First-Principles Insights into Surface and Ligand Effects in Stoichiometric HgTe Quantum Dots

Abstract: HgTe quantum dots are promising mid-infrared nanomaterials owing to their exceptional bandgap tunability, yet their electronic structure is strongly influenced by surface coordination and ligand passivation at ultrasmall sizes. Here, we employ atomistic simulations to systematically investigate stoichiometric HgTe nanoclusters with sizes 0.86 to 1.85 nm. The in silico exploration uncovers a transition from confinement-dominated electronic structures with delocalized frontier states in small self-passivated clusters to surface influenced characteristics in larger nanoclusters. Increased coordination and bond-length inhomogeneity in the larger nanoclusters generate localized near-gap states centered on undercoordinated surface atoms. At intermediate sizes, the band edge states become spatially separated on different regions of the cluster without forming deep gap states, marking the onset of surface induced electronic asymmetry. In larger clusters (1.8 nm), common neutral ligands like amines, thiols, phosphines, and alcohols effectively eliminate surface-derived localized states by restoring local coordination and altering the band edge electronic structure through ligand surface hybridization. The sensitivity of the bandgap to ligand identity and binding site underscores the interplay between surface coordination and ligand chemistry in shaping the electronic structure of these nanoclusters. These insights provide an atomistic understanding of size-dependent electronic structures in ultrasmall HgTe clusters. The study further establishes neutral ligands as powerful chemical handles for engineering frontier electronic states relevant to infrared optoelectronic functionality.

• The paper demonstrates that quantum confinement and surface coordination critically modulate electronic gap states in ultrasmall HgTe quantum dots.
• It shows that ligand passivation, via various neutral molecules, suppresses surface-localized states and effectively tunes bandgap sizes.
• The findings underscore that precise control over surface heterogeneity and ligand interactions is essential for designing efficient IR optoelectronic devices.

First-Principles Investigation of Size, Surface, and Ligand Effects in Stoichiometric HgTe Quantum Dots

Motivation and Background

HgTe quantum dots (QDs) have drawn interest as high-performance, size-tunable mid-infrared optoelectronic materials, particularly due to their unique band structure. Quantum confinement in HgTe—exhibiting bulk semimetallic character—induces a finite electronic gap and enables controllable spectral coverage from visible to long-wave IR. At ultrasmall sizes ($<$2 nm), a large fraction of atoms reside at the surface, rendering surface coordination, reconstruction, and ligand interactions pivotal in determining the quantum dot's electronic structure. The paper "First-Principles Insights into Surface and Ligand Effects in Stoichiometric HgTe Quantum Dots" (2606.08399) offers a systematic DFT-based elucidation of the interplay between size, surface heterogeneity, and ligand passivation in determining the electronic properties of stoichiometric HgTe nanoclusters.

Atomistic Model Construction and Electronic Structure Regimes

The authors constructed spherical, stoichiometric HgTe clusters comprising 14, 20, 38, 82, and 86 atoms (0.86–1.85 nm), ensuring sampling across the ultrasmall confinement regime, representative of the size range in colloidal synthesis. Structural relaxation using PBE-DFT (including D3(BJ) corrections) revealed that Hg preferentially occupies more internal positions, whereas Te is enriched at the outer shell, yielding an effectively Te-rich surface and partial self-passivation.

Electronic structure calculations—in particular HOMO-LUMO gaps, projected density of states (PDOS), real-space frontier orbital analysis, and inverse participation ratio (IPR)—demonstrate three distinct regimes:

• Confinement-Dominated Regime (14, 20 atoms): Relaxed clusters retain delocalized, molecular-like electronic states with clean gaps, and show no mid-gap states despite a high surface atom fraction. IPR values confirm delocalization, and PDOS reveals Te $p$-derived occupied and Hg $s$/Te $p$-hybridized unoccupied frontier states.
• Intermediate Regime (38 atoms): The HOMO and LUMO become spatially polarized on distinct regions (Te-rich vs. Hg-rich), producing an intrinsic electrostatic potential gradient akin to a built-in dipole. However, no deep gap states emerge, indicating that the onset of surface influence manifests as polarization, not defect formation.
• Surface-Influenced Regime (82, 86 atoms): Larger clusters exhibit shallow, surface-localized near-gap states with elevated IPR and real-space localization on undercoordinated surface regions. These arise from coordination and bond-length inhomogeneity at the cluster surface, not from charged or non-stoichiometric defects.

