Vibrational dynamics adiabatic representation

In contrast to the subsystem representation, the adiabatic basis depends on the environmental coordinates. As such, one obtains a physically intuitive description in terms of classical trajectories along Born-Oppenheimer surfaces. A variety of systems have been studied using QCL dynamics in this basis. These include the reaction rate and the kinetic isotope effect of proton transfer in a polar condensed phase solvent and a cluster [29-33], vibrational energy relaxation of a hydrogen bonded complex in a polar liquid [34], photodissociation of F2 [35], dynamical analysis of vibrational frequency shifts in a Xe fluid [36], and the spin-boson model [37,38], which is of particular importance as exact quantum results are available for comparison. 

Transitions between electronic states are formally equivalent to transitions between different vibrational or rotational states which were amply discussed in Chapters 9 11. Computationally, however, they are much more difficult to handle because they arise from the coupling between electronic and nuclear motions. The rigorous description of electronic transitions in polyatomic molecules is probably the most difficult task in the whole field of molecular dynamics (Siebrand 1976 Tully 1976 Child 1979 Rebentrost 1981 Baer 1983 Koppel, Domcke, and Cederbaum 1984 Whetten, Ezra, and Grant 1985 Desouter-Lecomte et al. 1985 Baer 1985b Lefebvre-Brion and Field 1986 Sidis 1989a,b Coalson 1989). The reasons will become apparent below. The two basic approaches, the adiabatic and the diabatic representations, will be outlined in Sections 15.1 and 15.2, respectively. Two examples, the photodissociation of CH3I and of H2S, will be discussed in Section 15.3. 

Since the dielectric continuum representation of the solvent has significant limitations, the molecular dynamics simulation of PCET with explicit solvent molecules is also an important direction. One approach is to utilize a multistate VB model with explicit solvent interactions [34-36] and to incorporate transitions among the adiabatic mixed electronic/proton vibrational states with the Molecular Dynamics with Quantum Transitions (MDQT) surface hopping method [39, 40]. The MDQT method has already been applied to a one-dimensional model PCET system [39]. The advantage of this approach for PCET reactions is that it is valid in the adiabatic and non-adiatic limits as well as in the intermediate regime. Furthermore, this approach is applicable to PCET in proteins as well as in solution. 

The adiabatic potential (11b.II) was first introduced by HIRSCHPELDER and WIGNER /6/ in the simplest case of a rectilinear (dynamically nonseparable) reaction coordinate and a quantized (high frequency) vibration normal to it. It is obviously also applicable, according to (11 a.II), to the case of a curvilinear reaction path and a classical (low frequency) y-vibration. The more general representation (9.II) of the adiabatic separation includes also the case of a quantized (enharmonic) vibration along the reaction coordinate in the reactant region of configuration space, in which E = E, pro-... 

We use the transformation matrix U R) to represent the potential energy matrix, dipole moment matrix, and photoionization amplitudes in the diabatic representation. Then the vibrational wavefunctions are computed in the diabatic representation, but can also be transformed with U R) when we wish to see the adiabatic functions. The vibrational wavepacket dynamics and time-resolved photoelectron spectroscopy of the system is treated in Sec. 5.4. 

Abstract In the present study, the effect of the potential energy surface representation on the infrared spectra features of the and Df clusters is investigated. For the spectral simulations, we adopted a recently proposed (Sanz-Sanz et al. in Phys Rev A 84 060502-1-4, 2011) two-dimensional adiabatic quantum model to describe the proton-transfer motion between the two H2 or D2 units. The reported calculations make use of a reliable on the fly DFT-based potential surface and the corresponding new dipole moment surface. The results of the vibrational predissociation dynamics are compared with earlier and recent experimental data available from mass-selected photodissociation spectroscopy, as well as with previous theoretical calculations based on an analytical ab initio parameterized surfaces. The role of the potential topology on the spectral features is studied, and general trends are discussed. 

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