Global integration of the Schrödinger equation within the wave operator formalism: the role of the effective Hamiltonian in multidimensional active spaces

• Published in: Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2016-05, Vol.49 (19), p.195305
• Main Authors: Jolicard, Georges, Leclerc, Arnaud, Viennot, David, Killingbeck, John P
• Format: Article
• Language: English
• Subjects: molecular quantum dynamics; numerical integration; Physics; Schrödinger equation; wave operator theory
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8113/49/19/195305

A global solution of the Schrödinger equation, obtained recently within the wave operator formalism for explicitly time-dependent Hamiltonians (Leclerc and Jolicard 2015 J. Phys. A: Math. Theor. 48 225205), 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.