Unexpected Reduction of a Coordinated Diazapyridinophane Ligand Bound to Chromium(III) Ion Leading to Delocalization of the Unpaired Electron across Two Isolated Pyridine Units.

In the tetraazamacrocyclic ligand N,N'-dimethyl-2,11-diaza-[3.3](2,6)pyridinophane (L-N4 Me2 ), the two pyridine units are separated from each other by sp3 -hybridized triatomic bridges. Such electronically isolated pyridine moieties are considerably less prone to reductions than di- or triimines. A detailed structural, magnetic, and spectroscopic investigation of the complexes [Cr(L-N4 Me2 )(OAc)2 ] and [Cr(L-N4 Me2 )(OAc)2 ](PF6 ), in combination with theoretical calculations, reveals that the reduced complex must be described as a chromium(III) ion coordinated to the anionic radical ligand (L-N4 Me2 )⋅- rather than a low-spin chromium(II) ion bound to closed-shell ligands. Thus, it is, to the best of our knowledge, only the second example of a stable and structurally characterized metal complex containing a reduced isolated pyridine unit. The stability is attributed to the delocalization of the unpaired electron across the two pyridine units, mediated by their interaction to the metal ion.

Development and Application of a Complete Active Space Spin-Orbit Configuration Interaction Program Designed for Single Molecule Magnets.

We present a spin-orbit configuration interaction program which has been tailored for the description of the magnetic properties of polynuclear metal complexes with partially filled d- and f-shells. The spin-orbit operators are directly included in the configuration interaction program based on Slater-determinants. The lowest states are obtained by a Block-Davidson-type diagonalisation. The usage of localised active orbitals enables the construction of start vectors from tensor products of single-center wave functions that already include spin-orbit interaction. This allows for an analysis of the role and the interplay of the different metal centres. Furthermore, in case of weak coupling of the metal centres these tensor products are already close to the final wave functions ensuring fast convergence. In combination with a two-layer hybrid parallelisation, this makes the program highly efficient. Based on the spin-orbit coupled wave functions, magnetic D-tensors, g-tensors and temperature-dependent susceptibilities can be calculated. The applicability and performance of the program is shown exemplarily on a trinuclear transition metal (CoII VII CoII ) complex.

Mn12 -Acetate Complexes Studied as Single Molecules.

The phenomenon of single molecule magnet (SMM) behavior of mixed valent Mn12 coordination clusters of general formula [MnIII 8 MnIV 4 O12 (RCOO)16 (H2 O)4 ] had been exemplified by bulk samples of the archetypal [MnIII 8 MnIV 4 O12 (CH3 COO)16 (H2 O)4 ] (4) molecule, and the molecular origin of the observed magnetic behavior has found support from extensive studies on the Mn12 system within crystalline material or on molecules attached to a variety of surfaces. Here we report the magnetic signature of the isolated cationic species [Mn12 O12 (CH3 COO)15 (CH3 CN)]+ (1) by gas phase X-ray Magnetic Circular Dichroism (XMCD) spectroscopy, and we find it closely resembling that of the corresponding bulk samples. Furthermore, we report broken symmetry DFT calculations of spin densities and single ion tensors of the isolated, optimized complexes [Mn12 O12 (CH3 COO)15 (CH3 CN)]+ (1), [Mn12 O12 (CH3 COO)16 ] (2), [Mn12 O12 (CH3 COO)16 (H2 O)4 ] (3), and the complex in bulk geometry [MnIII 8 MnIV 4 O12 (CH3 COO)16 (H2 O)4 ] (5). The found magnetic fingerprints - experiment and theory alike - are of a remarkable robustness: The MnIV 4 core bears almost no magnetic anisotropy while the surrounding MnIII 8 ring is highly anisotropic. These signatures are truly intrinsic properties of the Mn12 core scaffold within all of these complexes and largely void of the environment. This likely holds irrespective of bulk packing effects.

