Local Energy Decomposition Analysis of London Dispersion Effects: From Simple Model Dimers to Complex Biomolecular Assemblies.

ConspectusLondon dispersion (LD) forces are ubiquitous in chemistry, playing a pivotal role in a wide range of chemical processes. For example, they influence the structure of molecular crystals, the selectivity of organocatalytic transformations, and the formation of biomolecular assemblies. Harnessing these forces for chemical applications requires consistent quantification of the LD energy across a broad and diverse spectrum of chemical scenarios. Despite the great progress made in recent years in the development of experimental strategies for LD quantification, quantum chemical methods remain one of the most useful tools in the hand of chemists for the study of these weak interactions. Unfortunately, the accurate quantification of LD effects in complex systems poses many challenges for electronic structure theories. One of the problems stems from the fact that LD forces originate from long-range electronic dynamic correlation, and hence, their rigorous description requires the use of complex, highly correlated wave function-based methods. These methods typically feature a steep scaling with the system size, limiting their applicability to small model systems. Another core challenge lies in disentangling short-range from long-range dynamic correlation, which from a rigorous quantum mechanical perspective is not possible.In this Account, we describe our research endeavors in the development of broadly applicable computational methods for LD quantification in molecular chemistry as well as challenging applications of these schemes in various domains of chemical research. Our strategy lies in the use of local correlation theories to reduce the computational cost associated with complex electronic structure methods while providing at the same time a simple means of decomposition of dynamic correlation into its long-range and short-range components. In particular, the local energy decomposition (LED) scheme at the domain-based local pair natural orbital coupled cluster (DLPNO-CCSD(T)) level has emerged as a powerful tool in our research, offering a clear-cut quantitative definition of the LD energy that remains valid across a plethora of different chemical scenarios. Typical applications of this scheme are examined, encompassing protein-ligand interactions and reactivity studies involving many fragments and complex electronic structures. In addition, our research also involves the development of novel cost-effective methodologies, which exploit the LED definition of the LD energy, for LD energy quantification that are, in principle, applicable to systems with thousands of atoms. The Hartree-Fock plus London Dispersion (HFLD) scheme, correcting the HF interaction energy using an approximate CCSD(T)-based LD energy, is a useful, parameter-free electronic structure method for the study of LD effects in systems with hundreds of molecular fragments. However, the usefulness of the LED scheme reaches beyond providing an interpretation of the calculated DLPNO-CCSD(T) or DLPNO-MP2 interaction energies. For example, the dispersion energies obtained from the LED can be fruitfully used in order to parametrize semiempirical dispersion models. We will demonstrate this in the context of an emerging semiempirical method, namely, the Natural Orbital Tied Constructed Hamiltonian (NOTCH) method. NOTCH incorporates LED-derived LD energies and shows promising accuracy at a minimum amount of empiricism. Thus, it holds substantial promise for large and complex systems.

A perspective on the future of quantum chemical software: the example of the ORCA program package.

The field of computational chemistry has made an impressive impact on contemporary chemical research. In order to carry out computational studies on actual systems, sophisticated software is required in form of large-scale quantum chemical program packages. Given the enormous diversity and complexity of the methods that need to be implementation in such packages, it is evident that these software pieces are very large (millions of code lines) and extremely complex. Most of the packages in widespread use by the computational chemistry community have had a development history of decades. Given the rapid progress in the hardware and a lack of resources (time, workforce, money), it is not possible to keep redesigning these program packages from scratch in order to keep up with the ever more quickly shifting hardware landscape. In this perspective, some aspects of the multitude of challenges that the developer community faces are discussed. While the task at hand - to ensure that quantum chemical program packages can keep evolving and make best use of the available hardware - is daunting, there are also new evolving opportunities. The problems and potential cures are discussed with the example of the ORCA package that has been developed in our research group.

Oxygen-Donor Metalloligands Induce Slow Magnetization Relaxation in Zero Field for a Cobalt(II) Complex with {CoO4} Motif.

