Any order imaginary time propagation method for solving the Schrodinger equation

Details Any order imaginary time propagation method for solving the Schrodinger equation Any order imaginary time propagation method for solving the Schrodinger equation

2008-09-22

arxiv.org/abs/0809.3739v1

Physics

Condensed Matter

Materials Science

8 pages, 3 figures

Scientific paper

10.1016/j.cplett.2009.01.068

The eigenvalue-function pair of the 3D Schr\"odinger equation can be efficiently computed by use of high order, imaginary time propagators. Due to the diffusion character of the kinetic energy operator in imaginary time, algorithms developed so far are at most fourth-order. In this work, we show that for a grid based algorithm, imaginary time propagation of any even order can be devised on the basis of multi-product splitting. The effectiveness of these algorithms, up to the 12$^{\rm th}$ order, is demonstrated by computing all 120 eigenstates of a model C$_{60}$ molecule to very high precisions. The algorithms are particularly useful when implemented on parallel computer architectures.

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