Renner-Teller Hamiltonian

After these transformations, the Renner-Teller Hamiltonian adopts the following simple and very convenient aspect... 

We consider now the complete basis set of vibronic functions I f m, n) obtained as the direct product of the electronic functions l/+) and 1/1) by the phonons wave functions Im, n), where the integer numbers m and n (positive or zero) label the occupation numbers of the boson operators b b+ and b b, respectively. The Renner-Teller Hamiltonian (14) when applied to any vibronic function I f m,n) couples it with three states (at most) in fact it holds that ... 

The above results indicate that the Renner-Teller Hamiltonian (14) can be mapped exactly into a set of independent double chains of interacting states, as shown in Fig. 1. 

When the orbital functions are chosen as d-like or/-like, the axial symmetry of the molecule again leads to factorize the Renner-Teller Hamiltonian in a double chain. In effect the total angular momentum Jz remains a constant of motion and can be put in a diagonal form by means of the same type of canonical transformation, so we have... 

In Fig. 3, the computed vibronic energy levels are shown for 0vibronic energy levels without and with quartic terms is similar. However, with increasing g, relevant... 

Hamiltonian equations, 627-628 perturbative handling, 641-646 II electronic states, 631-633 vibronic coupling, 630-631 ABC bond angle, Renner-Teller effect, triatomic molecules, 611-615 ABCD bond angle, Renner-Teller effect, tetraatomic molecules, 626-628 perturbative handling, 641-646 II electronic states, 634-640 vibronic coupling, 630-631 Abelian theory, molecular systems, Yang-Mills fields ... 

Floquet theory principles, 35—36 single-surface nuclear dynamics, vibronic multiplet ordering, 24—25 Barrow, Dixon, and Duxbury (BDD) method, Renner-Teller effect tetraatomic molecules, Hamiltonian equations, 626-628 triatomic molecules, 618-621 Basis functions ... 

EWW Hamiltonian, Renner-Teller effect, triatomic molecules, 610—615 Expanding potential, molecular systems,... 

We wish to introduce here a very reliable calculation procedure to determine the eigenstates of a general Renner-Teller problem. It is convenient to start writing the matrix representation of the Hamiltonian of a Renner-Teller system on two degenerate p-like electronic states fx, fy and with the interaction part in the form given in Section 2, neglecting at the moment the quartic or higher order terms ... 

Renner-Teller Effect in Nonlinear Molecules Choice of Hamiltonian Minimal Models Pragmatic Models Benchmark Handling Effective Hamiltonians Beyond the Two-State Renner-Teller Effect... 

As discussed in Section 8.2.1, when nonadiabatic couplings cannot be neglected, the BO approximation is not reliable and coupled electronic states must be considered simultaneously with their interactions. For small systems, several full-dimensional approaches based on the vibronic or spin-rovibronic wavefunctions and taking into account simultaneously at least two electronic states have been developed [2, 100-104]. To quote some examples, the full vibronic Hamiltonians have been derived and employed for linear tetra-atomic molecules showing Renner-Teller interactions [103] or CXaY-like molecules of Csv symmetry showing Jahn-Teller interactions [104]. In the following, we will present the computational approaches based on the full rovibronic Carter-Handy Hamiltonian [100], developed for triatomic molecules and expressed in internal coordinates, which allows us to take into account up to three interacting electronic states [2, 100, 101]. 

J. M. Brown, The Renner-Teller effect The effective Hamiltonian approach, in Computational Molecular Spectroscopy, P. Jensen, P. R. Bunker, Eds., Wiley, Chichester, 2000, pp. 516-537. 

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