Most 3d metal-based single-molecule magnets (SMMs) use N-ligands or ligands with even softer donors to impart a particular coordination geometry and increase the zero-field splitting parameter |D|, while complexes with hard O-donor ligands showing slow magnetization relaxation are rare. Here, we report that a diamagnetic NiII complex of a tetradentate ligand featuring two N-heterocyclic carbene and two alkoxide-O donors, [LO,ONi], can serve as a {O,O'}-chelating metalloligand to give a trinuclear complex [(LO,ONi)Co(LO,ONi)](OTf)2 (2) with an elongated tetrahedral {CoIIO4} core, D = -74.3 cm-1, and a spin reversal barrier Ueff = 86.9 cm-1 in the absence of an external dc field. The influence of diamagnetic NiII on the electronic structure of the {CoO4} unit in comparison to [Co(OPh)4]2- (A) has been probed with multireference ab initio calculations. These reveal a contrapolarizing effect of the NiII, which forms stronger metal-alkoxide bonds than the central CoII, inducing a change in ligand field splitting and a 5-fold increase in the magnetic anisotropy in 2 compared to A, with an easy magnetization axis along the Ni-Co-Ni vector. This demonstrates a strategy to enhance the SMM properties of 3d metal complexes with hard O-donors by modulating the ligand field character via the coordination of diamagnetic ions and the benefit of robust metalloligands in that regard.

Molybdenum(VI) Nitrido Complexes with Tripodal Silanolate Ligands. Structure and Electronic Character of an Unsymmetrical Dimolybdenum µ-Nitrido Complex Formed by Incomplete Nitrogen Atom Transfer.

In contrast to a tungsten nitrido complex endowed with a tripodal silanolate ligand framework, which was reported in the literature to be a dimeric species with a metallacyclic core, the corresponding molybdenum nitrides 3 are monomeric entities comprising a regular terminal nitride unit, as proven by single-crystal X-ray diffraction (SC-XRD). Their electronic character is largely determined by the constraints imposed on the metal center by the podand ligand architecture. 95Mo nuclear magnetic resonance (NMR) and, to a lesser extent, 14N NMR spectroscopy allow these effects to be studied, which become particularly apparent upon comparison with the spectral data of related molybdenum nitrides comprising unrestrained silanolate, alkoxide, or amide ligands. Attempted nitrogen atom transfer from these novel terminal nitrides to [(tBuArN)3Mo] (Ar = 3,5-dimethylphenyl) as the potential acceptor stopped at the stage of unsymmetric dimolybdenum µ-nitrido complex 13a as the first intermediate along the reaction pathway. SC-XRD, NMR, electron paramagnetic resonance, and ultraviolet-visible spectroscopy as well as magnetometry in combination with density functional theory allowed a clear picture of the geometric and electronic structure of this mixed-valent species to be drawn. 13a is formally best described as an adduct of the type [(Mo[O])+III-(µN)-III-(Mo[N])+VI], S = 1/2 complex with (Mo[O])+III in the low-spin configuration, whereas related complexes such as [(AdS)3Mo-(µN)-Mo(NtBuAr)3] (19; Ad = 1-adamantyl) have previously been regarded in the literature as mixed-valent Mo+IV/Mo+V species. The spin population at the two Mo centers is uneven and notably larger at the more reduced Mo[O] atom, whereas the only spin present at the (µN) bridge is derived from spin polarization.

Elucidation of the exchange interaction in photoexcited three-spin systems - a second-order perturbational approach.

Photogenerated three-spin systems show great potential for applications in the field of molecular spintronics. In these systems, the exchange interaction in the electronically excited state dictates their magnetic properties. To design such molecules for specific applications, it is thus important to understand how the sign and magnitude of the exchange interaction can be controlled. For this purpose, we developed a perturbational approach, based on previous work by the groups of de Loth and Malrieu, that allows for the direct calculation of the exchange interaction and its individual contributions up to the second order and implemented it within the ORCA program package. Within this manuscript, we present the derivation of the individual second-order contributions, provide an overview of the implementation of the code and illustrate its performance. We show that, using this perturbational approach in combination with state-averaged orbitals from minimal active space calculations, accurate values for the exchange interaction can be computed for organic nitroxides. Further, we demonstrate that the weight of the ionic determinants in the orbital optimisation of the CASSCF procedure is crucial for the computation of accurate exchange couplings. In the case of photoexcited chromophore-radical systems, we find that the dynamic spin polarisation effect constitutes the most important contribution to the exchange interaction, whereby the sign of this contribution determines the sign of the exchange interaction.

