Basis set dependence of correlation corrections to protonation energies

The protonation energies of NH₃ and H₂O have been computed using a variety of basis sets. It is found that the effect of election correlation on these energies cannot reliably be determined without the use of large (triple-split and polarized) basis sets.     

Landmarks in graphs

Navigation can be studied in a graph-structured framework in which the navigating agent (which we shall assume to be a point robot) moves from node to node of a “graph space”. The robot can locate itself by the presence of distinctively labeled “landmark” nodes in the graph space. For a robot navigating in Euclidean space, visual detection of a distinctive landmark provides information about the direction to the landmark, and allows the robot to determine its position by triangulation. On a graph, however, there is neither the concept of direction nor that of visibility. Instead, we shall assume that a robot navigating on a graph can sense the distances to a set of landmarks.

Evidently, if the robot knows its distances to a sufficiently large set of landmarks, its position on the graph is uniquely determined. This suggests the following problem: given a graph, what are the fewest number of landmarks needed, and where should they be located, so that the distances to the landmarks uniquely determine the robot's position on the graph? This is actually a classical problem about metric spaces. A minimum set of landmarks which uniquely determine the robot's position is called a “metric basis”, and the minimum number of landmarks is called the “metric dimension” of the graph. In this paper we present some results about this problem. Our main new results are that the metric dimension of a graph with n nodes can be approximated in polynomial time within a factor of O(log n), and some properties of graphs with metric dimension two.     

Calculation of one-electron properties using limited configuration interaction techniques

One-electron properties may be evaluated by configuration interaction methods using analytical differentiation of the total energy with respect to an external perturbation parameter. Dipole moments are reported using such a method for CO and H₂CO. Inclusion of single substitutions does not change calculated dipole moments appreciably with this method. The differences between this method and the direct evaluation of an expectation value are discussed.     

Addition of water to Al5O4- determined by anion photoelectron spectroscopy and quantum chemical calculations

The anion photoelectron spectra of Al5O4- and Al5O5H2- are presented and interpreted within the context of quantum chemical calculations on these species. Experimentally, the electron affinities of these two molecules are determined to be 3.50(5) eV and 3.10(10) eV for the bare and hydrated cluster, respectively. The spectra show at least three electronic transitions crowded into a 1 eV energy window. Calculations on Al5O4- predict a highly symmetric near-planar structure with a singlet ground state. The neutral structure calculated to be most structurally similar to the ground state structure of the anion is predicted to lie 0.15 eV above the ground state structure of the neutral. The lowest energy neutral isomer does not have significant Franck-Condon overlap with the ground state of the anion. Dissociative addition of water to Al5O4- is energetically favored over physisorption. The ground state structure for the Al5O4- +H(2)O product forms when water adds to the central Al atom in Al5O4- with -H migration to one of the neighboring O atoms. Again, the ground state structures for the anion and neutral are very different, and the PE spectrum represents transitions to a higher-lying neutral structure from the ground state anion structure.     

A geometric programming approach to the Van der Waerden conjecture on doubly stochastic matrices

LetD _p be the set of all doubly stochastic square matrices of orderp i.e. the set of allp × p matrices with non-negative entries with row and column sums equal to unity. The permanent of ap × p matrixA = (a _ij ) is defined byP(A) = _Sp II _i=1 ^p a _i(i) whereS _p is the symmetric group of orderp. Van der Waerden conjectured thatP(A) p !/p ^p for all A AD _p with equality occurring if and only ifA = J _p , whereJ _p is the matrix all of whose entries are equal to 1/p.The validity of this conjecture has been shown for a few values ofp and for generalp under certain assumptions. In this paper the problem of finding the minimum of the permanent of a doubly stochastic matrix has been formulated as a reversed geometric program with a single constraint and an equivalent dual program is given. A related problem of reversed homogeneous posynomial programming problem is also studied.     

Comparison of nickel-group metal cyanides and acetylides and their anions using anion photoelectron spectroscopy and density functional theory calculations

The photoelectron spectra of NiCN-, PdCN-, PtCN-, HNiC2H-, Ni(C2H)2(-), PdC2H-, and PtC2H- are presented along with density functional theory calculations. Linear structures are predicted for all anions and neutrals. NiCN- and NiCN are predicted to have 3delta and 2delta ground states, respectively. HNiC2H- and Ni(C2H)2(-) are predicted to have 2delta and 2delta(g) anion and 3delta and 3pi(g) neutral ground states, respectively. The palladium and platinum cyanide and acetylides have 1sigma+ anion and 2sigma+ neutral ground states. Simulations generated from the calculated parameters are compared to observed spectra, and molecular orbital diagrams are presented to compare the bonding in these species.     

