Oscillator strengths and excited-state couplings for double excitations in time-dependent density functional theory

Although useful to extract excitation energies of states of double-excitation character in time-dependent density functional theory that are missing in the adiabatic approximation, the frequency-dependent kernel derived earlier [J. Chem. Phys. {\bf 120}, 5932 (2004)] was not designed to yield oscillator strengths. These are required to fully determine linear absorption spectra and they also impact excited-to-excited-state couplings that appear in dynamics simulations and other quadratic response properties. Here we derive a modified non-adiabatic kernel that yields both accurate excitation energies and oscillator strengths for these states. We demonstrate its performance on a model two-electron system, the Be atom, and on excited-state transition dipoles in the LiH molecule at stretched bond-lengths, in all cases producing significant improvements over the traditional approximations

Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What is Missing in, and Corrections to, the TD-DFT Adiabatic Approximation

In their famous paper Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of $N$ interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays however the realization that Nature is not always so nearsighted has driven us up Perdew's Jacob's ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very much like what the local density approximation (LDA) is to conventional ground-state DFT. While some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this article will focus on many-body corrections to LR-TD-DFT as one way to building hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.Comment: 56 pages, 17 figure

Electronic Structure of Excited States with Configuration Interaction Methods

Computational chemistry is routinely applied to ground state molecular systems to provide chemical insights. Accurate excited state calculations, however, still typically require carefully tailored calculations and sizeable computational resources. This work focuses on the development of methods and strategies that enable the calculation of excited state properties with more accuracy and on larger systems than ever before. The first two Chapters focus on the spin-flip configuration interaction family of methods. Chapter 2 introduces us to the quantities one can obtain with excited state methods, with a challenging example being the electronic structure of a possible intramolecular singlet fission system, a quinoidal bithiophene. The study assigns an experimentally observed long-lived exciton to a long-lived singlet multiexciton state with a combination of energetic and transition dipole moment quantities. The spin-flip methodology is extended in Chapter 3 to provide more insight into the energetic orderings of the multiexciton states of a tetracene dimer, a model singlet fission system, showing that triplet decoupling should occur spontaneously upon population of the intermediate multiexciton state, 1(TT). However, this extension enlarged the configuration spaces to the point that they became a limiting factor in the calculation of larger systems. Therefore, the latter two Chapters focus on investigating new strategies for identifying and eliminating unneeded configurations. Chapter 4 presents iterative submatrix diagonalization, a procedure for converging the Davidson diagonalization procedure with a reduced set of active orbitals. This is accomplished by generating a systematic series of submatrix approximations to the full configuration space and solving for eigenpairs within the series until convergence of eigenpairs is achieved. The method shows promise, converging eigenvalues with a considerable reduction in orbitals and total computational time. Chapter 5 applies heat-bath configuration interaction towards obtaining exact excitation energies and examines various ways in which convergence is signified. A new convergence metric based on the magnitude of the perturbative correction is developed and converged excitation energies are obtained for systems as large as hexatriene. These results involved treating configuration spaces with as many as 1038 configurations, a full 29 orders of magnitude over what is achievable with conventional configuration interaction methods and 10 orders beyond results reported by other recent state-of-art solvers. While there is still a great deal of work to be done before excited state computational chemistry will be routinely applicable to a wide variety of systems, the various methods investigated and extended here show significant promise, especially those presented in the latter Chapters as these are generally applicable to any configuration interaction method.PHDChemistryUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/140821/1/alandc_1.pd