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.

A Fock-operator complete active space self-consistent field (CAS-SCF) method combined with frozen-density embedding.

We report the implementation of a Fock-operator complete-active space self-consistent field (CAS-SCF) method combined with frozen-density embedding (FDE) into the KOALA quantum-chemistry program. The implementation is based on configuration interaction from an unrestricted reference determinant and is able to treat electronic configurations such as singlet, triplet, or quintet states embedded in a molecular environment. In order to account for possible spin polarization effects, the FDE contribution is extended to the unrestricted case. We assess the convergence obtained with the implementation at the example of a stretched lithium dimer with significant multi-reference character. The efficiency of the implementation enables the orbital optimization for 25 states in a state-average SA[S0-S10,T1-T12,Q1-Q2]-CAS(10,10)-SCF calculation for the retinal molecule using a def2-TZVP basis. The FDE ansatz leads to orbitals localized by definition on the target system, thus facilitating the orbital selection required for CAS methods in complex environments.

Interpretation of Coupled-Cluster Many-Electron Dynamics in Terms of Stationary States.

We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster (CC) theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion CC theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for He and Be atoms and for LiH, CH+, and LiF molecules show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration interaction (FCI) theory, provided that all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorates. Observing that populations computed from the linear response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations.

A state-specific multireference coupled-cluster method based on the bivariational principle.

A state-specific multireference coupled-cluster (MRCC) method based on Arponen's bivariational principle is presented, the bivar-MRCC method. The method is based on single-reference theory and therefore has a relatively straightforward formulation and modest computational complexity. The main difference from established methods is the bivariational formulation, in which independent parameterizations of the wave function (ket) and its complex conjugate (bra) are made. Importantly, this allows manifest multiplicative separability of the state (exact in the extended bivar-MRECC version of the method and approximate otherwise), and additive separability of the energy, while preserving polynomial scaling of the working equations. A feature of the bivariational principle is that the formal bra and ket references can be included as bivariational parameters, which eliminates much of the bias toward the formal reference. A pilot implementation is described, and extensive benchmark calculations on several standard problems are performed. The results from the bivar-MRCC method are comparable to established state-specific multireference methods. Considering the relative affordability of the bivar-MRCC method, it may become a practical tool for non-experts.

Magnetic anisotropy in trigonal planar Fe(ii) bis(trimethylsilyl)amido complexes of the type [Fe{N(SiMe3)2}2L]-experiment and theory.

Systematic ac (alternating current) magnetic investigations on four new trigonal planar high-spin Fe2+ complexes [Fe{N(SiMe3)2}2L] reveal that complexes which comprise a phosphine or arsine type ligand (L = PPh3, PMe3 and AsPh3) display slow magnetic relaxation at temperatures below 8 K under applied dc (direct current) fields, whereas a complex with a phosphine oxide ligand (L = OPPh3) does not. Accordingly, the parameters characteristic for magnetic anisotropy, derived both from dc magnetic measurements and quantum chemical calculations, reveal distinct differences for these two types of complexes. Extensive ab initio calculations of multi-reference wave function type were performed on the four new complexes listed above and the related reported ones with L = py, thf and PCy3 in order to get a reasonable description of the local electronic states involved in the magnetic relaxation. These calculations confirm that strong spin-orbit effects generate the magnetic anisotropy of complexes with L = PPh3, PMe3, AsPh3 and PCy3. On the other hand, the complexes with L = OPPh3, py and THF exhibit only small spin-orbit splittings, consistent with the fast relaxation found experimentally.

Field-Induced Co(II) Single-Ion Magnets with mer-Directing Ligands but Ambiguous Coordination Geometry.

