Magnitude of the First and Second Neighbour Magnetic Interactions in the Spin Chain Compound Li2CuO2

State-of-the-art molecular quantum chemical techniques have been applied to the solid-state compound Li2CuO2 in order to derive accurate estimates of the in-chain magnetic interactions. In the present work, the magnitude of the nearest neighbour and next nearest neighbour magnetic coupling constants is investigated from first principles embedded cluster calculations. The convergence of the results is carefully tested for the cluster size. In contrast to the earlier findings, it is predicted that J2 is only ~15% of J1. In particular, it is shown that a large J2 appears when the Li+ ions are not explicitly included in the calculation

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

Remarks on the exact energy functional for fermions: an analysis using the Löwdin partitioning technique

A comparison model based in the Löwdin partitioning technique is used to analyse the differences between the wave function and density functional models. This comparison model provides a tool, the Löwdin function f (E), to understand the structure of both theories and its discrepancies in terms of the subjacent mathematical structure and the necessary conditions of variationality required for the energy functional. It is argued that density functional theory (DFT) can be compared to the wave function theory (WFT) using the expressions of f (E) at E = 0. The WFT provides an explicit form of the exact energy functional for a fermion system from the full configuration interaction approach. The DFT can be seen as a special case of Löwdin function that does not satisfy all variational conditions on ρ(r) and also on the EXC[ρ] term. This analysis shows that ignoring the restrictions imposed by the spin and space symmetry requirements of the solutions when making a variational calculation implies that the correlations expressed by the ρ(r) function will be inconsistent with a γ1(r1; r′1) function derivable from a spin and space symmetry adapted wave function Ψ(r1s1, ¿, rnsn), even for a closed-shell system (i.e. an energy minimum that will exhibit the phenomenon of 'overcorrelation'). The comparison scheme also provides a new insight on the variational requirements in order to achieve a consistent description of the molecular electronic structure of both ground and excited states. Some numerical results are reported

Ab initio study of MF2 (M=Mn, Fe, Co, Ni) rutile-type compounds using the periodic unrestricted Hartree-Fock approach

The ab initio periodic unrestricted Hartree-Fock method has been applied in the investigation of the ground-state structural, electronic, and magnetic properties of the rutile-type compounds MF2 (M=Mn, Fe, Co, and Ni). All electron Gaussian basis sets have been used. The systems turn out to be large band-gap antiferromagnetic insulators; the optimized geometrical parameters are in good agreement with experiment. The calculated most stable electronic state shows an antiferromagnetic order in agreement with that resulting from neutron scattering experiments. The magnetic coupling constants between nearest-neighbor magnetic ions along the [001], [111], and [100] (or [010]) directions have been calculated using several supercells. The resulting ab initio magnetic coupling constants are reasonably satisfactory when compared with available experimental data. The importance of the Jahn-Teller effect in FeF2 and CoF2 is also discussed

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

Highly Adiabatic Time-Optimal Quantum Driving at Low Energy Cost

Time-efficient control schemes for manipulating quantum systems are of great importance in quantum technologies, where environmental forces rapidly degrade the quality of pure states over time. In this Letter, we formulate an approach to time-optimal control that circumvents the boundary-value problem that plagues the quantum brachistochrone equation at the expense of relaxing the form of the control Hamiltonian. In this setting, a coupled system of equations, one for the control Hamiltonian and another one for the duration of the protocol, realizes an ansatz-free approach to quantum control theory. We show how driven systems, in the form of a Landau-Zener type Hamiltonian, can be efficiently maneuvered to speed up a given state transformation in a highly adiabatic manner and with a low energy cost

Quantum Zermelo problem for general energy resource bounds

A solution to the quantum Zermelo problem for control Hamiltonians with general energy resource bounds is provided. Interestingly, the energy resource of the control Hamiltonian and the control time define a pair of conjugate variables that minimize the energy-time uncertainty relation. The resulting control protocol is applied to a single qubit as well as to a two-interacting qubit system represented by a Heisenberg spin dimer. For these low-dimensional systems, it is found that physically realizable control Hamiltonians exist only for certain quantized energy resource

