Date of Award

May 2020

Degree Type


Degree Name

Doctor of Philosophy (PhD)




Arindam Chakraborty


Chemical Structure, Computational Chemistry, Random Matrix Theory, Stochastic Sampling, Temperature Effect

Subject Categories

Physical Sciences and Mathematics


Temperature plays an incredibly important role in determining what values a quantum mechanical property of a chemical system can assume. The mechanism by which temperature and the other features of a chemical system’s environment effects observable properties is through their effect on the population of thermally-accessible structures. As temperature changes, the population of these thermally-accessible structures shifts, and correspondingly so do the distributions of quantum mechanical properties. Prediction, calculation, and analysis of these distributions are fundamental to the study of statistical mechanics, and are integral to understanding what role the chemical environment has on any quantum mechanical property that may be of interest. One of the largest ongoing challenges concerning the determination of quantum mechanical distributions is the need for 105 to 106 conformational samples from the population of structures in order to obtain accurate and reliable distributions of properties. For large chemical systems consisting of many electrons, performing ab-initio calculations on such a large number of structures is computationally infeasible using traditional quantum chemistry methods. This problem is even further exacerbated when distributions of excited electronic state properties such as electronic spectra are desired, due to the increased computational cost of ab-initio excited-state techniques.

To overcome this computational barrier, I have developed the Effective Stochastic Potential (ESP) method which addresses the challenge of conformational sampling. The ESP method is a first-principles technique which uses random matrix theory to treat noisy chemical environments of a system stochastically. In doing so, the computational cost of performing conformational sampling on the system can be drastically reduced. The accuracy of the ESP method has been confirmed by benchmarking against calculations of both ground and excited-state properties of H2O. I have applied the ESP method on various systems, including semiconductor nanoparticles to efficiently obtain temperature-dependent distributions of HOMO-LUMO gap energies, excitation energies, and exciton binding energies comprised of a million samples. For many of the systems studied, calculation of these distributions using traditional first-principle methods would be infeasible. Using the ESP method, it has been calculated that the distributions of excitation energies of PbS and CdSe nanoparticles have a pronounced red-shift as the temperature of the system increases. It has also been found that the excitation energy distributions in PbS nanoparticles exhibit sub-Gaussian characteristics at physically-relevant temperatures. These results highlight the ability of the ESP method to uncover unique temperature-dependent features of quantum mechanical distributions that may otherwise be impossible to obtain.


Open Access

Available for download on Sunday, August 15, 2021