A general unitary time evolution method for wave packets defined on a fixed ℒ2 basis is developed. It is based on the Lanczos reduction of the full N×N Hamiltonian to a p‐dimensional subspace defined by the application of H p−1 times to the initial vector. Unitary time evolution in the subspace is determined by exp{−iHpt}, retaining accuracy for a time interval τ, which can be estimated from the Lanczos reduced Hamiltonian Hp. The process is then iterated for additional time intervals. Although accurate results over long times can be obtained, the process is most efficient for large systems over short times. Time evolution employing this method in one‐ (unbounded) and two‐dimensional (bounded) potentials are done as examples using a distributed Gaussian basis. The one‐dimensional application is to direct evaluation of a thermal rate constant for the one‐dimensional Eckart barrier.
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15 November 1986
Research Article|
November 15 1986
Unitary quantum time evolution by iterative Lanczos reduction
Tae Jun Park;
Tae Jun Park
The Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, Illinois 60637
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J. C. Light
J. C. Light
The Department of Chemistry and the James Franck Institute, The University of Chicago, Chicago, Illinois 60637
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J. Chem. Phys. 85, 5870–5876 (1986)
Article history
Received:
June 24 1986
Accepted:
August 06 1986
Citation
Tae Jun Park, J. C. Light; Unitary quantum time evolution by iterative Lanczos reduction. J. Chem. Phys. 15 November 1986; 85 (10): 5870–5876. https://doi.org/10.1063/1.451548
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