Spin dynamics in single-molecule magnets and molecular qubits

Over recent decades, much effort has been made to lengthen spin relaxation/decoherence times of single-molecule magnets and molecular qubits by following different chemical design rules as maximizing the total spin value, controlling symmetry, enhancing the ligand field or inhibiting key vibrational modes. Simultaneously, electronic structure calculations have been employed to provide an understanding of the processes involved in the spin dynamics of molecular systems and served to refine or introduce new design rules. This review focuses on contemporary theoretical approaches focused on the calculation of spin relaxation/decoherence times, highlighting their main features and scope. Fundamental aspects of experimental techniques for the determination of key Single Molecule Magnet/Spin Qubit properties are also reviewed

DFT approaches to transport calculations in magnetic single-molecule devices

Electron transport properties of single-molecule devices based on the [Fe(tzpy)(2)(NCS)(2)] complex placed between two gold electrodes have been explored using three different atomistic DFT methods. This kind of single-molecule devices is quite appealing because they can present magnetoresistance effects at room temperature. The three employed computational approaches are: (i) self-consistent non-equilibrium Green functions (NEGF) with periodic models that can be described as the most accurate between the state-of-art methods, and two non-self-consistent NEGF approaches using either periodic or non-periodic description of the electrodes (ii and iii). The analysis of the transmission spectra obtained with the three methods indicates that they provide similar qualitative results. To obtain a reasonable agreement with the experimental data, it is mandatory to employ density functionals beyond the commonly employed GGA (i.e., hybrid functionals) or to include on-site corrections for the Coulomb repulsion (GGA+U method)

Exchange interactions on the highest-spin reported molecule: the mixed-valence Fe-42 complex

The finding of high-spin molecules that could behave as conventional magnets has been one of the main challenges in Molecular Magnetism. Here, the exchange interactions, present in the highest-spin molecule published in the literature, Fe-42, have been analysed using theoretical methods based on Density Functional Theory. The system with a total spin value S = 45 is formed by 42 iron centres containing 18 high-spin Fe-III ferromagnetically coupled and 24 diamagnetic low-spin Fe-II ions. The bridging ligands between the two paramagnetic centres are two cyanide ligands coordinated to the diamagnetic Fe-II cations. Calculations were performed using either small Fe-4 or Fe-3 models or the whole Fe-42 complex, showing the presence of two different ferromagnetic couplings between the paramagnetic Fe-III centres. Finally, Quantum Monte Carlo simulations for the whole system were carried out in order to compare the experimental and simulated magnetic susceptibility curves from the calculated exchange coupling constants with the experimental one. This comparison allows for the evaluation of the accuracy of different exchange-correlation functionals to reproduce such magnetic properties

Large magnetic anisotropy in mononuclear metal complexes

This review examines mononuclear metal complexes with high magnetic anisotropy and the theoretical approaches used to rationalize their magnetic properties. Electronic structure calculations based on CASSCF (or CASPT2/NEVPT2) methods provide a quantitative agreement of the zero- field splitting parameters either for mononuclear transition metal complexes or for equivalent lanthanide systems. To produce a more qualitative tool for predicting the magnetic anisotropy of metal complexes, we have developed a set of simple models. For transition metal systems, a simple model based on the splitting of the d orbitals, considering the coordination mode of the metal and its electronic configuration, is enough to qualitatively predict the system's magnetic anisotropy. A similar approach does not work with the f orbitals of the lanthanide complexes. As an alternative, we studied the electrostatic field generated by the ligands and found that this magnitude controls the shape and the orientation of the anisotropic electron density. This procedure allows us to rationalize and to predict whether the system will have a strong axial character, and also to determine the direction of the magnetic moment

Models to predict the magnetic properties of single- and multiple-bridged phosphate Cu-II systems: a theoretical DFT insight

