The linear carbon chains called the carbynes are possibly the most simple carbon molecular systems of interest as the potential materials for nanoelectronics. In a metallic cumulenic form of carbyne, the C atoms form the double bonds (... CC...), but the single and triple bonds alternate in the semiconducting polyynic structure (...−CC−CC−...). In this work, the ballistic electrical conductance of cumulenic and polyynic carbon chains C 40 , C 20 , and C 10 is calculated using the πelectron tight-binding methods. The transmission function and dependences of the current on the length of the carbon chain, the type of carbon bonds, material properties of the electrodes, bias voltage, and temperature are obtained. For the calculations of transmission function, we use the Schrodinger equation that meets the specified value of the energy E, the wave functions being the superposition of incident and reflected waves in the region of cathode, and describe the transmitted wave in the anode. For small bias voltages, the problem of calculating the transmission function in the cumulenic and polyynic chains is solved analytically by applying the difference schemes approach which permits us to pass from the tight-binding algebraic equations to the differential equations and to take advantage of their solutions. In the case of large voltages, we apply an iterative technique. The transmission functions τ(E,V) of the cumulenic and polyynic chains of similar composition differ dramatically. The energy regions of very high and low transparency of carbynes for electrons are obtained, and an oscillatory character of the energy dependence of transmission functions is pointed out. Each electronic level of the molecule corresponds to a peak in the energy dependence of transmission function with τ ≈ 1. The peaks are responsible for the resonant electron transfer between the electrodes. The voltage-dependent variations of the τ are initially quite weak, but at the higher voltages their effect is a drastic reduction of the carbyne transparency. One important feature of the current−voltage I−V characteristics is that the current initially increases with growth of the bias voltage, reaches a peak, and then drops to give rise to the negative conductance. On the typical I−V curves of the polyynic chains, there are both the peak and local minimum (valley) at higher voltages. Moreover, there are some oscillations of voltage dependences of conductance due to the discrete nature of the C chain electron energy levels. The π electron model results are compared with ab initio data on conductance of similar chains having only several C atoms. The presence of the negative resistance regions and valley in the curve I−V indicate the possibilities of design of the resonance tunneling devices based on the C chains.

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A computational method for the band structure of nanowires having approximately cylindrical symmetry is developed. The effective one‐electron potential is supposed to have spherical symmetry in the region of the atomic centres and is assumed to be constant in the interstitial region. The corresponding electronic density is supposed to be localised inside the region of cylindrical shape. The base wave functions are obtained by sewing together solutions of the Schrödinger equation for an electron in the empty cylinder (cylindrical waves) with spherically symmetrical solutions for the muffin‐tin spheres. Under the condition of the continuity of the base functions and their first derivatives overlap integrals and Hamiltonian matrix elements are obtained. Dispersion curves and electronic densities of states for chains of transition metals and those of nanowires from metals from K to Zn are calculated.

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