Extensive reference set and refined computational protocol for calculations of 57Fe Mössbauer parameters.

Mössbauer spectroscopy is a powerful technique for probing the local electronic structure of iron compounds, because it reports in an element-selective manner on both the oxidation state and coordination environment of the Fe ion. Computational prediction of the two main Mössbauer parameters, isomer shift (δ) and quadrupole splitting (ΔEQ), has long been targeted by quantum chemical studies, and useful protocols based on density functional theory have been proposed. Here we present an extensive curated reference set of Fe compounds that is considerably larger and more diverse than literature precedents. We make a distinction between low-temperature and high-temperature experimental subgroups. This set is employed for optimizing a refined computational protocol utilizing the scalar version of the exact 2-component (X2C) Hamiltonian with the finite nucleus approximation. Attention is devoted to having an accurate and flexible all-electron basis set for Fe. We assess the performance of several DFT methods that cover all representative families and rungs of functionals and find that hybrid functionals with ca. 25-30% exact exchange offer the best accuracy for isomer shifts. The work establishes a refined general protocol of wide applicability that achieves good performance for the prediction of isomer shifts in a wider variety of systems than before, but the limitations of DFT for quadrupole splittings are also highlighted. Finally, comparison of calculated values with high-temperature experimental results shows that the use of an empirical correction factor is required to account for the second-order Doppler shift and to achieve the same quality of correlation as with the low-temperature data.

A theoretical spectroscopy study of the photoluminescence properties of narrow band Eu2+-doped phosphors containing multiple candidate doping centers. Prediction of an unprecedented narrow band red phosphor.

We have previously presented a computational protocol that is based on an embedded cluster model and operates in the framework of TD-DFT in conjunction with the excited state dynamics (ESD) approach. The protocol is able to predict the experimental absorption and emission spectral shapes of Eu2+-doped phosphors. In this work, the applicability domain of the above protocol is expanded to Eu2+-doped phosphors bearing multiple candidate Eu doping centers. It will be demonstrated that this protocol provides full control of the parameter space that describes the emission process. The stability of Eu doping at various centers is explored through local energy decomposition (LED) analysis of DLPNO-CCSD(T) energies. This enables further development of the understanding of the electronic structure of the targeted phosphors, the diverse interactions between Eu and the local environment, and their impact on Eu doping probability, and control of the emission properties. Hence, it can be employed to systematically improve deficiencies of existing phosphor materials, defined by the presence of various intensity emission bands at undesired frequencies, towards classes of candidate Eu2+-doped phosphors with desired narrow band red emission. For this purpose, the chosen study set consists of three UCr4C4-based narrow-band phosphors, namely the known alkali lithosilicates RbNa[Li3SiO4]2:Eu2+ (RNLSO2), RbNa3[Li3SiO4]4:Eu2+ (RNLSO) and their isotypic nitridolithoaluminate phosphors consisting of CaBa[LiAl3N4]2:Eu2+ (CBLA2) and the proposed Ca3Ba[LiAl3N4]4:Eu2+ (CBLA), respectively. The theoretical analysis presented in this work led us to propose a modification of the CBLA2 phosphor that should have improved and unprecedented narrow band red emission properties. Finally, we believe that the analysis presented here is important for the future rational design of novel Eu2+-doped phosphor materials, with a wide range of applications in science and technology.

Valence-to-core X-ray emission spectroscopy of transition metal tetrahalides: mechanisms governing intensities.

Valence-to-core (VtC) X-ray emission spectroscopy offers the opportunity to probe the valence electronic structure of a system filtered by selection rules. From this, the nature of its ligands can be inferred. While a preceding 1s ionization creates a core hole, in VtC XES this core hole is filled with electrons from mainly ligand based orbitals. In this work, we investigated the trends in the observed VtC intensities for a series of transition metal halides, which spans the first row transition metals from manganese to copper. Further, with the aid of computational studies, we corroborated these trends and identified the mechanisms and factors that dictate the observed intensity trends. Small amounts of metal p contribution to the ligand orbitals are known to give rise to intensity of a VtC transition. By employing an LCAO (linear combination of atomic orbitals) approach, we were able to assess the amount of metal p contribution to the ligand molecular orbitals, as well as the role of the transition dipole moment and correlate these factors to the experimentally observed intensities. Finally, by employing an ano (atomic natural orbital) basis set within the calculations, the nature of the metal p contribution (3p vs. 4p) was qualitatively assessed and their trends discussed within the same transition metal halide series.