Three air-stable Co(II) mononuclear complexes with different aromatic substituents have been prepared and structurally characterized by single-crystal X-ray diffraction. The mononuclear complexes [Co(H2L1)2]·2THF (1), [Co(HL2)2] (2), and [Co(H2L3)2]·CH2Cl2 (3) (where H3L1, H2L2, and H3L3 represent 3-hydroxy-naphthalene-2-carboxylic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, nicotinic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, and 2-hydroxy-benzoic acid (6-hydroxymethyl-pyridin-2-ylmethylene) hydrazide, respectively) feature a distorted mer octahedral coordination geometry. Detailed magnetic studies of 1-3 have been conducted using direct and alternating current magnetic susceptibility data. Field-induced slow magnetic relaxation was observed for these three complexes. There are few examples of such behavior in (distorted) octahedral coordination geometry (OC) Co(II) mononuclear complexes with uniaxial anisotropy. Analysis of the six-coordinate Co(II) mononuclear single-ion magnets (SIMs) in the literature using the SHAPE program revealed that they all show what is best described as distorted trigonal prismatic (TRP) coordination geometry, and in general, these show negative D zero-field splitting (ZFS) values. On the other hand, all the Co(II) mononuclear complexes displaying what is best approximated as distorted octahedral (OC) coordination geometry show positive D values. In the new Co(II) mononuclear complexes we describe here, there is an ambiguity, since the rigid tridentate ligands confer what is best described for an octahedral complex as a mer coordination geometry, but the actual shape of the first coordination sphere is between octahedral and trigonal prismatic. The negative D values observed experimentally and supported by high-level electronic structure calculations are thus in line with a trigonal prismatic geometry. However, a consideration of the rhombicity as indicated by the E value of the ZFS in conjunction with the SHAPE analysis shows that in this case it is difficult to distinguish between the OC and TRP descriptions.

Magnetic anisotropy of a CoII single ion magnet with distorted trigonal prismatic coordination: theory and experiment.

The single ion magnetic properties of Co(ii) are affected by the details of the coordination geometry of the ion. Here we show that a geometry close to trigonal prismatic which arises when the ligand 6,6'-((1Z)-((piperazine-1,4-diylbis(propane-3,1-diyl))bis(azanylylidene))bis(methanylylidene))bis(2-methoxyphenol) coordinates to Co(ii) does indeed lead to enhanced single-ion behaviour as has previously been predicted. Synthesis of the compound, structural information, and static as well as dynamic magnetic data are presented along with an analysis using quantum chemical ab initio calculations. Though the complex shows a slight deviation from an ideal trigonal prismatic coordination, the zero-field splitting as well as the g-tensor are strongly axial with D = -41 cm-1 and E < 0.01 cm-1. For the lowest Kramers doublet (S = 1/2) g∥ = 7.86 and g⊥ < 0.05 were found. In contrast, the second Kramers doublet possesses a rhombic g-tensor with g∥ = 2.75 and g⊥ = 4.35. Due to large spin-orbit coupling resulting in very different g tensors, it is not possible to simulate the temperature dependence of the magnetic susceptibility with a spin Hamiltonian of the form H = D(Sz2 - S(S + 1)/3) + E(Sx2 - Sy2) + µBgS·B using an effective spin S = 3/2. Calculations on model complexes show the influence of the coordinating atoms and the deviation from the ideal trigonal prismatic coordination. As the distortion is reduced towards idealised D3h, the zero field splitting increases and the g-tensor of the second Kramers doublet also becomes axial.

Divergent Coordination Chemistry: Parallel Synthesis of [2×2] Iron(II) Grid-Complex Tauto-Conformers.

The coordination of iron(II) ions by a homoditopic ligand L with two tridentate chelates leads to the tautomerism-driven emergence of complexity, with isomeric tetramers and trimers as the coordination products. The structures of the two dominant [Fe(II) 4 L4 ](8+) complexes were determined by X-ray diffraction, and the distinctness of the products was confirmed by ion-mobility mass spectrometry. Moreover, these two isomers display contrasting magnetic properties (Fe(II) spin crossover vs. a blocked Fe(II) high-spin state). These results demonstrate how the coordination of a metal ion to a ligand that can undergo tautomerization can increase, at a higher hierarchical level, complexity, here expressed by the formation of isomeric molecular assemblies with distinct physical properties. Such results are of importance for improving our understanding of the emergence of complexity in chemistry and biology.

Field-Induced Slow Magnetic Relaxation in the Ni(I) Complexes [NiCl(PPh3)2]·C4H8O and [Ni(N(SiMe3)2)(PPh3)2].

Direct current (dc) and alternating current (ac) magnetic measurements have been performed on the three Ni(I) complexes: [NiCl(PPh3)3], [NiCl(PPh3)2]·C4H8O, and [Ni(N(SiMe3)2)(PPh3)2]. Fits of the dc magnetic data suggest an almost similar behavior of the three compounds, which display only moderate deviations from the spin-only values. The ac magnetic investigations reveal that the two complexes with trigonal planar coordination--[NiCl(PPh3)2]·C4H8O and [Ni(N(SiMe3)2)(PPh3)2]--display slow magnetic relaxation at low temperatures under applied dc fields, whereas tetrahedral [NiCl(PPh3)3] does not. Ground and excited states as well as magnetic data were calculated by ab initio wave function based multi-configurational methods, including dynamic correlation as well as spin-orbit coupling. The two trigonal planar complexes comprise well-isolated S = (1)/2 ground states, whereas two S = (1)/2 states with a splitting of less than 100 cm(-1) were found in the tetrahedral compound.

