Design of oxygen reduction bimetallic catalysts: ab-initio-derived thermodynamic guidelines

The Gibbs free energies of key elementary steps for the electrocatalytic oxygen reduction reaction (ORR) are calculated with B3LYP type of density functional theory: O2 + M + H+ + e- (0 eV) --> HOO-M (deltaG1), HOO-M + M --> HO-M + O-M (deltaG2), O2 + 2M + H+ + e- (0 eV) --> O-M + HO-M (deltaG3), and HO-M + O-M + 3H+ + 3e- (0 eV) --> 2H2O + 2M (deltaG4), where H+ is modeled as H3(+)O(H2O)3 and M stands for the adsorption site of a metal catalyst modeled by a single metal atom as well as by an M3 cluster. Taking Pt as a reference, deltaG4 is plotted against deltaG1 for 17 metals from groups V to XII. It is found that no single metal has both deltaG1 and deltaG4 more negative than Pt, although some of them have either more negative deltaG1 or more negative deltaG4. This enables us to explain thermodynamically why no other single metal catalyzes the ORR as effectively as Pt does. Moreover, a thermodynamic analysis reveals that the signs of delta deltaG (the difference between deltaG of other metals and deltaG of Pt) strongly correlate with the valence electronic structure of metals, i.e., delta deltaG1 < 0 and delta deltaG4 > 0 for metals M with vacant valence d orbitals, whereas delta deltaG1 > 0 and delta deltaG4 < 0 for metals M' with fully occupied valence d orbitals. Thus, a simple thermodynamic rule for the design of bimetallic catalysts for the ORR is proposed: couple a metal M (delta deltaG1 < 0) with a second metal M' (delta deltaG4 < 0) to form an alloy catalyst MM'3. The rationale behind this selection is based on M being more efficient for the rate-determining step, i.e., for the formation of the adsorbed species M-OOH, while M' can enhance the reductions of O and OH in the last three electron-transfer steps.     

On the girth of extremal graphs without shortest cycles

Let EX(ν;{C₃,…,C_n}) denote the set of graphs G of order ν that contain no cycles of length less than or equal to n which have maximum number of edges. In this paper we consider a problem posed by several authors: does G contain an n+1 cycle? We prove that the diameter of G is at most n−1, and present several results concerning the above question: the girth of G is g=n+1 if (i) ν≥n+5, diameter equal to n−1 and minimum degree at least 3; (ii) ν≥12, ν∉{15,80,170} and n=6. Moreover, if ν=15 we find an extremal graph of girth 8 obtained from a 3-regular complete bipartite graph subdividing its edges. (iii) We prove that if ν≥2n−3 and n≥7 the girth is at most 2n−5. We also show that the answer to the question is negative for ν≤n+1+⌊(n−2)/2⌋.     

Molecular dynamics simulations of surface oxide-water interactions on Pt(111) and Pt/PtCo/Pt3Co(111)

Classical molecular dynamics simulations of the interactions of water with oxidized Pt(111) and Pt/PtCo/Pt(3)Co(111) surfaces are performed by modeling water with the CF1 central force model that allows molecular dissociation and therefore the presence of other intermediates of the oxygen reduction reaction different from atomic oxygen. It is found that the water-surface oxide interactions do not affect the overall structure of the catalyst represented by an extended periodic slab. However, such interactions are affected by changes in the electrochemical potential which are simulated by higher values of the surface and atomic oxygen charges at increased oxygen coverage. Thus, electrochemical potential as well as the presence of protons and anions products of acid dissociation define the identity and the amount of oxygen reduction reaction intermediates such as OH or H(3)O. We observe agglomerations of water molecules over regions of the surface and the presence of OH and H(3)O in their vicinity. Our simulation model is able to qualitatively reproduce features of the degradation of the catalyst surface after oxidation and reduction cycles.     

Structural and reactivity properties of finite length cap-ended single-wall carbon nanotubes

The reaction of C2 with growing single-wall carbon nanotubes of different chiralities is investigated using density functional theory. It is found that the energy of the frontier orbitals for (5,5) and (6,6) armchair carbon nanotubes exhibits periodic behavior with an increasing number of carbon atoms in the nanotube. Such periodic behavior induces oscillations in the reaction energy released by adsorption of C2 to the nanotube open edge. In contrast, the energy of the frontier orbitals of the (6,5) chiral tube remains constant as the number of C atoms increases, and the same stability is observed in the adsorption energy. It is suggested that this may be one of the reasons for the low percent of armchair single-wall carbon nanotubes found in the experimental synthesis.     