Code generation in ORCA: progress, efficiency and tight integration.

An improved version of ORCA's automated generator environment (ORCA-AGE II) is presented. The algorithmic improvements and the move to C++ as the programming language lead to a performance gain of up to two orders of magnitude compared to the previously developed PYTHON toolchain. Additionally, the restructured modular design allows for far more complex code engines to be implemented readily. Importantly, we have realised an extremely tight integration with the ORCA host program. This allows for a workflow in which only the wavefunction Ansatz is part of the source code repository while all actual high-level code is generated automatically, inserted at the appropriate place in the host program before it is compiled and linked together with the hand written code parts. This construction ensures longevity and uniform code quality. Furthermore the new developments allow ORCA-AGE II to generate parallelised production-level code for highly complex theories, such as fully internally contracted multireference coupled-cluster theory (fic-MRCC) with an enormous number of contributing tensor contractions. We also discuss the automated implementation of nuclear gradients for arbitrary theories. All these improvements enable the implementation of theories that are too complex for the human mind and also reduce development times by orders of magnitude. We hope that this work enables researchers to concentrate on the intellectual content of the theories they develop rather than be concerned with technical details of the implementation.

Restricted Open-Shell Hartree-Fock Method for a General Configuration State Function Featuring Arbitrarily Complex Spin-Couplings.

In this work, we present a general spin restricted open-shell Hartree-Fock (ROHF) implementation that is able to generate self-consistent field (SCF) wave functions for an arbitrary configuration state function (CSF). These CSFs can contain an arbitrary number of unpaired electrons in arbitrary spin-couplings. The resulting method is named CSF-ROHF. We demonstrate that starting from the ROHF energy expression, for example, the one given by Edwards and Zerner, it is possible to obtain the values of the ROHF vector-coupling coefficients by setting up an open-shell for each group of consecutive parallel-coupled spins dictated by the unique spin-coupling pattern of any given CSF. To achieve this important and nontrivial goal, we employ the machinery of the iterative configuration expansion configuration interaction (ICE-CI) method, which is able to tackle general CI problems on the basis of spin-adapted CSFs. This development allows for the efficient generation of SCF spin-eigenfunctions for systems with complex spin-coupling patterns, such as polymetallic chains and metal clusters, while maintaining SCF scaling with system size (quadratic or less, depending on the specific algorithm and approximations chosen).

Palladium-catalysed electrophilic aromatic C-H fluorination.

Aryl fluorides are widely used in the pharmaceutical and agrochemical industries, and recent advances have enabled their synthesis through the conversion of various functional groups. However, there is a lack of general methods for direct aromatic carbon-hydrogen (C-H) fluorination. Conventional methods require the use of either strong fluorinating reagents, which are often unselective and difficult to handle, such as elemental fluorine, or less reactive reagents that attack only the most activated arenes, which reduces the substrate scope. A method for the direct fluorination of aromatic C-H bonds could facilitate access to fluorinated derivatives of functional molecules that would otherwise be difficult to produce. For example, drug candidates with improved properties, such as increased metabolic stability or better blood-brain-barrier penetration, may become available. Here we describe an approach to catalysis and the resulting development of an undirected, palladium-catalysed method for aromatic C-H fluorination using mild electrophilic fluorinating reagents. The reaction involves a mode of catalysis that is unusual in aromatic C-H functionalization because no organometallic intermediate is formed; instead, a reactive transition-metal-fluoride electrophile is generated catalytically for the fluorination of arenes that do not otherwise react with mild fluorinating reagents. The scope and functional-group tolerance of this reaction could provide access to functional fluorinated molecules in pharmaceutical and agrochemical development that would otherwise not be readily accessible.

