In silico chemistry : multiscale modeling from quantum mechanics to kinetics

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Chemical phenomena occur across a wide range of length and time scales. Atoms vibrate on the order of 10-15 seconds, while chemical reactions may take place anywhere between 10-12 seconds and hours (or as long as a chemist is willing to wait). Quantum mechanics governs the smallest of these scales, where the Schrödinger equation tells us how to compute observable properties of quantum systems. For such small systems, highly accurate calculations can be performed, though often with formidable computational cost. At intermediate scales with hundreds of atoms, approximate quantum mechanical methods can be used to define potential energy surfaces, which can be used in conjunction with Newtonian mechanics to simulate the trajectories that molecules move in. Kinetic models bridge to even larger, continuum scales, by utilizing a set of differential equations that relate macroscopic thermodynamic variables, such as temperature and pressure, to the concentrations of chemical species. The differential equations can be integrated to arbitrary points forward in time, providing predictions of how thermodynamic variables and concentrations change. Each of the aforementioned models yields a trade-off: high accuracy can be attained in the limit of the very small, while in the limit of the large, we are restricted to using coarser models. Connecting microscopic descriptions of molecules with models of macroscopic phenomena, as well as the reverse, can be informative for models at both scales. This dissertation aims to do precisely this, progressively working our way up from small length and time scales to macroscopic scales. First, we discuss research on improving the performance of electronic structure calculations such as Hartree-Fock by constructing approximations to the wavefunction through partitions of atoms into fragments. Then, we show how machine learning can be utilized to approximate effective Hamiltonian matrix elements. After, we discuss molecular dynamics integration, deriving multiple time step integration methods, showing how explicit integrators can be easily implemented, and how the accuracy of symplectic integrators can be analyzed in terms of the shadow Hamiltonian. Last, we make the connection of accelerated molecular dynamics simulations of nitromethane to kinetic models, which can be used to predict reaction pathways with varying thermodynamic conditions and time scales, allowing for comparison of predictions to experiments on computationally challenging time scales.


Type of resource text
Form electronic resource; remote; computer; online resource
Extent 1 online resource.
Place California
Place [Stanford, California]
Publisher [Stanford University]
Copyright date 2020; ©2020
Publication date 2020; 2020
Issuance monographic
Language English


Author Ford, Jason Elliot
Degree supervisor Martinez, Todd J. (Todd Joseph), 1968-
Thesis advisor Martinez, Todd J. (Todd Joseph), 1968-
Thesis advisor Dai, Hongjie, 1966-
Thesis advisor Markland, Thomas E
Degree committee member Dai, Hongjie, 1966-
Degree committee member Markland, Thomas E
Associated with Stanford University, Department of Chemistry


Genre Theses
Genre Text

Bibliographic information

Statement of responsibility Jason Elliot Ford.
Note Submitted to the Department of Chemistry.
Thesis Thesis Ph.D. Stanford University 2020.
Location electronic resource

Access conditions

© 2020 by Jason Elliot Ford
This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

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