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Pruned multi-configuration time-dependent Hartree methods

Banff International Research Station for Mathematical Innovation and Discovery

I shall present two pruned, nondirect product multi-configuration time dependent Hartree (MCTDH) methods for solving the Schr¨odinger equation. Both use a basis of products of natural orbitals. Standard MCTDH uses optimized 1D basis functions, called single particle functions, but the size of the basis scales exponentially with D, the number of coordinates.By replacing t → −iβ , β ∈ R>0 , we use the pruned methods to determine solutions of the time-independent Schroedinger equation. For a 12D Hamiltonian, we compare the pruned approach to standard MCTDH calculations for basis sizessmall enough that the latter are possible and demonstrate that pruning the basis reduces the CPU cost of computing vibrational energy levels of acetonitrile by more than two orders of magnitude. One of the pruned MCTDH methods uses an algebraic pruning constraint. The other uses a flexible basis that expands as the calculation proceeds. Results obtained with the expanded basis are compared to those obtained with the established multi-layer MCTDH (ML-MCTDH) scheme. Although ML-MCTDH is somewhat more efficient when low or intermediate accuracy is desired, pruned MCTDH is more efficient when high accuracy is required.

Mathematics; Quantum theory; Optics, electromagnetic theory; Mathematical physics

video/mp4

Author affiliation: Queen's University

2018-02-11

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64613

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/