Hamiltonian equation vibronic

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 ... 

II electronic states, 638-640 vibronic coupling, 628-631 triatomic molecules, 594-598 Hamiltonian equations, 612-615 pragmatic models, 620-621 Kramers doublets, geometric phase theory linear Jahn-Teller effect, 20-22 spin-orbit coupling, 20-22 Kramers-Kronig reciprocity, wave function analycity, 201 -205 Kramers theorem ... 

ABBA molecules, 631-633 HCCS radical, 633-640 perturbative handling, 641-646 theoretical principles, 625-633 Hamiltonian equation, 626-628 vibronic problem, 628-631 theoretical principles, 585-586 triatomic molecules ... 

In the present work we aim at a more accurate description and treat the Hamiltonian, equation (9), fully, with all JT and PJT couplings of Table 3 included. Only the inherently low-resolution experimental PE spectra of Refs. [4,6] are available for comparison which is thus confined to the gross overall features of the composite D — EYE band. Nevertheless, it proved necessary to adjust the vertical IPs, since their difference affects the computed vibronic structure [26]. Being a small difference of large numbers, we increased it from the ab initio value of 0.3 eV to a value of 0.45 eV. The PE spectral profile thus obtained with the MCTDH algorithm is depicted in Fig. 4, and compared there with the experimental recording of Ref. [6]. 

If the values of the parameters for the vibronic state ri,v) are known a priori, the spin-rotational energy levels can be calculated in a straightforward manner from the effective Hamiltonian, equation (7.183), computing the matrix elements in a suitable... 

Here f denotes the transition operator and E the energy transferred to the system (e.g., the photon energy in optical absorption). The initial state Pi) (with energy ,) can, but need not, belong to the set ifv> of vibronic states (with energies Ev) which constitute the set of final states given by the solutions of the vibronic Hamiltonian, equations (11)-(I4), or, in particular, equation (27) or equation (31). In all our later applications A,) will be the zero vibrational level of the electronic ground state and is assumed to be vibronically uncoupled from the excited states. 

The most consequent and the most straightforwaid realization of such a concept has been carried out by Handy, Carter, and Rosmus (HCR) and their coworkers. The final form of the vibration-rotation Hamiltonian and the handling of the corresponding Schrddinger equation in the absence of the vibronic... 

The two most useful sets are the bond displacements themselves, and the symmetry coordinates. The use of the latter leads naturally to a scheme in which the Hamiltonian for bent molecules is no longer diagonal in the total 0(4) quantum numbers (ti, x2), and thus one loses the simple form of the secular equation (Figure 4.11). The secular equation must be now diagonalized in the full space with dimensions that become rapidly larger. This scheme, developed by Leviatan and Kirson (1988), can be implemented only if the vibron numbers N are relatively small, N < 10. 

In dealing with the MO-LCAO wave function no additional assumptions concerning the vibronic matrix elements are necessary. The evaluation of the total molecular energy exactly copies the lower sheet of the adiabatic potential. This is a consequence of the well-known fact that the Hartree-Fock equations are equivalent to the statement of the Brillouin theorem the matrix elements of the electronic Hamiltonian between the ground-state and... 

Except for first-order perturbation theory, we did not use any approximation in obtaining equations (4) and (5). These results are based upon the assumption that the vibronic coupling part of the Hamiltonian, //JT, has the same high symmetry as... 

In the actual construction the vibronic constant taken as the coordinate derivative of non-diagonal matrix element in equation (5) took a form depending on the spin-Hamiltonian effective parameters ... 

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