Two-state Hamiltonian

The problem of nonadiabatic tunneling has been already formulated in section 3.5, and in this subsection we study how dissipation affects the conclusions drawn there. The two-state Hamiltonian for the system coupled to a bath is conveniently rewritten via the Pauli matrices... 

For the two-state Hamiltonian the adiabatic functions can be easily transformed into diabatic functions. In the latter representation the Hamiltonian is not diagonal, and the model is completely specified by the matrix Hik as a function of R. If, besides, the semiclassical approximation is adopted there will be only two essential functions AH(t) = Hn(t) — and... 

Now, the two-state Hamiltonian with approximations made can be simulated near Rx by the model Hamiltonian equation (26) with parameters cos 6 - h a - , Ae - Aeeft. The transition probability P can be obtained from equations (27) and (22) provided interference is neglected ... 

We consider a two-level system coupled to a bath of harmonic oscillators that will be referred to as a boson field. Two variations of this model, which differ from each other by the basis used to describe the two-level system, are frequently encountered. In one, the basis is made of the eigenstates of the two-state Hamiltonian that describes the isolated system. The full Hamiltonian is then written... 

The classical two-state Hamiltonian has been widely used by scientists. It is, for example, the same one that was classically used for the motion of planets (with elliptic diabatic orbitals instead of parabolic ones). One could easily imagine that there might be problems applying classical theory to the motion of electrons within... 

Warshel and co-workers > ° >i studied the dynamics of this Sn2 reaction using an interesting and different approach the empirical valence bond (EVB) method, which has been described in detail in a recent book by Warshel. The fundamental idea behind the application of the EVB method to this Sn2 reaction is that the reaction can be treated as a two state system, where the reactants and products are each taken to be separate quantum mechanical states with Hamiltonians and Hi- These states can be coupled together by an empirical coupling Hamiltonian so that when the two state Hamiltonian is diagonalized, the correct features of the ground state surface on which the reaction occurs are obtained. H, and H2 are taken by Warshel and coworkers to have analytic forms based on the gas phase parameters. 

The first term is a simple two-state Hamiltonian, resembling a spin operator... 

Two-state Hamiltonian based on the redueed axis method (RAM). 

Two-State Hamiltonian based on the fixed framework axis method (FFAM)... 

---