Wavepacket dynamics simulation

M. Quack Prof. Zewail and Gerber, when you make an interpretation of your femtosecond observations (detection signal as a function of excitation), would it not be necessary to try a full quantum dynamical simulation of your experiment in order to obtain a match with your molecular, mechanistic picture of the dynamics or the detailed wavepacket evolution Agreement between experimental observation and theoretical simulation would then support the validity of the underlying interpretation (but it would not prove it). The scheme is of the following kind ... 

In the photochemistry of benzene, the so-called channel 3 represents a well-known decay route along which fluorescence is quenched above a vibrational excess of 3000 cm [57], The decay takes place through a prefulvenic conical intersection characterized by an out of plane bending [52,58] and results in the formation of benzvalene and fulvene. The purpose of this study is to find distinct radiationless decay pathways that could be selected by exciting specific combinations of photoactive modes in the initial wavepacket created by a laser pulse. For this, we carry out quantum dynamics simulations on potential energy surfaces of reduced dimension, using the analysis outlined above for the choice of the coordinates. 

Basic questions are analyzed, as is the case for the photochemistry of formaldehyde. Contrary to previous results, direct quantum dynamics simulations showed that the H2 + CO H + HCO branching ratio in the Si/Sq nonadiabatic photodissociation of formaldehyde is controlled by the direction and size of the mean momentum of the wavepacket when it crosses the seam of conical intersection. In practice, if the wavepacket falls down from the barrier to the conical intersection with no initial momentum the system leads to H2 + CO, while an extra momentum toward products favors... 

To summarize, we have thus shown that an interplay of bond-softening and bond-hardening can be clearly seen in the snapshots of time-dependent QESs and wavepacket dynamics on them, which is clearly understood in terms of the quasi-classical approximation. In fact our simulation serves as a direct real-time demonstration of possibly competing bondsoftening and bond-hardening mechanisms, and moreover, has suggested a possible phenomenon, the inverse bond-hardening. The additional... 

This work prompted optimal control experiments on a large cyanine [88, 89], which confirmed that the branching ratio could be controlled by a pulse leading to excitation of the same skeletal deformations in the initial wavepacket (see Fig. 7.11). This control strategy was further validated in a quantum dynamics context with Gaussian-based direct dynamics simulations [90]. 

The time dependences of the wavepackets for the individual modes can be predicted by molecular-dynamics simulations even for comparatively complex molecules. Applications of the wavepacket treatment to resonance Raman spectroscopy are discussed in Chap. 12. 

Finally, some comments on two recent studies on methods for quantum dynamics simulations. In the first study, by Mendive-Tapia et al., the convergence of non-adiabatic direct dynamics in conjunction with frozen-width variational Gaussian product basis functions is evaluated. The simulation of non-adiabatic dynamics can be subdivided into two groups semi-classical methods (like the trajectory surface hopping approach) and wavepacket methods (for example, the... 

To add non-adiabatic effects to semiclassical methods, it is necessary to allow the trajectories to sample the different surfaces in a way that simulates the population transfer between electronic states. This sampling is most commonly done by using surface hopping techniques or Ehrenfest dynamics. Recent reviews of these methods are found in [30-32]. Gaussian wavepacket methods have also been extended to include non-adiabatic effects [33,34]. Of particular interest here is the spawning method of Martinez, Ben-Nun, and Levine [35,36], which has been used already in a number of direct dynamics studies. 

This article is organized as follows. In Section 2 ab initio molecular dynamics methods are described. Specifically, in Section 2.1 we discuss the extended Lagrangian atom-centered density matrix (ADMP) technique for simultaneous dynamics of electrons and nuclei in large clusters, and in Section 2.2 we discuss the quantum wavepacket ab initio molecular dynamics (QWAIMD) method. Simulations conducted and new insights obtained from using these approaches are discussed in Section 3 and the concluding remarks are given in Section 4. 

Although quantitative calculation of the accurate PESs remains a difficult task (see Section 20.1.2), the two-state-model describes the essential reaction dynamic process and is useful for a qualitative understanding. When the reaction coordinate is set to the adsorbate-surface distance (one-dimension), the two-state-model is called the Menzel-Gomer-Redhead [49] and/or Antoniewicz [50] model. We refer to them as the MGR models. The MGR models are often used successfully to analyze photodesorption on metal surfaces by assuming a short residential time on the excited PES. There are several methods to simulate the quantum dynamics of the MGR models, for example, stochastic wavepacket [51], open density matrix methods [52], and so on. 

For a complete treatment of a laser-driven molecule, one must solve the many-body, multidimensional time-dependent Schrodinger equation (TDSE). This represents a tremendous task and direct wavepacket simulations of nuclear and electronic motions under an intense laser pulse is presently restricted to a few bodies (at most three or four) and/or to a model of low dimensionality [27]. For a more general treatment, an approximate separation of variables between electrons (fast subsystem) and nuclei (slow subsystem) is customarily made, in the spirit of the BO approximation. To lay out the ideas underlying this approximation as adapted to field-driven molecular dynamics, we will consider from now on a molecule consisting of Nn nuclei (labeled a, p,...) and Ne electrons (labeled /, j,...), with position vectors Ro, and r respectively, defined in the center of mass (rotating) body-fixed coordinate system, in a classical field E(f) of the form Eof t) cos cot). The full semiclassical length gauge Hamiltonian is written, for a system of electrons and nuclei, as [4]... 

Recent advances in first-principles molecular dynamics (MD) calculations, which follow the Newtonian dynamics of classically treated nuclei, have made electronic-structure calculations applicable to the study of large systems where previously only classical simulations were possible. Examples of quantum-mechanical (QM) simulation methods are Born-Oppenheimer molecular dynamics (BOMD), Car-Parrinello molecular dynamics (CPMD), tight-binding molecular dynamics (TBMD), atom-centered density matrix propagation molecular dynamics (ADMPMD), and wavepacket ab idtb molecular dynamics (WPAIMD). 

Using the grid-based MCTDH method, simulations were performed, first in two dimensions [84], The resulting dynamics show that the 4CI point is reached very fast (in less than 30 fs after photoexcitation), and the wavepacket distributes over all states (see Fig. 7.9). 

---