Vibronic coupling dynamic

The dynamics associated with the Hamiltonian Eq. (8) or its variants Eq. (11) and Eq. (14) can be treated at different levels, ranging from the explicit quantum dynamics to non-Markovian master equations and kinetic equations. In the present context, we will focus on the first aspect - an explicit quantum dynamical treatment - which is especially suited for the earliest, ultrafast events at the polymer heterojunction. Here, the coherent vibronic coupling dynamics dominates over thermally activated events. On longer time scales, the latter aspect becomes important, and kinetic approaches could be more appropriate. 

Ru(cp)2, space group Dzh, site symmetry Dsh, C.S.25 Co(cp)2, space group Czh, site symmetry Dsd, C.S.24 vibronic coupling (dynamic Jahn-Teller effect) m orbitally degenerate Eig state suggested direction cosines determined ) two superimposed spectra observed, ... 

In this chapter we intend to give a brief exposition of the basic concepts of vibronic coupling theory. More detailed and comprehensive descriptions can be found in several monographs and review articles. We emphasize the numerical treatment of vibronic-coupling dynamics in the time as well as the frequency domain. A few applications will be reviewed which illustrate the present state of the art in this area. 

D. The Vibronic-Coupling Model Hamiltonian IV, Non-Adiabatic Molecular Dynamics... 

A further model Hamiltonian that is tailored for the treatment of non-adiabatic systems is the vibronic coupling (VC) model of Koppel et al. [65]. This provides an analytic expression for PES coupled by non-adiabatic effects, which can be fitted to ab initio calculations using only a few data points. As a result, it is a useful tool in the description of photochemical systems. It is also very useful in the development of dynamics methods, as it provides realistic global surfaces that can be used both for exact quantum wavepacket dynamics and more approximate methods. 

To demonstrate the basic ideas of molecular dynamics calculations, we shall first examine its application to adiabatic systems. The theory of vibronic coupling and non-adiabatic effects will then be discussed to define the sorts of processes in which we are interested. The complications added to dynamics calculations by these effects will then be considered. Some details of the mathematical formalism are included in appendices. Finally, examples will be given of direct dynamics studies that show how well the systems of interest can at present be treated. 

In the limit of strong vibronic coupling, F4S = 0, c = 5 /3, s=, c2 - s2 =, and the dynamic Jahn-Teller effect thus renders nugatory the orbital contributions to the angular momentum, and reduces the splitting, A, by a factor of two. Note in addition that the c and s quantities used in the vibronic treatment do not correspond to those of the adiabatic case, although the expressions are formally similar, so that the static distortion, A, cannot accurately be calculated from the c and s values deduced from the and 4 data. 

In the past decade, vibronic coupling models have been used extensively and successfully to explain the short-time excited-state dynamics of small to medium-sized molecules [200-202]. In many cases, these models were used in conjunction with the MCTDH method [203-207] and the comparison to experimental data (typically electronic absorption spectra) validated both the MCTDH method and the model potentials, which were obtained by fitting high-level quantum chemistry calculations. In certain cases the ab initio-determined parameters were modified to agree with experimental results (e.g., excitation energies). The MCTDH method assumes the existence of factorizable parameterized PESs and is thus very different from AIMS. However, it does scale more favorably with system size than other numerically exact quantum... 

Density functional theory, direct molecular dynamics, complete active space self-consistent field (CASSCF) technique, non-adiabatic systems, 404-411 Density operator, direct molecular dynamics, adiabatic systems, 375-377 Derivative couplings conical intersections, 569-570 direct molecular dynamics, vibronic coupling, conical intersections, 386-389 Determinantal wave function, electron nuclear dynamics (END), molecular systems, final-state analysis, 342-349 Diabatic representation ... 

Nuclear motion Schrodinger equation direct molecular dynamics, 363-373 vibronic coupling, adiabatic effects, 382-384 electronic states ... 

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