Extended formulations in mixed integer conic quadratic programming

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma et al. (INFORMS J Comput 20: 438–450, 2008) and Hijazi et al. (Comput Optim Appl 52: 537–558, 2012) to construct algorithms for MICQP that can provide a significant computational advantage. The first approach is based on an extended or lifted polyhedral relaxation of the Lorentz cone by Ben-Tal and Nemirovski (Math Oper Res 26(2): 193–205 2001) that is extremely economical, but whose approximation quality cannot be iteratively improved. The second is based on a lifted polyhedral relaxation of the euclidean ball that can be constructed using techniques introduced by Tawarmalani and Sahinidis (Math Programm 103(2): 225–249, 2005). This relaxation is less economical, but its approximation quality can be iteratively improved. Unfortunately, while the approach of Vielma, Ahmed and Nemhauser is applicable for general MICQP problems, the approach of Hijazi, Bonami and Ouorou can only be used for MICQP problems with convex quadratic constraints. In this paper we show how a homogenization procedure can be combined with the technique by Tawarmalani and Sahinidis to adapt the extended formulation used by Hijazi, Bonami and Ouorou to a class of conic mixed integer programming problems that include general MICQP problems. We then compare the effectiveness of this new extended formulation against traditional and extended formulation-based algorithms for MICQP. We find that this new formulation can be used to improve various LP-based algorithms. In particular, the formulation provides an easy-to-implement procedure that, in our benchmarks, significantly improved the performance of commercial MICQP solvers.     

Quantum entanglement between electronic and vibrational degrees of freedom in molecules

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.     

Compound prioritization methods increase rates of chemical probe discovery in model organisms

Preselection of compounds that are more likely to induce a phenotype can increase the efficiency and reduce the costs for model organism screening. To identify such molecules, we screened ~81,000 compounds in Saccharomyces cerevisiae and identified ~7500 that inhibit cell growth. Screening these growth-inhibitory molecules across a diverse panel of model organisms resulted in an increased phenotypic hit-rate. These data were used to build a model to predict compounds that inhibit yeast growth. Empirical and in silico application of the model enriched the discovery of bioactive compounds in diverse model organisms. To demonstrate the potential of these molecules as lead chemical probes, we used chemogenomic profiling in yeast and identified specific inhibitors of lanosterol synthase and of stearoyl-CoA 9-desaturase. As community resources, the ~7500 growth-inhibitory molecules have been made commercially available and the computational model and filter used are provided.     

Tunability of the M(II)M(III)/M(II)(2) and M(III)(2)/M(II)M(III) (M=Mn, Co) couples in bis-μ-O,O'-carboxylato-μ-OR bridged complexes

A comparison of the electrochemical properties of a series of dinuclear complexes [M(2)(L)(RCO(2))(2)](+) with M = Mn or Co, L = 2,6-bis(N,N-bis-(2-pyridylmethyl)-sulfonamido)-4-methylphenolato (bpsmp(-)) or 2,6-bis(N,N-bis(2-pyridylmethyl)aminomethyl)-4-tert-butylphenolato (bpbp(-)) and R = H, CH(3), CF(3) or 3,4-dimethoxybenzoate demonstrates: (i) The electron-withdrawing sulfonyl groups in the backbone of bpsmp(-) stabilize the [M(2)(bpsmp)(RCO(2))(2)](+) complexes in their M(II)(2) oxidation state compared to their [M(2)(bpbp)(RCO(2))(2)](+) analogues. Manganese complexes are stabilised by approximately 550 mV and cobalt complexes by 650 mV. (ii) The auxiliary bridging carboxylato ligands further attenuate the metal-based redox chemistry. Substitution of two acetato for two trifluoroacetato ligands shifts redox couples by 300-400 mV. Within the working potential window, reversible or quasi-reversible M(II)M(III)? M(II)(2) processes range from 0.31 to 1.41 V for the [Co(2)(L)(RCO(2))(2)](+/2+) complexes and from 0.54 to 1.41 V for the [Mn(2)(L)(RCO(2))(2)](+/2+) complexes versus Ag/AgCl for E(M(II)M(III)/M(II)(2)). The extreme limits are defined by the complexes [M(2)(bpbp)(CH(3)CO(2))(2)](+) and [M(2)(bpsmp)(CF(3)CO(2))(2)](+) for both metal ions. Thus, tuning the ligand field in these dinuclear complexes makes possible a range of around 0.9 V and 1.49 V for the one-electron E(M(II)M(III)/M(II)(2)) couple of the Mn and Co complexes, respectively. The second one-electron process, M(II)M(III)? M(III)(2) was also observed in some cases. The lowest potential recorded for the E°(M(III)(2)/M(II)M(III)) couple was 0.63 V for [Co(2)(bpbp)(CH(3)CO(2))(2)](2+) and the highest measurable potential was 2.23 V versus Ag/AgCl for [Co(2)(bpsmp)(CF(3)CO(2))(2)](2+).     

