English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Recently, a general expression for Eckart-frame Hamilton operators has beenobtained by the gateway Hamiltonian method ({\it J. Chem. Phys.} {\bf 142},174107 (2015); {\it ibid.} {\bf 143}, 064104 (2015)). The kinetic energyoperator in this general Hamiltonian is nearly identical with that of theEckart-Watson operator even when curvilinear vibrational coordinates areemployed. Its different realizations correspond to different methods ofcalculating Eckart displacements. There are at least two different methods forcalculating such displacements: rotation and projection. In this communicationthe application of Eckart Hamiltonian operators constructed by rotation andprojection, respectively, is numerically demonstrated in calculatingvibrational energy levels. The numerical examples confirm that there is no needfor rotation to construct an Eckart ro-vibrational Hamiltonian. The applicationof the gateway method is advantageous even when rotation is used, since itobviates the need for differentiation of the matrix rotating into the Eckartframe. Simple geometrical arguments explain that there are infinitely manydifferent methods for calculating Eckart displacements. The geometrical picturealso suggests that a unique Eckart displacement vector may be defined as theshortest (mass-weighted) Eckart displacement vector among Eckart displacementvectors corresponding to configurations related by rotation. Its length, asshown analytically and demonstrated by way of numerical examples, is equal toor less than that of the Eckart displacement vector one can obtain by rotationto the Eckart frame.

Eckart ro-vibrational Hamiltonians via the gateway Hamilton operator: theory and practice