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

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.

💡 Research Summary

The authors present a pioneering study of proton nuclear quantum effects (NQEs) on electronic excitations in a hydrogen‑bonded organic crystal, using a combined nuclear‑electronic orbital (NEO) approach with many‑body Green’s function methods (GW and the Bethe‑Salpeter Equation, BSE). The model system is the crystalline form of 5,6‑dihydroxyindole‑4 (DHI), a monomeric unit of eumelanin, which features a helical packing motif, extensive π‑π stacking, and a dense network of intermolecular hydrogen bonds. Three computational protocols are compared: (i) standard density‑functional theory (Std) where protons are treated as classical point charges, (ii) NEO‑DFT (NEO) where selected protons are quantized on the same footing as electrons, and (iii) Std:QGeom, a hybrid where the classical calculation uses the proton position expectation values obtained from the NEO run, thereby isolating purely geometric contributions.

NEO calculations reveal that the quantum delocalization of protons shifts their average positions by roughly 0.015 Å relative to the classical geometry. This leads to modest but systematic changes in bond lengths: C–H bonds elongate by ~0.03 Å, O–H hydrogen‑bond distances shorten by ~0.02 Å, and the overall H‑bond length contracts from 2.07 Å to 2.04 Å. When these geometries are fed into a GW quasiparticle (QP) calculation, the QP band gap shrinks from 5.95 eV (Std) to 5.89 eV (NEO), a reduction of about 0.05 eV. The BSE‑derived optical gap, however, is essentially unchanged (4.49 eV → 4.48 eV), indicating that the first bright singlet excitation is not directly sensitive to proton quantization. The exciton binding energy, defined as the difference between the QP gap and the optical gap, decreases from 1.46 eV (Std) to 1.41 eV (NEO). The Std:QGeom calculation yields an intermediate binding energy of 1.44 eV, confirming that most of the effect originates from the geometry change induced by quantum protons.

Optical absorption spectra (imaginary part of the dielectric function) for Std and NEO are qualitatively similar across the 4.5–8 eV range, but NEO introduces a modest red‑shift above 10 eV and enhances the intensity of several peaks (around 4.5, 5.0, and 6.2 eV). The near‑identical peak positions in the Std:QGeom spectrum demonstrate that these spectral changes are largely geometric in nature.

The most striking finding emerges from an analysis of exciton spatial distribution. Using the BSE wavefunctions, the authors compute Mulliken exciton populations for each of the four monomers in the unit cell, separately for the electron (particle) and hole components. In the classical Std case the populations are uniformly 0.25 on each monomer, with negligible variance, reflecting the high symmetry of the crystal. Quantizing protons (NEO) dramatically broadens the distribution: standard deviations increase by two orders of magnitude, and the populations deviate substantially from 0.25, indicating pronounced anisotropy. This anisotropy is especially evident for hydrogen‑bonded monomer pairs (Mol1‑Mol3 and Mol2‑Mol4), where the difference in particle or hole populations between the two partners can be sizable for specific excited states (e.g., the 51st excitation). The Std:QGeom results retain some anisotropy but differ from NEO, confirming that proton NQEs exert a direct electronic effect beyond mere structural relaxation.

These results imply that proton quantum delocalization can modulate exciton localization and directionality in hydrogen‑bonded organic solids, even when the overall optical gap remains unchanged. Such modulation could influence charge‑separation efficiencies, energy‑transfer pathways, and the design of organic optoelectronic devices that rely on hydrogen‑bond networks (e.g., organic LEDs, supramolecular aggregates, and bio‑inspired pigments). Methodologically, the work showcases the feasibility of integrating NEO with GW/BSE to treat both electronic correlation and nuclear quantum effects on equal footing, opening avenues for accurate excited‑state modeling of complex condensed‑phase systems where light nuclei play a pivotal role.