Spectra and structural polynomials of graphs of relevance to the theory of molecular conduction

In chemistry and physics, distortivity of π-systems (stabilisation of bond-alternated structures) is an important factor in the calculation of geometric, energetic, and electronic properties of molecules via graph theoretical methods. We use the spectra of paths and cycles with alternating vertex and edge weights to obtain the eigenvalues and eigenvectors for a class of linear and cyclic ladders with alternating rung and backbone edge weights. We derive characteristic polynomials and other structural polynomials formed from the cofactors of the characteristic matrix for these graphs. We also obtain spectra and structural polynomials for ladders with flipped weights and/or Möbius topology. In all cases, the structural polynomials for the composite graphs are expressed in terms of products of polynomials for graphs of half order. This form of the expressions allows global deductions about the transmission spectra of molecular devices in the graph-theoretical theory of ballistic molecular conduction

A simple model of ballistic conduction in multi-lead molecular devices

A fully analytical model is presented for ballistic conduction in a multi-lead device that is based on a π-conjugated carbon framework attached to a single source lead and several sink leads. This source-and-multiple-sink potential (SMSP) model is rooted in the Ernzerhof source-and-sink potential (SSP) approach and specifies transmission in terms of combinations of structural polynomials based on the molecular graph. The simplicity of the model allows insight into many-lead devices in terms of constituent two-lead devices, description of conduction in the multi-lead device in terms of structural polynomials, molecular orbital channels, and selection rules for active and inert leads and orbitals. In the wide-band limit, transmission can be expressed entirely in terms of characteristic polynomials of vertex-deleted graphs. As limiting cases of maximum connection, complete symmetric devices (CSD) and complete bipartite symmetric devices (CBSD) are defined and solved analytically. These devices have vanishing lead-lead interference effects. Illustrative calculations of transmission curves for model small-molecule systems are presented and selection rules are identified

Near omni-conductors and insulators: Alternant hydrocarbons in the SSP model of ballistic conduction

Within the source-and-sink-potential model, a complete characterisation is obtained for the conduction behaviour of alternant π-conjugated hydrocarbons (conjugated hydrocarbons without odd cycles). In this model, an omni-conductor has a molecular graph that conducts at the Fermi level irrespective of the choice of connection vertices. Likewise, an omni-insulator is a molecular graph that fails to conduct for any choice of connections. We give a comprehensive classification of possible combinations of omni-conducting and omni-insulating behaviour for molecular graphs, ranked by nullity (number of non-bonding orbitals). Alternant hydrocarbons are those that have bipartite molecular graphs; they cannot be full omni-conductors or full omni-insulators but may conduct or insulate within well-defined subsets of vertices (unsaturated carbon centres). This leads to the definition of "near omni-conductors" and "near omni-insulators." Of 81 conceivable classes of conduction behaviour for alternants, only 14 are realisable. Of these, nine are realised by more than one chemical graph. For example, conduction of all Kekulean benzenoids (nanographenes) is described by just two classes. In particular, the catafused benzenoids (benzenoids in which no carbon atom belongs to three hexagons) conduct when connected to leads via one starred and one unstarred atom, and otherwise insulate, corresponding to conduction type CII in the near-omni classification scheme

Molecular graphs and molecular conduction : the d-omni-conductors

Ernzerhof's source-and-sink-potential (SSP) model for ballistic conduction in conjugated π systems predicts transmission of electrons through a two-wire device in terms of characteristic polynomials of the molecular graph and subgraphs based on the pattern of connections. We present here a complete classification of conduction properties of all molecular graphs within the SSP model. An omni-conductor/omni-insulator is a molecular graph that conducts/insulates at the Fermi level (zero of energy) for all connection patterns. In the new scheme, we define d-omni-conduction/insulation in terms of Fermi-level conduction/insulation for all devices with graph distance d between connections. This gives a natural generalisation to all graphs of the concept of near-omni-conduction/insulation previously defined for bipartite graphs only. Every molecular graph can be assigned to a nullity class and a compact code defining conduction behaviour; each graph has 0, 1, >1 zero eigenvalues (non-bonding molecular orbitals), and three letters drawn from {C, I, X} indicate conducting, insulating or mixed behaviour within the sets of devices with connection vertices at odd, even and zero distances d. Examples of graphs (in 28 cases chemical) are given for 35 of the 81 possible combinations of nullity and letter codes, and proofs of non-existence are given for 42 others, leaving only four cases open