Analyzing Anisotropic Exchange in a Pentanuclear Os2 Ni3 Complex.

Spin Hamiltonian parameters of a pentanuclear Os 2 III Ni 3 II cyanometallate complex are derived from ab initio wave function based calculations, namely valence-type configuration interaction calculations with a complete active space including spin-orbit interaction (CASOCI) in a single-step procedure. While fits of experimental data performed so far could reproduce the data but the resulting parameters were not satisfactory, the parameters derived in the present work reproduce experimental data and at the same time have a reasonable size. The one-centre parameters (local g matrices and single-ion zero field splitting tensors) are within an expected range, the anisotropic exchange parameters obtained in this work for an Os-Ni pair are not exceedingly large but determine the low-T part of the experimental χT curve. Exchange interactions (both isotropic and anisotropic) obtained from CASOCI have to be scaled by a factor of 2.5 to obtain agreement with experiment, a known deficiency of such types of calculation. After scaling the parameters, the isotropic Os-Ni exchange coupling constant is J = - 4 . 2  cm-1 and the D parameter of the (nearly axial) anisotropic Os-Ni exchange is D = J ∥ - J ⊥ = 18 . 8 c m -1 , so anisotropic exchange is larger in absolute size than isotropic exchange. The negative value of the isotropic J (indicating antiferromagnetic coupling) seemingly contradicts the large-temperature behaviour of the temperature dependent susceptibility curve, but this is caused by the negative g value of the Os centres. This negative g value is a universal feature of a pseudo-octahedral coordination with t 2 g 5 configuration and strong spin-orbit interaction. Knowing the size of these exchange interactions is important because Os(CN) 6 3 - is a versatile building block for the synthesis of 5 d / 3 d magnetic materials.

TURBOMOLE: Modular program suite for ab initio quantum-chemical and condensed-matter simulations.

TURBOMOLE is a collaborative, multi-national software development project aiming to provide highly efficient and stable computational tools for quantum chemical simulations of molecules, clusters, periodic systems, and solutions. The TURBOMOLE software suite is optimized for widely available, inexpensive, and resource-efficient hardware such as multi-core workstations and small computer clusters. TURBOMOLE specializes in electronic structure methods with outstanding accuracy-cost ratio, such as density functional theory including local hybrids and the random phase approximation (RPA), GW-Bethe-Salpeter methods, second-order Møller-Plesset theory, and explicitly correlated coupled-cluster methods. TURBOMOLE is based on Gaussian basis sets and has been pivotal for the development of many fast and low-scaling algorithms in the past three decades, such as integral-direct methods, fast multipole methods, the resolution-of-the-identity approximation, imaginary frequency integration, Laplace transform, and pair natural orbital methods. This review focuses on recent additions to TURBOMOLE's functionality, including excited-state methods, RPA and Green's function methods, relativistic approaches, high-order molecular properties, solvation effects, and periodic systems. A variety of illustrative applications along with accuracy and timing data are discussed. Moreover, available interfaces to users as well as other software are summarized. TURBOMOLE's current licensing, distribution, and support model are discussed, and an overview of TURBOMOLE's development workflow is provided. Challenges such as communication and outreach, software infrastructure, and funding are highlighted.

Hyperfine tensors for a model system for the oxygen evolving complex of photosystem II: calculation of the anisotropy shift that occurs beyond the strong exchange limit.

Broken-symmetry density functional calculations have been used to calculate effective 55Mn hyperfine (A) tensors for a mixed-valence tetranuclear manganese complex, a model system for the S2 state of the oxygen-evolving complex of photosystem II. Recent investigations carried out in our laboratory showed that for calculations within the strong exchange limit, density functional calculations cannot reproduce the relative magnitude of the anisotropy of the hyperfine tensors of the MnIII center compared to the MnIV centers. In this work we therefore go beyond the strong exchange limit and investigate the effect of multiplet mixing, induced by zero-field splitting, on the effective hyperfine tensors through a perturbational treatment within the numerical spin projection procedure. Results show that the inclusion of zero-field splitting leads to a shift of the anisotropy from the MnIII ion towards the three MnIV ions, thus reconciling the calculated and experimentally observed anisotropy pattern. However, the final results are quite sensitive to the energy gap between the ground (doublet) and the first excited (quartet) state and therefore critically depend on the appropriate choice of the isotropic exchange coupling constants.

