Adiabatic Quantum Computing for Random Satisfiability Problems

The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables, the adiabatic method gives solution probabilities close to 1 for problem sizes feasible to evaluate via simulation on current computers. However, for these sizes the minimum energy gaps of most instances are fairly large, so the good performance scaling seen for small problems may not reflect asymptotic behavior where costs are dominated by tiny gaps. Moreover, the resulting search costs are much higher than for other methods. Variants of the quantum algorithm that do not match the adiabatic limit give lower costs, on average, and slower growth than the conventional GSAT heuristic method.Comment: added discussion of discrete adiabatic method, and simulations with 30 bits 8 pages, 8 figure

Inter-cluster reactivity of Metallo-aromatic and anti-aromatic Compounds and Their Applications in Molecular Electronics: A Theoretical Investigation

Local reactivity descriptors such as the condensed local softness and Fukui function have been employed to investigate the inter-cluster reactivity of the metallo-aromatic (Al4Li- and Al4Na-) and anti-aromatic (Al4Li4 and Al4Na4) compounds. We use the concept of group softness and group Fukui function to study the strength of the nucleophilicity of the Al4 unit in these compounds. Our analysis shows that the trend of nucleophilicity of the Al4 unit in the above clusters is as follows; Al4Li- > Al4Na- > Al4Li4 > Al4Na 4 For the first time we have used the reactivity descriptors to show that these clusters can act as electron donating systems and thus can be used as a molecular cathode.Comment: 23 pages, 1 figure and 1 table of conten

Bose-Einstein condensation of correlated atoms in a trap

The Bose-Einstein condensation of correlated atoms in a trap is studied by examining the effect of inter-particle correlations to one-body properties of atomic systems at zero temperature using a simplified formula for the correlated two body density distribution. Analytical expressions for the density distribution and rms radius of the atomic systems are derived using four different expressions of Jastrow type correlation function. In one case, in addition, the one-body density matrix, momentum distribution and kinetic energy are calculated analytically, while the natural orbitals and natural occupation numbers are also predicted in this case. Simple approximate expressions for the mean square radius and kinetic energy are also given.Comment: 14 pages, 19 figures, 1 Table, RevTe

Solid-phase molecular recognition of cytosine based on proton-transfer reaction. Part II. supramolecular architecture in the cocrystals of cytosine and its 5-Fluoroderivative with 5-Nitrouracil

<p>Abstract</p> <p>Background</p> <p>Cytosine is a biologically important compound owing to its natural occurrence as a component of nucleic acids. Cytosine plays a crucial role in DNA/RNA base pairing, through several hydrogen-bonding patterns, and controls the essential features of life as it is involved in genetic codon of 17 amino acids. The molecular recognition among cytosines, and the molecular heterosynthons of molecular salts fabricated through proton-transfer reactions, might be used to investigate the theoretical sites of cytosine-specific DNA-binding proteins and the design for molecular imprint.</p> <p>Results</p> <p>Reaction of cytosine (Cyt) and 5-fluorocytosine (5Fcyt) with 5-nitrouracil (Nit) in aqueous solution yielded two new products, which have been characterized by single-crystal X-ray diffraction. The products include a dihydrated molecular salt (CytNit) having both ionic and neutral hydrogen-bonded species, and a dihydrated cocrystal of neutral species (5FcytNit). In CytNit a protonated and an unprotonated cytosine form a triply hydrogen-bonded aggregate in a self-recognition ion-pair complex, and this dimer is then hydrogen bonded to one neutral and one anionic 5-nitrouracil molecule. In 5FcytNit the two neutral nucleobase derivatives are hydrogen bonded in pairs. In both structures conventional N-H^...O, O-H^...O, N-H^+...N and N-H^...N^-intermolecular interactions are most significant in the structural assembly.</p> <p>Conclusion</p> <p>The supramolecular structure of the molecular adducts formed by cytosine and 5-fluorocytosine with 5-nitrouracil, CytNit and 5FcytNit, respectively, have been investigated in detail. CytNit and 5FcytNit exhibit widely differing hydrogen-bonding patterns, though both possess layered structures. The crystal structures of CytNit (D<it>p</it>k_a= -0.7, molecular salt) and 5FcytNit (D<it>p</it>k_a= -2.0, cocrystal) confirm that, at the present level of knowledge about the nature of proton-transfer process, there is not a strict correlation between the D<it>p</it>k_avalues and the proton transfer, in that the acid/base <it>p</it>k_astrength is not a definite guide to predict the location of H atoms in the solid state. Eventually, the absence in 5FcytNit of hydrogen bonds involving fluorine is in agreement with findings that covalently bound fluorine hardly ever acts as acceptor for available Brønsted acidic sites in the presence of competing heteroatom acceptors.</p