| The simulation of many-electron systems plays a vital role in understanding condensed matter. Yet, even with modern computational power, exact quantum mechanical calculations are limited to a few electrons. This reality has fueled the development of a wide variety of approximate methods to reduce the number of electronic degrees of freedom in a calculation while maintaining accuracy. A prominent member in this class of methods is pseudopotential theory. In pseudopotential theory, most electrons are treated implicitly by enforcing the orthogonality between themselves and the explicitly treated electrons through the use of a repulsive potential. Unfortunately, the calculation of the pseudopotential itself is computationally intensive, and this has limited the use of exact pseudopotential theory. Instead, approximate methods are often used.;In this dissertation, a new analytically exact reformulation of pseudopotential theory is presented. This formalism has two principle advantages. First, it is physically transparent and provides a direct geometric interpretation of pseu- is physically transparent and provides a direct geometric interpretation of pseudopotential theory. Second (and most importantly), it is significantly more computationally efficient. This efficiency results from the ability of the formalism to solve for the exact pseudopotential without ever requiring the calculation of the potential energy operator. As a demonstration of the method, the one-electron pseudopotential for a tetrohydrofuran molecule interacting with an excess electron is calculated. To the best of my knowledge, this is the largest molecule for which an exact pseudopotential has been calculated, and, with this new formalism, the pseudopotential was calculated in less than 15 seconds.;These types of pseudopotentials (i.e. a molecule interacting with an excess electron) are frequently used to calculate the behavior of excess electrons in condensed phase environments. Thus, in conclusion, this dissertation will explore the effect of electronic symmetry on the behavior of the charge-transfer-to-solvent (CTTS) reaction through the use of mixed quantum/classical molecular dynamics simulations. This work reduces the system to a one-electron problem where the remainder of the electrons is treated via a pseudopotential developed by other researchers. This work illustrates the importance of pseudopotential theory in enabling the calculation of condensed-phase systems. |
