Darling

Physically, why does a temi like the Darling-Dennison couplmg arise We have said that the spectroscopic Hamiltonian is an abstract representation of the more concrete, physical Hamiltonian fomied by letting the nuclei in the molecule move with specified initial conditions of displacement and momentum on the PES, with a given total kinetic plus potential energy. This is the sense in which the spectroscopic Hamiltonian is an effective Hamiltonian, in the nomenclature used above. The concrete Hamiltonian that it mimics is expressed in temis of particle momenta and displacements, in the representation given by the nomial coordinates. Then, in general, it may contain temis proportional to all the powers of the products of the... 

Flowever, if only the Darling-Deimison conplmg is important for the conpled stretches, what is its importance telling ns about the internal molecnlar motion It turns out that the right kind of analysis of the spectroscopic fitting Flamiltonian reveals a vast amonnt about the dynamics of the molecnle it allows ns to decipher the story encoded in the spectrum of what the molecule is really doing in its internal motion. We will approach this spectral cryptology from two complementary directions ... 

Dennison coupling produces a pattern in the spectrum that is very distinctly different from the pattern of a pure nonnal modes Hamiltonian , without coupling, such as (Al.2,7 ). Then, when we look at the classical Hamiltonian corresponding to the Darling-Deimison quantum fitting Hamiltonian, we will subject it to the mathematical tool of bifiircation analysis [M]- From this, we will infer a dramatic birth in bifiircations of new natural motions of the molecule, i.e. local modes. This will be directly coimected with the distinctive quantum spectral pattern of the polyads. Some aspects of the pattern can be accounted for by the classical bifiircation analysis while others give evidence of intrinsically non-classical effects in the quantum dynamics. 

We have seen that resonance couplings destroy quantum numbers as constants of the spectroscopic Hamiltonian. Widi both the Darling-Deimison stretch coupling and the Femii stretch-bend coupling in H2O, the individual quantum numbers and were destroyed, leaving the total polyad number n + +... 

George R Darling, Stephen Holloway and Charles Rettner... 

Wang Z S, Darling G R and Holloway S 2000 Translation-to-rotational energy transfer in seattering of H2 moleeules from Cu(111) surfaees Surf. Sc/. 458 63... 

Darling G R and Holloway S 1994 The role of parallel momentum in the dissociative adsorption of H2 at highly corrugated surfaces Surf. Sc/. 304 L461... 

Kay M, Darling G R, Holloway S, White J A and Bird D M 1995 Steering effects in non-activated adsorption Chem. Phys. Lett 245 311... 

Darling G R and Holloway S 1995 Tlie dissociation of diatomic molecules Prog. Phys.. 58 1595... 

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