Abstract
Grid-based schemes for simulating quantum dynamics, such as the multi-configuration time-dependent Hartree (MCTDH) method, provide highly accurate predictions of the coupled nuclear and electronic dynamics in molecular systems. Such approaches provide a multi-dimensional, time-dependent view of the system wavefunction represented on a coordinate grid; in the case of non-adiabatic simulations, additional information about the state populations adds a further layer of complexity. As such, wavepacket motion on potential energy surfaces which couple many nuclear and electronic degrees-of-freedom can be extremely challenging to analyse in order to extract physical insight beyond the usual expectation-value picture. Here, we show that non-linear dimensionality reduction (NLDR) methods, notably diffusion maps, can be adapted to extract information from grid-based wavefunction dynamics simulations, providing insight into key nuclear motions which explain the observed dynamics. This approach is demonstrated for 2-D and 9-D models of proton transfer in salicylaldimine, as well as 8-D and full 12-D simulations of cis-trans isomerization in ethene; these simulations demonstrate how NLDR can provide alternative views of wavefunction dynamics, and also highlight future developments.
Highlights
Simulating wavefunction evolution describing the coupled nuclear/electronic dynamics of molecules following photo-excitation remains a frontier challenge in computational chemistry; refs. [1,2,3,4,5,6,7,8,9] the computational expense associated with accurately modelling excited state electronic structure, as well as that associated with representing and propagating time-dependent wavefunctions, means that there remain opportunities for algorithm development
Methods enable identification of important reaction-coordinates which might not be immediately obvious from simple time-series of individual atomic or molecular coordinates; the reduction from the enormous number of atomic coordinates used in biophysical simulations to just a few key coordinates provides a further advantage to analysis. Building on these previous demonstrations of the utility of non-linear dimensionality reduction (NLDR) in other settings, we aim to investigate the use of NLDR in grid-based wavefunction propagation schemes; in particular, our goal in this article is to assess the utility of DMs in extracting important molecular motions from time-dependent wavefunctions as a route to understanding photo-induced chemical reaction mechanisms, and we demonstrate this approach in a series of grid-based simulations of multi-dimensional molecular systems
We demonstrate our overall simulation scheme, and the possibilities offered by DMs, in large-scale simulations of salicylaldimine and ethene; notably, we perform the first direct, full-dimensional (12-D, three electronic states) multi-configuration time-dependent Hartree (MCTDH) simulations of ethene, and use the DM NLDR strategy to compare our results to previous trajectory-based simulations of the same system
Summary
Simulating wavefunction evolution describing the coupled nuclear/electronic dynamics of molecules following photo-excitation remains a frontier challenge in computational chemistry; refs. [1,2,3,4,5,6,7,8,9] the computational expense associated with accurately modelling excited state electronic structure, as well as that associated with representing and propagating time-dependent wavefunctions, means that there remain opportunities for algorithm development. Simulating wavefunction evolution describing the coupled nuclear/electronic dynamics of molecules following photo-excitation remains a frontier challenge in computational chemistry; refs. [1,2,3,4,5,6,7,8,9] the computational expense associated with accurately modelling excited state electronic structure, as well as that associated with representing and propagating time-dependent wavefunctions, means that there remain opportunities for algorithm development. Grid-based schemes in particular, where a time-dependent wavefunction is generally represented as a series of complex values on a coordinate-grid, broadly represent the most accurate strategy for modelling quantum molecular dynamics, refs. As well as modelling wavefunction evolution on a single Born-Oppenheimer electronic state, this scheme can be readily expanded to account for non-adiabatic simulations on multiple electronic states (using either the single-set or multi-set formulation [6]), enabling direct quantum dynamics simulations of molecular systems following photoexcitation
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