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

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

Multi-component symmetry-projected approach for molecular ground state correlations

The symmetry-projected Hartree--Fock ansatz for the electronic structure problem can efficiently account for static correlation in molecules, yet it is often unable to describe dynamic correlation in a balanced manner. Here, we consider a multi-component, systematically-improvable approach, that accounts for all ground state correlations. Our approach is based on linear combinations of symmetry-projected configurations built out of a set of non-orthogonal, variationally optimized determinants. The resulting wavefunction preserves the symmetries of the original Hamiltonian even though it is written as a superposition of deformed (broken-symmetry) determinants. We show how short expansions of this kind can provide a very accurate description of the electronic structure of simple chemical systems such as the nitrogen and the water molecules, along the entire dissociation profile. In addition, we apply this multi-component symmetry-projected approach to provide an accurate interconversion profile among the peroxo and bis($\mu$-oxo) forms of [Cu$_2$O$_2$]$^{2+}$, comparable to other state-of-the-art quantum chemical methods

Quality Control of the Thermal Properties of Superstructures in Accommodation Spaces in Naval Constructions

The application of passive design strategies in ships, such as the use of superstructures with high thermal insulation, allows the energy demand of heating, ventilation, and air conditioning systems to be reduced. There is a knowledge gap in the scientific literature on the possibilities to thermally characterize superstructures. Knowing such possibilities would make a methodology available for the quality control of naval constructions and for the inspection of the appropriate state of insulations in existing ships. For this purpose, a total of three different typologies of ship superstructures were monitored, and the data obtained were analyzed by using various existing approaches for the thermal characterization of facades: the heat flow meter method and temperature measurement methods. The results showed that the heat flow meter method constitutes a valid methodology to obtain representative results. In addition, guaranteeing a thermal gradient dependent of the wall typology and placing probes in zones not influenced by thermal bridges ensure that representative results are achieved