Spin-orbit coupling (SOC) and hybrid-functional (HSE) calculations confirm the robustness of these findings; relativistic and exchange effects modulate the energetic crowding of frontier states but do not remove the surface-induced localization trend.

Ligand Passivation and Site-Dependent Electronic Tuning

The passivation of 86-atom clusters with common neutral ligands—methylamine, methanethiol, methylphosphine, and methanol—reveals two tightly correlated phenomena:

1. Suppression of Surface-Localized States: Ligand coordination to undercoordinated Hg surface sites reduces bond-length dispersion, stabilizes surface motifs, and eliminates surface-derived localized near-gap states, restoring clean band gaps. The elimination of surface states is robust across all ligand types and adsorption geometries, as validated through DOS/IPR analysis.
2. Bandgap and Frontier-Level Modulation: The electronic gap size is strongly ligand- and site-dependent. Methanol yields the widest bandgap (0.88 eV), followed by methanethiol (0.82 eV), methylphosphine (0.77 eV), and methylamine (0.73 eV).

• The trend reflects the energetic alignment of ligand-localized orbitals relative to the QD band edges and the degree of ligand-surface orbital hybridization.
• Oxygen and phosphorus ligands minimally perturb the band edge, while nitrogen and sulfur ligands, characterized by greater orbital overlap, yield more pronounced bandgap reduction.
• The effect is also sensitive to adsorption site: local coordination environment and surface polarity (as represented by Face 1 vs. Face 2 domains) produce significant heterogeneity in both binding energies and electronic gaps.

Site-dependent partial passivation preserves or shifts localized near-gap states, underscoring that passivation must address all electronically vulnerable sites to effect complete surface state elimination. Binding energies per ligand ($-1.56$ to $-1.61$ eV) are relatively insensitive to ligand type at full coverage, but site selectivity emerges at lower coverage.

Theoretical and Practical Implications

This work establishes that electronic structure in ultrasmall stoichiometric HgTe QDs is an emergent property of the entangled effects of quantum confinement, coordination chemistry, and ligand-induced perturbations. The clear, size-dependent progression from delocalized to surface-localized states—culminating in strong ligand and adsorption-site dependence—demonstrates that:

• Ligands are active electronic modulators rather than simple passivants or stabilizers, with their orbital character and local dielectric environment directly responsible for band-edge engineering.
• Surface reconstruction and heterogeneity can dominate frontier state localization for clusters in the 1.5–2 nm regime, a critical consideration in device design and predictive modeling for HgTe QDs.
• Robustness to relativistic and hybrid-functional corrections reinforces that the observed surface effects are not artifacts of DFT approximations, but rather fundamental electronic features of these nanoclusters.

From an optoelectronic perspective, these trends have direct consequences in determining carrier trapping, exciton recombination rates, and spectral signatures—factors essential for the realization of high-efficiency photodetectors, NIR/SWIR emitters, and quantum optics devices.

Future Directions

Open research directions concern the extension of this atomistic understanding to:

• Non-stoichiometric and doped clusters, where excess carriers or vacancies could further complicate surface chemistry,
• Dynamic ligand exchange and competitive adsorption under operando synthetic or device-relevant conditions,
• Explicit inclusion of environmental effects (e.g., solvents, embedding matrices) and their effect on surface charge trapping or release,
• Scaling trends towards even larger cluster sizes, linking the ultrasmall regime to bulk-like nanocrystal behavior.

The methodology deployed here— DFT-based atomistic modeling with comprehensive surface and ligand sampling—provides a critical framework for subsequent studies bridging molecular and materials science perspectives.

Conclusion

The paper delivers a rigorous first-principles mapping of size, surface, and ligand effects in the electronic structure of stoichiometric HgTe QDs. Ligand chemistry and surface coordination emerge as decisive levers for tuning band edges and suppressing electronic inhomogeneity, with implications for the synthetic design of QDs tailored for specific optoelectronic functions. This work significantly advances the atomistic understanding of surface and ligand control in ultrasmall quantum dot systems, establishing foundational principles for the precision engineering of IR-active nanomaterials.