Proton Quantum Effects on Electronic Excitation in Hydrogen-bonded Organic Solid: A First-Principles Green's Function Theory Study

TL;DR

Proton nuclear quantum effects (NQEs) on electronic excitations in a hydrogen-bonded organic solid are investigated using first-principles Green's-function theory, treating protons quantum mechanically with the nuclear-electronic orbital (NEO) method within GW-BSE. The study applies single-shot $G_0W_0$ quasiparticle calculations and solves the Bethe-Salpeter equation (BSE) in the Tamm-Dancoff approximation to obtain exciton energies and densities, including exciton density $\rho_n(\mathbf{r_h},\mathbf{r_e})$ and Mulliken populations that quantify delocalization across four hydrogen-bonded monomers. It finds that quantizing protons lowers the quasiparticle gap from $E_{gap}^{QP} = 5.95$ eV to $E_{gap}^{QP} = 5.89$ eV and reduces the exciton binding energy from $E_b = 1.46$ eV to $1.41$ eV, while the optical gap remains nearly unchanged; analysis shows most changes are geometry-driven, though proton quantum motion induces pronounced exciton anisotropy in several excited states. The approach demonstrates a practical route to study NQEs on electronic excitations in extended organic solids and highlights ongoing limitations such as neglect of proton-electron correlation beyond the epc functional and high computational cost.

Abstract

Nuclear quantum effects of protons on electronic excitations in hydrogen-bonded organic materials remains underexplored. In theoretical studies, modeling excitons in these extended systems is particularly difficult because they tend to have a large exciton binding energy and sometimes exhibit charge transfer character. We demonstrate how first-principles Green's function theory combined with the nuclear-electronic orbital method enables us to examine the nature of excitons in a prototypical organic solid of eumelanin, for which the extensive hydrogen bonds have been proposed to facilitate the formation of delocalized excitons. We investigate how the quantization of protons impacts electronic excitations. We discuss the extent to which the resulting proton quantum effects can be described as being derived from structure and how they induce molecular-level anisotropy for the excitons in the organic solid.

Figures (5)

• Figure 1: (a) DHI crystal structure with the unit cell shown as a black box. The organic solid has the helical packing with the herringbone pattern in the crystal. (b) Monomer units in the unit cell are highlighted in yellow. Inset shows the position expectation values of quantum protons are highlighted in blue, overlaid on classical proton positions shown in pink. Mol1-Mol3 and Mol2-Mol4 monomer pairs are hydrogen-bonded.
• Figure 2: (a) Quasi-particle (QP) density of states (DOS) obtained from $GW$ calculations. The x-axis shows QP energy in eV, and the DOS is aligned with respect to the HOMO as a reference (0.0 eV). Gaussian broadening with a FWHM value of 0.025 eV was used. (b) Comparison of the optical absorption spectra for Std (in blue) and NEO (in grey) calculations obtained using BSE@$GW$ calculations. (c) Comparison of the optical absorption spectra for NEO (in grey) and Std:QGeom (in red) calculations obtained using BSE@$GW$ calculations. The x-axis shows the excitation energy in eV, and the optical absorption spectrum for the solids is given by the imaginary part of dielectric function in the y-axis.
• Figure 3: Distribution of Mulliken exciton populations for individual monomers, $P^{p/h}_{Mol}$, for (a) Std, (b) NEO, and (c) Std:QGeom calculations. The Mulliken exciton populations are shown for the particle and hole of the excitons in blue and green, respectively. Each circle indicates $P^{p/h}_{Mol}$ for individual excited state $n$. In (a)-(c), the box heights correspond to the standard deviation of the Mulliken population distributions (see Eq. \ref{['eq:spread']}). In (a), the inset shows a magnified y-axis to highlight the standard deviation for Std calculation. The horizontal lines passing through the boxes shows the average value given by $\mu^{p/h}_{P_{Mol}}$. Deviations of the values from 0.25 indicate that the excitons are spatially more heterogeneously distributed among the four monomers in the unit cell.
• Figure 4: The spatial anisotropy of excitons for hydrogen-bonded monomer units is quantified by $|P^{p/h}_{Mol(A), n}-P^{p/h}_{Mol(B), n}|$ where $A$ and $B$ are hydrogen-bonded pairs, for (a) particle and (b) hole. The dark shades are indicative of the exciton anisotropy. Both figures show the results for Std, Std:QGeom, and NEO calculations. Horizontal axes show the excitation number for the first 55 excitations, and the results for the higher excited states are provided in Figure S5 in the Supporting Information.
• Figure 5: Exciton particle and hole probability densities are shown for the 1$^{\mathrm{st}}$ and 51$^{\mathrm{st}}$ excited states. The corresponding excitation energies are $E_1^{\mathrm{Std}} = 4.49$ eV and $E_1^{\mathrm{NEO}} = 4.48$ eV, and $E_{51}^{\mathrm{Std}} = 6.14$ eV and $E_{51}^{\mathrm{NEO}} = 6.09$ eV. Particle and hole densities are shown in blue and green, respectively. Panels (a,c) correspond to Std calculations, while panels (b,d) correspond to NEO calculations. The black box indicate the unit cell.