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Article Dans Une Revue Journal of Chemical Physics Année : 2023

Analytical high-dimensional operators in canonical polyadic finite basis representation (CP-FBR)

Résumé

In the present work, we introduce a simple means of obtaining an analytical (i.e., grid-free) canonical polyadic (CP) representation of a multidimensional function that is expressed in terms of a set of discrete data. For this, we make use of an initial CP guess, even not fully converged, and a set of auxiliary basis functions [finite basis representation (FBR)]. The resulting CP-FBR expression constitutes the CP counterpart of our previous Tucker sum-of-products-FBR approach. However, as is well-known, CP expressions are much more compact. This has obvious advantages in high-dimensional quantum dynamics. The power of CP-FBR lies in the fact that it requires a grid much coarser than the one needed for the dynamics. In a subsequent step, the basis functions can be interpolated to any desired density of grid points. This is useful, for instance, when different initial conditions (e.g., energy content) of a system are to be considered. We show the application of the method to bound systems of increased dimensionality: H 2 (3D), HONO (6D), and CH 4 (9D).

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Chimie
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Dates et versions

hal-04064119 , version 1 (11-04-2023)

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Nataša Nadoveza, Ramón L Panadés-Barrueta, Lei Shi, Fabien Gatti, Daniel Peláez. Analytical high-dimensional operators in canonical polyadic finite basis representation (CP-FBR). Journal of Chemical Physics, 2023, 158 (11), pp.114109. ⟨10.1063/5.0139224⟩. ⟨hal-04064119⟩
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