Global integration of the Schr\"odinger equation within the wave operator formalism: The role of the effective Hamiltonian in multidimensional active spaces

TL;DR

This paper extends a wave operator approach to solve the time-dependent Schrödinger equation in multidimensional active spaces, improving the description of complex quantum dynamics and dissipation in molecular systems.

Contribution

It generalizes the wave operator formalism to multidimensional active spaces and develops an iterative algorithm for effective Hamiltonian computation.

Findings

Multidimensional active spaces improve the accuracy of quantum dynamics simulations.

The method effectively describes dissipative processes like photodissociation.

Choosing appropriate active spaces enhances cyclic dynamics and prevents divergences.

Abstract

A global solution of the Schr\"odinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians [J. Phys. A: Math. Theor. 48, 225205 (2015)], is generalized to take into account the case of multidimensional active spaces. An iterative algorithm is derived to obtain the Fourier series of the evolution operator issuing from a given multidimensional active subspace and then the effective Hamiltonian corresponding to the model space is computed and analysed as a measure of the cyclic character of the dynamics. Studies of the laser controlled dynamics of diatomic models clearly show that a multidimensional active space is required if the wavefunction escapes too far from the initial subspace. A suitable choice of the multidimensional active space, including the initial and target states, increases the cyclic character and avoids divergences occuring when one-dimensional active spaces are used. The method is also proven to be efficient in describing dissipative processes such as photodissociation.