Electronic structure of copper phthalocyanine from $G_0{W}_0$ calculations

We present all-electron $G_0{W}_0$ calculations for the electronic structure of the organic semiconductor copper phthalocyanine, based on semilocal and hybrid density-functional theory (DFT) starting points. We show that $G_0{W}_0$ calculations improve the quantitative agreement with high resolution photoemission and inverse photoemission experiments. However, the extent of the improvement provided by $G_0{W}_0$ depends significantly on the choice of the underlying DFT functional, with the hybrid functional serving as a much better starting point than the semilocal one. In particular, strong starting-point dependence is observed in the energy positions of highly localized molecular orbitals. This is attributed to self-interaction errors (SIE), due to which the orbitals obtained from semilocal DFT do not approximate the quasi-particle (QP) orbitals as well as those obtained from hybrid DFT. Our findings establish the viability of the $G_0{W}_0$ approach for describing the electronic structure of metal-organic systems, given a judiciously chosen DFT-based starting point.

Figure 1

Schematic illustration of a CuPc molecule.

Figure 2

Quasi-particle HOMO energies obtained from $G_0{W}_0$ based on semilocal and hybrid starting points with increasingly large basis sets, compared to the experimental ionization potential.[2, 3, 5]

Figure 3

Calculated DFT and QP spectra, obtained from computed energy levels (shown as sticks) by broadening via convolution with a 0.35-eV-wide Gaussian, compared to gas phase UPS of Evangelista et al.[2] and to thin film IPES data of (a) Murdey et al.[17] (shown with curve fitting results) and (b) Hill et al.[8] DFT spectra were shifted so as to align the HOMO and LUMO levels with computed ionization potential and electron affinity values—see text for details. Experimental IPES spectra were shifted so as to align the LUMO peak with the computed GW@PBEh LUMO peak.

Figure 4

Calculated DFT and QP spectra, broadened by convolution with a 0.15-eV-wide Gaussian, compared to high-resolution gas phase UPS data.[2] The DFT spectra were shifted as in Fig. 3.

Figure 5

Visualizations of selected leading molecular orbitals of CuPc. Also shown is the density difference between the $b_{1g\uparrow }$ orbitals obtained at the PBEh and PBE levels of theory, multiplied by a factor of ten for clarity of visualization. In the density difference plot, dark gray indicates a higher density in the PBE orbital and light gray indicates a higher density in the PBEh orbital.

Figure 6

QP corrections as a function of DFT energies for both the PBE the PBEh starting points.