Computer simulations are an increasingly important pillar of science, along with exper-

iment and traditional pencil and paper theoretical work. Indeed, the development of the

needed approximations and methods needed to accurately calculate the properties of the

range of materials from molecules to nanostructures to bulk materials has been a great tri-

umph of the last 50 years and has led to an increased role for computation in science. The

need for quantitatively accurate predictions of material properties has never been greater,

as technology such as computer chips and photovoltaics require rapid advancement in the

control and understanding of the materials that underly these devices. As more accuracy is

needed to adequately characterize, e.g. the energy conversion processes, in these materials,

improvements on old approximations continually need to be made. Additionally, in order

to be able to perform calculations on bigger and more complex systems, algorithmic devel-

opment needs to be carried out so that newer, bigger computers can be maximally utilized

to move science forward.

In this work we discuss our endeavors to improve approximations and algorithms to an-

swer the challenge of better describing material properties. After an introduction to define

and discuss all the important concepts that appear later, we first discuss the calculation of

so-called satellite properties in the photoemission spectra (PES) of doped graphene. While

the GW approximation accurately produces the quasiparticle energies across a range of

materials from nanostructures and molecules to bulk metals and semiconductors, it does

not accurately produce the satellite properties seen in PES experiments. We find that a

more advanced treatment of the Green’s function, the cumulant expansion, is needed to

adequately describe the satellite properties of doped graphene on SiC. In addition to this

more advanced Green’s function treatment, a novel technique is devised for including the

screening due to the SiC substrate on which the doped graphene is placed. This more ad-

vanced treatment of the substrate is also crucial for obtaining agreement with experiment.

Next, we show how the cumulant expansion can be used to accurately predict the ARPES

spectra of bulk Si and the time-domain capacitance spectra of two-dimensional electron

gases (2DEGs) in semiconductor quantum wells, with both the quasiparticle and satellite

features given correctly (unlike in GW theory, in which only the quasiparticle properties

are predicted accurately). We then discuss carrier lifetimes from the GW approximation

in bulk Si and GaAs, showing how theory can provide access to detailed microscopic in-

formation that could be of use in designing more efficient photovoltaics. In chapter 6, we

discuss the effect of the pseudopotential approximation on excited-state GW calculations.

Finding a small amount of error due to the use of nodeless pseudowavefunctions when us-

ing pseudopotentials, we are able to understand the tendency of GW calculations that use

pseudowavefunctions to overestimate the band gap in many common semiconductors. We

quantify this error and suggest improved techniques for applications where this error is

too large. In the last section on research, we discuss the effect of self-consistency in GW

calculations. Chapter 7 is on computational algorithm development, and there we discuss

some algorithmic advances made in improving the BerkeleyGW code. A technique for bet-

ter distributing the data during the calculation of the inverse dielectric matrix is discussed

and shown to give very good performance improvements, especially for the large systems

that are becoming increasingly common. Other small improvements that allow for a more

accurate calculation of quasiparticle lifetimes are also discussed. Finally, a few appendices

are included for completeness.