Assessment of the similarity-transformed equation of motion (STEOM) for open-shell organic and transition metal molecules.

This study benchmarks the newly re-implemented single-reference excited-state methods, IP-EOM-CCSD, EA-EOM-CCSD, and STEOM-CCSD, in ORCA6.0, with a focus on open-shell systems. We compare STEOM against EOM-CCSD, CC3, and CCSDT across a range of systems, including small organic radicals, hydrated transition metal (TM) ions, and TM diatomic systems with both closed and open-shell configurations. For organic radicals, STEOM and EOM-CCSD show comparable performance, aligning closely with CC3 and CCSDT results. In the case of hydrated TM ions, IP-EOM closely matches DLPNO-CCSD results, while deviations from DLPNO-CCSD(T) are consistent. For open-shell TM systems, IP-EOM exhibits a blueshift relative to both the DLPNO-CCSD methods, while EA-EOM-CCSD shows better agreement. When comparing STEOM and CC3 to CCSDT, STEOM shows slightly larger deviations in closed-shell systems but shows excellent agreement in open-shell systems. Computational efficiency is also assessed, revealing a significant speedup in ORCA 6.0 compared to ORCA 5.0, with optimizations improving computation times. This study provides valuable insights into the performance and efficiency of STEOM in various chemical environments, highlighting its strengths and limitations.

Does Serial Femtosecond Crystallography Depict State-Specific Catalytic Intermediates of the Oxygen-Evolving Complex?

Recent advances in serial femtosecond crystallography (SFX) of photosystem II (PSII), enabled by X-ray free electron lasers (XFEL), provided the first geometric models of distinct intermediates in the catalytic S-state cycle of the oxygen-evolving complex (OEC). These models are obtained by flash-advancing the OEC from the dark-stable state (S1) to more oxidized intermediates (S2 and S3), eventually cycling back to the most reduced S0. However, the interpretation of these models is controversial because geometric parameters within the Mn4CaO5 cluster of the OEC do not exactly match those expected from coordination chemistry for the spectroscopically verified manganese oxidation states of the distinct S-state intermediates. Here we focus on the first catalytic transition, S1 → S2, which represents a one-electron oxidation of the OEC. Combining geometric and electronic structure criteria, including a novel effective oxidation state approach, we analyze existing 1-flash (1F) SFX-XFEL crystallographic models that should depict the S2 state of the OEC. We show that the 1F/S2 equivalence is not obvious, because the Mn oxidation states and total unpaired electron counts encoded in these models are not fully consistent with those of a pure S2 state and with the nature of the S1 → S2 transition. Furthermore, the oxidation state definition in two-flashed (2F) structural models is practically impossible to elucidate. Our results advise caution in the extraction of electronic structure information solely from the literal interpretation of crystallographic models and call for re-evaluation of structural and mechanistic interpretations that presume exact correspondence of such models to specific catalytic intermediates of the OEC.

Nature of S-States in the Oxygen-Evolving Complex Resolved by High-Energy Resolution Fluorescence Detected X-ray Absorption Spectroscopy.

Photosystem II, the water splitting enzyme of photosynthesis, utilizes the energy of sunlight to drive the four-electron oxidation of water to dioxygen at the oxygen-evolving complex (OEC). The OEC harbors a Mn4CaO5 cluster that cycles through five oxidation states Si (i = 0-4). The S3 state is the last metastable state before the O2 evolution. Its electronic structure and nature of the S2 → S3 transition are key topics of persisting controversy. Most spectroscopic studies suggest that the S3 state consists of four Mn(IV) ions, compared to the Mn(III)Mn(IV)3 of the S2 state. However, recent crystallographic data have received conflicting interpretations, suggesting either metal- or ligand-based oxidation, the latter leading to an oxyl radical or a peroxo moiety in the S3 state. Herein, we utilize high-energy resolution fluorescence detected (HERFD) X-ray absorption spectroscopy to obtain a highly resolved description of the Mn K pre-edge region for all S-states, paying special attention to use chemically unperturbed S3 state samples. In combination with quantum chemical calculations, we achieve assignment of specific spectroscopic features to geometric and electronic structures for all S-states. These data are used to confidently discriminate between the various suggestions concerning the electronic structure and the nature of oxidation events in all observable catalytic intermediates of the OEC. Our results do not support the presence of either peroxo or oxyl in the active configuration of the S3 state. This establishes Mn-centered storage of oxidative equivalents in all observable catalytic transitions and constrains the onset of the O-O bond formation until after the final light-driven oxidation event.

