Vibrational Energies of the Hydrogen Bonds of H₃O₂⁻ and H₅O₂⁺

We approximate the vibrational energies of the symmetric and asymmetric stretches of the hydrogen bonds of the molecules H_3O_2^- and H_5O_2^+ by applying an improvement to the standard time-independent Born-Oppenheimer approximation. These two molecules are symmetric around a central hydrogen which participates in hydrogen bonding. Unlike the standard Born-Oppenheimer approximation, this approximation appropriately scales the hydrogen nuclei differently than the heavier oxygen nuclei. This results in significantly more accurate approximations for the stretching vibrational energies, which we compare to experimental measurements.

Name thesis:degree_name

Master of Science

Level thesis:degree_level

masters

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2016

Author dc:creator

• Gamble, Stephanie Nicole

Chair dc:contributor.committeechair

• Hagedorn, George A.

Committee members dc:contributor.committeemember

• Crawford, T. Daniel
• Valeyev, Eduard Faritovich

• hydrogen bond
• double well
• vibrational energies

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:8423

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/71454