Magnetic coupling constants in three electrons three centres problems from effective Hamiltonian theory and validation of broken symmetry based approaches

In the most general case of three electrons in three symmetry unrelated centres with localized magnetic moments, the low energy spectrum consists of one quartet ( ) and two doublet ( , ) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants , and . However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin adapted states, since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated (JCTC 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a -conjugated purely organic triradica

Post-B3LYP Functionals Do Not Improve the Description of Magnetic Coupling in Cu(II) Dinuclear Complexes

The accuracy of post-B3LYP functionals is analyzed using an open-shell database of Cu(II) dinuclear complexes with well-defined experimental values of the magnetic coupling constants. This database provides a sound open-shell training set to be used to improve the fitting schemes in defining new functionals or when reparametrizing the existing ones. For a large set of representative hybrid exchange-correlation functionals, it is shown that the overall description of moderate-to-strong antiferromagnetic interactions is significantly more accurate than the description of ferromagnetic or weakly antiferromagnetic interactions. In the case of global hybrids, the most reliable ones have 25-40% Fock exchange with SOGGA and PBEO being the most reliable and M06 the exception. For range-corrected hybrids, the long-range corrected CAM-B3LYP and omega B97XD provide acceptable results, and M11 is comparable but more erratic. It is concluded that the reliability of the calculated values is system and range-dependent, and this fact introduces a serious warning on the blind use of a single functional to predict magnetic coupling constants. Hence, to extract acceptable magnetostructural correlations, a 'standardization' of the method to be used is advised to choose the optimal functional

Understanding and predicting magnetic coupling in complex systems: from inorganic complexes to organic polyradicals

[spa] Esta tesis presenta un estudio teórico y computacional sobre la predicción precisa de constantes de acoplamiento magnético en una serie de sistemas complejos. Estos incluyen dos familias de compuestos principales. La primera familia está formada por complejos de coordinación inorgánicos, los cuales presentan centros magnéticos localizados sobre los átomos metálicos y estructuras cristalinas bien definidas. El segundo grupo se trata de radicales puramente orgánicos, con conjugación del sistema π, los cuales presentan una flexibilidad estructural mucho mayor y una deslocalización de los electrones desapareados más extensa. La tesis tiene dos partes principales. La primera se dedica a establecer una estrategia para la extracción de constantes de acoplamiento magnético, lo cual se lleva a cabo en una serie de complejos de coordinación heterodinucleares y homotrinucleares. La estrategia se basa la propuesta de una formulación alternativa del mapping approach, que evita el uso de un proyector de espín y con ello las deficiencias derivadas de ello, en comparación con la formulación inicial propuesta por Noodleman. Esta propuesta es aplicada al problema de tres-electrones tres-centros, y validada por comparación con el experimento y a través de le teoría del Hamiltoniano efectivo. La segunda parte de la tesis se centra en compuestos radicalarios puramente orgánicos π—conjugados, que presentan interacción entre los electrones desapareados a través de enlace. Con el objetivo de promover la estabilidad química de los centros radicalarios, diferentes unidades básicas son consideradas. En base a diferentes esquemas de acoplamiento de estas unidades, y del papel de la flexibilidad estructural, el principal objetivo es establecer los principales factores electrónicos y estructurales para aumentar la estabilidad del radical y promover una interacción ferromagnética robusta entre ellos. Las principales conclusiones de la tesis son dos: primero, la propuesta para extraer constantes de acoplamiento en sistemas complejos resulta en valores consistentes; segundo, esta tesis propone utilizar poliradicales lineales π-conjugados, basados en unidades moleculares derivados de poliarylmethyl radicales, para lograr propiedades ferromagnéticas robustas en sistemas puramente orgánicos estables.[eng] This thesis presents a theoretical and computational approach to the accurate description of magnetic exchange interactions in a variety of complex systems. These include two main families of compounds. The first family is formed by inorganic coordination complexes, presenting localized magnetic centres and well-defined crystal structures. The second family consists of purely organic, π−conjugated odd alternant neutral polyradicals, which display a much larger structural flexibility and greater delocalization of the unpaired electrons over the π system. The thesis has two main parts. The first one refers to the adopted strategy for the accurate extraction of magnetic exchange interactions. The systems used to investigate this issue are coordination compounds of increasing complexity, including heterobinuclear and homotrinuclear complexes, for which experimental crystal structures and magnetic data are available. The adopted strategy is based on the mapping approach, which relies on a one to one correspondence between the non-relativistic, time-independent exact Hamiltonian and two model spin Hamiltonians, the so-called HDVV and Ising. Ultimately, the mapping approach consists on describing both the energy and the wave function of the pure spin states by means of broken symmetry functions, using a spin projector to establish a univocal relation. In this thesis, a detailed analysis of the mapping approach has enabled establishing an alternative and accurate manner for extracting magnetic interactions in complex systems. By pointing out two main deficiencies that make the standard mapping approach proposed by Noodleman not appropriate to certain systems, and following previous work in our group, we propose an alternative approach. This is based on a direct use of the energy of the broken symmetry solutions which are mapped into the energy expectation values of the corresponding broken symmetry solutions of the HDVV Hamiltonian. This strategy relies on the one-to-one correspondence of the diagonal terms of the HDVV and Ising matrix representations. This proposal has been applied to the three-centre three-electron problem, and is further verified by comparison of the calculated coupling constants with the available experimental data and by means of effective Hamiltonian theory. The exchange coupling constant values obtained with this approach are consistent. Additionally, effective Hamiltonian theory offers the possibility to check whether the system can be described as a Heisenberg system. The second part of the thesis deals with purely organic π−conjugated neutral radicals interacting through-bond, and applies the strategy developed for inorganic molecules to extract the magnetic coupling constants between the unpaired electrons in these compounds. On the basis of chemical stability, different building blocks are investigated. Then, by considering different coupling schemes (strategies to assemble them leading to different dimensionalities) and the role of structural flexibility, the main goal of the investigation is to establish the main electronic and structural factors to enhance the stability of the radical centres and promote a robust ferromagnetic interaction among them. Thus, Chapter 1 compares explicitly through-space and through-bond interacting organic radicals, providing experimental arguments for the choice of the latter as building blocks. Chapter 2 introduces the theoretical foundations on which all computational methodologies used in this thesis are based. Chapter 3 provides an analysis of electronic structure methods to establish an accurate scheme to compute magnetic coupling constants in complex systems with well-defined structural parameters. Based on different studies on organic polyradicals, Chapter 4 offers reliable arguments to design purely π−conjugated organic polyradical interacting through-bond, with large S value, high-spin ground state, robust ferromagnetic properties, strong magnetic anisotropy and chemical stability. The appearance of a secondary structure in these flexible molecules is found to be crucial for stabilizing the polyradical high-spin ground state. Altogether, the main conclusions of this thesis are that the proposed strategy for the extraction of magnetic exchange interactions provides consistent results and the proposal for using linear π-conjugated polyradicals, based on molecular units derived from triarylmethyl radicals, to achieve robust ferromagnetic properties in stable purely organic systems