Magnetostructural correlation in isolated trinuclear iron(iii) oxo acetate complexes.

We elucidate the correlation between geometric structures and magnetic couplings in trinuclear iron(iii) oxo acetate complexes [Fe3O(OAc)6(Py)n]+ (n = 0, 1, 2, 3) when isolated and trapped as gaseous ions. Structural information arises from Infra Red-Multiple Photon Dissociation (IR-MPD) and Collision Induced Dissociation (CID) experiments in conjuction with Density Functional Theory (DFT) based calculations. We simulate the antiferromagnetic couplings between the FeIII (d5) centers by employing a Broken Symmetry approach within our DFT calculations, and we extract the associated antiferromagnetic coupling constants. Coordination of one, two or three axial pyridine ligands to the [Fe3O(OAc)6]+ subunit distorts the geometry of the triangular Fe3O core. The Fe-Ocentral bond lengths are enlarged or shortened depending on number of coordinated pyridine ligands. This significantly affects the antiferromagnetic coupling constants between the FeIII centers ranging from -62 cm-1 to -28 cm-1 in [Fe3O(OAc)6(Py)n]+ (n = 0, 1, 2, 3). A detailed analysis of the associated exchange couplings indicates a switching of magnetic ground states by pyridine coordination. The total spin ST in the ground states of [Fe3O(OAc)6(Py)n]+ raises from ST = 1/2 (n = 0) to 3/2 (n = 1) and 5/2 (n = 2). Coordination of the third pyridine ligand (n = 3) re-establishes a spin ground state of ST = 1/2. We thus identify a coordination controlled switching of magnetic ground states.

Spectroscopic, Structural, and Kinetic Investigation of the Ultrafast Spin Crossover in an Unusual Cobalt(II) Semiquinonate Radical Complex.

A comprehensive spectroscopic and structural investigation of [CoII (l-N4 tBu2 )(dbsq)][B(p-C6 H4 Cl)4 ] (1, l-N4 tBu2 =N,N'-di-tert-butyl-2,11-diaza[3.3](2,6)pyridinophane, dbsq1- =3,5-di-tert-butylsemiquinonate), the first known octahedral complex with a low-spin (ls) CoII semiquinonate ground state, is reported. Above 200 K, solids as well as solutions of 1 exhibit thermally induced spin-crossover (SCO) from the ls to the high-spin (hs) CoII semiquinonate state instead of the frequently observed valence tautomerism from ls CoIII catecholate to hs CoII semiquinonate. DFT calculations demonstrate that the (closed shell) CoIII catecholate suffers from a triplet instability leading to the ls CoII semiquinonate ground state. The thorough temperature-dependent spectroscopic study of the SCO enables a photophysical investigation. Thus, by selective photoexcitation of the ls fraction of 1 in solution at room temperature, ultrafast conversion to the hs state is observed using femtosecond electronic and IR-vibrational (infrared) transient absorption spectroscopy. The kinetics of the photocycle is described by a stretched exponential with τ=3.3-3.6 ps and ß=0.52-0.54, representing an upper limit for the hs-ls relaxation time. This is, to our knowledge, the fastest interconversion ever determined for a SCO complex, and is attributed to the special situation that in 1 a CoII complex is coordinated to a π-radical ligand allowing very efficient coupling between the ls and hs spin states.

Spin-Free CC2 Implementation of Induced Transitions between Singlet Ground and Triplet Excited States.

