Spectroscopic signatures of bond-breaking internal rotation. II. Rotation-vibration level structure and quantum monodromy in HCP

Journal of Chemical Physics

Volumn 114, Issue 1, 2001, Pages 262-275

  Jacobson, Matthew P ^a   Child, Mark S ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRONIC STRUCTURE; GROUND STATE; HYDROGEN; ISOMERIZATION; MOLECULAR SPECTROSCOPY; MOLECULAR VIBRATIONS; QUANTUM THEORY;

BOND-BREAKING INTERNAL ROTATION; SADDLE POINTS;

CHEMICAL BONDS;

EID: 0035151876     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1330746     Document Type: Article

References (22)

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11. We wish to comment briefly on why the semiclassically inverted effective bending potential reproduces the HCP rotational constants more accurately than a simple adiabatic treatment. The first critical point is that deficiencies of the adiabatic approximation to the full ab initio PES are due to the adiabatic approximation, and not the PES itself, which reproduces the observed rotational constants with good accuracy. The second critical point is that the semiclassically inverted potential reproduces the quantum bending energies by design, but its ability to reproduce the rotational constants is nontrivial, and implies that the inversion procedure partially corrects for certain deficiencies in the crude adiabatic approximation. Why is this so? We suspect, but cannot prove, that the success of the inversion is related to the structure of the fitted effective Hamiltonian, which includes only a single resonant interaction, the Fermi 2:1 resonance between the CP stretch and bend. The inclusion of this resonance effectively deperturbs the zero-order CP stretch and bend energies. However, no resonant interaction is included between the bend and the CH stretch. This fact does not imply that there is no interaction between the bend and CH stretch, only that this interaction need not be accounted for by an explicit off-diagonal resonance (i.e., that its effects can be accounted for by perturbation theory). Thus, we suspect that our inverted effective bending potential, because it is derived from the effective Hamiltonian, implicitly corrects for weak (i.e., nonresonant) coupling between the CH stretch and bend; this coupling is manifested in the eigenvectors of the ab initio surface by the fact that the nodes of the "pure bend" states do not align precisely along the minimum energy isomerization pathway, but oscillate slightly in the hydrogen stretch dimension. Whether the nonresonant CH/bend coupling at low energies translates into direct, resonant coupling at higher energies is unclear.
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18. We wish to mention briefly a curious fact. Our effective bending potential, or indeed the minimum energy isomerization potential on the ab initio surface, has a highly "kinked" form in Jacobi coordinates but is very close to a simple pendulum in bond-angle coordinates. We can think of no reason why this must be so. However, this does imply that the effects of the "kink" must somehow be accounted for by the much more complicated kinetic energy operator in bond-angle coordinates, thus providing a different perspective on the dynamics. Thus far, we have not pursued this direction further.
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