## New Theoretical Developments in Exploring Electronically Excited States: Including Localized Configuration Interaction Singles and Application to Large Helium Clusters

- Author(s): Closser, Kristina Danielle
- Advisor(s): Head-Gordon, Martin
- et al.

## Abstract

This thesis presents new developments in excited state electronic structure theory. Contrasted with the ground state, the electronically excited states of atoms and molecules often are unstable and have short lifetimes, exhibit a greater diversity of character and are generally less well understood.

The very unusual excited states of helium clusters motivated much of this work. These clusters consist of large numbers of atoms (experimentally 10^3-10^9 atoms) and bands of nearly degenerate excited states. For an isolated atom the lowest energy excitation energies are from 1s->2s and 1s->2p transitions, and in clusters describing the lowest energy band minimally requires four states per atom. In the ground state the clusters are weakly bound by van der Waals interactions, however in the excited state they can form well-defined covalent bonds.

The computational cost of quantum chemical calculations rapidly becomes prohibitive as the size of the systems increase. Standard excited-state methods such as configuration interaction singles (CIS) and time-dependent density functional theory (TD-DFT) can be used with ~100 atoms, and are optimized to treat only a few states. Thus, one of our primary aims is to develop a method which can treat these large systems with large numbers of nearly degenerate excited states. Additionally, excited states are generally formed far from their equilibrium structures. Vertical excitations from the ground state induce dynamics in the excited states. Thus, another focus of this work is to explore the results of these forces and the fate of the excited states.

Very little was known about helium cluster excited states when this work began, thus we first investigated the excitations in small helium clusters consisting of 7 or 25 atoms using CIS. The character of these excited states was determined using attachment/detachment density analysis and we found that in the n = 2 manifold the excitations could generally be interpreted as superpositions of atomic states with surface states appearing close to the atomic excitation energies and interior states being blue shifted by up to ~2 eV.

The dynamics resulting from excitation of He_7 were subsequently explored using ab initio molecular dynamics (AIMD). These simulations were performed with classical adiabatic dynamics coupled to a new state-following algorithm on CIS potential energy surfaces. Most clusters were found to completely dissociate and resulted in a single excited atomic state (90%), however, some trajectories formed bound, He*_2 (3%), and a few yielded excited trimers (<0.5%). Comparisons were made with available experimental information on much larger clusters.

Various applications of this state following algorithm are also presented. In addition to AIMD, these include excited-state geometry optimization and minimal energy path finding via the growing string method. When using state following we demonstrate that more physical results can be obtained with AIMD calculations. Also, the optimized geometries of three excited states of cytosine, two of which were not found without state following, and the minimal energy path between the lowest two singlet excited states of protonated formaldimine are offered as example applications.

Finally, to address large clusters, a local variation of CIS was developed. This method exploits the properties of absolutely localized molecular orbitals (ALMOs) to limit the total number of excitations to scaling only linearly with cluster size, which results in formal scaling with the third power of the system size. The derivation of the equations and design of the algorithm are discussed in detail, and computational timings as well as a pilot application to the size dependence of the helium cluster spectrum are presented.