In most organic molecules, phosphorescence has its origin in transitions from triplet exited states to the singlet ground state, which are spin-forbidden in nonrelativistic quantum mechanics. A sufficiently accurate description of phosphorescence lifetimes for molecules that contain only light elements can be achieved by treating the spin-orbit coupling (SOC) with perturbation theory (PT). We present an efficient implementation of this approach for the approximate coupled cluster singles and doubles model CC2 in combination with the resolution-of-the-identity approximation for the electron repulsion integrals. The induced oscillator strengths and phosphorescence lifetimes from SOC-PT are computed within the response theory framework. In contrast to previous work, we employ an explicitly spin-coupled basis for singlet and triplet operators. Thereby, a spin-orbital treatment can be entirely avoided for closed-shell molecules. For compounds containing only light elements, the phosphorescence lifetimes obtained with SOC-PT-CC2 are in good agreement with those of exact two-component (X2C) CC2, whereas the calculations are roughly 12 times faster than with X2C. Phosphorescence lifetimes computed for two thioketones with the SOC-PT-CC2 approach agree very well with reference results from experiment and are similar to those obtained with multireference spin-orbit configuration interaction and with X2C-CC2. An application to phosphorescent emitters for metal-free organic light-emitting diodes (OLEDs) with almost 60 atoms and more than 1800 basis functions demonstrates how the approach extends the applicability of coupled cluster methods for studying phosphorescence. The results indicate that other decay channels like vibrational relaxation may become important in such systems if lifetimes are large.

The spin and orbital contributions to the total magnetic moments of free Fe, Co, and Ni clusters.

We present size dependent spin and orbital magnetic moments of cobalt (Con (+), 8 ≤ n ≤ 22), iron (Fen (+), 7 ≤ n ≤ 17), and nickel cluster (Nin (+), 7 ≤ n ≤ 17) cations as obtained by X-ray magnetic circular dichroism (XMCD) spectroscopy of isolated clusters in the gas phase. The spin and orbital magnetic moments range between the corresponding atomic and bulk values in all three cases. We compare our findings to previous XMCD data, Stern-Gerlach data, and computational results. We discuss the application of scaling laws to the size dependent evolution of the spin and orbital magnetic moments per atom in the clusters. We find a spin scaling law "per cluster diameter," ∼n(-1/3), that interpolates between known atomic and bulk values. In remarkable contrast, the orbital moments do likewise only if the atomic asymptote is exempt. A concept of "primary" and "secondary" (induced) orbital moments is invoked for interpretation.

Intersystem-crossing and phosphorescence rates in fac-Ir(III)(ppy)3: a theoretical study involving multi-reference configuration interaction wavefunctions.

We have employed combined density functional theory and multi-reference configuration interaction methods including spin-orbit coupling (SOC) effects to investigate the photophysics of the green phosphorescent emitter fac-tris-(2-phenylpyridine)iridium (fac-Ir(ppy)3). A critical evaluation of our quantum chemical approaches shows that a perturbational treatment of SOC is the method of choice for computing the UV/Vis spectrum of this heavy transition metal complex while multi-reference spin-orbit configuration interaction is preferable for calculating the phosphorescence rates. The particular choice of the spin-orbit interaction operator is found to be of minor importance. Intersystem crossing (ISC) rates have been determined by Fourier transformation of the time correlation function of the transition including Dushinsky rotations. In the electronic ground state, fac-Ir(ppy)3 is C3 symmetric. The calculated UV/Vis spectrum is in excellent agreement with experiment. The effect of SOC is particularly pronounced for the metal-to-ligand charge transfer (MLCT) band in the visible region of the absorption spectrum which does not only extend its spectral onset towards longer wavelengths but also experiences a blue shift of its maximum. Pseudo-Jahn-Teller interaction leads to asymmetric coordinate displacements in the lowest MLCT states. Substantial electronic SOC and a small energy gap make ISC an ultrafast process in fac-Ir(ppy)3. For the S1↝T1 non-radiative transition, we compute a rate constant of kISC = 6.9 × 10(12) s(-1) which exceeds the rate constant of radiative decay to the electronic ground state by more than six orders of magnitude, in agreement with the experimental observation of a subpicosecond ISC process and a triplet quantum yield close to unity. As a consequence of the geometric distortion in the T1 state, the T1 → S0 transition densities are localized on one of the phenylpyridyl moieties. In our best quantum chemical model, we obtain phosphorescence decay times of 264 µs, 13 µs, and 0.9 µs, respectively, for the T1,I, T1,II, and T1,III fine-structure levels in dichloromethane (DCM) solution. In addition to reproducing the correct orders of magnitude for the individual phosphorescence emission probabilities, our theoretical study gives insight into the underlying mechanisms. In terms of intensity borrowing from spin-allowed transitions, the low emission probability of the T1,I substate is caused by the mutual cancellation of contributions from several singlet states to the total transition dipole moment. Their contributions do not cancel but add up in case of the much faster T1,III → S0 emission while the T1,II → S0 emission is dominated by intensity borrowing from a single spin-allowed process, i.e., the S2 → S0 transition.

