Darling-dennison

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... 

Lehmann, K. K. (1983), On the Relation of Child and Lawton s Harmonically Coupled Anharmonic-Oscillator Model and Darling-Dennison Coupling, J. Chem. Phys. 79, 1098. 

Figure 4. Within a bend Darling-Dennison stack of zero-order levels, H,y increases and AEy decreases as u4 increases. The spike in Hij/ Ey occurs where the zero-order energies crash near Ubend = 16-...

Figure 5. Within a bend Darling-Dennison stack, Hi/ increases but AEj. increases more rapidly as vz increases, resulting in a gradually decreasing mixing angle, Hy/AEy.

Figure 6. The entire bend Darling-Dennison stack, which contains the ZOBS, pulls away from the other Darling-Dennison stacks as V2 increases. The different stacks are connected by the 3, 245 anharmonic resonance, Although the inter-stack Hy increase as V2 increases, the Hy increase more slowly than A -, thus the mixing angle decreases slowly as vz increases.

Figure la illustrates some of the dynamics in the state space of the [ns = 1, nres = 11, / = 0] polyad illuminated at t = 0 via the (0, 1, 0, 8°, 0 )° ZOBS [2]. The four panels of this figure depict the survival probability of the ZOBS (upper left), die probability of transfer to the two most important first-tier states [coupled by the bend Darling-Dennison interaction upper right (0, 1, 0, 6+2, 2-2)0 and lower left (0, 1, 0, 6°, 2°), and the transfer probability to one of the dynamically most remote dark states in the polyad (1, 0, 0, 0°, 6°)° (lower right), which occurs via a minimum of four anharmonic coupling steps ( 1, 244 followed by 44,55 three times). 

M. S. Child I have moreover a question for Prof. Field. Given that the Darling-Dennison resonance between the symmetric and antisym-... 

For the water molecule, data on D.O and HDO were also used for H,S and H,Se no isotopic data were used, v is the Darling-Dennison resonance parameter. All data are in cm-1 errors in values are given in the last digits quoted. 

In Section 9.4.12.4 the simplest possible local mode HlqCAL, expressed in terms of four independently adjustable parameters (the Morse De and a parameters, and two 1 1 kinetic and potential energy coupling parameters, Grr and km,), is transformed to the simplest possible normal mode H )oRMAL, which is also expressed in terms of four independent parameters. However, the interrelationships between parameters, based on the 1 1 coupled local Morse oscillator model, result in only 3 independent fit parameters. This paradox is resolved when one realizes that the 4 parameter local-Morse model generates the Darling-Dennison 2 2 coupling term in the normal mode model. However, the full effects of this (A ssaa/16hc)[(at + as)2(a+ + aa)2] coupling term are not taken into account in the local mode model. 

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