Compton scattering beyond the impulse approximation

We treat the non-relativistic Compton scattering process in which an incoming photon scatters from an N-electron many-body state to yield an outgoing photon and a recoil electron, without invoking the commonly used frameworks of either the impulse approximation (IA) or the independent particle model (IPM). An expression for the associated triple differential scattering cross section is obtained in terms of Dyson orbitals, which give the overlap amplitudes between the N-electron initial state and the (N-1) electron singly ionized quantum states of the target. We show how in the high energy transfer regime, one can recover from our general formalism the standard IA based formula for the cross section which involves the ground state electron momentum density (EMD) of the initial state. Our formalism will permit the analysis and interpretation of electronic transitions in correlated electron systems via inelastic x-ray scattering (IXS) spectroscopy beyond the constraints of the IA and the IPM.Comment: 7 pages, 1 figur

Chemical tools for study of phosphohistidine: generation of selective Τ‐phosphohistidine and Π‐phosphohistidine antibodies

Non-hydrolysable stable analogues of τ-phosphohistidine (τ-pHis) and π-pHis have been designed aided by electrostatic surface potential calculations, and subsequently synthesized. The τ-pHis and π-pHis analogues (phosphopyrazole 8 and pyridyl amino amide 13, respectively) were used as haptens to generate pHis polyclonal antibodies. Both τ-pHis and π-pHis conjugates in the form of a BSA-glutaraldehyde-τ-pHis and BSA-glutaraldehyde-π-pHis were synthesized and characterized by 31P NMR spectroscopy. Commercially available τ-pHis (SC56-2) and π-pHis (SC1-1; SC50-3) monoclonal antibodies were used to show that the BSA-G-τ-pHis and BSA-G-π-pHis conjugates could be used to assess the selectivity of pHis antibodies in a competitive ELISA. Subsequently, the selectivity of the generated pHis antibodies generated using phosphopyrazole 8 and pyridyl amino amide 13 as haptens was assessed by competitive ELISA against His, pSer, pThr, pTyr, τ-pHis and π-pHis. Antibodies generated using the phosphopyrazole 8 as a hapten were found to be selective for τ-pHis, and antibodies generated using the pyridyl amino amide 13 were found to be selective for π-pHis. Both τ- and π-pHis antibodies were shown to be effective in immunological experiments, including ELISA, western blot, and immunofluorescence. The τ-pHis antibody was also shown to be useful in the immunoprecipitation of proteins containing pHis

Structure elucidation of dimethylformamide-solvated alkylzinc cations in the gas phase

Organozinc iodides, useful for the synthesis of nonproteinogenic amino acids, are investigated in the gas phase by a combination of electrospray (ESI)-MS/MS, accurate ion mass measurements, and infrared multiphoton dissociation (IRMPD) spectroscopy employing a free electron laser. ESI allowed the full characterization of a set of dimethylformamide (DMF)-solvated alkylzinc cations formed by formal loss of F in the gas phase. Gas phase ion structures of the organozinc cations were identified and optimized by computations at the B3LYP/6-311G** level of theory. The calculations indicate that the zinc cation in gas phase alkylzine-DMF species preferentially adopts a tetrahedral coordination sphere with four ligands, namely the alkyl group, any internal coordinating group, and DMF (the number of which depends on the number of internal coordinating groups present). Besides the sequential loss of coordinated DMF, collision-induced dissociation (CID) patterns demonstrate that the zinc-DMF interaction in tetrahedral four-coordinate mono-DMF-zinc complex ions can be even stronger than covalent bonds. The IRMPD spectra of the alkylzine-DMF species examined show a rich pattern of indicative bands in the range of 1000-1800 cm(-1). All major features of the recorded IRMPD spectra are consistent with the computed IR spectra of the respective gas phase ion structures predicted by theory, allowing identification and assignment

