Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study

Most {\em ab initio} calculations on fullerene molecules have been carried out based on the paradigm of the H\"uckel model. This is consistent with the restricted nature of the independent-particle model underlying such calculations, even in single-reference-based correlated approaches. On the other hand, previous works on some of these molecules using model Hamiltonians have clearly indicated the importance of short-range inter-atomic spin-spin correlations. In this work, we consider {\em ab initio} non-collinear Hartree--Fock (HF) solutions for representative fullerene systems: the bowl, cage, ring, and pentagon isomers of C$_{20}$, and the larger C$_{30}$, C$_{36}$, C$_{60}$, C$_{70}$, and C$_{84}$ fullerene cages. In all cases but the ring we find that the HF minimum corresponds to a truly non-collinear solution with a torsional spin density wave. Optimized geometries at the generalized HF (GHF) level lead to fully symmetric structures, even in those cases where Jahn-Teller distortions have been previously considered. The nature of the GHF solutions is consistent with the $\pi$-electron space becoming polyradical in nature: each $p$-orbital remains effectively singly occupied. The spin frustration, induced by the pentagon rings in an otherwise anti-ferromagnetic background, is minimized at the HF level by aligning the spins in non-collinear arrangements. The long-range magnetic ordering observed is reminiscent of the character of broken symmetry HF solutions in polyacene systems.Comment: 16 figure

Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model

A multi-reference configuration mixing scheme is used to describe the ground state, characterized by well defined spin and space group symmetry quantum numbers as well as doping fractions $N_{e}/N_{sites}$, of one dimensional Hubbard lattices with nearest-neighbor hopping and periodic boundary conditions. Within this scheme, each ground state is expanded in a given number of nonorthogonal and variationally determined symmetry-projected configurations. The results obtained for the ground state and correlation energies of half-filled and doped lattices with 30, 34 and 50 sites, compare well with the exact Lieb-Wu solutions as well as with the ones obtained with other state-of-the-art approximations. The structure of the intrinsic symmetry-broken determinants resulting from the variational procedure is interpreted in terms of solitons whose translational and breathing motions can be regarded as basic units of quantum fluctuations. It is also shown that in the case of doped 1D lattices, a part of such fluctuations can also be interpreted in terms of polarons. In addition to momentum distributions, both spin-spin and density-density correlation functions are studied as functions of doping. The spectral functions and density of states, computed with an ansatz whose quality can be well-controlled by the number of symmetry-projected configurations used to approximate the $N_{e} \pm 1$ electron systems, display features beyond a simple quasiparticle distribution, as well as spin-charge separation trends.Comment: 16 pages, 11 figure

Relación entre el tipo de percha y el comportamiento de agresividad en el lagarto Norops polylepis (Squamata: Dactyloidae)

A intensidade da agressão contra intrusos por detentores de um território tem sido relacionada ao tipo de recurso disponível para um indivíduo no interior de seu território. A influência das características do poleiro sobre o comportamento de agressão de machos residentes de Norops polylepis na presença de um macho intruso foi investigada neste estudo. Em cada poleiro, foram conduzidos encontros nos quais foi registrado o comportamento agressivo dos machos residentes, além do diâmetro do poleiro e o número de poleiros das proximidades. O comportamento agressivo de machos residentes aumentou em poleiros maiores e em algum grau em áreas com maior densidade de plântulas ao redor. São discutidas explicações potenciais para o alto grau de comportamento de agressão de N. polylepis em poleiros grandes e com elevado número de plântulas ao redor.The intensity of aggression against intruders by owners of a territory has been related to the type of resources available to an individual within its territory. The influence of perch-site characteristics on aggressive behavior of resident male Norops polylepis in presence of an intruder male was investigated in this study. At each perch site, pairwise encounters were conducted in which the aggressive behavior of resident males was recorded, along with the diameter of the perch and the number of nearby perches. Aggressive behavior of resident males increased on larger perches and to some extent in areas having greater density of nearby saplings. Potential explanations for the high aggressive behavior of N. polylepis on broad perches with high number of neighboring saplings are explored.La intensidad de agresión por individuos que son dueños de un territorio hacia los intrusos se ha relacionado con el tipo de recurso disponible en sus territorios. La influencia de las características del sitio de percha con el comportamiento de agresividad de los machos residentes de Norops polylepis en presencia de un macho intruso se investigó en este estudio. En cada sitio de percha se registró el comportamiento agresivo de los residentes, junto con los diámetros de percha y árboles jóvenes alrededor. Se encontró evidencia de que la agresión de los residentes incrementó en perchas con mayor diámetro y áreas con mayor densidad de árboles jóvenes. Explicaciones potenciales por el alto nivel de agresividad de N. polylepis en perchas anchas y con mayor número de árboles jóvenes alrededor fueron exploradas

Small scale fracture behaviour of multilayer TiN/CrN systems: Assessment of bilayer thickness effects by means of ex-situ tests on FIB-milled micro-cantilevers

TiN/CrN multilayered PVD coatings are known to exhibit outstanding micromechanical properties and wear resistance. On the other hand, information on their small scale fracture behaviour is rather scarce. The present work aims to address it by testing to failure FIB-milled microbeams of multilayer TiN/CrN systems with different bilayer periods (8, 19 and 25 nm). In doing so, these micrometric specimens are first FIB notched, and thus deflected by means of a nanoindentation system. It is found that multilayer architecture translates into a beneficial synergic effect regarding critical load for reaching unstable failure; and thus, on energy absorption at fracture. Such behaviour is associated with small scale crack deflection as main toughening mechanism.Peer ReviewedPostprint (author's final draft

Excited electronic states from a variational approach based on symmetry-projected Hartree--Fock configurations

Recent work from our research group has demonstrated that symmetry-projected Hartree--Fock (HF) methods provide a compact representation of molecular ground state wavefunctions based on a superposition of non-orthogonal Slater determinants. The symmetry-projected ansatz can account for static correlations in a computationally efficient way. Here we present a variational extension of this methodology applicable to excited states of the same symmetry as the ground state. Benchmark calculations on the C$_2$ dimer with a modest basis set, which allows comparison with full configuration interaction results, indicate that this extension provides a high quality description of the low-lying spectrum for the entire dissociation profile. We apply the same methodology to obtain the full low-lying vertical excitation spectrum of formaldehyde, in good agreement with available theoretical and experimental data, as well as to a challenging model $C_{2v}$ insertion pathway for BeH$_2$. The variational excited state methodology developed in this work has two remarkable traits: it is fully black-box and will be applicable to fairly large systems thanks to its mean-field computational cost