#### Date of Award

8-2014

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Chemistry

#### Advisor(s)

Arindam Chakraborty

#### Keywords

electron-hole correlation length, excited electronic states, explicitly correlated wave functions, ligand-induced quantum-confined Stark effect, quantum-confined Stark effect, quantum dots

#### Subject Categories

Chemistry | Physical Sciences and Mathematics

#### Abstract

The two main objectives of this dissertation are the systematic development of explicitly correlated electron-hole wave function based methods and the application of these methods to chemical systems with an

emphasis on nanoparticles.

The understanding of the basic physics of excited electronic states is an important consideration when developing new methods and applications. In this dissertation, excited electronic states were studied using the electron-hole quasiparticle representation. Theoretical treatment of electronic excitation in large quantum dots and nanoparticles is challenging because of the large number of electrons in the system. The quasiparticle representation provides an alternative representation that can partially alleviate the computational bottleneck associated with investigating these systems. However, in this representation, the effects of electron-hole correlation must be understood in order to accurately describe the system's optical and electronic properties.

The electron-hole wave function consists of two separate mathematical components which are the explicitly correlated part of the wave function and the reference wave function which is operated on by the explicitly correlated operator. This dissertation presents theoretical development of both of these components. In the first part, a systematic formulation for deriving the explicitly correlated form of the electron-hole wave function was performed. Towards that goal, the electron-hole correlation length was defined using the electron-hole cumulant. The construction of explicitly correlated wave function was improved by the introduction of the electron-hole correlation length which was determined using the electron-hole cumulant. The electron-hole correlation length allowed the determination of parameters in the explicitly correlated operator without the performance of energy minimizations. In the second part, the electron-hole reference wave function was improved by combining full configuration electron-hole wave function with the explicitly correlated operator.

The developed methods were used to investigate the quantum-confined Stark effect (QCSE) and the effect of pH on the optical properties of quantum dots. The effect of applied electric fields on nanoparticles is known as the quantum-conﬁned Stark effect. In this dissertation, the effect of both homogeneous and inhomogeneous electric fields on the optical and electronic properties of quantum dots was investigated. The effect of electric fields on the optical and electronic properties of a GaAs quantum dot was determined by combining the variational polaron transformation with the explicitly correlated electron-hole wave function. The presence of charged ligands also influenced the optical properties of quantum dot and this effect is known as the ligand-induced quantum-confined Stark effect. In this dissertation, the effect of pH on the optical properties of functionalized quantum dots were investigated by first calculating the charged states of the surface ligands at a given pH and then performing electron-hole explicitly correlated wave function based calculations in the electrostatic field generated by the charged ligands.

Theoretical methods developed in this dissertation have impacted the field of computational nanoscience by reducing the computational bottleneck to investigate nanoparticles and by providing novel avenues for improving accuracy of existing methods.

#### Access

Open Access

#### Recommended Citation

Blanton, Christopher Jon, "Theoretical investigation of the quantum-confined Stark effect" (2014). *Dissertations - ALL*. 160.

https://surface.syr.edu/etd/160