Abstract
The rotation-vibration (Coriolis) coupling contribution to variationally computed rovibrational energy levels is investigated, employing triatomic AB{}_{2} molecules as models. In particular, calculations are performed for H{}_{2}{}^{16}O, across a range of vibrational and rotational excitations, both with and without the Coriolis contribution. A variety of different embedding choices are considered, together with a hierarchy of increasingly severe approximations culminating in a generalized version of the so-called “centrifugal sudden” method. Several surprising and remarkable conclusions are found, including that the Eckart embedding is not the best embedding choice.
Highlights
The rotation-vibration (Coriolis) coupling contribution to variationally computed rovibrational energy pleevrefolsrims iendvfeosrtiHga21t6eOd,aecmropslsoayirnagntgreiaotfovmibicraAtBio2nmaloalencdurloestaatsiomnoadl eexlsc.itInatpioanrtsi,cubloatrh, cwailtchulaantdiownsitahroeut the Coriolis contribution
They claim[30] that they made the first step at discussing the different operators’ relative advantages, to really compare their efficacy it is necessary to calculate ro-vibrational energy levels[30], a task performed during this sctouodryd.iInnat1e9f7r4am, MewcGorukir, efoarntdhrKeoe-uartiodmev(ealtoopme+d tdhiaet“ojmz c)oqnusaenrtvuinmg”sccaetntetrriifnuggcaallscuudladteionnasp32p;rionxtihmeastaiomneiyneaarJ,aPcaocbki published his paper on related “sudden approximation” methods[31], comparing space-fixed and body-fixed formulations
The Coriolis-free approximation does not lead to new symmetries; it provides no significant numerical advantages over exact calculations, it may be useful for state labeling
Summary
The rotation-vibration (Coriolis) coupling contribution to variationally computed rovibrational energy pleevrefolsrims iendvfeosrtiHga21t6eOd,,aecmropslsoayirnagntgreiaotfovmibicraAtBio2nmaloalencdurloestaatsiomnoadl eexlsc.itInatpioanrtsi,cubloatrh, cwailtchulaantdiownsitahroeut the Coriolis contribution. It is natural to consider KEO approximations that separate rotational and vibrational motions within these blocks in some form. If the full ĤVR is used, converged numerical rovibrational energy levels should be independent of the choice of the vibrational coordinates and the embedding.
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