We investigate hole (empty electron position) transfer in open cumulenic and polyynic carbynes, i.e., atomic carbon nanowires, with Real-Time Time-Dependent Density-Functional Theory (RT-TDDFT), through the open-source computer package NWChem.
We study molecules with 6 carbon atoms. One cumulenic with coplanar methylene end-groups, which we symbolize cu6co (cumulenic coplanar with 6 carbon atoms) and three polyynic molecules: One starts with short bond length and is symbolized by pol6sl (polyynic short-long with 6 carbon atoms) and the other two start with long bond length, which are subdivided into with staggered and eclipsed methyl end-groups and are denoted by pol6lss and pol6lse, respectively (polyynic long-short staggered and polyynic long-short eclipsed). In Density Functional Theory (DFT), we use the basis sets 6-31G*, cc-pVDZ, cc-pVTZ and the B3LYP exchange and correlation functional. First, we optimize the geometry, to find their static ground state. In the optimized geometry, we perform DFT for the calculation of the energy, from where we obtain the Löwdin charge distribution in each site of the static geometry of the molecules. As sites we choose the intermediate C atoms, while, the extreme sites consist of C atoms together with the H atoms with which they are connected. Thus, the extreme sites are CH, CH2, CH3, depending on the case.
We study the transfer of an additional hole along the chain, which we artificially insert in the initial site of the chain, using CDFT (constrained DFT), and the Löwdin charge population analysis. We take into account the molecular vibrations and calculate the eigenvectors and eigenfrequencies of the normal modes of vibration via the Hessian matrix. We generate distorted geometries for each molecule, combining all the normal modes of vibration in the harmonic approximation, based on the Bose-Einstein distribution and, in this way, we obtain the vibrational microstates of the system. Each geometry of the set of microstates is created by the total displacement of the normal modes, in the direction of all eigenvectors, where each mode has a specific probability weight. The set of these geometries gives the fluctuations of the system at constant temperature. We obtain RT-TDDFT results for all deformed geometries at temperatures 0 K and 300 K. For each molecule, we calculate, for the static and the mean vibrational state of each deformed geometry:
- The mean over time probabilities to find the hole at each site.
- The frequency content, i.e., the main oscillation frequencies of the dipole moment along the axis of the molecule and the corresponding oscillation amplitudes with FFT analysis.
- The maximum transfer percentage.
- The mean transfer rate.
transfer, carnbynes, geometries, vibrations, charge, dipole moment