We investigate hole transfer in open carbynes, i.e., carbon atomic nanowires, using Real-Time Time-Dependent Density Functional Theory (RT-TDDFT). The nanowire is made of N carbon atoms. We use the functional B3LYP and the basis sets 3-21G, 6-31G*, cc-pVDZ, cc-pVTZ, cc-pVQZ. We also utilize a few Tight-Binding (TB) wire models, a very simple model with all sites equivalent and transfer integrals given by the Harrison ppπ">ppπ expression (TBI) as well as a model with modified initial and final sites (TBImod) to take into account the presence of one or two or three hydrogen atoms at the edge sites. To achieve similar site occupations in cumulenes with those obtained by converged RT-TDDFT, TBImod is sufficient. However, to achieve similar frequency content of charge and dipole moment oscillations and similar coherent transfer rates, the TBImod transfer integrals have to be multiplied by a factor of four (TBImodt4times). An explanation for this is given. Full geometry optimization at the B3LYP/6-31G* level of theory shows that in cumulenes bond length alternation (BLA) is not strictly zero and is not constant, although it is symmetrical relative to the molecule center. BLA in cumulenic cases is much smaller than in polyynic cases, so, although not strictly, the separation to cumulenes and polyynes, approximately, holds. Vibrational analysis confirms that for N even all cumulenes with coplanar methylene end groups are stable, for N odd all cumulenes with perpendicular methylene end groups are stable, and the number of hydrogen atoms at the end groups is clearly seen in all cumulenic and polyynic cases. We calculate and discuss the Density Functional Theory (DFT) ground state energy of neutral molecules, the CDFT (Constrained DFT) “ground state energy” of molecules with a hole at one end group, energy spectra, density of states, energy gap, charge and dipole moment oscillations, mean over time probabilities to find the hole at each site, coherent transfer rates, and frequency content, in general. We also compare RT-TDDFT with TB results.

This paper was published online on 12 December 2016 with an incorrect panel in Fig. 2. Figure 2 has been replaced as of 20 July 2020. The figure is incorrect in the printed version of the journal.

We study hole transfer in open cumulenic and polyynic nanowires made of N carbon atoms, using real-time time-dependent density functional theory (RT-TDDFT) and tight-binding (TB) wire models. For RT-TDDFT, we mainly use functional B3LYP and basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ, obtaining clear convergence; cc-pVTZ is the smallest basis set of sufficient quality; cc-pVQZ is better with a higher computational cost. For TB, we use a simplistic wire model where all sites are equivalent (TBI) and models with modified initial and final sites, mimicking the existence of one or two or three hydrogens at edge sites (TBImod, TBImodt4times). We compare the ground state energy, EGS, obtained by density functional theory (DFT) for cumulenic molecules with coplanar (co) or perpendicular (pe) methylene end groups as well as polyynic molecules starting with short (sl) or with long (ls) C–C bonds. For odd N, cumulenic pe molecules have lower EGS than cumulenic co molecules, that are probably transition states. We examine energy spectra, density of states, energy gap, charge oscillations, mean over time probabilities to find the hole at each site, coherent transfer rates, electric dipole moment, and frequency content. DFT shows that due to the impact of end groups, there exists a cumulenic energy gap, smaller than the polyynic one. TBI and TBImod reproduce approximately the magnitude of the energy gap in the polyynic case at the limit of large N. TBImod is capable of predicting the same site occupations with the nicely converged RT-TDDFT ones for the cumulenic case. However, charge and dipole moment oscillations as well as transfer rates by RT-TDDFT are approximately four times faster than those by TBImod. The site occupations of polyynic sl and of polyynic ls molecules are modified relative to cumulenic molecules; the trends can be explained qualitatively.