Calculating eigenvalues and eigenvectors of parameter-dependent Hamiltonians using an adaptative wave operator method
Abstract
We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices using an adaptative active subspace. We consider a Hamiltonian that depends on external adjustable or adiabatic parameters, using adaptative projectors that follow the successive eigenspaces when the adjustable parameters are modified. The method can also handle non-Hermitian Hamiltonians. An iterative algorithm is derived and tested through comparisons with a standard wave operator algorithm using a fixed active space and with a standard block-Davidson method. The proposed approach is competitive; it converges within a few dozens of iterations at constant memory cost. We first illustrate the abilities of the method on a 4D-coupled oscillator model Hamiltonian. A more realistic application to molecular photodissociation under intense laser fields with varying intensity or frequency is also presented. Maps of photodissociation resonances of H2+ in the vicinity of exceptional points are calculated as an illustrative example.
- Publication:
-
Journal of Chemical Physics
- Pub Date:
- May 2020
- DOI:
- 10.1063/5.0008947
- arXiv:
- arXiv:2005.13611
- Bibcode:
- 2020JChPh.152t4107L
- Keywords:
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- Physics - Computational Physics;
- Physics - Chemical Physics;
- Quantum Physics
- E-Print:
- 30 pages, 4 figures