Selective G-quadruplex DNA stabilizing agents based on bisquinolinium and bispyridinium derivatives of 1,8-naphthyridine

Various biologically relevant G-quadruplex DNA structures offer a platform for therapeutic intervention for altering the gene expression or by halting the function of proteins associated with telomeres. One of the prominent strategies to explore the therapeutic potential of quadruplex DNA structures is by stabilizing them with small molecule ligands. Here we report the synthesis of bisquinolinium and bispyridinium derivatives of 1,8-naphthyridine and their interaction with human telomeric DNA and promoter G-quadruplex forming DNAs. The interactions of ligands with quadruplex forming DNAs were studied by various biophysical, biochemical, and computational methods. Results indicated that bisquinolinium ligands bind tightly and selectively to quadruplex DNAs at low ligand concentration (～0.2-0.4 μM). Furthermore, thermal melting studies revealed that ligands imparted higher stabilization for quadruplex DNA (an increase in the T(m) of up to 21 °C for human telomeric G-quadruplex DNA and >25 °C for promoter G-quadruplex DNAs) than duplex DNA (ΔT(m) ≤ 1.6 °C). Molecular dynamics simulations revealed that the end-stacking binding mode was favored for ligands with low binding free energy. Taken together, the results indicate that the naphthyridine-based ligands with quinolinium and pyridinium side chains form a promising class of quadruplex DNA stabilizing agents having high selectivity for quadruplex DNA structures over duplex DNA structures.     

Hydrogen-bonding interactions in peptide nucleic acid and deoxyribonucleic acid: a comparative study

Peptide nucleic acid (PNA) is a synthetic analogue of deoxyribonucleic acid (DNA) capable of tightly binding to itself and DNA with high specificity. Using hybrid density functional methods, hydrogen-bond (H-bond) strengths have been evaluated for isolated Watson-Crick base pairs, PNA base pairs, and charged as well as neutral DNA base pairs. Heterogeneous base pairs of PNA with charged and neutral DNA have also been investigated. The competing effects of short-range H-bonding and long-range Coulombic repulsions in charged DNA base pairs have been analyzed. Polarizable continuum models have been employed to evaluate solvation effects on the binding energies.     

A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees

Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, the problem of computing a low-weight spanning tree such that the degree of each vertex is at most its specified bound is considered. In particular, modifying a given spanning treeTusingadoptionsto meet the degree constraints is considered. A novel network-flow-based algorithm for finding a good sequence of adoptions is introduced. The method yields a better performance guarantee than any previous algorithm. If the degree constraintd(v) for eachvis at least 2, the algorithm is guaranteed to find a tree whose weight is at most the weight of the given tree times 2 − min{(d(v) − 2)/(deg_T(v) − 2) : deg_T(v) > 2}, where deg_T(v) is the initial degree ofv. Equally importantly, it takes this approach to the limit in the following sense: if any performance guarantee that is solely a function of the topology and edge weights of a given tree holds foranyalgorithm at all, then it also holds for the given algorithm. Examples are provided in which no lighter tree meeting the degree constraint exists. Linear-time algorithms are provided with the same worst-case performance guarantee. ChoosingTto be a minimum spanning tree yields approximation algorithms with factors less than 2 for the general problem on geometric graphs with distances induced by variousL_pnorms. Finally, examples of Euclidean graphs are provided in which the ratio of the lengths of an optimal Traveling Salesman path and a minimum spanning tree can be arbitrarily close to 2.     

Grafting of methacrylates and styrene on to polystyrene backbone via a “grafting from” ATRP process at ambient temperature

Well defined graft copolymers are prepared by “grafting from” atom transfer radical polymerization (ATRP) at room temperature (30 °C). The experiments were aimed at grafting methacrylates and styrene at latent initiating sites of polystyrene. For this purpose, the benzylic hydrogen in polystyrene was subjected to allylic bromination with N‐bromosuccinimide and azobisisobutrylnitirle to generate tertiary bromide ATRP initiating sites (Br? C? PS). The use of Br? C? PS with lesser mol % of bromide initiating groups results in better control and successful graft copolymerization. This was used to synthesize a series of new graft copolymers such as PS‐g‐PBnMA, PS‐g‐PBMA, PS‐g‐GMA, and PS‐g‐(PMMA‐b‐PtBA) catalyzed by CuBr/PMDETA system, in bulk, at room temperature. The polymers are characterized by GPC, NMR, FTIR, TEM, and TGA. Graft copolymerization followed by block polymerization enabled the synthesis of highly branched polymer brush, in which the grafting density can be adjusted by appropriate choice of bromide concentration in the polystyrene. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3818–3832, 2007