Revealing molecule-internal mechanisms that control phonon heat transport through single-molecule junctions by a genetic algorithm

Abstract

Measurements of the thermal conductance of single-molecule junctions have recently been reported for the first time. It is presently unclear, how much the heat transport can be controlled through molecule-internal effects. The search for molecules with lowest and highest thermal conductance is complicated by the gigantic chemical space. Here we describe a systematic search for molecules with a low or a high phononic thermal conductance using a genetic algorithm. Beyond individual structures of well performing molecules, delivered by the genetic algorithm, we analyze patterns and identify the different physical and chemical mechanisms to suppress or enhance phonon heat flow. In detail, mechanisms revealed to reduce phonon transport are related to the choice of terminal linker blocks, substituents and corresponding mass disorder or destructive interference, meta couplings and molecule-internal twist. For a high thermal conductance, the molecules should instead be rather uniform and chain-like. The identified mechanisms are systematically analyzed at different levels of theory, and their significance is classified. Our findings are expected to be important for the emerging field of molecular phononics.

Figures (9)

• Figure 1: Genetic encoding of molecules. The general scheme is shown in the top row. The encoding consists of molecular blocks, derived from pristine building blocks by attaching substituents, and couplings. The molecule, depicted in the middle, is encoded according to this scheme in the bottom row. Dashed gray lines mark the block limits. Throughout this study the substituents are shown in the following colors: fluorine, cyan; chlorine, green; bromine, red; iodine, purple. Substituents may be attached at the positions that are indicated by black numbers for each block. Hydrogen atoms or the corresponding substituents are specified after a '#' token in the encoding in the numbered order. Anchor groups, i.e. a sulfur atom (yellow) on the left and right side of the molecule, are omitted from the encoding, since they are always the same and thus redundant. Gold tips of the envisioned metal-molecule-metal junction are represented by yellow triangles. Depending on the simulation, we may add a single gold atom (yellow, larger diameter than sulfur atoms), as shown here, or saturate the sulfur anchors with a single hydrogen at each side.
• Figure 2: Pristine molecular building blocks used to construct molecules. Green-colored carbon atoms indicate the "left" coupling point. Red carbon atoms mark the para-coupling position on the "right", whereas cyan carbon atoms mark the meta-coupling position. Blocks with only red carbon atoms, see blocks 1 and 2, do not differ in para and meta connection. For the sake of clarity the multiplicity of bonds is not shown.
• Figure 3: Results of different evolution runs optimizing molecules for low phononic thermal conductance. (a) Fitness plotted as a function of the generation for evolution runs A to K. Parameters used for the fitness function in equation \ref{['main:eq:fitness_low-kappa']} are listed in table \ref{['main:tab:run_configuration']}. (b) Thermal conductance $\kappa_\mathrm{ph}(T)$ at $T=600$ K plotted against the generation number. The inset shows an enlarged section of the plot at high generations. Candidates in the initial populations show typically thermal conductance values larger than $25~\mathrm{pW/K}$. (c) Molecular structures of the fittest individuals in the last generation of each evolution run. (d) SA for each generation and evolution run. For the assessment of the SA, terminal gold atoms are removed and replaced by hydrogens, yielding isolated molecules with SH termination. The inset shows an enlarged section of the plot at high generations. (e) Shannon entropy for all evolution runs. (f) Same as (e) but for the cumulated dihedral angle. In panels (a), (b), (d), (e) and (f), solid lines show the values of the fittest individual and shaded regions around the solid lines visualize the scatter range of the four best performing candidates.
• Figure 4: Analysis of the evolution run I in figure \ref{['main:fig:result_overview']}, leading to the lowest overall heat conductance. (a) Fitness values of the whole population as a function of generation. Crosses mark molecular candidates evolved through selection, crossover and mutation, dots indicate randomly generated individuals. The black solid line shows the mean fitness. Relative frequency of (b) all molecular building blocks and (c) building blocks in the first and last positions of the encoding string for each generation. (d) Statistics of coupling classes for each generation, defined by counting the number of meta couplings in each molecular structure. Remaining couplings are in para configuration. Panel (b) shows the statistics of the whole generation, in panels (c) and (d) the statistics consider the top $20$ individuals of each generation. For panels (b) and (c), block numbers in the legend correspond to those in figure \ref{['main:fig:molecular_blocks']}.
• Figure 5: Optimization of molecules for high phonon thermal conductance. (a) Fitness values as a function of generation. Crosses mark molecular candidates evolved through selection, crossover and mutation. Dots indicate randomly generated individuals. The black line shows the mean fitness value. According to equation \ref{['main:eq:fitness_high-kappa']} the fitness is directly proportional to the thermal conductance $\kappa_\mathrm{ph}(600~\mathrm{K})$, measured in units of $\kappa_0=1$ pW/K. (b) The best performing molecule of the last generation. (c) Relative frequency of molecular blocks for each generation, considering the top $20$ individuals of each generation. Block numbers in the legend correspond to those of figure \ref{['main:fig:molecular_blocks']}. (d) Shannon entropy of the best performing molecule with the highest thermal conductance in each generation. Shaded regions visualize the scatter range of the best four individuals.