An Exploration of Theoretical Spectra

Thesis (Ph.D.)--University of Washington, 2023This thesis presents an exploration of theoretical spectra, both in their creation andinterpretation, with a focus on coupled cluster methods and an emphasis on the importance of relativistic effects. Throughout this work the X2C Hamiltonian is utilized to produce the reference wavefunction, including both scalar relativistic effects and spin-orbit coupling variationally in the presented schemes. First, a relativistic equation-of-motion coupled-cluster with single and double excitations(X2C-EOM-CCSD) formalism is presented including a discussion of the massively parallelized implementation available in the ChronusQuatum software package. In order to evaluate the accuracy of X2C-EOM-CCSD, we compare calculated, experimental, and TDDFT results, looking at zero-field splitting values. In addition to calculating the excitation energies for this low energy region, the oscillator strength of each excitation is calculated. This enables the simulation of absorption spectra, the observation of which excited states are populated, and the comparison of other general spectral features in the low energy UV-Visible region in order to benchmark the accuracy. Additionally, a relativistic time-dependent equation-of-motion coupled-cluster with singleand double excitations (TD-EOM-CCSD) formalism is presented. Unlike other explicitly time-dependent quantum chemical methods, the present approach considers the time correlation function of the dipole operator, as opposed to the expectation value of the timedependent dipole moment. The accuracy of X2C-TD-EOM-CCSD is evaluated by comparing zero-field splitting in atomic absorption spectra of open-shell systems (Na, K, Mg+, and Ca+) with values obtained from experiment. In closed-shell species (Na+, K+, Mg2+, and Ca2+), singlet triplet mixing is observed in the X2C-TD-EOM-CC calculations, which results from the use of the X2C reference. The effects of the X2C reference are evaluated by comparing spectra derived from X2C-TD-EOM-CC calculations to those from TD-EOM-CC calculations using a complex generalized Hartree-Fock (C-GHF) reference. The interpretation of spectra is an arduous task that can be simplified with the use ofspectral analysis tools. The Python library, fasma, is presented as a tool to help simplify this problem. By breaking down spectra into angular momentum character or molecular orbital contributions, along with giving information about the excitation order of each transition, various regions of the spectra can be interpreted and features of interest can be quickly identified. While keeping ease of use in mind, this library also allows extensive customization of analysis by the user through the quantity of information from electronic structure calculations that is made into easily accessible Python objects

Short Iterative Lanczos Integration in Time-Dependent Equation-of-Motion Coupled-Cluster Theory

A time-dependent (TD) formulation of equation-of-motion coupled-cluster (EOM-CC) theory can provide excited-state information over an arbitrarily wide energy window with a reduced memory footprint relative to conventional, frequency-domain EOM-CC theory. However, the floating-point costs of the time-integration required by TD-EOM-CC are generally far larger than those of the frequency-domain form of the approach. This work considers the potential of the short iterative Lanczos (SIL) integration scheme [J. Chem. Phys.1986,85, 5870-5876] to reduce the floating-point costs of TD-EOM-CC simulations. Low-energy and K-edge absorption features for small molecules are evaluated using TD-EOM-CC with single and double excitations, with the time-integrations carried out via SIL and fourth-order Runge-Kutta (RK4) schemes. Spectra derived from SIL- and RK4-driven simulations are nearly indistinguishable, and with an appropriately chosen subspace dimension, the SIL requires far fewer floating-point operations than are required by RK4. For K-edge spectra, SIL is the more efficient scheme by an average factor of 7.2

Relativistic Real-Time Time-Dependent Equation-of-Motion Coupled-Cluster

We present a relativistic time-dependent equation-of-motion coupled-cluster with single and double excitations (TD-EOM-CCSD) formalism. Unlike other explicitly time-dependent quantum chemical methods, the present approach considers the time correlation function of the dipole operator, as opposed to the expectation value of the time-dependent dipole moment. We include both scalar relativistic effects and spin-orbit coupling variationally in this scheme via the use of the exact two-component (X2C) wave function as the reference that enters the coupled-cluster formalism. In order to evaluate the accuracy of X2C-TD-EOM-CCSD, we compare zero-field splitting in atomic absorption spectra of open-shell systems (Na, K, Mg+, and Ca+) with values obtained from experiment. In closed-shell species (Na+, K+, Mg2+, and Ca2+), we observe singlet-triplet mixing in the X2C-TD-EOM-CC calculations, which results from the use of the X2C reference. The effects of the X2C reference are evaluated by comparing spectra derived from X2C-TD-EOM-CC calculations to those from TD-EOM-CC calculations using a complex generalized Hartree-Fock (C-GHF) reference

A Heterogeneous CPU + GPU Algorithm for Variational Two-Electron Reduced-Density Matrix Driven Complete Active Space Self-Consistent Field Theory

We present a heterogeneous CPU+GPU algorithm for the direct variational optimization of the two-electron reduced-density matrix (2RDM) under two-particle N-representability conditions. This variational 2RDM (v2RDM) approach is the driver for a polynomially-scaling approximation to configuration-interaction-driven complete active space self-consistent field (CASSCF) theory. For v2RDM-based CASSCF com- putations involving an active space consisting of 50 electrons in 50 orbitals [denoted (50e,50o)], we observe a speedup of a factor of 3.7 when the code is executed on a combination of an NVIDIA TITAN V GPU and an Intel Core i7-6850k CPU, relative to the case when the code is executed on the CPU alone. We use this GPU-accelerated v2RDM-CASSCF algorithm to explore the electronic structure of the 3,k-circumacene and 3,k-periacene series (k=2–7) and compare indicators of polyradical character in the lowest-energy singlet states to those observed for oligoacene molecules. The singlet states in larger circumacene and periacene molecules display the same polyradical characteristics observed in oligoacenes, with the onset of this behavior occuring at smallest k for periacenes, followed by the circumacenes and then the oligoacenes. However, the unpaired electron density that accumulates along the zig-zag edge of the circumacenes is slightly less than that which accumulates in the oligoacenes, while periacenes clearly exhibit the greatest build-up of unpaired electron density in this region.</div