Browsing by Subject "Vibronic coupling"
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Item Development of a computational framework for quantitative vibronic coupling and its application to the NO₃ radical(2012-05) Simmons, Christopher Scott; Stanton, John (John F.); Rossky, Peter J.; Wyatt, Robert E.; Anslyn, Eric V.; Miranker, Daniel P.The Born-Oppenheimer approximation is a mainstay in molecular physics and chemistry and can be considered a two step process. The first step is to solve the electronic problem with nuclei fixed in space while the second step is to then determine the nuclear dynamics on a given electronic potential energy surface. This first-step calculation of the wavefunction and electronic energies for fixed nuclei has been at the center of modern quantum chemistry for decades. While the majority of chemical processes can be investigated by considering these single electronic surface dynamics, there exist problems in which the dynamics are not constrained to a single electronic surface. One such problem that justifies going beyond the typical adiabatic approximation is the determination of energy levels in systems with strongly coupled electronic states. While some work has been done using diabatic or quasidiabatic Hamiltonians to describe such systems, the work has historically been of qualitative accuracy. Model Hamiltonians have been constructed using experimental data to help calibrate the model parameters aided by the use of lower level adiabatic calculations to help inform the model. It is only within the last few years that theorists have been able to attempt parameterization of such models using only ab initio methods. The goal of this work is to develop a computational framework for the parameterization of quantitatively accurate quasidiabatic Hamiltonians based purely on ab initio information and apply it to a notoriously difficult problem that has plagued the theoretical community for decades -- high accuracy treatment of the energy levels of the NO₃ radical. In this dissertation, high-level ab initio calculations that employ the equation-of-motion coupled-cluster method in the single, doubles and triples (EOMIP-CCSDT) have been used in conjunction with a quasidiabatic ab initio approximation to construct a vibronic Hamiltonian for the strongly coupled X²A'₂ and B²E' states of the NO₃ radical. A quartic vibronic coupling model potential of the form advocated by Köppel et al. has been used to determine the energy levels of this system to quantitative accuracy when compared to experimental data. In order to obtain sufficiently accurate potential energy surfaces necessary to parameterize a quantitatively accurate model Hamiltonian, thousands of large calculations had to be run that do not fit in memory on even the largest HPC systems. The resulting large, out-of-core solves do not map to traditional systems in a way to enable any reasonable parallelization. As a result, a new MPI-based utility has been developed to support out-of-core methods on distributed memory systems. This and other advances in scientific computing form the basis of the developed computational framework.Item Extending the reach of algorithms for the calculation of molecular vibronic spectra(2016-12) Rabidoux, Scott Michael; Stanton, John (John F.); Eijkhout, Victor; Arbogast, Todd; van de Geijn, Robert; Makarov, DmitriiTheoretical spectroscopy is an important field of chemistry that can help extract useful information about the properties of a molecule from experimental spectral data. Ab initio calculations of molecular spectra can be performed and compared against experimental data to determine the validity of various calculated molecular properties. Unfortunately, the computational cost of these spectral simulations rises quickly with the number of atoms in the molecule of interest. As a result, current techniques for simulating molecular spectra are often limited for use with only the smallest of molecules. The main purpose of this work is to develop new computational tools in an effort to extend the reach of current state-of-the-art spectral simulation algorithms and allow for the spectroscopic study of larger molecules than is currently feasible. The calculation of vibronic spectra requires the solution of the time-independent Schrödinger equation to obtain the vibronic energy levels of a molecule and their corresponding transition intensities. When the Born-Oppenheimer approximation is applicable for the solution of the time-independent Schrödinger equation, the vibrational energy levels of a molecule can be easily determined analytically, if the harmonic approximation is used. What remains, then, for a spectral simulation, is the calculation of the transition intensities associated with each energy level. Under the harmonic approximation, the transition intensities (also known as Franck-Condon factors) can be calculated via a set of recurrence equations developed by Doktorov, Malkin, and Manko. The implementation of these recurrence equations, though, can be computationally intensive for medium-to-large molecules, especially for finite-temperature simulations. In this work, I present a new algorithm for the calculation of Franck-Condon factors via the Doktorov recurrence equations that achieves significantly better computational performance than existing implementations, with speedups of roughly thirty times on a single processor. When the Born-Oppenheimer approximation is not applicable, vibronic coupling effects must be accounted for to achieve an accurate spectral simulation. A common approach for treating vibronic coupling effects is to solve the time-independent Schrödinger equation using a model Hamiltonian developed by Köppel, Domcke, and Cederbaum (KDC). Using the KDC approach, the problem of solving the Schrödinger equation becomes a problem of solving for the eigenstates of a large, sparse matrix. The computational difficulty of this problem is then dependent on the size of the matrix. Unfortunately, the size of the matrix at hand grows exponentially with the number of vibrational modes of the molecule of interest, and matrix dimensions can easily reach upwards of one billion and beyond. In an attempt to make tractable problems involving very large matrices, I present in this work a distributed-memory parallelization strategy for the KDC approach. The resulting parallel algorithm achieves impressive parallel scalability and has been used to study several previously intractable spectroscopic problems. I conclude this work by presenting ab initio calculations and spectral simulations for the molecule trans-1,3-butadiene. The spectroscopy of butadiene has been studied by expermentalists and theorist alike, but a complete KDC spectral model has yet to be achieved due in part to the large size of the resulting matrices. Using the newly-developed parallel algorithm described above, I am able to present spectra from simulations using the most complete KDC model for butadiene to date and discuss what these results may tell us about butadiene’s electronic structure.