Magnetic coupling constants in three electrons three centres problems from effective Hamiltonian theory and validation of broken symmetry based approaches

In the most general case of three electrons in three symmetry unrelated centres with localized magnetic moments, the low energy spectrum consists of one quartet ( ) and two doublet ( , ) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants , and . However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin adapted states, since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated (JCTC 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a -conjugated purely organic triradica

The triplet-singlet gap in the m -Xylylene radical:A not so simple One

Meta-benzoquinodimethane (MBQDM) or m-xylylene provides a model for larger organic diradicals, the triplet-singlet gap being the key property. In the present work this energy difference has been the object of a systematic study by means of several density functional theory-based methods including B3LYP, M06, M06-2X, HSE and LC-omega PBE potentials and a variety of wave function-based methods such as complete active space self consistent field (CASSCF), Multireference second-order Moller-Plesset (MRMP), difference dedicated configuration interaction (DDCI), and Multireference configuration interaction (MRCI). In each case various basis sets of increasing quality have been explored, and the effect of the molecular geometry is also analyzed. The use of the triplet and broken symmetry (BS) solutions for the corresponding optimized geometries obtained from B3LYP and especially M06-2X functionals provide the value of the adiabatic triplet-singlet gap closer to experiment when compared to the reported value of Wenthold, Kim, and Lineberger, (J. Am. Chem. Soc. 1997, 119, 1354) and also for the electron affinity. The agreement further improves using the full pi-valence CASSCF(8,8) optimized geometry as an attempt to correct for the spin contamination effects on the geometry of the BS state. The CASSCF, MRMP, and MRCI, even with the full pi valence CAS(8,8) as reference and relatively large basis set, systematically overestimate the experimental value indicating either that an accurate description must go beyond this level of theory, including a electrons and higher order polarization functions, or perhaps that the measured value is affected by the experimental conditions