Multiple spawning method

The standard semiclassical methods are surface hopping and Ehrenfest dynamics (also known as the classical path (CP) method [197]), and they will be outlined below. More details and comparisons can be found in [30-32]. The multiple spawning method, based on Gaussian wavepacket propagation, is also outlined below. See [1] for further infomiation on both quantum and semiclassical non-adiabatic dynamics methods. 

A more comprehensive Gaussian wavepacket based method has been introduced by Martinez et al. [35,36,218]. Called the multiple spawning method, it has already been used in direct dynamics studies (see Section V.B), and shows much promise. It has also been applied to adiabatic problems in which tunneling plays a role [219], as well as the interaction of a... 

The multiple spawning method described in Section IV.C has been applied to a number of photochemical systems using analytic potential energy surfaces. As well as small scattering systems [36,218], the large retinal molecule has been treated [243,244]. It has also been applied as a direct dynamics method. 

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

Hudock et al. [126] used the ab initio molecular dynamics multiple spawning method to go beyond the static picture based on PES and include the time dependent dynamical behavior and predict time-resolved photoelectron spectroscopy results. According to these results the first ultrafast component of the photoelectron spectra of uracil corresponds to relaxation on the S2 minimum rather than nonadiabatic transitions to the Si state. The authors suggest that the radiationless relaxation from... 

In this light surface hopping methods are akin to the LAND-map approach except they throw away a lot of information in the interest of developing an efficient method to model the approximate dynamics of the diagonal densities. The multiple spawning methods developed by Martinez and coworkers [51-55]... 

In the multiple spawning method of Martfnez at al., the time-dependent Gaussian nuclear wavefunction basis x t) are supposed to be parametrized... 

Ben-Nun M, Martinez TJ (1998) Nonadiabatic molecular dynamics validation of the multiple spawning method for a multidimensional problem. J Chem Phys 108 7244... 

Other quantum mechanical approaches based on Gaussian wavepackets or coherent-state basis sets are those by Methiu and co-workers [46] and Martinazzo and co-workers [47] as well as the multiple spawning method developed by Martinez et al. [48] by which the moving wavepacket is expanded on a variable number of frozen Gaussians. Elsewhere [49] such an approach, especially conceived to be run on the fly, has been utilized for computing the ethylene spectrum by directly coupling it with electronic structure calculations. 

The conceptual framework for the - semiclassical simulation of ultrafast spectroscopic observables is provided by the Wigner representation of quantum mechanics [2, 3]. Specifically, for the ultrafast pump-probe spectroscopy using classical trajectories, methods based on the semiclassical limit of the Liouville-von Neumann equation for the time evolution of the vibronic density matrix have been developed [4-8]. Our approach [4,6-8] is related to the Liouville space theory of nonlinear spectroscopy developed by Mukamel et al. [9]. It is characterized by the ability to approximately describe quantum phenomena such as optical transitions by averaging over the ensemble of classical trajectories. Moreover, quantum corrections for the nuclear dynamics can be introduced in a systematic manner, e.g. in the framework of the entangled trajectory method [10,11]. Alternatively, these effects can be also accounted for in the framework of the multiple spawning method [12]. In general, trajectory-based methods require drastically less computational effort than full quantum mechanical calculations and provide physical insight in ultrafast processes. Additionally, they can be combined directly with quantum chemistry methods for the electronic structure calculations. 

Molecular Dynamics Validation of the Multiple Spawning Method for a Multidimensional Problem. 

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