The Observation of Four Separate Fluxional Processes in [Re3(CO)10H3]2-, including an Example of the Rotation of a Re=Re Fragment on ReH(CO)4

Magnetization transfer 13C n.m.r. mesurements have been used to investigate the fluxionality of [Re3(CO)10H3]2\u2013 in CD3CN, the lowest energy process being the local scrambling of the carbonyls of the doubly hydride bridged H2Re(CO)3 unit; the next process can be viewed as \u2018olefin\u2019 ReH(CO)4, rotation about the \u2018acetylene\u2019[(CO)3Re(\ub5-H)2- Re(CO)3]2\u2013, followed by the single hydride moving to the unbridged edge and finally local carbonyl scrambling on the ReH(CO)4

Evidence for the role of tetramethylethylenediamine in aqueous Negishi cross-coupling: synthesis of nonproteinogenic phenylalanine derivatives on water

The structure of the alkylzinc−tetramethylethyl-enediamine (TMEDA) cluster cation 3 has been determined in the gas phase by a combination of tandem mass spectrometry, infrared multiphoton dissociation (IRMPD) spectroscopy, and DFT calculations. Both sets of experimental results establish the existence of a strongly stabilizing interaction of TMEDA with the zinc cation. High-level DFT calculations on the alkylzinc−TMEDA cluster cation 3 allowed the identification of two low energy conformers, each featuring a four-coordinate zinc atom with a bidentate TMEDA ligand, and internal coordination from the carbonyl group of the Boc group to zinc. The experimental IRMPD spectrum is reproduced with an appropriately weighted combination of the IR spectra of the two conformers identified by theory. DFT calculations on the structure of the alkylzinc halide 2 with coordinated TMEDA using the PCM model of water solvent suggest that TMEDA can promote ionization of the zinc−iodine bond in organozinc iodides under aqueous conditions, providing a credible explanation for the role of TMEDA in stabilizing the carbon−zinc bond. Reaction of the serine-derived iodide 1 with aryl iodides "on water", promoted by nano zinc in the presence of PdCl2(Amphos)2 (5 mol %) and TMEDA, leads to the formation of protected phenylalanine derivatives 4 in reasonable yields. In the case of ortho-substituted aryl iodides and aryl iodides that are solids at room temperature, conducting the reaction at 65 °C gives improved results. In all cases, the product 5 of reductive dimerization of the iodide 1 is also isolated

Gas-phase study of new organozinc reagents by IRMPD-spectroscopy, computational modelling and tandem-MS

An extensive set of organozinc iodides, useful for Negishi-type cross-coupling reactions, are investigated as respective cations after formal loss of iodide in the gas phase. Firstly, two new alkylzinc compounds derived from Tyrosine (Tyr) and Tryptophan (Trp) are closely examined. Secondly, the influence of specific protecting groups on the subtle balance between intra- and intermolecular coordination of zinc in these reagents is probed through trifluoroacetyl (TFA)-derivatized alkylzinc compounds. Finally, the influence of the strongly coordinating bidentate ligand N,N,N′,N′-tetramethylethylenediamine (TMEDA) on the structure of alkylzinc cations is further explored in order to better understand the stability of the respective complexes towards water. A combination of electrospray (ESI)-MS/MS, accurate ion mass measurements, infrared multiple-photon dissociation (IRMPD) spectroscopy and computational modelling allowed the full characterisation of all dimethylformamide (DMF)-solvated and TMEDA-coordinated alkylzinc cations in the gas phase. The calculations indicate that the zinc cation in gas-phase alkylzinc-DMF or TMEDA-complex ions preferentially adopts a tetrahedral coordination sphere with four ligands. Additionally, conformers with only three binding partners bound to zinc but with effectively combined hydrogen-bond interactions are also found. Collision induced dissociation (CID) patterns demonstrate that the zinc-DMF interaction in tetrahedral four-coordinate mono-DMF-zinc complex ions as well as the interaction between TMEDA and zinc in the corresponding complex ions is even stronger than typical covalent bonds. In most cases, all major features of the IRMPD spectra are consistent with only a single major isomer, allowing secured identification and assignment