Alexander Onipko

Spectrum of π Electrons in Graphene as a Macromolecule

We report the exact solution of the spectral problem for a graphene sheet framed by two armchair- and two zigzag-shaped boundaries. The solution is found for the pi electron Hamiltonian and gives, in particular, a closed analytic expression of edge-state energies in graphene. It is shown that the lower symmetry of graphene, in comparison with C6h of 2D graphite, has a profound effect on the graphene band structure. This and other results obtained have far-reaching implications for the understanding of graphene electronics. Some of them are briefly discussed.

Spectrum ofπelectrons in graphene as an alternant macromolecule and its specific features in quantum conductance

An exact description of

Ab initio calculations of equilibrium geometries and vibrational excitations of helical ethylene-glycol oligomers: application to modeling of monolayer infrared spectra

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Effect of length and geometry on the highest occupied molecular orbital-lowest unoccupied molecular orbital gap of conjugated oligomers: An analytical Hückel model approach

electrons based on the tight-binding model of graphene as an alternant, plane macromolecule is presented. The model molecule can contain an arbitrary number of benzene rings and has armchair- and zigzag-shaped edges. This suggests an instructive alternative to the most commonly used approach, where the reference is made to the honeycomb lattice periodic in its A and B sublattices. Several advantages of the macromolecule model are demonstrated. The newly derived analytical relations detail our understanding of

Tunneling across molecular wires: an analytical exactly solvable model

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Long-Chain Alkylthiol Assemblies Containing Buried In-Plane Stabilizing Architectures

electron nature in achiral graphene ribbons and carbon tubes and classify these structures as quantum wires.

Analytical one-particle approach to the π electronic structure of heterocyclic polymers

The density functional theory methods are used to calculate the equilibrium molecular structures and vibrational spectra of helical H(CH2CH2O)nH (OEG) oligomers (n = 4-7) at a level of precision th ...

Quantum conductance of achiral graphene ribbons and carbon tubes

It is shown that the asymptotic behavior of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap of conjugated oligomers of types M−(M)N−2−M and M−(M)N−2−M1 with M = M1−M2, where M, M1, and M2 are alternant but otherwise arbitrary monomers described by the Huckel Hamiltonian, is ruled by the law ΔHL(N)=ΔHL(∞)+const⋅N−2. On this basis we suggest an approximate expression for the HOMO-LUMO gap as a function of oligomer length, that is exact for minimal- and infinite-length oligomers. Two parameters of this function determine the dependence of ΔHL(N) on the oligomer geometry. By comparing the proposed approximation with the exact model results for oligomers of polyene, polyparaphenylene (PPP), and polyparaphenylenevinylene (PPV) (some experimental data and results of more elaborate calculations have been also used for this purpose) the proposed approximation is proven to give a useful estimate of the conjugation length and geometry effect on the HOMO-LUMO gap of the mole...

From acene to graphene spectrum of π electrons with the use of the Green's function

Abstract On the basis of the Landauer approach and Green function technique we have developed an exactly solvable analytical model that gives a quick and reliable estimate of (ohmic) tunnel conductance in metal–molecular heterojunctions. The model covers conjugated oligomers of types M–M–⋯–M and M 1 –M 2 –M 1 –⋯–M 2 –M 1 connecting metal pads in molecular contacts. Based on a realistic Hamiltonian for these kinds of oligomers we obtain an analytical expression for the tunnel conductance: (2 e 2 / h ) g 0 ( E F ) g mol 0 ( E F )e −2 δ ( E F ) N , where N is the number of the structural units M (or M 1 ). The pre-exponential factor g 0 ( E F ) depends on the metal and metal–molecule coupling characteristics only, whereas g mol 0 ( E F ) and the exponential decay constants are explicit functions of the Green function matrix elements of monomers M (or M 1 and M 2 ). This formula provides, for the first time, an analytical relationship between a realistic description of the molecular electronic structure and the heterojunction resistance. The results obtained from this formula are of immediate use for probing currents through single molecules, e.g. by scanning tunneling microscope (STM) techniques as well as for measurements of electron transfer rates in donor/bridge/acceptor systems.

Green function of conjugated oligomers: the exact analytical solution with an application to the molecular conductance

A series of alkylthiol compounds were synthesized to study the formation and structure of complex self-assembled monolayers (SAMs) consisting of interchanging structural modules stabilized by intermolecular hydrogen bonds. The chemical structure of the synthesized compounds, HS(CH(2))(15)CONH(CH(2)CH(2)O)(6)CH(2)CONH-X, where X refers to the extended chains of either -(CH(2))(n)CH(3) or -(CD(2))(n)CD(3), with n = 0, 1, 7, 8, 15, was confirmed by NMR and elemental analysis. The formation of highly ordered, methyl-terminated SAMs on gold from diluted ethanolic solutions of these compounds was revealed using contact angle goniometry, null ellipsometry, cyclic voltammetry, and infrared reflection absorption spectroscopy. The experimental work was complemented with extensive DFT modeling of infrared spectra and molecular orientation. New assignments were introduced for both nondeuterated and deuterated compounds. The latter set of compounds also served as a convenient tool to resolve the packing, conformation, and orientation of the buried and extended modules within the SAM. Thus, it was shown that the lower alkyl portion together with the hexa(ethylene glycol) portion is stabilized by the two layers of lateral hydrogen bonding networks between the amide groups, and they provide a structurally robust support for the extended alkyls. The presented system can be considered to be an extension of the well-known alkyl SAM platform, enabling precise engineering of nanoscopic architectures on the length scale from a few to approximately 60 A for applications such as cell membrane mimetics, molecular nanolithography, and so forth.