Analysis of the Geometrical Evolution in On-the-Fly Surface-Hopping Nonadiabatic Dynamics with Machine Learning Dimensionality Reduction Approaches: Classical Multidimensional Scaling and Isometric Feature Mapping

Abstract

On-the-fly trajectory-based nonadiabatic dynamics simulation has become an important approach to study ultrafast photochemical and photophysical processes in recent years. Because a large number of trajectories are generated from the dynamics simulation of polyatomic molecular systems with many degrees of freedom, the analysis of simulation results often suffers from the large amount of high-dimensional data. It is very challenging but meaningful to find dominating active coordinates from very complicated molecular motions. Dimensionality reduction techniques provide ideal tools to realize this purpose. We apply two dimensionality reduction approaches (classical multidimensional scaling and isometric feature mapping) to analyze the results of the on-the-fly surface-hopping nonadiabatic dynamics simulation. Two representative model systems, CHNH and the phytochromobilin chromophore model, are chosen to examine the performance of these dimensionality reduction approaches. The results show that these approaches are very promising, because they can extract the major molecular motion from complicated time-dependent molecular evolution without preknown knowledge.

QM/MM Benchmarking of Cyanobacteriochrome Slr1393g3 Absorption Spectra

“…Furthermore, Matute et al employed TD-DFT to predict the chromophore conformations, when they are bound to the proteins [21,45]. Also the photochemistry of related chromophore models was investigated by several groups [46,47,48,49] and more details on this topic, which involves an ultrafast double-bond isomerization, can be found in a recent review [50].…”

Recent Advances and Perspectives on Nonadiabatic Mixed Quantum–Classical Dynamics

“…This situation imposes significant challenges for analysis, which must be automatized, with clear quantitative classification criteria. [455][456][457] The second strategy to reduce computational costs commonly adopted is to downgrade the electronic structure level. NA-MQC dynamics are often run with small double- basis sets, with methods providing an incomplete treatment of electron correlation, as CASSCF (which misses dynamical electron correlation) or TDDFT (which misses nondynamical electron correlation).…”

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).…”

“…The dimensionality reduction can then be accomplished by simply picking the desired number of vectors and discarding the rest. Related approaches are, e.g., multidimensional scaling (MDS), 16 ISOMAP, 16 or diffusion map, 11,14,19 which all construct different kinds of matrices and find the reduced space via their eigenvectors.…”