Strain engineering has emerged as a powerful tool for modulating quantum confinement effects in nanostructures, enabling precise control over electronic and optical properties. Computational studies using density functional theory (DFT) and molecular dynamics (MD) simulations provide critical insights into how mechanical strain alters band structures, carrier confinement, and excitonic behavior in quantum dots, nanowires, and two-dimensional materials. These approaches allow researchers to predict strain-dependent phenomena without the need for extensive experimental trial and error.

DFT simulations have been particularly effective in studying strain-induced modifications to quantum confinement due to their ability to calculate electronic structures with high accuracy. For quantum dots, DFT studies reveal that compressive strain typically increases the bandgap by enhancing carrier localization, while tensile strain reduces it by delocalizing wavefunctions. In CdSe quantum dots, for example, a 2% compressive strain can increase the bandgap by approximately 0.1 eV, whereas tensile strain of the same magnitude decreases it by a comparable amount. The nonlinear relationship between strain and bandgap arises from the interplay between quantum confinement and strain-induced deformation potentials.

For nanowires, DFT calculations demonstrate that uniaxial strain along the growth axis modifies both the direct and indirect bandgaps differently depending on the crystallographic orientation. In Ge/Si core-shell nanowires, simulations show that compressive strain in the Ge core induces a transition from indirect to direct bandgap behavior at certain critical strain values. This occurs because strain shifts the conduction band minima relative to the valence band maxima, altering the fundamental gap nature. The strain distribution in such heterostructures is highly nonuniform, with the core experiencing different strain states than the shell, leading to complex modifications of the electronic structure.

Two-dimensional materials exhibit particularly strong strain sensitivity due to their atomic thinness. DFT studies of monolayer MoS2 reveal that biaxial tensile strain reduces the direct bandgap at the K point while increasing the spin-orbit splitting. At approximately 3% biaxial strain, the direct gap decreases by around 0.3 eV, significantly modifying the optical absorption spectrum. Uniaxial strain along specific crystallographic directions can even induce a direct-to-indirect bandgap transition in MoS2, fundamentally changing its optoelectronic properties. The strain response differs between monolayer and few-layer cases due to interlayer coupling effects.

Molecular dynamics simulations complement DFT by providing the atomic configurations under strain before electronic structure calculations. For nanostructures with significant lattice mismatch or complex strain distributions, MD can accurately predict the relaxed atomic positions prior to DFT analysis. This combined approach is essential for systems like core-shell nanowires where interface strain affects the entire electronic structure. MD simulations also reveal how strain propagates through nanostructures at finite temperatures, accounting for thermal fluctuations that pure DFT cannot capture.

The strain response of quantum confinement also depends strongly on the material system. In III-V semiconductor quantum dots like InAs, strain primarily affects the heavy-hole and light-hole splitting, while in II-VI materials like CdTe, the effect on exciton binding energy dominates. DFT calculations can quantify these differences by computing the strain-dependent effective masses and dielectric constants that govern confinement strength. For nanowires, the diameter plays a crucial role – thinner wires show greater strain sensitivity due to stronger quantum confinement effects competing with strain perturbations.

In transition metal dichalcogenides beyond MoS2, such as WS2 or WSe2, strain modifies both the bandgap and the valley polarization properties important for valleytronics applications. DFT simulations predict that certain strain configurations can enhance or suppress the valley splitting, enabling strain-engineered valley polarization. The spin-orbit coupling in these materials also changes with strain, affecting the spin texture of the bands near the valleys. These effects are particularly pronounced under nonuniform strain distributions that break symmetry differently than uniform strain.

For heterostructured nanomaterials, the interplay between quantum confinement and strain becomes even more complex. In quantum dot solids or stacked 2D materials, strain affects both the intraparticle confinement and the interparticle coupling simultaneously. DFT calculations must account for both aspects to predict the overall electronic structure modifications. In Moiré superlattices formed by strained 2D material bilayers, the resulting potential landscape creates additional confinement effects that depend sensitively on the strain state and twist angle.

The computational challenges in these studies include accurately describing the exchange-correlation effects under strain, especially for excited states and optical properties. Advanced DFT methods like hybrid functionals or GW approximations improve the bandgap predictions compared to standard local density approximation. For larger systems or dynamic strain processes, machine learning potentials trained on DFT data enable longer MD simulations while maintaining quantum mechanical accuracy. These approaches are particularly valuable for studying strain relaxation processes or defect formation under strain.

Temperature effects add another layer of complexity, as thermal expansion and electron-phonon coupling modify the strain response. Ab initio MD simulations can capture these effects by sampling the configuration space at finite temperatures before electronic structure analysis. The temperature-dependent strain coefficients obtained from such simulations often differ significantly from zero-temperature DFT predictions, especially for soft nanomaterials with strong anharmonicity.

The predictive power of these computational studies enables targeted design of strain-engineered nanomaterials for specific applications. By calculating how strain modifies the density of states, carrier mobility, or optical transition strengths, researchers can identify optimal strain configurations for devices like strained quantum dot lasers or tunable 2D material photodetectors. The combination of DFT and MD provides a comprehensive framework for understanding and harnessing strain-induced modifications to quantum confinement across diverse nanomaterial systems.

Future directions in this field include extending these methods to study dynamic strain processes, such as those induced by surface acoustic waves or ultrafast laser pulses. The development of more efficient computational workflows will also enable high-throughput screening of strain effects across material libraries, accelerating the discovery of novel strain-engineered nanomaterials with tailored quantum confinement properties. As computational power and methods continue advancing, these studies will provide even deeper insights into the fundamental physics of strain-coupled quantum phenomena at the nanoscale.