A Conserved Second Sphere Residue Tunes Copper Site Reactivity in Lytic Polysaccharide Monooxygenases.

Lytic polysaccharide monooxygenases (LPMOs) are powerful monocopper enzymes that can activate strong C-H bonds through a mechanism that remains largely unknown. Herein, we investigated the role of a conserved glutamine/glutamate in the second coordination sphere. Mutation of the Gln in NcAA9C to Glu, Asp, or Asn showed that the nature and distance of the headgroup to the copper fine-tune LPMO functionality and copper reactivity. The presence of Glu or Asp close to the copper lowered the reduction potential and decreased the ratio between the reduction and reoxidation rates by up to 500-fold. All mutants showed increased enzyme inactivation, likely due to changes in the confinement of radical intermediates, and displayed changes in a protective hole-hopping pathway. Electron paramagnetic resonance (EPR) and X-ray absorption spectroscopic (XAS) studies gave virtually identical results for all NcAA9C variants, showing that the mutations do not directly perturb the Cu(II) ligand field. DFT calculations indicated that the higher experimental reoxidation rate observed for the Glu mutant could be reconciled if this residue is protonated. Further, for the glutamic acid form, we identified a Cu(III)-hydroxide species formed in a single step on the H2O2 splitting path. This is in contrast to the Cu(II)-hydroxide and hydroxyl intermediates, which are predicted for the WT and the unprotonated glutamate variant. These results show that this second sphere residue is a crucial determinant of the catalytic functioning of the copper-binding histidine brace and provide insights that may help in understanding LPMOs and LPMO-inspired synthetic catalysts.

The SHARK integral generation and digestion system.

In this paper, the SHARK integral generation and digestion engine is described. In essence, SHARK is based on a reformulation of the popular McMurchie/Davidson approach to molecular integrals. This reformulation leads to an efficient algorithm that is driven by BLAS level 3 operations. The algorithm is particularly efficient for high angular momentum basis functions (up to L = 7 is available by default, but the algorithm is programmed for arbitrary angular momenta). SHARK features a significant number of specific programming constructs that are designed to greatly simplify the workflow in quantum chemical program development and avoid undesirable code duplication to the largest possible extent. SHARK can handle segmented, generally and partially generally contracted basis sets. It can be used to generate a host of one- and two-electron integrals over various kernels including, two-, three-, and four-index repulsion integrals, integrals over Gauge Including Atomic Orbitals (GIAOs), relativistic integrals and integrals featuring a finite nucleus model. SHARK provides routines to evaluate Fock like matrices, generate integral transformations and related tasks. SHARK is the essential engine inside the ORCA package that drives essentially all tasks that are related to integrals over basis functions in version ORCA 5.0 and higher. Since the core of SHARK is based on low-level basic linear algebra (BLAS) operations, it is expected to not only perform well on present day but also on future hardware provided that the hardware manufacturer provides a properly optimized BLAS library for matrix and vector operations. Representative timings and comparisons to the Libint library used by ORCA are reported for Intel i9 and Apple M1 max processors.

Quantum computing in pharma: A multilayer embedding approach for near future applications.

Quantum computers are special purpose machines that are expected to be particularly useful in simulating strongly correlated chemical systems. The quantum computer excels at treating a moderate number of orbitals within an active space in a fully quantum mechanical manner. We present a quantum phase estimation calculation on F2 in a (2,2) active space on Rigetti's Aspen-11 QPU. While this is a promising start, it also underlines the need for carefully selecting the orbital spaces treated by the quantum computer. In this work, a scheme for selecting such an active space automatically is described and simulated results obtained using both the quantum phase estimation (QPE) and variational quantum eigensolver (VQE) algorithms are presented and combined with a subtractive method to enable accurate description of the environment. The active occupied space is selected from orbitals localized on the chemically relevant fragment of the molecule, while the corresponding virtual space is chosen based on the magnitude of interactions with the occupied space calculated from perturbation theory. This protocol is then applied to two chemical systems of pharmaceutical relevance: the enzyme [Fe] hydrogenase and the photosenzitizer temoporfin. While the sizes of the active spaces currently amenable to a quantum computational treatment are not enough to demonstrate quantum advantage, the procedure outlined here is applicable to any active space size, including those that are outside the reach of classical computation.

