Influence of molecular geometry on the adsorption orientation for oligophenylene-ethynylenes on Au(111)

The adsorption structures formed from a class of oligophenylene-ethynylenes on Au(111) under ultrahigh vacuum conditions is compared based on high-resolution scanning tunneling microscopy (STM) measurements. The molecules consist of three or four benzene rings connected by ethynylene spokes and are all functionalized identically with an aldehyde, a hydroxyl, and a bulky tert-butyl group. Compounds with the conjugated spokes placed in the para, meta, and threefold configurations were previously found to exclusively form molecular layers with flat-lying adsorption geometries. In contrast, the associated compound with spokes in the ortho configuration surprisingly differs in its adsorption by forming only structures with an upright adsorption orientation. The packing density for the structures formed by the compound with the ortho configuration is less dense than that in conventional self-assembled monolayers while still keeping the conducting backbone in an upright orientation. These structures are thus interesting from the perspective of performing single-molecule conduction measurements on the oligophenylene-ethynylene backbones.     

Self-assembly of monodispersed, chiral nanoclusters of cysteine on the Au(110)-(1 x 2) surface

The self-assembly of monodispersed supramolecular nanoclusters was observed by scanning tunneling microscopy (STM). The clusters form from the naturally occurring amino acid cysteine by vapor deposition onto the Au(110)-(1 x 2) surface under ultrahigh vacuum conditions. Enantiomerically pure l- and d-cysteine yields clusters with mirror-image STM signatures. Racemic ld-cysteine segregates into homochiral clusters, evidencing specific intermolecular interactions during the self-assembly process.     

Locally ideal formulations for piecewise linear functions with indicator variables

In this paper, we consider mixed integer linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context.     

The impact of sampling methods on bias and variance in stochastic linear programs

Stochastic linear programs can be solved approximately by drawing a subset of all possible random scenarios and solving the problem based on this subset, an approach known as sample average approximation (SAA). The value of the objective function at the optimal solution obtained via SAA provides an estimate of the true optimal objective function value. This estimator is known to be optimistically biased; the expected optimal objective function value for the sampled problem is lower (for minimization problems) than the optimal objective function value for the true problem. We investigate how two alternative sampling methods, antithetic variates (AV) and Latin Hypercube (LH) sampling, affect both the bias and variance, and thus the mean squared error (MSE), of this estimator. For a simple example, we analytically express the reductions in bias and variance obtained by these two alternative sampling methods. For eight test problems from the literature, we computationally investigate the impact of these sampling methods on bias and variance. We find that both sampling methods are effective at reducing mean squared error, with Latin Hypercube sampling outperforming antithetic variates. For our analytic example and the eight test problems we derive or estimate the condition number as defined in Shapiro et al. (Math. Program. 94:1–19, 2002). We find that for ill-conditioned problems, bias plays a larger role in MSE, and AV and LH sampling methods are more likely to reduce bias.     

Lift-and-project cuts for convex mixed integer nonlinear programs

We describe a computationally effective method for generating lift-and-project cuts for convex mixed-integer nonlinear programs (MINLPs). The method relies on solving a sequence of cut-generating linear programs and in the limit generates an inequality as strong as the lift-and-project cut that can be obtained from solving a cut-generating nonlinear program. Using this procedure, we are able to approximately optimize over the rank one lift-and-project closure for a variety of convex MINLP instances. The results indicate that lift-and-project cuts have the potential to close a significant portion of the integrality gap for convex MINLPs. In addition, we find that using this procedure within a branch-and-cut solver for convex MINLPs significantly reduces the total solution time for many instances. We also demonstrate that combining lift-and-project cuts with an extended formulation that exploits separability of convex functions yields significant improvements in both relaxation bounds and the time to calculate the relaxation. Overall, these results suggest that with an effective separation routine, like the one proposed here, lift-and-project cuts may be as effective for solving convex MINLPs as they have been for solving mixed-integer linear programs.     

Long jumps in the surface diffusion of large molecules

We have studied the diffusion of the two organic molecules DC and HtBDC on the Cu(110) surface by scanning tunneling microscopy. Surprisingly, we find that long jumps, spanning multiple lattice spacings, play a dominating role in the diffusion of these molecules--the root-mean-square jump lengths are as large as 3.9 and 6.8 lattice spacings, respectively. The presence of long jumps is revealed by a new and simple method of analysis, which is tested by kinetic Monte Carlo simulations.     

Global and local expression of chirality in serine on the Cu{110} surface

Establishing a molecular-level understanding of enantioselectivity and chiral resolution at the organic-inorganic interfaces is a key challenge in the field of heterogeneous catalysis. As a model system, we investigate the adsorption geometry of serine on Cu{110} using a combination of low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. The chirality of enantiopure chemisorbed layers, where serine is in its deprotonated (anionic) state, is expressed at three levels: (i) the molecules form dimers whose orientation with respect to the substrate depends on the molecular chirality, (ii) dimers of L- and D-enantiomers aggregate into superstructures with chiral (-1 ?2; 4 0) lattices, respectively, which are mirror images of each other, and (iii) small islands have elongated shapes with the dominant direction depending on the chirality of the molecules. Dimer and superlattice formation can be explained in terms of intra- and interdimer bonds involving carboxylate, amino, and β-OH groups. The stability of the layers increases with the size of ordered islands. In racemic mixtures, we observe chiral resolution into small ordered enantiopure islands, which appears to be driven by the formation of homochiral dimer subunits and the directionality of interdimer hydrogen bonds. These islands show the same enantiospecific elongated shapes those as in low-coverage enantiopure layers.