aWe propose the design of a single-molecule diode with a rectification ratio exceeding a million. The employed mechanism is based on coherent resonant charge transport across a molecule that consists of four conjugated sites coupled by non-conjugated bridges. Using density functional theory calculations, we rationalize the design of the molecule and demonstrate the crucial role of aligning the sites at a specific voltage. Rectification ratios are calculated for a series of chemical substituents and demonstrate that with careful molecular design, high rectification ratios can be achieved. Finally, we comment on the shortcomings of our approach, how further improvements can be obtained and discuss some of the experimental challenges.Molecular diodes have been attracting much attention recently, both in self-assembled monolayers 1-7 and on the single-molecule scale. [8][9][10][11][12][13][14][15][16] Even though the rectifier has been the seminal device which launched the field of single-molecule electronics, 17 up to date, their performance have many shortcomings. In particular, their rectification ratios (RR) are orders of magnitude lower than typical semiconducting rectifiers. The highest RR reported experimentally on a single-molecule junction 15 is about 600, and is no match for a semiconducting diode where ratios exceeding 10 6 are common. In that study, a molecular backbone was considered which consisted of two identical, weakly-coupled conjugated parts. In such a system, current flows coherently when both halves are on resonance, i.e., the sites are aligned with each other within the bias window. The alignment of the two sites can be modified by applying a bias voltage and/or by chemical substituents. With proper design, one can align the sites at zero bias, while misaligning them at finite bias, yielding negative differential conductance. 18 One can also align the sites at a finite bias, 15,19-22 and achieve single-molecule rectification.Based on a similar principle, here we investigate theoretically how the rectification ratio of single-molecule diodes can be significantly enhanced by the addition of more sites in series, as shown in as presented in Fig. 1b. Low RR are primarily caused by a high reverse current. Adding more sites in series leads to a strong suppression of the reverse current, thereby drastically improving the RR. However, the addition of sites comes at the cost of an increased molecular complexity and number of model parameters. In this study, we first focus on the design of a molecule which behaves as having four sites in series. For this purpose, we use density functional theory (DFT) calculations. We then investigate how the molecule can be engineered by the means of chemical substitution to align the sites at a particular bias voltage. We eventually show that the molecule designed with four sites represents a drastic improvement compared to a two-site molecule, with RR approaching 10 6 , competitive with siliconbased diodes.1 Design guidelines Fig. 1 depicts the concept of a rectifier...