Fermi level alignment in molecular nanojunctions and its relation to charge transfer

The alignment of the Fermi level of a metal electrode within the gap of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a molecule is a key quantity in molecular electronics, which can vary the electron transparency of a single-molecule junction by orders of magnitude. We present a quantitative analysis of the relation between this level alignment (which can be estimated from charging free molecules) and charge transfer for bipyridine and biphenyl dithiolate (BPDT) molecules attached to gold leads based on density functional theory calculations. For bipyridine the charge distribution is defined by a balance between electrostatic repulsion effects and the filling of the LUMO, where the molecule loses electrons to the leads. BPDT, on the other hand, gains electrons. As a direct consequence the Fermi level of the metal is found at the energetically higher end of the gap in the transmission function for bipyridine and at its lower end for BPDT.

Figure 1

(Color online) A bipyridine (left) and BPDT (right) molecule suspended between Au electrodes. The middle lower panel shows the alignment of the molecular levels with the metal Fermi energy [red (gray) line] by equalizing vacuum potentials of the isolated molecules and surfaces where the HOMO and LUMO are marked with dashed and the other MOs with solid lines. The left and right lower panels show transmission functions for the coupled systems for bipyridine and BPDT, respectively.

Figure 2

(Color online) MO1 energies (relative to $E_F$ of the Au surface) depending on the distance $d$ between the molecule and the Au surfaces for (a) bipyridine and (b) BPDT. The black solid curves are taken from the coupled systems; for the gray (red) curves estimates from the charged free molecules have been used. The dashed line shows the position from vacuum alignment without charging $\left({ϵ}_{\mathit{vac}\text{−}\mathit{align}}\right)$, which was obtained from a free-molecule calculation and the work function of the metal slab. MO1 in its dependence on the charge for the free molecules is shown as insets.

Figure 3

(Color online) Charge density difference $\Delta n\left(x_z\right)$ (black solid line, summed up parallel to the surface plane) and its integral (black dashed line) for bipyridine coupled to Au atoms $(d=2.63\mathrm{\AA })$. $\Delta n\left(x_z\right)$ constructed only from contributions of the bipyridine HOMO (see inset) and the Au $s$ and $d$ $\left(z^2\right)$ states is also given for comparison [gray (green) line].