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

Sampreeti Bhattacharya, Jianhang Xu+2 more|arXiv (Cornell University)|Feb 8, 2026

melanin and skin pigmentation0 citations

TL;DR

The paper uses the nuclear-electronic orbital (NEO) method within the Bethe-Salpeter equation (BSE) on GW calculations to study how proton quantum effects modify electronic excitations in a hydrogen-bonded eumelanin-like organic crystal, highlighting geometry-derived and anisotropy effects on excitons.

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.

Motivation & Objective

• Motivate understanding of nuclear quantum effects (NQEs) on electronic excitations in hydrogen-bonded organic materials.
• Demonstrate how the NEO method integrated with BSE@GW can quantify proton quantum effects on excitations.
• Assess whether observed effects are primarily geometry-derived or intrinsically electronic.
• Characterize exciton anisotropy and localization across monomer units in the crystal.
• Provide insights into how proton quantization alters exciton binding energy and spectra.

Proposed method

• Combine first-principles Green’s function theory (GW/BSE) with the nuclear-electronic orbital (NEO) approach to quantize protons.
• Compute quasi-particle energies with G0W0 and solve the BSE in the Tamm-Dancoff approximation.
• Use the NEO-DFT framework to obtain proton position expectation values and corresponding basis sets for protons.
• Analyze excitons via exciton probability density and Mulliken exciton populations on monomer units.
• Compare Std, NEO, and Std:QGeom scenarios to separate geometry-derived from direct quantum effects.
• Quantify exciton anisotropy through Mulliken populations and monitor changes across the 4 monomers in the unit cell.

Experimental results

Research questions

• RQ1 How do proton quantum effects influence the quasi-particle gap and optical gap in a hydrogen-bonded organic solid?
• RQ2 To what extent are proton quantum effects on excitations geometry-derived versus intrinsic to the electronic Hamiltonian?
• RQ3 Do proton quantum effects induce anisotropy or localization of excitons among monomer units?
• RQ4 How is exciton binding energy affected by proton quantization in a crystalline organic solid?
• RQ5 Can NEO-BSE@GW capture changes in peak intensities and distribution of exciton densities beyond the overall spectra?

Key findings

• Proton quantization reduces the quasi-particle gap from 5.95 eV (Std) to 5.89 eV (NEO).
• Optical gap changes are small: 4.49 eV (Std) vs 4.48 eV (NEO).
• Exciton binding energy decreases from 1.46 eV (Std) to 1.41 eV (NEO); Std:QGeom gives 1.44 eV.
• The overall optical absorption spectrum shape is largely unchanged; proton quantum effects mainly produce geometry-derived shifts, with some peak-height changes.
• Exciton anisotropy among monomers increases when protons are quantized, evidenced by broader Mulliken population distributions and localization patterns in specific excited states (e.g., state 51).
• NEO protons introduce delocalization of proton density while smoothing the effective potential, leading to more homogeneous electronic structure than Std:QGeom, yet not purely geometric in origin.