This article presents a new complex absorbing potential (CAP) block Lanczos method for computing scattering eigenfunctions and reaction probabilities. The method reduces the problem of computing energy eigenfunctions to solving two energy dependent systems of equations. An energy independent block Lanczos factorization casts the system into a block tridiagonal form, which can be solved very efficiently for all energies. We show that CAP-Lanczos methods exhibit instability due to the non-normality of CAP Hamiltonians and may break down for some systems. The instability is not due to loss of orthogonality but to non-normality of the Hamiltonian matrix. While use of a Woods–Saxon exponential CAP—as opposed to a polynomial CAP—reduced non-normality, it did not always ensure convergence. Our results indicate that the Arnoldi algorithm is more robust for non-normal systems and less prone to break down. An Arnoldi version of our method is applied to a nonadiabatic tunneling Hamiltonian with excellent results, while the Lanczos algorithm breaks down for this system.
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21 July 2008
Research Article|
July 21 2008
Non-normal Lanczos methods for quantum scattering
Reza Rajaie Khorasani;
Reza Rajaie Khorasani
Department of Chemistry,
McMaster University
, 1280 Main St. W. Hamilton, Ontario L8S 4M1, Canada
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Randall S. Dumont
Randall S. Dumont
a)
Department of Chemistry,
McMaster University
, 1280 Main St. W. Hamilton, Ontario L8S 4M1, Canada
Search for other works by this author on:
a)
Electronic mail: [email protected].
J. Chem. Phys. 129, 034110 (2008)
Article history
Received:
April 15 2008
Accepted:
May 16 2008
Citation
Reza Rajaie Khorasani, Randall S. Dumont; Non-normal Lanczos methods for quantum scattering. J. Chem. Phys. 21 July 2008; 129 (3): 034110. https://doi.org/10.1063/1.2940733
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