Reversible and selective O2 chemisorption in a porous metal-organic host material

The metal-organic host material [{Co(III)(2)(bpbp)(O(2))}(2)bdc](PF(6))(4) (1·2O(2); bpbp(-) = 2,6-bis(N,N-bis(2-pyridylmethyl)aminomethyl)-4-tert-butylphenolato; bdc(2-) = 1,4-benzenedicarboxylato) displays reversible chemisorptive desorption and resorption of dioxygen through conversion to the deoxygenated Co(II) form [{Co(II)(2)(bpbp)}(2)bdc](PF(6))(4) (1). Single crystal X-ray diffraction analysis indicates that the host lattice 1·2O(2), achieved through desorption of included water guests from the as-synthesized phase 1·2O(2)·3H(2)O, consists of an ionic lattice containing discrete tetranuclear complexes, between which lie void regions that allow the migration of dioxygen and other guests. Powder X-ray diffraction analyses indicate that the host material retains crystallinity through the dioxygen desorption/chemisorption processes. Dioxygen chemisorption measurements on 1 show near-stoichiometric uptake of dioxygen at 5 mbar and 25 °C, and this capacity is largely retained at temperatures above 100 °C. Gas adsorption isotherms of major atmospheric gases on both 1 and 1·2O(2) indicate the potential suitability of this material for air separation, with a O(2)/N(2) selectivity factor of 38 at 1 atm. Comparison of oxygen binding in solution and in the solid state indicates a dramatic increase in binding affinity to the complex when it is incorporated in a porous solid.     

Facile charge-displacement at silicon gives spaced-out reaction

Adsorbates on metals, but not previously on semiconductors, have been observed to display long-range repulsive interactions. On metals, due to efficient dissipation, the repulsions are weak, typically on the order of 5 meV at 10 ?. On the 7×7 reconstruction of the Si(111) surface, charge transport through the surface has been demonstrated by others using charge injection by STM tips. Here we show that for both physisorbed brominated molecules, and for chemisorbed Br-atoms, induced charge-transfer in the Si(111)-7×7 surface can lead to a strong repulsive interaction between adsorbates, calculated as 200 meV at 13.4 ?. This large repulsive interaction must be channeled through the surface since it causes widely spaced "one-per-corner-hole" patterns of physisorption (three cases--directly observed here) and subsequent chemisorption (four cases observed). The patterns were observed by ultrahigh vacuum scanning tunneling microscopy for four different brominated hydrocarbon adsorbates; 1,2-dibromoethane, 1-bromopropane, 1-bromopentane, and bromobenzene, deposited individually on the surface. In every case, adsorbates were overwhelmingly more likely to be found singly than multiply adjacent to a corner-hole, constituting a distinctive pattern having a probability p = 7 × 10(-5) compared to a random distribution.     

Bond alternation, polarizability, and resonance detuning in methine dyes

We derive structure-property relationships for methine ("Brooker") dyes relating the color of the dye and its symmetric parents to its bond alternation in the ground state and also to the dipole properties associated with its low-lying charge-resonance (or charge-transfer) transition. We calibrate and test these relationships on an array of different protonation states of the green fluorescent protein chromophore motif (an asymmetric halochromic methine dye) and its symmetric parent dyes. The relationships rely on the assumption that the diabatic states that define the Platt model for methine dye color [J. R. Platt, J. Chem. Phys. 25, 80 (1956)] can also be distinguished by their single-double bond alternation and by their charge localization character. These assumptions are independent of the primary constraint that defines the diabatic states in the Platt model--specifically, the Brooker deviation rule for methine dyes [L. G. S. Brooker, Rev. Mod. Phys. 14, 275 (1942)]. Taking these assumptions, we show that the Platt model offers an alternate route to known structure-property relationships between the bond length alternation and the quadratic nonlinear polarizability β. We show also that the Platt model can be parameterized without the need for synthesis of the symmetric parents of a given dye, using the dipole data obtained through spectroscopic measurements. This suggests that the Platt model parameters may be used as independent variables in free-energy relationships for chromophores whose symmetric parents cannot be synthesized or chromophores strongly bound to biomolecular environments. The latter category includes several recently characterized biomolecular probe constructs. We illustrate these concepts by an analysis of previously reported electroabsorption and second-harmonic generation experiments on green fluorescent proteins.     

Differences in actinide metal-ligand orbital interactions: comparison of U(IV) and Pu(IV) β-ketoiminate N,O donor complexes

Syntheses and characterization of UCl(2)((Ar)acnac)(2), UI(2)((Ar)acnac)(2), and PuI(2)((Ar)acnac)(2) are reported ((Ar)acnac denotes a bis-phenyl β-ketoiminate ligand where Ar = 3,5-(t)Bu(2)C(6)H(3)). Structural analyses and computations show significant metal-ligand orbital interaction differences in U(IV) vs. Pu(IV) bonding.