Two New Methods To Generate Internal Coordinates for Molecular Wave Packet Dynamics in Reduced Dimensions

Abstract

The curse of dimensionality still remains as the central challenge of molecular quantum dynamical calculations. Either compromises on the accuracy of the potential landscape have to be made or methods must be used that reduce the dimensionality of the configuration space of molecular systems to a low dimensional one. For dynamic approaches such as grid-based wave packet dynamics that are confined to a small number of degrees of freedom this dimensionality reduction can become a major part of the overall problem. A common strategy to reduce the configuration space is by selection of a set of internal coordinates using chemical intuition. We devised two methods that increase the degree of automation of the dimensionality reduction as well as replace chemical intuition by more quantifiable criteria. Both methods reduce the dimensionality linearly and use the intrinsic reaction coordinate as guidance. The first one solely relies on the intrinsic reaction coordinate (IRC), whereas the second one uses semiclassical trajectories to identify the important degrees of freedom.

Identification of Important Normal Modes in Nonadiabatic Dynamics Simulations by Coherence, Correlation, and Frequency Analyses

“…This was mainly done in order to be compatible with the eventual generation of an LVC model based on the set of identified most important normal modes, in order to carry out MCTDH simulations in a way comparable to recent simulations. [29][30][31] Unlike the dimensionality-reduction techniques mentioned above (PCA, ISOMAP, diffusion map), 4,[11][12][13][14][15][16] our goal here is not to find an optimal arbitrary coordinate basis, but rather to identify the most important modes within the employed normal mode basis.…”

“…11 One of the most convenient ways to generate such lowdimensional models is by applying some dimensionalityreduction techniques to full-dimensional AIMD trajectories. A significant body of literature was published on this topic, see, e.g., References 4,[11][12][13][14][15][16][17]. One of the most common approaches is to take the coordinate data from the trajectories, compute the covariance matrix, and perform a principal component analysis (PCA).…”

“…One of the most common approaches is to take the coordinate data from the trajectories, compute the covariance matrix, and perform a principal component analysis (PCA). 4,15,17,18 In this way, the coordinate space is transformed into a vector basis where most of the statistical variance is contained in a subspace spanned by the first few vectors. The dimensionality reduction can then be accomplished by simply picking the desired number of vectors and discarding the rest.…”

“…While the mentioned dimensionality reduction approaches have successfully been employed in molecular dynamics simulations from small organic molecules 15 to large proteins, 18 they all have in common that they exclusively consider the distribution of nuclear geometries. Here, we propose that for nonadiabatic dynamics this might not be the only important aspect of the simulations.…”

Constructing Grids for Molecular Quantum Dynamics Using an Autoencoder

“…The protonization of the oxygen on the far side of the chlorine is much more stable. Since this system requires about two to three degrees of freedom to be appropriately described, 3 Since we used trajectory data points to construct these two autoencoder subspaces, it would not be expected that any low-dimensional projection would reconstruct the IRC exactly. However, we would expect that, as long as an increase in dimensionality is very beneficial for the description, the distance of projected IRCs would decrease significantly.…”