Exchange Interactions and Magnetic Properties of a Molecular Mn18 -Ring Complex.

[Mn3 O(OAc)7 (HOAc)]6 ⋅ x AcOH (x=6-9) represents a rare example of a compound containing molecular Mn18 -rings. These are formed by Mn3 (µ3 -O) subunits in which the high-spin Mn(III) centers are bridged by three pairs of acetate anions (AcO- ). An AcOH molecule coordinates to one of the Mn atoms leading to [Mn3 (µ3 -O)(µ2 -OAc)6 (AcOH)]-units, designated in short as Mn3 -units, that are interconnected by acetate anions via the other two Mn atoms to form Mn18 -rings. Magnetic measurements show weak ferromagnetic interactions between them that are suppressed in strong magnetic field. Quantum-chemical calculations on Mn3 model complexes using independently DFT and ab-initio multi reference methods (CASSCF/NEVPT2) show a correlation between the orientation of the pseudo-Jahn-Teller axes of pairs of Mn(III) magnetic centers and corresponding exchange coupling energies. Weak coupling between Mn3 -units within the Mn18 -ring allowed to simulate the magnetic susceptibility versus temperature dependence in terms of basically uncoupled magnetic moments of each Mn3 -unit within the ring.

Theoretical Magnetic Relaxation and Spin-Phonon Coupling Study in a Series of Molecular Engineering Designed Bridged Dysprosocenium Analogues.

A detailed computational study of hypothetical sandwich dysprosium double-decker complexes, bridged by various numbers of aliphatic linkers, was performed to evaluate the effect of the structural modifications on their ground-state magnetic sublevels and assess their potential as candidates for single-molecule magnets (SMMs). The molecular structures of seven complexes were optimized using the TPSSh functional, and the electronic structure and magnetic properties were investigated using the complete active space self-consistent field method (CASSCF). Estimates of the magnetic moment blocking barrier (Ueff) and blocking temperatures (TB) are reported. In addition, a new method based on computed derivatives of effective demagnetization barriers Ueff with respect to vibrational normal modes was introduced and applied to evaluate the impact of spin-phonon coupling on the SMM properties. On the basis of the computed parameters, we have identified promising candidates with properties superior to those of the existing single-molecule magnets.

On the Single-Molecule Magnetic Behavior of Linear Iron(I) Arylsilylamides.

The rational design of 3d-metal-based single-molecule magnets (SMM) requires a fundamental understanding of their intrinsic electronic and structural properties and how they translate into experimentally observable features. Here, we determined the magnetic properties of the linear iron(I) silylamides K{crypt}[FeL2] and [KFeL2] (L = -N(Dipp)SiMe3; crypt = 4,7,13,16,21,24-Hexaoxa-1,10-diazabicyclo[8.8.8]hexacosan). For the former, slow-relaxation of the magnetization with a spin reversal barrier of Ueff = 152 cm-1 as well as a closed-waist magnetic hysteresis and magnetic blocking below 2.5 K are observed. For the more linear [KFeL2], in which the potassium cation is encapsulated by the aryl substituents of the amide ligands, the relaxation barrier and the blocking temperature increase to Ueff = 184 cm-1 and TB = 4.5 K, respectively. The increase is rationalized by a more pronounced axial anisotropy in [KFeL2] determined by dc-SQUID magnetometry. The effective relaxation barrier of [KFeL2] is in agreement with the energy spacing between the ground and first-excited magnetic states, as obtained by field-dependent IR-spectroscopy (178 cm-1), magnetic measurements (208 cm-1), as well as theoretical analysis (212 cm-1). In comparison with the literature, the results show that magnetic coercivity in linear iron(I) silylamides is driven by the degree of linearity in conjunction with steric encumbrance, whereas the ligand symmetry is a marginal factor.