%2pi(g) and 34%2sigma(g)+) A state, a omega = 12 (34%2pi(g) and 66%2sigma(g)+) B state, a omega = 52(2delta(g))C state, and a omega = 32(99%2delta(g))D state. The X-A, X-B, X-C, and X-D transition energies are 485, 3715, 17 246, and 20 110 cm(-1), respectively. The B97-2, B3LYP, and PBE0 functionals overestimate by approximately 100% the X 2pi(g)-2sigma(g)+T(e) but provide a qualitative energetic ordering in good agreement with ACPF results. B3LYP with variable exchange leads to a 42% optimal Hartree-Fock exchange for transition energies but all equilibrium geometries get worsened. Asymptotic corrections to B3LYP do not provide improved values. The nature of the bonding in the X 2pi(g) state is very different from that of CuCl2 since the Mulliken charge on the metal is 1.1 while the spin density is only 0.35. DFT strongly delocalizes the spin density providing even smaller values of around 0.18 on Ag not only for the ground state, but also for the 2sigma(g)+ state.     

Spin-orbit Coupling and Intersystem Crossing in 4H-Pyran-4-thione： CASSCF//TD-B3LYP Study

The intersystem crossing channels of gaseous 4H-pyran-4-thione were investigated using the CASSCF//TD-B3LYP methods and group theory. Using the effective one-electron spin-orbit Harniltonian, the strengths of spin-orbit coupling were estimated, which plays an essential role in the spin transitions between different spin states. Calculated results show that phosphorescence and non-radiative decay via intersystem crossing to the So state are concurrent processes occurring at the T1 state. A rapid depletion of the S1 state via intersystem crossing to the T1 state can be mediated by the T2 state, if spin relaxation is fast within the triplet levels. Our calculated results are in close agreement with experimental observations.     

Magnetic and optical studies on an S = 6 ground-state cluster [Cr12O9(OH)3(O2CCMe3)15]: determination of,and the relationship between,single-ion and cluster spin Hamiltonian parameters

The dodecametallic Cr(III) cluster [Cr(12)O(9)(OH)(3)(O(2)CCMe(3))(15)] has a ground spin state of S = 6 characterized by the spin Hamiltonian parameters g(ZZ)() = 1.965, g(XX)() = g(YY)() = 1.960, D(S=)()(6) = +0.088 cm(-)(1), and E(S=)()(6) = 0 (where D and E are the axial and rhombic zero-field splitting parameters, respectively) as determined by multifrequency EPR spectroscopy and magnetization studies. Micro-SQUID magnetization studies reveal steps due to the fine structure of the ground state, with the spacing between the steps in excellent agreement with the D(S=)()(6) value determined by EPR. Analysis of high-resolution optical data (MCD) allows us to determine the single-ion g values and D value (= -1.035 cm(-)(1)) of the constituent Cr(III) ions directly. A vector coupling analysis demonstrates that the cluster ZFS is almost entirely due to the single-ion component. Thus, the relative orientations of the local and cluster magnetic axes can lead to a cluster ZFS of opposite sign to the single-ion value, even when this is the only significant contribution.     

Singlet and triplet potential surfaces for the O2+C2H4 reaction

Electronic structure calculations at the CASSCF and UB3LYP levels of theory with the aug-cc-pVDZ basis set were used to characterize structures, vibrational frequencies, and energies for stationary points on the ground state triplet and singlet O(2)+C(2)H(4) potential energy surfaces (PESs). Spin-orbit couplings between the PESs were calculated using state averaged CASSCF wave functions. More accurate energies were obtained for the CASSCF structures with the MRMP2/aug-cc-pVDZ method. An important and necessary aspect of the calculations was the need to use different CASSCF active spaces for the different reaction paths on the investigated PESs. The CASSCF calculations focused on O(2)+C(2)H(4) addition to form the C(2)H(4)O(2) biradical on the triplet and singlet surfaces, and isomerization reaction paths ensuing from this biradical. The triplet and singlet C(2)H(4)O(2) biradicals are very similar in structure, primarily differing in their C-C-O-O dihedral angles. The MRMP2 values for the O(2)+C(2)H(4)→C(2)H(4)O(2) barrier to form the biradical are 33.8 and 6.1 kcal/mol, respectively, for the triplet and singlet surfaces. On the singlet surface, C(2)H(4)O(2) isomerizes to dioxetane and ethane-peroxide with MRMP2 barriers of 7.8 and 21.3 kcal/mol. A more exhaustive search of reaction paths was made for the singlet surface using the UB3LYP/aug-cc-pVDZ theory. The triplet and singlet surfaces cross between the structures for the O(2)+C(2)H(4) addition transition states and the biradical intermediates. Trapping in the triplet biradical intermediate, following (3)O(2)+C(2)H(4) addition, is expected to enhance triplet→singlet intersystem crossing.