Density functional theory has become an indispensable tool for investigating the electronic and structural properties of semiconductor and metallic nanowires. The method provides atomic-scale insights into quantum confinement effects, surface states, and strain-induced modifications that govern nanowire behavior. Unlike bulk materials, nanowires exhibit unique characteristics due to their reduced dimensionality, making DFT particularly valuable for understanding their fundamental properties.

Quantum confinement effects in nanowires arise when the wire diameter approaches the de Broglie wavelength of charge carriers. DFT calculations reveal how confinement along different crystallographic directions alters electronic structure. For silicon nanowires oriented along the [110] direction, bandgap widening occurs as diameters decrease below 5 nm, with the direct-to-indirect bandgap transition disappearing below 2 nm. GaN nanowires show similar trends but maintain direct bandgap characteristics even at small diameters due to stronger quantum confinement of electrons in the conduction band. Metallic nanowires such as gold exhibit discrete electronic states and conductance quantization when diameters approach 1 nm, as predicted by DFT-calculated local density of states.

Surface states play a critical role in nanowire properties due to their high surface-to-volume ratio. DFT enables accurate modeling of surface reconstructions and their impact on electronic behavior. Silicon nanowires with [111] orientation develop surface states within the bandgap when passivated with hydrogen, while unpassivated surfaces show metallic character due to dangling bonds. GaN nanowires exhibit Fermi level pinning caused by nitrogen vacancies at surfaces, as confirmed by DFT-calculated defect formation energies. For metallic nanowires like platinum, surface states contribute to enhanced catalytic activity, with DFT revealing the relationship between surface coordination numbers and adsorption energies.

Strain engineering in nanowires can be systematically studied using DFT through controlled application of tensile or compressive strains. Silicon nanowires under 2% axial strain show significant changes in effective mass, with electron mobility increasing by up to 30% under tensile strain. GaN nanowires demonstrate piezoelectric effects under strain, with DFT predicting polarization-induced charge separation at rates of 0.03 C/m² per percent strain. Metallic nanowires exhibit modified d-band centers under strain, altering their chemical reactivity. DFT calculations on gold nanowires reveal that 1% compressive strain shifts the d-band center upward by 0.2 eV, increasing CO adsorption energy by 15%.

Conductance quantization and contact effects in nanowires are accurately captured by DFT combined with non-equilibrium Green's function methods. For gold nanowires with diameters below 1 nm, DFT predicts integer multiples of the quantum conductance unit G0 = 2e²/h, with the exact value depending on the number of conduction channels. Contact geometry significantly affects transport properties, as shown by DFT studies of silicon nanowires bonded to aluminum electrodes, where interface states reduce conductance by 40% compared to ideal contacts. The method also reveals how atomic-scale defects at contacts create scattering centers that degrade performance.

Case studies demonstrate DFT's predictive power for specific nanowire systems. Silicon nanowires with diamond cubic structure show diameter-dependent bandgap variations:
Diameter (nm) | Bandgap (eV)
1.5 | 2.1
3.0 | 1.4
5.0 | 1.1

GaN nanowires in wurtzite structure exhibit spontaneous polarization effects, with DFT calculating built-in electric fields of 3 MV/cm along the [0001] direction. Metallic copper nanowires display size-dependent stability, with DFT predicting a transition from face-centered cubic to pentagonal symmetry below 2 nm diameter.

Modeling extended defects in nanowires presents significant challenges for DFT due to computational limitations. Dislocations in silicon nanowires require supercells containing thousands of atoms to properly represent strain fields, pushing the boundaries of current computational resources. Surface reconstructions add further complexity, as seen in gold nanowires where the equilibrium surface geometry changes from {100} to {111} facets below 3 nm diameter, requiring large-scale DFT calculations to capture the transition accurately.

The accuracy of DFT predictions depends critically on exchange-correlation functional selection. For semiconductor nanowires, hybrid functionals like HSE06 provide better bandgap estimates compared to standard LDA or GGA, at the cost of increased computational expense. Metallic nanowires require careful treatment of van der Waals interactions for surface and interface properties, with optB88-vdW functional showing good agreement with experimental data for noble metal nanowires.

Future developments in DFT methodology will address current limitations in nanowire modeling. Linear-scaling algorithms and machine learning potentials promise to extend accessible system sizes while maintaining quantum mechanical accuracy. Improved treatment of excited states will enhance predictions of optical properties and hot carrier effects in nanowires. As computational power increases, DFT will enable more comprehensive studies of defect dynamics and finite-temperature effects in these nanostructured systems.

The application of DFT to semiconductor and metallic nanowires has provided fundamental insights that guide their use in electronic devices, sensors, and energy applications. By connecting atomic-scale structure to macroscopic properties, DFT serves as a bridge between theoretical understanding and practical nanowire engineering. Continued methodological advances will further strengthen its role in nanomaterial design and optimization.