Adjacency matrices of polarity graphs and of other C 4-free graphs of large size

In this paper we give a method for obtaining the adjacency matrix of a simple polarity graph G _q from a projective plane PG(2, q), where q is a prime power. Denote by ex(n; C ₄) the maximum number of edges of a graph on n vertices and free of squares C ₄. We use the constructed graphs G _q to obtain lower bounds on the extremal function ex(n; C ₄), for some n < q ² + q + 1. In particular, we construct a C ₄-free graph on ${n=q^2 -\sqrt{q}}$ vertices and ${\frac{1}{2} q(q^2-1)-\frac{1}{2}\sqrt{q} (q-1) }$ edges, for a square prime power q.     

On Superconnectivity of (4, g)-Cages

A (k, g)-cage is a graph that has the least number of vertices among all k-regular graphs with girth g. It has been conjectured (Fu et?al. in J. Graph Theory, 24:187?C191, 1997) that all (k, g)-cages are k-connected for every k??? 3. A k-connected graph G is called superconnected if every k-cutset S is the neighborhood of some vertex. Moreover, if G?S has precisely two components, then G is called tightly superconnected. In this paper, we prove that every (4, g)-cage is tightly superconnected when g ???11 is odd.     

Addition reactions of alkyl and carboxyl radicals to vinylidene fluoride

The addition reactions of alkyl radicals CF3* and CH3* and carboxyl radicals C2H5O*, C2H5OCOO*, CF3COO*, and CH3COO* to a vinylidene fluoride (VDF) molecule are studied using ab initio calculations. These radicals were selected because they are intermediate or final products of diacyl peroxides decomposition in the initiation reactions of VDF polymerization. Two combinations of methods for energetics and structure optimization are applied: QCISD/6-311G(d,p)//HF/6-31G(d) and B3LYP/6-311G+(3df, 2p)//B3LYP/6-31G(d). It is found that the formed bond length of the product, the forming bond length of the transition state, and the attack angle of the product structures are not sensitive to the level of theory even though the attack angle of the transition state structures is. Early transition states are obtained upon attack at both high-substituted and nonsubstituted carbon atom VDF ends. Kinetic and thermodynamic control rules play different roles on governing the reactivity of the addition with the studied radicals. Both theoretical methods yield the same trends for the preferential attack site in terms of regioselectivity, barrier energies, and reaction enthalpies. It is shown that the addition reactions of the intermediate radicals C2H5OCOO*, CF3COO*, and CH3COO* of the decomposition of diethyl peroxydicarbonate, trifluoroacetyl peroxide, and diacetyl peroxide initiators yield smaller energy barriers than the additions of the corresponding final radicals, C2H5O*, CF3*, and CH3*; therefore, the reactions of the intermediate radicals should not be ignored when analyzing the initiation process of the VDF polymerization using those initiators.     

Vibrational spectra of anhydrous and monohydrated caffeine and theophylline molecules and crystals

Density functional theory and classical molecular dynamics simulations are used to investigate the vibrational spectra of caffeine and theophylline anhydrous and monohydrate molecules and those of their crystalline anhydrous and monohydrated states, with emphasis in the terahertz region of the spectra. To better understand the influence of water in the monohydrate crystal spectra, we analyze the vibrational spectra of water monomer, dimer, tetramer, and pentamer, and also those of liquid water at two different temperatures. In small water clusters, we observe the progressive addition of translational and librational modes to the terahertz region of the spectra. The water spectra predicted by rigid and flexible water models is examined with classical molecular dynamics, and the respective peaks, especially in the terahertz region, are compared with those found in the small clusters. Similar analysis done for caffeine and theophylline monohydrate molecules using density functional theory clearly shows the presence of water modes in the librational states and in the water stretching region. Molecular dynamics of caffeine and theophylline anhydrous and monohydrate crystals reveal the influence of vibrations from the molecule-molecule (caffeine or theophylline) crystal stacks and those from the water-molecule interactions found in the monohydrate molecules and new modes from molecule-molecule, water-molecule, and water-water hydrogen bonding interactions arising from collective effects in the crystal structure. Findings illustrate challenges of terahertz technology for the detection of specific substances in condensed phases.