Molecular systems wave packets

Gaussian wavepackets multiple spawning, 402 propagation, 380-381 molecular systems, component amplitude analysis, wave packet construction, 229-230... 

As a last example of a molecular system exhibiting nonadiabatic dynamics caused by a conical intersection, we consider a model that recently has been proposed by Seidner and Domcke to describe ultrafast cis-trans isomerization processes in unsaturated hydrocarbons [172]. Photochemical reactions of this type are known to involve large-amplitode motion on coupled potential-energy surfaces [169], thus representing another stringent test for a mixed quantum-classical description that is complementary to Models 1 and II. A number of theoretical investigations, including quantum wave-packet studies [163, 164, 172], time-resolved pump-probe spectra [164, 181], and various mixed... 

The photochemical excitation delivered by a narrowly defined pump laser pulse achieves three indispensable things it sets time = 0, energizes the reactant molecules, and localizes them in space. It induces molecular coherence as excitation of each of the individual molecules involved leads to a coherent superposition of separate wave packets, a highly locahzed, geometrically well-defined and moving packet—analogous to a classical system, one that can be described using classical concepts of atomic positions and momentum. 

A statistical relationship between the above description and the standard one can be obtained. In a molecular sample at time t, the nuclei are statistically s-tributed. Each molecule shows its own particular energy gap between the electronic states involved in the process. On the average, things may look like as an electro-nuclear adiabatic process which could be modelled as a wave packet propagating on an adiabatic potential energy surface. This is the point where standard BO simulations of reaction processes [40] and the present view can be tied together. Individual systems are sensing electronic processes while the molecular... 

Baumert, T., Grosser, M., Thalweiser, R., and Gerber, G. (1991). Femtosecond time-resolved wave packet motion in molecular multiphoton ionization and fragmentation The Na2 system, Phys. Rev. Lett. 67, 3753. 

So far we have treated only the case of wave packets constructed from pure states. Consider now the control of a molecular system in a mixed state in which the initial states are distributed at a finite temperature. The time evolution of the system density operator pit) is determined by the Liouville equation,... 

For 4-atom systems such as formaldehyde the photodissociation dynamics have yet to be established. A fully quantal description of the photodissociation is still very expensive computationally. So far 6-dimensional wave packet studies have been applied only to one electronic surface, for example for scattering of a molecule or atoms on surfaces or collisions of molecules. Currently, for molecular systems with more than four atoms, a reduced dimensionality model must be used. This means that certain degrees of freedom are fixed throughout the dynamical simulation. 

One has to emphasize that Eqs. (82) and (83) do not involve the Born-Oppenheimer approximation although the nuclear motion is treated classically. This is an important advantage over the quantum molecular dynamics approach [47-54] where the nuclear Newton equations (82) are solved simultaneously with a set of ground-state KS equations at the instantaneous nuclear positions. In spite of the obvious numerical advantages one has to keep in mind that the classical treatment of nuclear motion is justified only if the probability densities (R, t) remain narrow distributions during the whole process considered. The splitting of the nuclear wave packet found, e.g., in pump-probe experiments [55-58] cannot be properly accounted for by treating the nuclear motion classically. In this case, one has to face the complete system (67-72) of coupled TDKS equations for electrons and nuclei. 

As has been mentioned above, a new method for the treatment of the dynamics of mixed classical quantum system has been recently suggested by Jung-wirth and Gerber [50,51]. The method uses the classically based separable potential (CSP) approximation, in which classically molecular dynamics simulations are used to determine an effective time-dependent separable potential for each mode, then followed by quantum wave packet calculations using these potentials. The CSP scheme starts with "sampling" the initial quantum state of the system by a set of classical coordinates and momenta which serve as initial values for MD simulations. For each set j (j=l,2,...,n) of initial conditions a classical trajectory [q (t), q 2(t),..., q N(t)] is generated, and a separable time-dependent effective potential V (qj, t) is then constructed for each mode i (i=l,2,...,N) in the following way ... 

By changing the frequency and the intensity of the steady state laser, we can vary the width and the displacement of the excited wave packet. With this example, we want to demonstrate how the space-dependence of a dipole coupling can be used to steer the transfer of a wave packet to an excited molecular potential. However, this is only one example out of many possible. This method is by no means restricted to a model system consisting of harmonic oscillators but can be easily applied to any form of one-dimensional potential curves. Possible applications might be steering of a reaction to one side of a potential barrier by displacing the excited wave packet to the desired side, or coupling to a dissociative state in order to steer the dissociation of a molecule. 

We wish to describe the preparation of a nuclear wave packet corresponding to coherent molecular pseudorotation in the electronic ground state by a sequence of nonresonant light pulses [30], The system is driven by a pair of vibrationally abrupt pulses... 

In these wave packet simulations, the molecular axis of the FHF system is assumed to be aligned along the space-fixed axis Z electric field vector. This assumption involves a maximum interaction of the IR and UV laser pulses with the system. Recalling that the time-dependent interaction potential is given by the scalar product of the electric field vector and the dipole vector, i.e. (t) /j, cos 9, it is clear that for field polarizations perpendicular to the molecular axis [9 = 90°) the interaction of the IR laser pulse with the anion vanishes, and for any molecular orientation different from 0= 0° or 180° the interaction is less efficient. Consider now an ensemble of randomly oriented FHF molecules, as in Fig. 4.13(c). Since the UV pulse is tuned to match the energy gap between anion and neutral... 

In gas-phase dynamics, the discussion is focused on the TD quantum wave packet treatment for tetraatomic systems. This is further divided into two different but closed related areas molecular photofragmentation or half-collision dynamics and bimolecular reactive collision dynamics. Specific methods and examples for treating the dynamics of direct photodissociation of tetraatomic molecules and of vibrational predissociation of weakly bound dimers are given based on different dynamical characters of these two processes. TD methods such as the direct projection method for direct photodissociation, TD golden rule method and the flux method for predissociation are presented. For bimolecular reactive scattering, the use of nondirect product basis and the computation of the initial state-selected total reaction probabilities by flux calculation are discussed. The descriptions of these methods are supported by concrete numerical examples and results of their applications. 

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