Recent improvements in energy resolution for electron energy-loss spectroscopy in the scanning transmission electron microscope (STEM-EELS) allow novel effects in the low-loss region of the electron energy-loss spectrum to be observed. This dissertation explores what new information can be obtained with the combination of meV EELS energy resolution and atomic spatial resolution in the STEM. To set up this up, I review nanoparticle shape effects in the electrostatic approximation and compare the “classical” and “quantum” approaches to EELS simulation. Past the electrostatic approximation, the imaging of waveguide-type modes is modeled in ribbons and cylinders (in “classical" and “quantum" approaches, respectively), showing how the spatial variations of such modes can now be imaged using EELS. Then, returning to the electrostatic approximation, I present microscopic applications of low-loss STEM-EELS. I develop a “classical” model coupling the surface plasmons of a sharp metallic nanoparticle to the dipolar vibrations of an adsorbate molecule, which allows expected molecular signal enhancements to be quantified and the resultant Fano-type asymmetric spectral line shapes to be explained, and I present “quantum” modelling for the charged nitrogen-vacancy (NV-) and neutral silicon-vacancy (SiV0) color centers in diamond, including cross-sections and spectral maps from density functional theory. These results are summarized before concluding.

Many of these results have been previously published in Physical Review B. The main results of Ch. 2 and Ch. 4 were packaged as “Enhanced vibrational electron energy-loss spectroscopy of adsorbate molecules” (99, 104110), and much of Ch. 5 appeared as “Prospects for detecting individual defect centers using spatially resolved electron energy loss spectroscopy” (100, 134103). The results from Ch. 3 are being prepared for a forthcoming article in the Journal of Chemical Physics.

Phase problem has been long-standing in x-ray diffractive imaging. It is originated from the fact that only the amplitude of the scattered wave can be recorded by the detector, losing the phase information. The measurement of amplitude alone is insufficient to solve the structure. Therefore, phase retrieval is essential to structure determination with X-ray diffractive imaging. So far, many experimental as well as algorithmic approaches have been developed to address the phase problem. The experimental phasing methods, such as MAD, SAD etc, exploit the phase relation in vector space. They usually demand a lot of efforts to prepare the samples and require much more data. On the other hand, iterative phasing algorithms make use of the prior knowledge and various constraints in real and reciprocal space. In this thesis, new approaches to the problem of direct digital phasing of X-ray diffraction patterns from two-dimensional organic crystals were presented. The phase problem for Bragg diffraction from two-dimensional (2D) crystalline monolayer in transmission may be solved by imposing a compact support that sets the density to zero outside the monolayer. By iterating between the measured stucture factor magnitudes along reciprocal space rods (starting with random phases) and a density of the correct sign, the complex scattered amplitudes may be found (J. Struct Biol 144, 209 (2003)). However this one-dimensional support function fails to link the rod phases correctly unless a low-resolution real-space map is also available. Minimum prior information required for successful three-dimensional (3D) structure retrieval from a 2D crystal XFEL diffraction dataset were investigated, when using the HIO algorithm. This method provides an alternative way to phase 2D crystal dataset, with less dependence on the high quality model used in the molecular replacement method.

Photosystem II (PSII) is a large protein-cofactor complex. The first step in

photosynthesis involves the harvesting of light energy from the sun by the antenna (made

of pigments) of the PSII trans-membrane complex. The harvested excitation energy is

transferred from the antenna complex to the reaction center of the PSII, which leads to a

light-driven charge separation event, from water to plastoquinone. This phenomenal

process has been producing the oxygen that maintains the oxygenic environment of our

planet for the past 2.5 billion years.

The oxygen molecule formation involves the light-driven extraction of 4 electrons

and protons from two water molecules through a multistep reaction, in which the Oxygen

Evolving Center (OEC) of PSII cycles through 5 different oxidation states, S0 to S4.

Unraveling the water-splitting mechanism remains as a grant challenge in the field of

photosynthesis research. This requires the development of an entirely new capability, the

ability to produce molecular movies. This dissertation advances a novel technique, Serial

Femtosecond X-ray crystallography (SFX), into a new realm whereby such time-resolved

molecular movies may be attained. The ultimate goal is to make a “molecular movie” that

reveals the dynamics of the water splitting mechanism using time-resolved SFX (TRSFX)

experiments and the uniquely enabling features of X-ray Free-Electron Laser

(XFEL) for the study of biological processes.

This thesis presents the development of SFX techniques, including development of

new methods to analyze millions of diffraction patterns (~100 terabytes of data per XFEL

experiment) with the goal of solving the X-ray structures in different transition states.

ii

The research comprises significant advancements to XFEL software packages (e.g.,

Cheetah and CrystFEL). Initially these programs could evaluate only 8-10% of all the

data acquired successfully. This research demonstrates that with manual optimizations,

the evaluation success rate was enhanced to 40-50%. These improvements have enabled

TR-SFX, for the first time, to examine the double excited state (S3) of PSII at 5.5-Å. This

breakthrough demonstrated the first indication of conformational changes between the

ground (S1) and the double-excited (S3) states, a result fully consistent with theoretical

predictions.

The power of the TR-SFX technique was further demonstrated with proof-of principle

experiments on Photoactive Yellow Protein (PYP) micro-crystals that high

temporal (10-ns) and spatial (1.5-Å) resolution structures could be achieved.

In summary, this dissertation research heralds the development of the TR-SFX

technique, protocols, and associated data analysis methods that will usher into practice a

new era in structural biology for the recording of ‘molecular movies’ of any biomolecular

process.

One of the most important issues in femtosecond free electron laser X-ray diraction is to reconstruct the 3D charge density of molecule from a mass of diraction snapshots. In order to determine the orientation of single molecule from diraction patterns, we rst determine the moments and products of inertia of this from 2D experiment data (diraction patterns or EM images to obtain the elements of the inertia tensor. If diraction patterns from uniformly random orientations or some preferred orientations are collected, the principal axes of the molecule can be extracted, together with the Euler angles which relate the principal axes of the molecule to the laboratory frame axes. This is achieved by nding the maximum and minimum values for the measured moments from many single-molecule patterns. Simulations for GroEL protein indicates that the calculation of the autocorrelation help eliminate the Poisson noise in Cryo- EM images and can make correct orientation determination. The eect of water jacket surrounding the protein molecule is studied based on molecular dynamics simulation result. The intensities from water and interference is found to suppress those from protein itself. A method is proposed and applied to the simulation data to show the possibility for it to overcome the water background problem. The scattering between Bragg re ections from nanocrystals is used to aid solution of the phase problem. We describe a method for reconstructing the charge density of a typical molecule within a single unit cell, if suciently nely-sampled diraction data are available from many nanocrystals of dierent sizes lying in the same orientations without knowledge of the distribution of particle size or requiring atomic-resolution data. Triple correlation of the diraction patterns are made use of to reconiii