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We review techniques for simulating fully quantum nonadiabatic dynamics usingthe frozen-width moving Gaussian basis functions to represent the nuclearwavefunction. A choice of these basis functions is primarily motivated by theidea of the on-the-fly dynamics that will involve electronic structurecalculations done locally in the vicinity of each Gaussian center and thusavoiding the "curse of dimensionality" appearing in large systems. For quantumdynamics involving multiple electronic states there are several aspects thatneed to be addressed. First, the choice of the electronic state representationis one of most defining in terms of formulation of resulting equations ofmotion. We will discuss pros and cons of the standard adiabatic and diabaticrepresentations as well as the relatively new moving crude adiabaticrepresentation. Second, if the number of electronic states can be fixedthroughout the dynamics, the situation is different for the number of Gaussiansneeded for an accurate expansion of the total wavefunction. The latterincreases its complexity along the course of the dynamics and a protocolextending the number of Gaussians is needed. We will consider two commonapproaches for the extension: 1) spawning and 2) cloning. Third, equations ofmotion for individual Gaussians can be chosen in different ways, implicationsfor the energy conservation related to these ways will be discussed. Finally,to extend the success of moving basis approaches to quantum dynamics of opensystems we will consider the Non-stochastic Open System Schr\"odinger Equation(NOSSE).

Nonadiabatic Quantum Dynamics with Frozen-Width Gaussians