Mechanism of Cu/Pd-catalyzed decarboxylative cross-couplings: a DFT investigation.

The reaction mechanism of decarboxylative cross-couplings of benzoates with aryl halides to give biaryls, which is cooperatively catalyzed by copper/palladium systems, was investigated with DFT methods. The geometries and energies of all starting materials, products, intermediates, and transition states of the catalytic cycle were calculated for the two model reactions of potassium 2- and 4-fluorobenzoate with bromobenzene in the presence of a catalyst system consisting of copper(I)/1,10-phenanthroline and the anionic monophosphine palladium complex [Pd(PMe3)Br](-). Several neutral and anionic pathways were compared, and a reasonable catalytic cycle was identified. The key finding is that the transmetalation has a comparably high barrier as the decarboxylation, which was previously believed to be solely rate-determining. The electronic activation energy of the transmetalation is rather reasonable, but the free energy loss in the initial Cu/Pd adduct formation is high. These results suggested that research aimed at further improving the catalyst should target potentially bridging bidentate ligands likely to assist in the formation of bimetallic intermediates. Experimental studies confirm this somewhat counterintuitive prediction. With a bidentate, potentially bridging ligand, designed to support the formation of bimetallic adducts, the reaction temperature for decarboxylative couplings was reduced by 70 °C to only 100 °C.

Broken symmetry approach to density functional calculation of zero field splittings including anisotropic exchange interactions.

The broken symmetry approach to the calculation of zero field splittings (or magnetic anisotropies) of multinuclear transition metal complexes is further developed. A procedure is suggested how to extract spin Hamiltonian parameters for anisotropic exchange from a set of broken symmetry density functional calculations. For isotropic exchange coupling constants Jij, the established procedure is retrieved, and anisotropic (or pseudodipolar) exchange coupling tensors Dij are obtained analogously. This procedure only yields the sum of the individual single-ion zero field splitting tensors Di. Therefore, a procedure based on localized orbitals has been developed to extract the individual single-ion contributions. With spin Hamiltonian parameters at hand, the zero field splittings of the individual spin multiplets are calculated by an exact diagonalization of the isotropic part, followed by a spin projection done numerically. The method is applied to the binuclear cation [LCr(OH)3CrL](3 +) (L = 1,4,7-trimethyl-1,4,7-triazanonane) for which experimental zero field splittings for all low-energy spin states are known, and to the single-molecule magnet [Fe4(CH3C(CH2O)3)2(dpm)6] (Hdpm = 2,2,6,6-tetramethylheptane-3,5-dione). In both these 3d compounds, the single-ion tensors mainly come from the spin-orbit interaction. Anisotropic exchange is dominated by the spin-dipolar interaction only for the chromium compound. Despite the rather small isotropic exchange couplings in the iron compound, spin-orbit and spin-dipolar contributions to anisotropic exchange are of similar size here.

