Can model Hamiltonians describe the electron–electron interaction in π-conjugated systems?: PAH and graphene

Model Hamiltonians have been, and still are, a valuable tool for investigating the electronic structure of systems for which mean field theories work poorly. This review will concentrate on the application of Pariser–Parr–Pople (PPP) and Hubbard Hamiltonians to investigate some relevant properties of polycyclic aromatic hydrocarbons (PAH) and graphene. When presenting these two Hamiltonians we will resort to second quantisation which, although not the way chosen in its original proposal of the former, is much clearer. We will not attempt to be comprehensive, but rather our objective will be to try to provide the reader with information on what kinds of problems they will encounter and what tools they will need to solve them. One of the key issues concerning model Hamiltonians that will be treated in detail is the choice of model parameters. Although model Hamiltonians reduce the complexity of the original Hamiltonian, they cannot be solved in most cases exactly. So, we shall first consider the Hartree–Fock approximation, still the only tool for handling large systems, besides density functional theory (DFT) approaches. We proceed by discussing to what extent one may exactly solve model Hamiltonians and the Lanczos approach. We shall describe the configuration interaction (CI) method, a common technology in quantum chemistry but one rarely used to solve model Hamiltonians. In particular, we propose a variant of the Lanczos method, inspired by CI, that has the novelty of using as the seed of the Lanczos process a mean field (Hartree–Fock) determinant (the method will be named LCI). Two questions of interest related to model Hamiltonians will be discussed: (i) when including long-range interactions, how crucial is including in the Hamiltonian the electronic charge that compensates ion charges? (ii) Is it possible to reduce a Hamiltonian incorporating Coulomb interactions (PPP) to an 'effective' Hamiltonian including only on-site interactions (Hubbard)? The performance of CI will be checked on small molecules. The electronic structure of azulene and fused azulene will be used to illustrate several aspects of the method. As regards graphene, several questions will be considered: (i) paramagnetic versus antiferromagnetic solutions, (ii) forbidden gap versus dot size, (iii) graphene nano-ribbons, and (iv) optical properties.

Electrochemical analysis of the performance of carbon supported Pd nanoparticles for direct formic acid fuel cells: from gold supported electrodes to catalyst-coated membranes

In this work carbon supported Pd nanoparticles were prepared and used as electrocatalysts for formic acid electrooxidation fuel cells. The influence of some relevant parameters such as the nominal Pt loading, the Nafion/total solids ratio as well as the Pd loading towards formic acid electrooxidation was evaluated using gold supported catalytic layer electrodes which were prepared using a similar methodology to that employed in the preparation of conventional catalyst coated membranes (CCM). The results obtained show that, for constant Pd loading, the nominal Pd loading and the Nafion percentage on the catalytic layer do not play an important role on the resulting electrocatalytic properties. The main parameter affecting the electrocatalytic activity of the electrodes seems to be the Pd loading, although the resulting activity is not directly proportional to the increased Pd loading. Thus, whereas the Pd loading is multiplied by a factor of 10, the activity is only twice which evidences an important decrease in the Pd utilization. In fact, the results obtained suggest the active layer is the outer one being clearly independent of the catalytic layer thickness. Finally, catalyst coated membranes with Pd catalyst loadings of 0.1, 0.5 and 1.2 mg cm-2 were also tested in a breathing direct formic acid fuel cell.