Copper(II) phosphate bridged compounds have been studied by DFT methods in order to gain a better understanding of the magnetic exchange interactions through 1,1 and 1,3-bridges, which vary with the bonding modes of the ligand. In many cases phosphate is only one among several bridging ligands making it difficult to identify the predominant exchange pathway. This work proposes a graphical analysis, based on the unrestricted corresponding orbitals (UCO), and the derived 'magnetic orbitals' to identify the predominant exchange pathway. Models for the 1,1- and 1,3-bridging modes allow establishing the angle or dihedral dependence of the J values. For the 1,1-bridging mode the theta Cu-O-Cu angle was used. For the 1,3-phosphate the correlation was established with a D-P-O-i-Cu-i dihedral angle (tau) where D is a dummy atom. Using models with different D-P-O-i-Cu-i dihedral angles a predictive scheme was generated. Eleven copper(II) phosphate bridged structures were used to validate the proposed model. The study has shown that antiferromagnetic exchange interactions are primarily produced by phosphate bridges due to the possibility of this ligand that always enables a degree of overlap between the magnetic orbitals

Tuning Single-Molecule Conductance in Metalloporphyrin-Based Wires via Supramolecular Interactions.

Nature has developed amazing supramolecular constructs to deliver outstanding charge transport capabilities using metalloporphyrin-based supramolecular stacks.1 Here we are incorporating simple, naturally inspired supramolecular interactions via the axial complexation of metalloporphyrins into the formation of a single-molecule wire in a nanoscale gap to dissect the resulting electron pathways through the final chemical adduct. We observe that small structural changes in the axial coordinating linkers result in dramatic changes in the transport properties through the metalloporphyrin-based wire. The increased flexibility of a pyridine-4-yl-methanethiol ligand due to an extra methyl group as compared to a more rigid mercaptopyridine linker allows the former to adopt an unexpected highly conductive stacked structure between the two junction electrodes and the metalloporphyrin ring. DFT calculations reveal a molecular junction structure composed of a shifted stack of the three molecular backbones; the two pyridine ligands sandwiching the metalloporphyrin ring, which is stabilized by a combination of the porphyrin metal center coordinating the pyridinic N and the pyridine/porphyrin overlapping. Contrarily, the more rigid 4-mercaptopyridine ligand presents a more expected octahedral coordination of the metalloporphyrin metal center, leading to much lower conductance. Furthermore, we show that a mechanical forced imposed along the molecular wire axis results in a variety of more extended supramolecular structures between the pyridine linkers and the porphyrin ring spanning the tunneling gap and scoring relatively high conductance values. This works sets an example of the use of supramolecular chemistry in the construction of efficient molecular conduits towards the development of supramolecular electronics, a concept already exploited in natural organisms

Transporte Cuántico y Magnetismo en Sistemas Inorgánicos: Un Estudio Computacional

