Low-lying quasibound rovibrational states of H₂¹⁶O^**

Abstract

A complex coordinate scaling (CCS) method is described allowing the quantum chemical computation of quasibound (also called resonance or metastable) rovibrational states of strongly bound triatomic molecules. The molecule chosen to test the method is H₂ ¹⁶O, for which an accurate global potential energy surface, a previous computation of a few resonance states via the complex absorbing potential (CAP) method, and some Feshbach (J = 0, where J is the quantum number characterising overall rotations of the molecule) and shape (J ≠ 0) resonances measured via a state-selective, triple-resonance technique are all available. Characterisation of the computed resonance states is performed via probability density plots based on CCS rovibrational wavefunctions. Such plots provide useful details about the physical nature of the resonance states. Based on the computations and the resonance plots, the following useful facts about the resonance states investigated are obtained: (a) Feshbach resonances are formed by accumulation of a large amount of energy in either the non-dissociative bending or symmetric streching modes, excitations by more than five quanta are not uncommon; (b) there are several resonance states with low and medium bending excitation, the latter are different from the states observed somewhat below dissociation by the same triple-resonance technique; (c) several types of dissociation bahavior can be identified, varying greatly among the states; (d) several pairs of J = 0 and J = 1 Feshbach resonance states can be identified which differ by rigid-rotor type energies; and (e) the lifetimes of the assigned J = 1 rovibrational Feshbach resonances are considerably longer than the lifetimes of their J = 0 vibrational counterparts.

Keywords:

• complex absorbing potential (CAP)
• complex coordinate scaling (CCS)
• water molecule
• Feshbach and shape resonances
• probability density plots
• tunneling

Acknowledgements

The work received support from the Scientific Research Fund of Hungary (OTKA, grant no. NK83583) and by an ERA-Chemistry grant awarded to AGC. The authors are grateful to Professor Jonathan Tennyson for useful discussions on the topic of the paper.

This paper is dedicated to Professor Martin Quack, who made numerous experimental as well as theoretical contributions to advanced areas of molecular physics and physical chemistry. For us, particularly instructive has been his work on the complex motions of highly excited molecules studied via high-resolution molecular spectroscopy

Notes

^a Results are taken from Ref. 44 and they correspond to those reported in Ref. 40. The bold capital letter labels given in parentheses are taken from table 1 of Ref. 44.

^b Values obtained using the (100 120 55) basis set, see Section 3 for details.

^c Convergence (conv.) is with respect to results obtained with the (95 115 55) basis set.

^d The < symbol indicates that the eigenvalue trajectory cusp used to identify the resonance eigenvalue is partly located in the negative Г region of the complex energy plane; thus, Г is only approximated taking into account the size of the region the trajectory samples near the cusp.

^a Results taken from Ref. [44].

^b Values were obtained using the (100 120 55) basis set, see Section 3 for details.

^c Convergence is with respect to results obtained with the (95 115 55) basis set, missing convergence values indicate that those resonances were only identified using the largest (100 120 55) basis set.

^d Values were obtained using the (85 105 50) basis set, see Section 3 for details.

^e Convergence is with respect to results obtained with the (75 95 50) basis set, missing convergence values indicate that those resonances were only identified using the (85 105 50) basis set.

^fThe < symbol indicates that the eigenvalue trajectory cusp used to identify the resonance eigenvalue is partly located in the negative Г region of the complex energy plane; thus, Г is only approximated taking into account the size of the region the trajectory samples near the cusp.

^aValues were obtained using the (85 105 50) basis set, see Section 3 for details.

^bThe < symbol indicates that the eigenvalue trajectory cusp used to identify the resonance eigenvalue is partly located in the negative Г region of the complex energy plane; thus, Г is only approximated taking into account the size of the region the trajectory samples near the cusp.