Single-particle Green's function method is a direct way of calculating electron binding energy, which relies on expanding the Fock subspace in a finite single-particle basis. However, these methods suffer from slow asymptotic decay of basis set incompleteness error. An energy-dependent explicitly correlated (F12) formalism for Green's function is presented that achieves faster convergence to the basis set limit. The renormalized second-order Green's function method (NR2-F12) scales as iterative N^5 where N is the system size. These methods are tested on a set of small (O21) and medium-sized (OAM24) organic molecules. The basis set incompleteness error in ionization potential (IP) obtained from the NR2-F12 method and aug-cc-pVDZ basis for OAM24 is 0.033 eV compared to 0.067 eV for NR2 method and aug-cc-pVQZ basis. Hence, accurate electron binding energies can be calculated at a lower cost using NR2-F12 method. For aug-cc-pVDZ basis, the electron binding energies obtained from NR2-F12 are comparable to EOM-IP-CCSD method that uses a CCSD reference and scales as iterative N^6. / Master of Science / Solving the non-relativistic time-independent Schrödinger equation is a central problem in quantum chemistry with the primary goal of finding the exact electronic wave function. Like all many-body problems, the applications of highly accurate electronic structure methods are limited to small molecules since they are computationally expensive. With scalable algorithms and parallel implementation of computer programs, the chemistry of large molecular systems can be investigated. Electron binding energies give an insight into the orbital picture of a molecule, which is manifested in chemical structure and properties of a molecule.
Green’s function provides an alternative to wave function based methods to calculate ionization potential and electron affinity directly rather than solving for the wave function itself. For accurate electron binding energies, the wave function needs to be represented by large number of basis functions, which make these methods computationally expensive.
Explicitly correlated electronic structure methods are designed to produce accurate results at a smaller basis set. This work investigates the use of explicitly correlated Green’s function methods to calculate electron binding energies of small and medium sized organic molecules. These results are compared to coupled cluster methods, which are known to provide accurate benchmarks in quantum chemistry.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/101962 |
| Date | 29 July 2019 |
| Creators | Teke, Nakul Kushabhau |
| Contributors | Chemistry, Valeyev, Eduard Faritovich, Mayhall, Nicholas J., Crawford, T. Daniel, Troya, Diego |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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