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Monte Carlo Methods for the Study of the Ro-Vibrational States of Highly Fluxional Molecules

Petit, Andrew S
http://rave.ohiolink.edu/etdc/view?acc_num=osu1366136698

Abstract Details

2013, Doctor of Philosophy, Ohio State University, Chemical Physics.
Molecular spectroscopy remains a powerful tool for obtaining insights into fundamental chemical processes, studying the properties of reactive intermediates, and investigating the chemistry of the interstellar medium. The spectra of semi-rigid molecules are often well-described using spectroscopic Hamiltonians obtained from the application of perturbation theory to the full rotation-vibration Hamiltonian. However, the presence of large amplitude vibrational motions causes the perturbation theory expansion to become slow to converge or even divergent. As a result, the spectra of fluxional systems become difficult to interpret and a proper theoretical description of the nuclear dynamics challenging to achieve. The majority of the work reported in this thesis involves diffusion Monte Carlo (DMC), an approach that has been shown to successfully describe the ground state properties of highly fluxional systems and, through the fixed-node approximation, vibrationally excited states. In this thesis, we first describe an extension of fixed-node DMC to the study of the rotationally excited states of symmetric and asymmetric top molecules that undergo large amplitude vibrational motions. The nodal surfaces used to impose rotational excitation into the DMC calculations are obtained from the roots of the rigid rotor wave functions. Despite using a zeroth-order description of the nodal surfaces and without placing any constraints in the vibrational coordinates, the fixed-node DMC approach is able to capture the effects of rotation-vibration coupling in highly fluxional molecules for states with J as large as 12. One limitation of DMC is the need to perform the simulations in Cartesian coordinates, requiring the use of a full-dimensional potential energy surface and preventing the possibility of restricting the calculations to the subset of coordinates that are physically relevant to the questions being asked. As a first step towards overcoming this limitation, we describe the development of an internal coordinate extension of DMC in which the calculations can be performed in any set of independent internal coordinates. We will benchmark the approach on the ground and ν=1 vibrationally excited states of H3+ and its isotopologues. Additionally, we will discuss fundamental properties of the nodal surfaces of vibrationally excited states as well as demonstrate that analysis of ground state DMC probability distributions can aid in the identification of the set of coordinates that are less strongly coupled and therefore for more suitable for use as nodal coordinates in fixed-node DMC calculations. Finally, we will present a new approach for the calculation of low-quanta vibrationally excited states of strongly anharmonic systems. By using a set of evolving basis functions, the size of which effectively grows with each iteration due to the incorporation of information obtained from the previous diagonalization of the Hamiltonian matrix, a significant smaller basis is required than in other variational approaches. Additionally, Monte Carlo importance sampling is used to limit the number of necessary electronic structure evaluations and achieve an improved scaling with system size relative to grid based approaches. A thorough testing of this method on model one and two-dimensional systems will be described.
Anne McCoy (Advisor)
Terry Miller (Committee Member)
Frank De Lucia (Committee Member)
226 p.
Physical Chemistry
Diffusion Monte Carlo; fluxionality; anharmonicity; rotation-vibration coupling; theoretical spectroscopy

Recommended Citations

Citations

  • Petit, A. S. (2013). Monte Carlo Methods for the Study of the Ro-Vibrational States of Highly Fluxional Molecules [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366136698

    APA Style (7th edition)

  • Petit, Andrew. Monte Carlo Methods for the Study of the Ro-Vibrational States of Highly Fluxional Molecules. 2013. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1366136698.

    MLA Style (8th edition)

  • Petit, Andrew. "Monte Carlo Methods for the Study of the Ro-Vibrational States of Highly Fluxional Molecules." Doctoral dissertation, Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366136698

    Chicago Manual of Style (17th edition)

osu1366136698
589
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This open access ETD is published by The Ohio State University and OhioLINK.