Nonadiabatic effects Hamiltonian

The effective hamiltonian in formula 29 incorporates approximations that we here consider. Apart from a term V"(R) that originates in nonadiabatic effects [67] beyond those taken into account through the rotational and vibrational g factors, other contributions arise that become amalgamated into that term. Replacement of nuclear masses by atomic masses within factors in terms for kinetic energy for motion both along and perpendicular to the internuclear axis yields a term of this form for the atomic reduced mass. 

That effective hamiltonian according to formula 29, with neglect of W"(R), appears to be the most comprehensive and practical currently available for spectral reduction when one seeks to take into account all three principal extramechanical terms, namely radial functions for rotational and vibrational g factors and adiabatic corrections. The form of this effective hamiltonian differs slightly from that used by van Vleck [9], who failed to recognise a connection between the electronic contribution to the rotational g factor and rotational nonadiabatic terms [150,56]. There exists nevertheless a clear evolution from the advance in van Vleck s [9] elaboration of Dunham s [5] innovative derivation of vibration-rotational energies into the present effective hamiltonian in formula 29 through the work of Herman [60,66]. The notation g for two radial functions pertaining to extra-mechanical effects in formula 29 alludes to that connection between... 

Equation (1-6) does not show when the off diagonal terms on the right hand side become important. To judge the importance of the nonadiabatic effects it is most convenient to use the perturbation theory37- 40. The Hamiltonian tK can be represented by the sum... 

In this connection, it is of interest to note that when nonadiabatic effects are small, as in strongly coupled systems at low energy or substantial vibronic angular momentum, a semi-classical quantization scheme beginning with the adiabatic nuclear Hamiltonian yields fairly... 

Schwenke, D.W. A first principle effective Hamiltonian for including nonadiabatic effects for H2-I-and HD+, J. Chem. Phys. 2001,114,1693-9. 

Herman, R. M. and Ogilvie, J. F. (1998). An effective Hamiltonian to treat adiabatic and nonadiabatic effects in the rotational and vibrational spectra of diatomic molecules. Adv. Chem. Phys., 103, 187-215. 

Consider a physically acceptable system of the complex-level structure that involves the Born-Oppenheimer basis, consisting of the ground electronic state g) = 0) and a single doorway state s) that is coupled via nonadiabatic intramolecular interactions Hvib to a background of J) states, and where both the states s) and the manifold I) are characterized by the radiative and nonradiative decay widths Ys and Yj. respectively (see Figure 6.2). The effective Hamiltonian responsible for this system is... 

Both the initial- and the final-state wavefunctions are stationary solutions of their respective Hamiltonians. A transition between these states must be effected by a perturbation, an interaction that is not accounted for in these Hamiltonians. In our case this is the electronic interaction between the reactant and the electrode. We assume that this interaction is so small that the transition probability can be calculated from first-order perturbation theory. This limits our treatment to nonadiabatic reactions, which is a severe restriction. At present there is no satisfactory, fully quantum-mechanical theory for adiabatic electrochemical electron-transfer reactions. 

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