Semiconductor nanoparticles (NPs) are a class of nanoscopic materials with highly tunable optical and electronic properties. The electronic density of states of these NPs depends strongly on both shape and size and has allowed semiconductor NPs to be tailored for applications in various fields including photovoltaics, solid-state lighting, and biological labeling. This work presents investigation of the effect of shape on excitonic properties of electronically excited NPs. Specifically, this work focuses on isovolumetric NPs and addresses the question of how optical properties of NPs are impacted by isovolumetic deformation of NP shapes. The effects of three shapes, representing 1D, 2D, and 3D quantum confinement, for three sizes and four semiconductor materials (CdSe, CdS, CdTe, and PbS) were studied. The electronic excitation in these NPs was described using electron−hole (eh) quasiparticle representation, and exciton binding energies, ehjoint probabilities, and eh-separation distances were calculated using the eh explicitly correlated Hartree−Fock method. The calculations demonstrated that increased anisotropy in the confinement potential resulted in decreased exciton binding energy in the NPs. Within a specific volume, it was found that nanorods exhibited lower exciton binding energies than did nanodisks and that nanodisks exhibited lower exciton binding energies than nanospheres of identical volume. In contrast, the trend for eh-joint probability was found to be opposite that of exciton binding energies. These results demonstrate that a relatively small change in NP structure can result in a substantial change in the excitonic properties of these nanomaterials.

The relationship between structure and property is central to chemistry and enables the understanding of chemical phenomena and processes. Need for an efficient conformational sampling of chemical systems arises from the presence of solvents and the existence of non-zero temperatures. However, conformational sampling of structures to compute molecular quantum mechanical properties is computationally expensive because a large number of electronic structure calculations are required. In this work, the development and implementation of the effective stochastic potential (ESP) method is presented to perform efficient conformational sampling of molecules. The overarching goal of this work is to alleviate the computational bottleneck associated with performing a large number of electronic structure calculations required for conformational sampling. We introduce the concept of a deformation potential and demonstrate its existence by the proof-by-construction approach. A statistical description of the fluctuations in the deformation potential due to non-zero temperature was obtained using infinite-order moment expansion of the distribution. The formal mathematical definition of the ESP was derived using the functional minimization approach to match the infinite-order moment expansion for the deformation potential. Practical implementation of the ESP was obtained using the random-matrix theory method. The developed method was applied to two proof-of-concept calculations of the distribution of HOMO-LUMO gaps in water molecules and solvated CdSe clusters at 300 K. The need for large sample size to obtain statistically meaningful results was demonstrated by performing 10 ESP calculations. The results from these prototype calculations demonstrated the efficacy of the ESP method for performing efficient conformational sampling. We envision that the fundamental nature of this work will not only extend our knowledge of chemical systems at non-zero temperatures but also generate new insights for innovative technological applications.

Electron-hole or quasiparticle representation plays a central role in describing electronic excitations in many-electron systems. For charge-neutral excitation, the electron-hole interaction kernel is the quantity of interest for calculating important excitation properties such as optical gap, optical spectra, electron-hole recombination, and electron-hole binding energies. The electron-hole interaction kernel can be formally derived from the density-density correlation function using both Green's function and time-dependent density functional theory (TDDFT) formalism. The accurate determination of the electron-hole interaction kernel remains a significant challenge for precise calculations of optical properties in the GW+BSE formalism. From the TDDFT perspective, the electron-hole interaction kernel has been viewed as a path to systematic development of frequency-dependent exchange-correlation functionals. Traditional approaches, such as many-body perturbation theory formalism, use unoccupied states (which are defined with respect to Fermi vacuum) to construct the electron-hole interaction kernel. However, the inclusion of unoccupied states has long been recognized as the leading computational bottleneck that limits the application of this approach for larger finite systems. In this work, an alternative derivation that avoids using unoccupied states to construct the electron-hole interaction kernel is presented. The central idea of this approach is to use explicitly correlated geminal functions for treating electron-electron correlation for both ground and excited state wave functions. Using this ansatz, it is derived using both diagrammatic and algebraic techniques that the electron-hole interaction kernel can be expressed only in terms of linked closed-loop diagrams. It is proved that the cancellation of unlinked diagrams is a consequence of linked-cluster theorem in real-space representation. The electron-hole interaction kernel derived in this work was used to calculate excitation energies in many-electron systems, and results were found to be in good agreement with the EOM-CCSD and GW+BSE methods. The numerical results highlight the effectiveness of the developed method for overcoming the computational barrier of accurately determining the electron-hole interaction kernel to applications of large finite systems such as quantum dots and nanorods.

Obtaining statistical distributions by sampling a large number of conformations is vital for an accurate description of temperature-dependent properties of chemical systems. However, constructing distributions with 10 5 −10 6 samples is computationally challenging because of the prohibitively high computational cost of performing first-principles quantum mechanical calculations. In this work, we present a new technique called the effective stochastic potential configuration interaction singles (ESP-CIS) method to obtain excitation energies. The ESP-CIS method uses random matrix theory for the construction of an effective stochastic representation of the Fock operator and combines it with the CIS method. Excitedstate energies of PbS quantum dots (0.75−1.75 nm) at temperatures of 10−400 K were calculated using the ESP-CIS method. Results from a total of 27 million excitation energy calculations revealed the distributions to be sub-Gaussian in nature with negative skewness, which progressively became red-shifted with increasing temperature. This study demonstrates the efficacy of the ESP-CIS method as a general-purpose method for efficient excited-state calculations.

Bare aluminum metal surfaces are highly reactive, which leads to the spontaneous formation of a protective oxide surface layer. Because many subsequent corrosive processes are mediated by water, the structure and dynamics of water at the oxide interface are anticipated to influence corrosion kinetics. Using molecular dynamics simulations with a reactive force field, we model the behavior of aqueous aluminum metal ions in water adsorbed onto aluminum oxide surfaces across a range of ion concentrations and water film thicknesses corresponding to increasing relative humidity. We find that the structure and diffusivity of both the water and the metal ions depends strongly on the humidity of the environment and the relative height within the adsorbed water film.Aqueous aluminum ion diffusion rates in water films corresponding to a typical indoor relative humidity of 30% are found to be more than two orders of magnitude slower than self-diffusion of water in the bulk limit. Connections between metal ion diffusivity and corrosion reaction kinetics are assessed parametrically with a reductionist model based on a 1D continuum reaction-diffusion equation. Our results highlight the importance of incorporating the properties specific to interfacial water in predictive models of aluminum corrosion.