Instanton theory for modelling the effect of tunneling in molecular systems

doctoral thesis

• Title (croatian): Teorija instantona za modeliranje učinka tuneliranja u molekularnim sustavima
• Author: Mihael Eraković
• Mentor: Marko-Tomislav Cvitaš (mentor)
• Committee member: Tomica Hrenar (predsjednik povjerenstva)
• Committee member: Stuart C. Althorpe https://orcid.org/0000-0003-1288-8070 (član povjerenstva)
• Committee member: Ivan Ljubić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Chemistry); Zagreb
• Defense date and country: 2022-09-29, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Chemistry
• Universal decimal classification (UDC): 54 - Chemistry. Crystallography. Mineralogy

Abstract

Tunneling is a quantum mechanical effect in which wavepacket passes through regions which are classically inaccessible, due to the insufficient energy of the system. Tunneling causes splitting of the vibrational levels in systems which possess several symmetry-related minima. Modelling of tunneling effect using quantum mechanical methods is extremely challenging due to its sensitivity on the potential’s and wavefunction’s shapes. Instanton theory is a semiclassical method known to provide a good description of tunneling in the ground vibrational state. The goal of this thesis is to develop and improve instanton theory so that it can be applied to vibrationally excited states, systems with asymmetric potential energy wells and used with ab initio potentials. Additionally, the goal is to apply the developed theory to compute tunneling splittings in malonaldehyde and small water clusters, as well as on the molecules in which a part of identical atoms is substituted with different isotopes.

Abstract (croatian)

Tuneliranje je kvantnomehanički efekt prolaska valnog paketa kroz regije u prostoru u kojima prema klasičnoj mehanici takav prolazak ne bi bio moguć zbog nedovoljne energije sustava. Tuneliranje uzrokuje pojavu cijepanja vibracijskih nivoa u sustavima koji sadrže nekoliko simetrijski povezanih minimuma. Modeliranje tuneliranja kvantnomehaničkim metodama
iznimno je teško zbog velike osjetljivosti na potencijal i oblik valne funkcije. Teorija instantona je poluklasična metoda koja pruža dobar opis tuneliranjem uzrokovanog cijepanja vibracijskih stanja za osnovno vibracijsko i rotacijsko stanje molekula. Cilj ove disertacije je razviti i poboljšati teoriju instantona kako bi bila primjenjiva na pobuđena vibracijska i rotacijska stanja, sustave s asimetričnim potencijalnim jamama te ab initio potencijale. Dodatno, cilj je primijeniti razvijenu metodu kako bi se opisalo tuneliranjem uzrokovano cijepanje u molekuli malonaldehida, malih grozdovima vode te djelomično izotopno supstituiranim sustavima.

• Keywords: instanton; path integral; tunneling
• Keywords (english): instanton; teorija integrala po stazama; tuneliranje
• Language: english
• URN:NBN: urn:nbn:hr:217:944213
• Promotion: 2022
• Study programme: Title: Doctoral study in chemistry; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje kemija (doktor/doktorica znanosti, područje prirodnih znanosti, polje kemija)
• Type of resource: Text
• Extent: XXXVI, 134 str. ; 30 cm
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2024-09-29
• Created on: 2022-11-02 13:33:20