Configuration interaction (CI) methods are a cornerstone of quantum mechanical calculations for studying multiexciton states in nanoparticles, particularly in semiconductor quantum dots and other nanoscale systems. These methods provide a systematic framework for capturing electron-electron and electron-hole interactions, which are critical for understanding optical and electronic properties. The CI approach expands the wavefunction as a linear combination of Slater determinants, allowing for the inclusion of electron correlation effects beyond mean-field approximations like Hartree-Fock or density functional theory.

The foundation of CI lies in constructing a basis of excited-state configurations from a reference wavefunction, typically the ground state. For multiexciton states, such as biexcitons or triexcitons, the method accounts for interactions between multiple electron-hole pairs. Single-reference CI starts from one dominant configuration, usually the Hartree-Fock solution, and includes excitations of varying degrees, such as singles (CIS), doubles (CID), or up to full CI (FCI) where all possible excitations are considered. While single-reference CI is computationally tractable for small systems, it can fail for strongly correlated states where multiple configurations contribute significantly. This limitation is addressed by multi-reference CI (MRCI), which uses a set of reference configurations to better describe degenerate or near-degenerate states.

In nanoparticles, particularly quantum dots, CI methods are indispensable for predicting excitonic properties. The confinement of charge carriers in these systems leads to discrete energy levels and enhanced Coulomb interactions, making multiexciton states experimentally observable. For example, biexciton binding energies—the energy difference between two excitons and a biexciton—are a key metric for quantum dot applications in lasers and light-emitting devices. CI calculations have shown that biexciton binding energies in CdSe quantum dots range from 10 to 30 meV, depending on dot size and shape. These values align with experimental measurements, validating the CI approach.

Auger processes, where non-radiative recombination of an exciton transfers energy to another carrier, are another area where CI methods provide critical insights. Auger recombination rates are sensitive to the overlap of electron and hole wavefunctions, which CI accurately captures through explicit inclusion of electron correlation. Studies on PbS and CdTe quantum dots reveal Auger lifetimes on the order of picoseconds, consistent with time-resolved spectroscopy data. The ability of CI to model these processes is vital for designing quantum dots with suppressed Auger recombination, a requirement for applications like single-photon sources.

Comparisons between single-reference and multi-reference CI highlight their respective strengths. Single-reference CI is computationally efficient and suitable for weakly correlated systems, but it struggles with states involving multiple excitations or near-degenerate configurations. MRCI, while more accurate, demands higher computational resources due to the larger configuration space. For instance, MRCI studies of InP quantum dots demonstrate significant improvements in predicting absorption spectra compared to single-reference methods, particularly for higher-energy transitions. However, the computational cost scales rapidly with system size, limiting MRCI to smaller nanoparticles or simplified models.

II-VI semiconductor nanoparticles, such as CdSe and CdTe, have been extensively studied using CI methods. These materials exhibit strong quantum confinement and sizable biexciton binding energies. CI calculations reveal that reducing quantum dot size increases Coulomb interactions, leading to larger biexciton binding energies. For CdSe dots with diameters below 5 nm, binding energies can exceed 20 meV, a trend corroborated by photoluminescence spectroscopy. Similarly, III-V semiconductors like InAs and GaAs show distinct multiexciton behavior due to their different dielectric constants and effective masses. CI studies predict biexciton binding energies in InAs dots to be lower than in II-VI counterparts, typically around 5-15 meV, reflecting weaker confinement effects.

Computational limitations of CI methods remain a challenge. The factorial scaling of the configuration space with the number of electrons and basis functions restricts applications to moderately sized systems. For nanoparticles beyond a few nanometers, approximations like truncated CI or selected CI are necessary. Parallel computing and algorithmic optimizations have extended the reach of CI, but full CI remains impractical for large nanoclusters. Recent advances in stochastic CI and machine learning-assisted selection of configurations offer promising avenues to mitigate these limitations.

In summary, configuration interaction methods are a powerful tool for investigating multiexciton states in nanoparticles. Their ability to capture electron correlation and electron-hole interactions makes them indispensable for predicting optical properties, biexciton binding energies, and Auger processes. While single-reference CI provides a balance between accuracy and computational cost, multi-reference CI is essential for strongly correlated systems. Applications to II-VI and III-V quantum dots demonstrate the method's success in reproducing experimental observations, though computational constraints necessitate ongoing methodological developments. As nanotechnology advances, CI methods will continue to play a central role in understanding and designing nanoscale materials with tailored excitonic properties.