Date of Award

Spring 5-6-2021

Document Type

Honors Project

Degree Name

Bachelor of Science


Chemistry and Physics

Department Chair or Program Director

Asper, Janet

First Advisor

Makhija, Varun

Major or Concentration



The recent development of attosecond laser pulses provides a direct path to observing the electronic dynamics of excited molecules. Recently proposed experimental methods re- quire that the measurements be made in the molecular frame, that is, that the molecule is in a fixed orientation. However, quantum mechanics does not allow this. Here we examine instead the full dimensional, laboratory frame, time evolving probability distribution gen- erated by resonant excitation of a molecular sample. Quantum dynamics are driven by both the populations of quantum states and the coherences between them. Since the total angular momentum of an isolated system is conserved, we are able to form a general formalism to examine these aspects by introducing a new operator, the Angular Momentum Coherence Operator (AMCO). We use these to study coherences between excited electronic states as well as photoionization from rotational coherences excited in the ground electronic state.

In order to investigate electronic coherences in the laboratory frame, we identified and cal- culated the off diagonal density matrix elements in the laboratory frame. We find that these matrix elements are composed of the Electronic Angular Distribution Moments (EADMs), which are expectation values of the AMCOs. The EADMs determine the angular distribu- tion of electronic coherences in the laboratory frame. We find that the time dependence of this laboratory frame angular distribution is synchronized with electronic coherences in the molecular frame. Demonstrative calculations were carried out for the molecule 4-amino- 4’-nitrostilbene resonantly excited by an attosecond pulse.

Additionally, rotational coherences in the electronic ground state are also characterized by the AMCOs. We used rotational coherences to develop a mathematical protocol for re- constructing molecular frame photoelectron distributions (MFPADs) from laboratory frame measurements for polyatomic molecules. MFPADs give the probability of removing (ion- izing) an electron at a specific angle with respect to the molecular axis and have been shown to be effective probes of molecular electronic dynamics. We numerically demonstrated this MFPAD reconstruction method for the molecules N2 and C2H4. The new technique is expected to be generally applicable for a range of MF reconstruction problems involving photoionization of polyatomic molecules.

Thus, the AMCOs provide a generalized framework to analyze angular momentum co- herences in molecular dynamics.

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