Lyuba Malysheva

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.

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

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 ...

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

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...

Tunneling across molecular wires: an analytical exactly solvable model

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.

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

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.

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

The one-electron description of heterocyclic five-membered ring polymers is derived on the basis of the Su–Schrieffer–Heeger–Huckel type Hamiltonian which accounts for the electronic interaction of the heteroatom p-orbital lone pair with the π band structure of the carbon backbone. An explicit form of the fifth order equation, the solutions of which determine the dispersion relations for five π electron bands and closed expressions of molecular orbitals, is obtained. The main accent is put on the gross π electronic polymer structure. It is shown that there exists one-to-one correspondence between the structure considered as a function of basic system parameters [such as the electron on-site energies at carbon (C) and heteroatom (X), and resonance integrals associated with C–C and X–C bonds] and zeros of the Green function of polymer building blocks—monomers. This interrelation is expressed in the form of certain equations for the monomer Green function matrix elements, which predict the values of system p...

Quantum conductance of achiral graphene ribbons and carbon tubes

Explicit expressions of the band spectrum near the neutrality point are derived for armchair and zigzag graphene ribbons and carbon tubes. Several spectral features, which were previously observed only in numerical calculations, are given an adequate analytic description in terms of elementary functions. The obtained dispersion relations are used for a comparison of conductance ladders of graphene-based wires; these relations are also beneficial for many other applications.

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

The origin of the spectrum of TT electrons that results from the coupling of N N-long acenes via C-C covalent bonding has been traced with the use of the Green function formalism. Exact expressions of acene and graphene Greens functions, which are useful for analysis of the electronic properties of these macromolecules, are obtained and advanced to a form suitable for instructive applications.

Ab Initio Modeling of Defect Signatures in Infrared Reflection-Absorption Spectra of SAMs Exposing Methyl- and Hydrogen-Terminated Oligo(ethylene glycols)

Extensive ab initio modeling has been performed to explain quantitatively the apparent shapes of characteristic bands, which are systematically observed in the fingerprint region of infrared (IR) reflection-absorption (RA) spectra of oligo(ethylene glycol) (OEG)-terminated SAMs. The presence of defects was thoroughly examined by modeling the RA spectra using the DFT method BP86/6-31G* for all-helical and all-trans conformers of HS(CH2CH2O)nR (n = 5, 6, R = H, CH3) and HS(CH2)15CONH(CH2CH2O)6H molecules and for several defect-containing conformers. These data were then used to simulate RA spectra of SAMs with different content of defects and to compare them with experiments. It is shown that for SAMs of HS(CH2CH2O)nCH3 (n = 5, 6) the pronounced asymmetry of the dominating band can be attributed to the multimode nature of COC stretching vibrations of helical conformers combined with the contribution from few percent of all-trans conformers. Arguments are presented which disprove appreciable amounts of helical conformers with single trans and/or gauche defects. Much more complex combination of factors, which can come into play in the formation of the high-frequency shoulder of COC band, is exemplified by self-assemblies of OEG-terminated amide-bridged alkanethiolates. In particular, spectral signatures of defects with inverted OH terminus are compared with other contributions to the apparent shape of COC band formation. For this family of SAMs, the presence of about 10% of all-trans conformers gives a satisfactory quantitative agreement between the calculated RA spectra and experimental observations.

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

The exact analytical expression of the Green function of oligomers M-M-...-M and M-1-M-2-M-1-...-M-2-M-1, where M M-1, and M-2 are monomers of arbitrary pi electronic structure described by the tight-binding Hamiltonian, is derived for the first time. This result makes possible to address relevant spectral and electron transport properties of large linear molecules on the basis of realistic exactly solvable models. The power of the approach is exemplified by obtaining a number of explicit relations between the transport related quantities, in particular, through molecule tunneling decay constant, and the molecular electronic structure for a wide family of potential molecular wires