Calculating eigenvalues and eigenvectors of parameter-dependent hamiltonians using an adaptative wave operator method

Calcul de valeurs propres et vecteurs propres de Hamiltoniens paramétriques en utilisant une méthode d'opérateur d'onde adaptative

Arnaud Leclerc (1) , Georges Jolicard (2)

1 LPCT - Laboratoire de Physique et Chimie Théoriques
2 UTINAM - Univers, Transport, Interfaces, Nanostructures, Atmosphère et environnement, Molécules (UMR 6213)

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 which depends on external adjustable or adiabatic parameters , using adaptative projectors which 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 dozen iterations at constant memory cost. We first illustrate the abilities of the method on a 4-D 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 H + 2 in the vicinity of exceptional points are calculated as an illustrative example.

Domaines: Physique Quantique [quant-ph]; Physique [physics]; Chimie théorique et/ou physique; Chimie-Physique [physics.chem-ph]

Arnaud Leclerc, Georges Jolicard. Calculating eigenvalues and eigenvectors of parameter-dependent hamiltonians using an adaptative wave operator method. Journal of Chemical Physics, 2020, 152 (20), pp.204107. ⟨10.1063/5.0008947⟩. ⟨hal-02636974⟩