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

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.