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This dissertation explores the time-dependent equation-of-motion coupled-cluster (TD-EOM-CC)framework for the accurate calculation of the excited electronic states within molecules, with a focus on lowering the computational cost of the TD-EOM-CC time simulation. Chapter 1 is an introductory chapter, presenting the mathematical foundation for the methods discussed, descriptions of the treatment of the electronic ground state in Hartree-Fock and coupled-cluster theories, and discussing the ways in which electronic excited states can be calculated in electronic structure theory. Chapters 2 and 3 cover ways to reduce the computational cost of a TD-EOM-CC procedure. First, because the choice of integrator has a significant effect on the cost of the simulation, we study an implementation of the short iterative Lanczos (SIL) scheme as an integrator for TD- EOM-CC methods and benchmark the cost and accuracy compared to the previously utilized 4th order Runge-Kutta scheme. We then discuss the use of the core-valence separation (CVS) approximation within the TD-EOM-CC framework for the calculation of core-electron excited states of molecular systems. Chapter 4 outlines a TD-EOM-CC framework for the calculation of molecular absorption spectra in the presence of finite external electric fields, and compares the stability of propagation within a finite field and propagation where the light is treated perturbatively when complex eigenvalues are present within the eigenspectrum.