Electronic structure and properties of multifunctional systems: bisdithiazolyl-based materials

[cat] Els materials orgànics moleculars cada vegada tenen més aplicacions en la fabricació de dispositius electrònics per les seves propietats òptiques i de conducció. Quan els elements moleculars són radicals, cal tenir en compte alhora la càrrega i l'espín de l'electró desaparellat. La racionalització de l'estructura i de les propietats d'aquests materials multifuncionals requereix una descripció acurada de la seva estructura electrònica. En aquest treball s'analitza l'aplicabilitat dels models actuals en la modelització de la conducció elèctrica d'aquests materials, emprant tota una família de compostos derivats del bisditiazolil com a sistemes model.[eng] Molecular organic materials are finding increasing application in the manufacture of electronic devices thanks to their optical and conduction properties. When the molecular moieties are radicals, both charge and spin of the unpaired electron should be taken into account. The full rationalization of the structure and properties of these multifunctional materials requires a careful description of their electronic structure. In this paper, the applicability of the current models in the modeling of the electrical conduction of these materials is analyzed, using the family of bisdithiazolyl-based compounds as model systems

Existence of multi-radical and closed-shell semiconducting states in post-graphene organic Dirac materials

Post-graphene organic Dirac (PGOD) materials are ordered two-dimensional networks of triply bonded sp2 carbon nodes spaced by π-conjugated linkers. PGOD materials are natural chemical extensions of graphene that promise to have an enhanced range of properties and applications. Experimentally realised molecules based on two PGOD nodes exhibit a bi-stable closed-shell/multi-radical character that can be understood through competing Lewis resonance forms. Here, following the same rationale, we predict that similar states should be accessible in PGOD materials, which we confirm using accurate density functional theory calculations. Although for graphene the semimetallic state is always dominant, for PGOD materials this state becomes marginally meta-stable relative to open-shell multiradical and/or closed-shell states that are stabilised through symmetry breaking, in line with analogous molecular systems. These latter states are semiconducting, increasing the potential use of PGOD materials as highly tuneable platforms for future organic nanoelectronics and spintronics

How does thickness affect magnetic coupling in Ti-based MXenes

The magnetic nature of Ti2C, Ti3C2, and Ti4C3 MXenes is determined from periodic calculations within density functional theory and using the generalized gradient approximation based PBE functional, the PBE0 and HSE06 hybrids, and the on-site Hubbard corrected PBE+U one, in all cases using a very tight numerical setup. The results show that all functionals consistently predict a magnetic ground state for all MXenes, with spin densities mainly located at the Ti surface atoms. The analysis of solutions corresponding to different spin orderings consistently show that all functionals predict an antiferromagnetic conducting ground state with the two ferromagnetic outer (surface) Ti layers being antiferromagnetically coupled. A physically meaningful spin model is proposed, consistent with the analysis of the chemical bond, with closed shell, diamagnetic, Ti2+ like ions in inner layers and surface paramagnetic Ti+ like centers with one unpaired electron per magnetic center. From a Heisenberg spin model, the relevant isotropic magnetic coupling constants are extracted from an appropriate mapping of total energy differences per formula unit to the expected energy values of the spin Hamiltonian. While the numerical values of the magnetic coupling constants largely depend on the used functional, the nearest neighbor intralayer coupling is found to be always ferromagnetic, and constitutes the dominant interaction, although two other non-negligible interlayer antiferromagnetic terms are involved, implying that the spin description cannot be reduced to NN interaction only. The influence of the MXene thickness is noticeable for the dominant ferromagnetic interaction, increasing its value with the MXene width. However, the interlayer interactions are essentially due to the covalency effects observed in all metallic solutions which, as expected, decay with distance. Within the PBE+U approach, a U value of 5 eV is found to closely simulate the results from hybrid functionals for Ti2C and less accurately for Ti3C2 and Ti4C3