En esta tesis doctoral se presentan estudios computacionales basados en métodos de estructura electrónica de propiedades magnéticas en sistemas inorgánicos moleculares y extendidos. La primera sección incluye un trabajo sobre transporte electrónico a través de uniones moleculares constituidas por complejos de transición, se empleó la metodología de las funciones de Green fuera del equilibrio en combinación con cálculos basados en la teoría del funcional de la densidad (NEGF+DFT). En el artículo se analizaron las propiedades de transporte electrónico polarizado de espín a través de un compuesto con transición de espín de hierro(II). El segundo bloque está compuesto por tres trabajos acerca de la modulación de las propiedades de transición de espín en redes metalo-orgánicas porosas tipo clatrato de Hofmann. Los estudios teóricos fueron realizados mediante cálculos DFT periódicos. Se analizó la red {[FeII(pirazina)][PtII(CN)4]} en presencia de diferentes moléculas pequeñas (disulfuro de carbono, dióxido de azufre, tiourea, tiofeno, pirrol, furano, pirazina y yodo). Las distorsiones geométricas calculadas para la red en presencia de las diferentes moléculas huésped fueron comparadas con las estructuras determinadas mediante difracción de rayos X. Las modificaciones en la temperatura experimental de transición de espín fueron comparadas con los cambios en energía electrónica calculados. La naturaleza de las interacciones huésped-anfitrión fue estudiada a través del cálculo de energías de interacción y análisis de la densidad de estados (curvas COD). El tercer bloque trata sobre propiedades magnéticas en compuestos de coordinación de lantánidos. Los estudios teóricos fueron realizados mediante cálculos CASSCF+RASSI. En el primer trabajo se investigó un grupo de veinte compuestos mononucleares de disprosio(III) que presentan comportamiento de imán unimolecular (SMM), SMM inducido por campo o ausencia de este comportamiento. Las propiedades magnéticas calculadas comparadas con información experimental. El efecto del entorno de coordinación en las propiedades SMM fue estudiado mediante medidas continuas de forma y cálculos CASSCF+RASSI en estructuras modelo, a partir de esta información se sugirieron la condiciones que favorecen el comportamiento SMM. En los otros trabajos de este bloque se investigan las propiedades magnéticas de compuestos polinucleares de lantánidos a través de cálculos CASSCF+RASSI y ajustes de constantes de acoplamiento mediante el modelo de Lines, se discutió acerca del papel de la anisotropía magnética en el comportamiento SMM y de las contribuciones de intercambio y dipolar en la interacción entre centros magnéticos. En la cuarta sección se presentan tres artículos sobre interacciones de intercambio en complejos polinucleares de metales de transición y lantánidos estudiados a través de métodos DFT (aproximación Broken Symmetry), las propiedades magnéticas de los compuestos (curvas de magnetización y susceptibilidad) fueron simuladas a través de la diagonalización del Hamiltoniano de Heisenberg-Dirac-Van Vleck y métodos de Monte Carlo cuántico. El primer artículo trata de las propiedades magnetocalóricas de compuestos polinucleares de gadolinio con metales de transición. El signo y la magnitud de las constantes de acoplamiento calculadas fueron comparados con los valores ajustados a datos experimentales y relacionados con la geometría y coordinación de los caminos de intercambio. El efecto de las interacciones de intercambio respecto a las propiedades magnetocalóricas de los compuestos fue evaluada a través del cálculo de la variación de la entropía magnética. Finalmente, las condiciones que favorecen la aparición de un efecto magnetocalórico pronunciado fueron discutidas. En el segundo y tercer trabajo se comparan las propiedades magnéticas experimentales y calculadas de un complejo de cobre y otro de hierro. Las constantes de acoplamiento fueron analizadas en función la geometría y tipo de grupos puente a través de correlaciones magnetoestructurales conocidas.This thesis presents theoretical studies based on electronic structure methods about magnetic properties of molecular and extended inorganic systems. First section presents an article about electronic transport in molecular junctions based on coordination compounds. Calculations were performed employing the Non-Equilibrium Green’s Functions in conjunction with DFT method. The study discusses the magnetotransport properties of an iron(II) spin-crossover complex. Second block deals with tunability of spin crossover properties in a porous metalorganic framework by small molecule absorption. The systems were modeled employing DFT calculations. Eight different guest moleclules were considered (CS2, I2, furan, thiourea, SO2, pyrazine, thiophene and pyrrole). Changes in experimental spin transition temperature were related with differences in electronic energy between spin states. Specific host-guest interactions were studied by interaction energy calculations and Crystal Orbital Displacent curves. Third section focus on magnetic properties of lanthanide complexes calculated by the CASSCF+RASSI method. The first article analyzes the single molecule magnet (SMM) properties of 20 mononuclear disprosium(III) complexes. The calculated magnetic parameters were compared with published AC susceptibility measurements. The effect of the coordination environment on SMM properties was further studied by model systems. Favorable environments for enhancing SMM behavior are suggested. The other three articles of this section deal with magnetic properties of polynuclear lanthanide complexes. The role of anisotropy on SMM properties and the nature of interactions between magnetic centers (exchange and dipolar) are discussed. The last block is about exchange interactions in polynuclear complexes. Coupling constants were calculated by means of DFT calculations (Broken Symmetry approximation). Simulated susceptibility and magnetization curves were obtained by exact diagonalization of the spin Hamiltonian and quantum Monte Carlo methods. The first work of this section is about the influence of exchange on magnetocaloric properties of gadolinium compounds. The magnitude of magnetocaloric effect was evaluated by the calculation of the magnetic entropy change. Favorable conditions for enhancing magnetocaloric response are discussed. Las two articles focus on magnetic exchange in polynuclear transition metal compounds. Calculated coupling constants were analyzed in terms of geometry through established magnetostructural correlations