Slow magnetic relaxation in trigonal-planar mononuclear Fe(II) and Co(II) bis(trimethylsilyl)amido complexes--a comparative study.

Alternating current magnetic investigations on the trigonal-planar high-spin Co(2+) complexes [Li(15-crown-5)] [Co{N(SiMe3)2}3], [Co{N(SiMe3)2}2(THF)] (THF = tetrahydrofuran), and [Co{N(SiMe3)2}2(PCy3)] (Cy = -C6H13 = cyclohexyl) reveal that all three complexes display slow magnetic relaxation at temperatures below 8 K under applied dc (direct current) fields. The parameters characteristic for their respective relaxation processes such as effective energy barriers Ueff (16.1(2), 17.1(3), and 19.1(7) cm(-1)) and relaxation times τ0 (3.5(3) × 10(-7), 9.3(8) × 10(-8), and 3.0(8) × 10(-7) s) are almost the same, despite distinct differences in the ligand properties. In contrast, the isostructural high-spin Fe(2+) complexes [Li(15-crown-5)] [Fe{N(SiMe3)2}3] and [Fe{N(SiMe3)2}2(THF)] do not show slow relaxation of the magnetization under similar conditions, whereas the phosphine complex [Fe{N(SiMe3)2}2(PCy3)] does, as recently reported by Lin et al. (Lin, P.-H.; Smythe, N. C.; Gorelsky, S. I.; Maguire, S.; Henson, N. J.; Korobkov, I.; Scott, B. L.; Gordon, J. C.; Baker, R. T.; Murugesu, M. J. Am. Chem. Soc. 2011, 135, 15806.) Distinctly differing axial anisotropy D parameters were obtained from fits of the dc magnetic data for both sets of complexes. According to density functional theory (DFT) calculations, all complexes possess spatially nondegenerate ground states. Thus distinct spin-orbit coupling effects, as a main source of magnetic anisotropy, can only be generated by mixing with excited states. This is in line with significant contributions of excited determinants for some of the compounds in complete active space self-consistent field (CASSCF) calculations done for model complexes. Furthermore, the calculated energetic sequence of d orbitals for the cobalt compounds as well as for [Fe{N(SiMe3)2}2(PCy3)] differs significantly from the prediction by crystal field theory. Experimental and calculated (time-dependent DFT) optical spectra display characteristic d-d transitions in the visible to near-infrared region. Energies for lowest transitions range from 0.19 to 0.35 eV; whereas, for [Li(15-crown-5)][Fe{N(SiMe3)2}3] a higher value is found (0.66 eV). Zero-field (57)Fe Mößbauer spectra of the three high-spin iron complexes exhibit a doublet at 3 K with small and similar values of the isomer shifts (δ), ranging between 0.57 and 0.59 mm/s, as well as an unusual small quadrupole splitting (ΔEQ = 0.60 mm/s) in [Li(15-crown-5)][Fe{N(SiMe3)2}3].

Switching of a coupled spin pair in a single-molecule junction.

Single-molecule spintronics investigates electron transport through magnetic molecules that have an internal spin degree of freedom. To understand and control these individual molecules it is important to read their spin state. For unpaired spins, the Kondo effect has been observed as a low-temperature anomaly at small voltages. Here, we show that a coupled spin pair in a single magnetic molecule can be detected and that a bias voltage can be used to switch between two states of the molecule. In particular, we use the mechanically controlled break-junction technique to measure electronic transport through a single-molecule junction containing two coupled spin centres that are confined on two Co(2+) ions. Spin-orbit configuration interaction methods are used to calculate the combined spin system, where the ground state is found to be a pseudo-singlet and the first excitations behave as a pseudo-triplet. Experimentally, these states can be assigned to the absence and occurrence of a Kondo-like zero-bias anomaly in the low-temperature conductance data, respectively. By applying finite bias, we can repeatedly switch between the pseudo-singlet state and the pseudo-triplet state.