Quantitative predictions of photoelectron spectra in amorphous molecular solids from multiscale quasiparticle embedding

We present a first-principles-based multiscale simulation framework for quantitative predictions of the high-energy part of the ultraviolet photoelectron spectroscopy (UPS) spectra of amorphous molecular solids. The approach combines a deposition simulation, many-body Green's function theory, polarizable film embedding, and multimode electron-vibrational coupling and provides a molecular-level view on the interactions and processes giving rise to spectral features. This insight helps bridging the current gap between experimental UPS and theoretical models as accurate analyses are hampered by the energetic disorder, surface sensitivity of the measurement, and the complexity of excitation processes. In particular, this is relevant for the unambiguous determination the highest occupied molecular orbital energy (HOMO) of organic semiconductors, a key quantity for tailoring and engineering new optoelectronic devices. We demonstrate the capabilities of the simulation approach studying the spectrum of two isomers of 2-methyl-9,10-bis(naphthalen-2-yl)anthracene as archetypical materials showing a clearly separated HOMO peak in experiment. The agreement with experiment is excellent, suggesting that our approach provides a route for determining the HOMO energy with an accuracy better than 0.1 eV.

Figure 1

Experimental UPS spectra obtained using He-I radiation (21.2 eV ) for (a) $\alpha$-MADN and (b) $\beta$-MADN, respectively. For both systems, the peak associated to the HOMO, at about $-6.1$ eV, is clearly separated from the deeper levels.

Figure 2

Schematic representation of the potential energy surfaces for the neutral (blue) and the cation (red) states, respectively, for a specific vibrational mode $k$, as a function of the (dimensionless) vibrational coordinate $q_k$. Adiabatic transitions are the results of coupling of particlelike excitations (vertical transition) with molecular vibrations, observed as the total reorganization energy ${\lambda }_{\text{tot}}={\sum }_k{\lambda }_k$. Within the full-quantum treatment of carrier-vibrational mode coupling, employed in this paper, the detailed mode-specific coupling strengths ${\lambda }_k$ are included in the expression for the spectral shape shift and broadening function $S_{\text{el-vib}}^{\text{FQ}}\left(\mathrm{\Delta }E\right)$ [Eq. (14)].

Figure 3

Comparison of the quasiparticle HOMO energies ${\varepsilon }_{\text{HOMO}}$ obtained using different molecular mechanics embedding schemes, as a function of the cutoff radius $r_{\mathrm{c}}$ up to which electrostatic effects are included, for (a) a surface and (b) a bulk molecule in the $\beta$-MADN thin film. For the cutoff-based $GW$/aMM (blue line) and $GW$/sMM (red line) methods, the cutoff length $r_{\text{c}}$ is varied showing only a slow convergence. The value at $r_{\text{c}}=\infty$ indicates the result after periodic embedding ($GW$/pMM scheme). In all cases, only the quasiparticle state is considered polarizable while the molecules in the MM region are described by static point charges.

Figure 4

Layer-resolved energy levels of (a) $\alpha$-MADN and (b) $\beta$-MADN obtained from vacuum KS (0), vacuum $GW$ (1), static (2), and polarizable (3) $GW/\text{pMM}$ calculations, respectively. The error bars correspond to the range of $\pm$ one standard deviation.

Figure 5

Frontier orbital surface density of states before (SDOS) and after adiabatic correction (ad-SDOS), as well as the simulated UPS spectra within the full-quantum model (ad-$\mathrm{SDOS}+\mathrm{FQ}$) for both $\alpha$-MADN (a) and $\beta$-MADN (b) as obtained from the polarizable $GW/\text{pMM}$ calculations. (c) Shows for $\beta$-MADN the shift of single-molecule vertical HOMO level to the adiabatic one at lower binding energies, and the subsequent application of the line-shape function $S_{\text{el-vib}}^{\text{FQ}}\left(\mathrm{\Delta }E\right)$ [Eq. (14)] which leads to a pronounced broadening (FWHM: 0.25 eV) and shift to higher binding energies with respect to ${\varepsilon }_{\text{HOMO}}^{\text{ad}}$.

Figure 6

UPS spectra for $\alpha$-MADN (a) and $\beta$-MADN (b). Curves 0–3 give the UPS as depth weighted DOS with vertical-to-adiabatic shift and vibrational broadening via Eq. (14) predicted from vacuum KS (0), $GW$ (1), static (2), and polarizable $GW/\text{pMM}$ (3) calculations, respectively. The closed circles give the experimental spectra, obtained using He-I radiation (21.2 eV). The experimental resolution is $\sigma$ = 0.05 eV, and has no significant effect on the final spectral width.