Measuring the conductance of single-molecule junctions, which feature in a range of photovoltaic and energy-harvesting devices, is essential to gain better insights into the energy and charge-transfer processes of the molecule, in order to optimize the devices themselves. But accurately calculating the conductance is no mean feat. Now, by applying a correction to a standard modelling method used to make measurements in such systems, an international group of researchers has demonstrated qualitatively and quantitatively correct solutions for a compound known as “porphyrin” for the first time, thereby enabling predictive modelling of complex molecular junctions.

Porphyrins are cyclic organic compounds that are commonly used as a “single molecule junction” wherein – a single organic molecule connected to macroscopic metallic electrodes. Standard methods predict erroneous electron orbitals for transition metals in porphyrin molecules, as well as overestimating the conductance by an order of magnitude. In the new work, the team tackled both inaccuracies using a modified “hybrid” formulation of the “density functional theory” (DFT) – a computational quantum mechanical modelling method that looks at the electronic structure of many-body systems.

"The hybrid functional is the only pragmatically feasible method we can employ to correct both errors at the same time," says Zhenfei Liu, a postdoctoral researcher at the Molecular Foundry and Materials Sciences Division at the Lawrence Berkeley National Laboratory. "Other approaches need two stages to correct the qualitative and quantitative inaccuracies."

Metal centres

Porphyrins usually have a transition metal at the centre, which as Liu stresses has an important impact on the molecule's properties. "For catalysis, for example, the metal centre is key to make the porphyrin work as it's supposed to," he says. Calculating the properties of transition metals has some known nuances. To deal with these, chemists developed a mathematical formulation known as the "exact exchange", which was incorporated into DFT over a decade ago, and is responsible for more accurate calculations of the electronic bandgap, charge transfer and other properties of these systems.

"The functional was already known but had not been applied to molecular junctions," says Liu. "But we knew you need the exact exchange to make DFT work for transition metals, so we used a combination of standard functional and an exact exchange. This additional component – the exact exchange – gives the qualitatively correct calculations."

Liu, working with Jeff Neaton at the Molecular Foundry at Lawrence Berkeley Lab and the University of California, Berkeley, along with Latha Venkataraman, Luis M Campos and colleagues at Columbia University in New York and Yonsei University in Korea, incorporated a previously developed modification known as "DFT+Σ", which corrects inaccuracies that arise due to underestimating the alignment of energy levels in the junction.

Experiment versus theory

The researchers synthesized different types of porphyrin with cobalt, copper, nickel or no metal at the centre. Solutions of the porphyrins were deposited on a gold-on-mica substrate and a gold scanning tunnelling microscopy tip was dipped into the solution and pulled out to create a break junction. Comparisons of measured conductances with calculated values favoured the accuracy of the researchers' newly modified formulation over standard DFT.

Liu explains that the team’s novel hybrid approach can be applied to other systems as well. "For example, in organic metallic interfaces the junction has two interfaces on each side – probably a more common scenario in nanoscience."

He also describes previously published work on a study of the conductance of similar junctions but with graphite as one of the electrodes instead of gold. Breaking the symmetry of the system in this way gives rise to rectification in the junction – when the bias is reversed, the conductance value changes, which can be useful for energy-harvesting devices.

The work is published in Nano Letters.