Why spin contamination is a major problem in the calculation of spin-spin coupling in triplet biradicals.

In organic triplet biradicals, zero field splitting is dominated by the spin-dipolar interaction. While it has been observed before that spin-unrestricted density functional calculations give huge errors for systems with small D values, a consistent explanation was still missing. Using model systems, this work demonstrates how spin contamination creates unphysical one-center terms in the two-particle density matrix that spoil the calculated results.

Structure-reactivity relationships in the hydrogenation of carbon dioxide with ruthenium complexes bearing pyridinylazolato ligands.

Pyridinylazolato (N-N') ruthenium(II) complexes of the type [(N-N')RuCl(PMe3)3] have been obtained in high yields by treating the corresponding functionalised azolylpyridines with [RuCl2 (PMe3)4] in the presence of a base. (15)N NMR spectroscopy was used to elucidate the electronic influence of the substituents attached to the azolyl ring. The findings are in agreement with slight differences in the bond lengths of the ruthenium complexes. Furthermore, the electronic nature of the azolate moiety modulates the catalytic activity of the ruthenium complexes in the hydrogenation of carbon dioxide under supercritical conditions and in the transfer hydrogenation of acetophenone. DFT calculations were performed to shed light on the mechanism of the hydrogenation of carbon dioxide and to clarify the impact of the electronic nature of the pyridinylazolate ligands.

Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments. II. The importance of gauge invariance for large-core semi-local pseudopotentials.

In a previous paper we pointed out that core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation [P. Schwerdtfeger, B. Assadollahzadeh, U. Rohrmann, R. Schäfer, and J. R. Cheeseman, J. Chem. Phys. 134, 204102 (2011)]. In a recent paper van Wüllen showed that additional terms arising from the gauge-invariant condition for the semi-local part of a pseudopotential operator can lead to non-negligible contributions to the magnetizability tensor, which are sensitive to the gauge origin and basis set chosen [C. van Wüllen, J. Chem. Phys. 136, 114110 (2012)]. These terms were neglected in previous calculations as they were assumed to be small. In this paper we analyze the importance of the gauge-dependent semi-local pseudopotential correction term in detail for AuF and clusters of Sn showing that it leads indeed to very large corrections to the paramagnetic term for large-core pseudopotentials. Without this correction the results become very sensitive to the basis set applied. This now resolves some of the unusual large paramagnetic contributions reported before for both AuF and Sn(2).

On the use of effective core potentials in the calculation of magnetic properties, such as magnetizabilites and magnetic shieldings.

State-of-the art effective core potentials (ECPs) that replace electrons of inner atomic cores involve non-local potentials. If such an effective core potential is added to the Hamiltonian of a system in a magnetic field, the resulting Hamiltonian is not gauge invariant. This means, magnetic properties such as magnetisabilities and magnetic shieldings (or magnetic susceptibilities and nuclear magnetic resonance chemical shifts) calculated with different gauge origins are different even for exact solutions of the Schrödinger equation. It is possible to restore gauge invariance of the Hamiltonian by adding magnetic field dependent terms arising from the effective core potential. Numerical calculations on atomic and diatomic model systems (potassium mono-cation and potassium dimer) clearly demonstrate that the standard effective core potential Hamiltonian violates gauge invariance, and this affects the calculation of magnetisabilities more strongly than the calculation of magnetic shieldings. The modified magnetic field dependent effective core potential Hamiltonian is gauge invariant, and therefore it is the correct starting point for distributed gauge origin methods. The formalism for gauge including atomic orbitals (GIAO) and individual gauge for localized orbitals methods is worked out. ECP GIAO results for the potassium dimer are presented. The new method performs much better than a previous ECP GIAO implementation that did not account for the non-locality of the potential. For magnetic shieldings, deviations are clearly seen, but they amount to few ppm only. For magnetisabilities, our new ECP GIAO implementation is a major improvement, as demonstrated by the comparison of all-electron and ECP results.