Exchange interactions on the highest-spin reported molecule: the mixed-valence Fe-42 complex

The finding of high-spin molecules that could behave as conventional magnets has been one of the main challenges in Molecular Magnetism. Here, the exchange interactions, present in the highest-spin molecule published in the literature, Fe-42, have been analysed using theoretical methods based on Density Functional Theory. The system with a total spin value S = 45 is formed by 42 iron centres containing 18 high-spin Fe-III ferromagnetically coupled and 24 diamagnetic low-spin Fe-II ions. The bridging ligands between the two paramagnetic centres are two cyanide ligands coordinated to the diamagnetic Fe-II cations. Calculations were performed using either small Fe-4 or Fe-3 models or the whole Fe-42 complex, showing the presence of two different ferromagnetic couplings between the paramagnetic Fe-III centres. Finally, Quantum Monte Carlo simulations for the whole system were carried out in order to compare the experimental and simulated magnetic susceptibility curves from the calculated exchange coupling constants with the experimental one. This comparison allows for the evaluation of the accuracy of different exchange-correlation functionals to reproduce such magnetic properties

Increasing the effective energy barrier promoted by the change of a counteranion in a Zn-Dy-Zn SMM: slow relaxation via the second excited state

The trinuclear complex [ZnCl(l-L)Dy(l-L)ClZn]PF6 exhibits a single- molecule magnetic behaviour under zero field with a relatively large effective energy barrier of 186 cm1. Ab initio calculations reveal that the relaxation of the magnetization is symmetry-driven (the DyIII ion possesses a C2 symmetry) and occurs via the second excited state

Lanthanide Tetrazolate complexes combining single-molecule magnet and luminescence properties: the effect of the replacement of Tetrazolate N3 by β-Diketonate ligands on the anisotropy energy barrier

Three new sets of mononuclear Ln(III) complexes of general formulas [LnL(3)]CH3OH [Ln(III)=Yb (1), Er (2), Dy (3), Gd (4), and Eu (5)], [LnL(2)(tmh)(CH3OH)]nH(2)OmCH(3)OH [Ln(III)=Yb (1b), Er (2b), Dy (3b), Gd (4b)], and [LnL(2)(tta)(CH3OH)]CH3OH [Ln(III)=Yb (1c), Er (2c), Dy (3c), Gd (4c)] were prepared by the reaction of Ln(CF3SO3)nH(2)O salts with the tridentate ligand 2-(tetrazol-5-yl)-1,10-phenanthroline (HL) and, for the last two sets, additionally with the -diketonate ligands 2,2,6,6-tetramethylheptanoate (tmh) and 2-thenoyltrifluoroacetonate (tta), respectively. In the [LnL(3)]CH3OH complexes the Ln(III) ions are coordinated to three phenanthroline tetrazolate ligands with an LnN(9) coordination sphere. Dynamic ac magnetic measurements on 1-3 reveal that these complexes only exhibit single-molecule magnet (SMM) behavior when an external dc magnetic field is applied, with U-eff values of 11.7K (1), 16.0K (2), and 20.2K (3). When the tridentate phenanthroline tetrazolate ligand is replaced by one molecule of methanol and the -diketonate ligand tmh (1b-3b) or tta (1c-3c), a significant increase in U-eff occurs and, in the case of the Dy-III complexes 3b and 3c, out-of-phase signals below 15 and 10K, respectively, are observed in zero dc magnetic field. CASSCF+RASSI ab initio calculations performed on the Dy-III complexes support the experimental results. Thus, for 3 the ground Kramers' doublet is far from being axial and the first excited state is found to be very close in energy to the ground state, so the relaxation barrier in this case is almost negligible. Conversely, for 3b and 3c, the ground Kramers' doublet is axial with a small quantum tunneling of the magnetization, and the energy difference between the ground and first Kramers' doublets is much higher, which allows these compounds to behave as SMMs at zero field. Moreover, these calculations support the larger U-eff observed for 3b compared to 3c. Additionally, the solid-state photophysical properties of 1, 2, 4, and 5 show that the phenanthroline tetrazolate ligand can act as an effective antenna to sensitize the characteristic Yb-III, Er-III, and Eu-III emissions through an energy-transfer process