Gaussian wavepacket dynamics

S.l. Vetchinkin, A.S. Vetchinkin, V.V. Eryomin, and I.M. Umanskii, Gaussian Wavepacket Dynamics in an Anharmonic System , Chem. Phys. Lett. 215, 11... 

To remedy this diflSculty, several approaches have been developed. In some metliods, the phase of the wavefunction is specified after hopping [178]. In other approaches, one expands the nuclear wavefunction in temis of a limited number of basis-set fiinctions and works out the quantum dynamical probability for jumping. For example, the quantum dynamical basis fiinctions could be a set of Gaussian wavepackets which move forward in time [147]. This approach is very powerfLil for short and intemiediate time processes, where the number of required Gaussians is not too large. 

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. 

The Gaussian wavepacket based spawning method, mentioned above, has also been used in direct dynamics where it is called ab initio multiple spawning... 

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. 

Both the BO dynamics and Gaussian wavepacket methods described above in Section n separate the nuclear and electronic motion at the outset, and use the concept of potential energy surfaces. In what is generally known as the Ehrenfest dynamics method, the picture is still of semiclassical nuclei and quantum mechanical electrons, but in a fundamentally different approach the electronic wave function is propagated at the same time as the pseudoparticles. These are driven by standard classical equations of motion, with the force provided by an instantaneous potential energy function... 

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... 

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. 

One can also ask about the relationship of the FMS method, as opposed to AIMS, with other wavepacket and semiclassical nonadiabatic dynamics methods. We first compare FMS to previous methods in cases where there is no spawning, and then proceed to compare with previous methods for nonadiabatic dynamics. We stress that we have always allowed for spawning in our applications of the method, and indeed the whole point of the FMS method is to address problems where localized nuclear quantum mechanical effects are important. Nevertheless, it is useful to place the method in context by asking how it relates to previous methods in the absence of its adaptive basis set character. There have been many attempts to use Gaussian basis functions in wavepacket dynamics, and we cannot mention all of these. Instead, we limit ourselves to those methods that we feel are most closely related to FMS, with apologies to those that are not included. A nice review that covers some of the... 

Eckart conditions, Renner-Teller effect, triatomic molecules, 610-615 Ehrenfest dynamics, direct molecular dynamics error sources, 403—404 Gaussian wavepacket propagation, 378-383 molecular mechanics valence bond (MMVB), 409-411... 

Heller equations, direct molecular dynamics, Gaussian wavepackets and multiple spawning, 399-402 Hellmann-Feynman theorem ... 

Independent Gaussian approximation (IGA), direct molecular dynamics, Gaussian wavepacket propagation, 379-383... 

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