Density functional theory has become an indispensable tool for modeling the optoelectronic properties of nanostructures due to its balance between computational efficiency and accuracy. The method provides insights into electronic structure, optical transitions, and excited-state properties critical for understanding light-matter interactions at the nanoscale. When applied to low-dimensional systems, DFT reveals quantum confinement effects, dielectric screening modifications, and interfacial phenomena that govern optoelectronic performance.

Exciton binding energy calculations represent one of the most important applications of DFT in nanostructure characterization. The reduced dielectric screening in nanostructures compared to bulk materials leads to significantly enhanced exciton binding energies. For monolayer transition metal dichalcogenides like MoS2, DFT calculations predict binding energies in the range of 300-600 meV, consistent with experimental measurements. The accurate determination of these energies requires careful treatment of electron-hole interactions through approaches such as the GW approximation, which corrects DFT's underestimation of band gaps. In perovskite nanocrystals such as CsPbBr3, DFT reveals how quantum confinement increases exciton binding energies from approximately 40 meV in bulk to over 150 meV in 5 nm particles.

Optical absorption spectra predictions benefit from DFT's ability to calculate dipole-allowed transitions between valence and conduction bands. Standard DFT methods using the random phase approximation can qualitatively reproduce absorption features but often require scissor operators to align theoretical and experimental band gaps. More advanced approaches solve the Bethe-Salpeter equation, which explicitly includes electron-hole interactions missing in independent-particle approximations. This method successfully reproduces measured absorption spectra in systems like CdSe quantum dots, including the size-dependent blue shift of absorption edges and fine structure splitting. For 2D heterobilayers such as MoSe2-WS2, the Bethe-Salpeter equation reveals interlayer exciton formation with lifetimes exceeding those of intralayer excitons by orders of magnitude.

Quantum efficiency estimations rely on DFT-derived parameters including radiative recombination rates, non-radiative pathways, and exciton dissociation probabilities. In lead halide perovskite nanocrystals, DFT calculations show how surface termination affects trap state formation, explaining experimental observations of near-unity quantum yields in properly passivated systems. For carbon quantum dots, DFT helps identify emission mechanisms by correlating functional group configurations with photoluminescence quantum yields. The method also quantifies Auger recombination rates in quantum dots, a critical factor limiting quantum efficiency at high excitation densities.

The Bethe-Salpeter equation approach extends beyond standard DFT by treating excitonic effects through a two-particle Green's function formalism. This proves essential for accurate modeling of systems with strong electron-hole correlations, such as organic semiconductors or 2D materials. The equation's kernel contains direct Coulomb attraction and exchange terms that modify optical transition energies and oscillator strengths. In graphene nanoribbons, this approach reveals dark exciton states invisible to standard absorption measurements but important for thermalization processes. For transition metal dichalcogenide monolayers, it explains the large A and B exciton splitting observed in circular dichroism experiments.

Strain engineering of nanostructures represents another area where DFT provides critical insights. Applied strain modifies band edges through deformation potential coupling and changes in orbital overlap. In black phosphorus nanosheets, DFT predicts a transition from direct to indirect gap under 3% uniaxial strain. For core-shell quantum dots like CdSe/CdS, strain-induced band bending affects carrier localization and recombination dynamics. Perovskite nanocrystals exhibit particularly strong strain sensitivity, with DFT calculations showing that just 2% compressive strain can increase photoluminescence quantum yield by enhancing radiative recombination rates.

Heterostructure band alignment studies benefit from DFT's ability to handle interface effects and charge transfer. The method accurately predicts type I, II, or III band alignments in 2D material heterostacks based on layer composition and stacking angle. In MoS2/WS2 vertical heterostructures, DFT reveals a type II alignment with 0.4 eV conduction band offset, enabling efficient charge separation. For perovskite nanocrystal assemblies, DFT helps understand energy transfer mechanisms by quantifying exciton coupling between neighboring particles. The inclusion of van der Waals corrections proves essential for accurate alignment predictions in weakly coupled systems.

Perovskite nanocrystals serve as an excellent test case for DFT's capabilities in nanoscale optoelectronics. Calculations on CsPbI3 nanocrystals reproduce the size-dependent band gap tuning from 1.73 eV in bulk to 2.45 eV in 5 nm particles. The method also explains the unusual defect tolerance of these materials by showing that intrinsic defects form shallow rather than deep traps. For mixed halide perovskites, DFT reveals halide segregation mechanisms under illumination through calculation of migration barriers and cluster formation energies.

2D material heterobilayers demonstrate DFT's power in modeling interlayer phenomena. In twisted bilayer graphene, the method predicts moiré superlattice effects that modify optical selection rules. For transition metal dichalcogenide heterostacks like MoSe2/WSe2, DFT calculates interlayer exciton binding energies exceeding 200 meV due to reduced dielectric screening. The inclusion of spin-orbit coupling proves critical for accurate predictions in these heavy-element systems, explaining valley polarization effects observed in time-resolved spectroscopy.

While DFT provides powerful insights into nanoscale optoelectronics, several challenges remain. The accurate description of charge transfer excitons requires large supercells that strain computational resources. Treatment of temperature effects on optical properties often relies on approximate phonon coupling models. Despite these limitations, continued improvements in exchange-correlation functionals and computational algorithms ensure DFT's central role in nanomaterial design and characterization. The method's ability to connect atomic-scale structure with macroscopic optoelectronic properties makes it indispensable for both fundamental studies and technological applications of nanostructures.