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Manuscript Title: Qprop: A Schrödinger-solver for intense laser-atom interaction
Authors: Dieter Bauer, Peter Koval
Program title: QPROP
Catalogue identifier: ADXB_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 174(2006)396
Programming language: C++.
Computer: PC Pentium IV, Athlon.
Operating system: Linux.
RAM: Memory requirements depend on the number of propagated orbitals and on the size of the orbitals. For instance, time-propagation of a hydrogenic wavefunction in the perturbative regime requires about 64 KByte RAM (4 radial orbitals with 1000 grid points). Propagation in the strongly nonperturbative regime providing energy spectra up to high energies may need 60 radial orbitals, each with 30000 grid points, i.e., about 30 MByte. Examples are given in the article.
Word size: Real and complex valued numbers of double precision are used.
Keywords: Time-dependent Schrodinger equation, split operator, Crank-Nicolson approximant, window-operator.
Classification: 2.5, 4.3.

External routines: The program uses the well established libraries BLAS, LAPACK, and F2C.

Nature of problem:
Atoms put into the strong field of modern lasers display a wealth of novel phenomena that are not accessible to conventional perturbation theory where the external field is considered small as compared to inneratomic forces. Hence, the full ab initio solution of the time-dependent Schrödinger equation is desirable but in full dimensionality, only feasible for no more than two (active) electrons. If many-electron effects come into play or effective ground state potentials are needed, (time-dependent) density functional theory may be employed. Qprop aims at providing tools for
  1. the time-propagation of the wavefunction according to the time-dependent Schrödinger equation,
  2. the time-propagation of Kohn-Sham orbitals according to the time-dependent Kohn-Sham equations,
  3. the energy-analysis of the final one-electron wavefunction (or the Kohn-Sham orbitals).

Solution method:
An expansion of the wavefunction in spherical harmonics leads to a coupled set of equations for the radial wavefunctions. These radial wavefunctions are propagated using a split-operator technique and the Crank-Nicolson approximation for the short-time propagator. The initial ground state is obtained via imaginary time-propagation for spherically symmetric (but otherwise arbitrary) effective potentials. Excited states can be obtained through the combination of imaginary time-propagation and orthogonalization. For the Kohn-Sham scheme a multipole expansion of the effective potential is employed. Wavefunctions can be analyzed using the window-operator technique, facilitating the calculation of electron spectra, either angular-resolved or integrated.

The coupling of the atom to the external field is treated in dipole approximation. The time-dependent Schrödinger solver is restricted to the treatment of a single active electron. As concerns the time-dependent density functional mode of Qprop, the Hartree-potential (accounting for the classical electron-electron repulsion) is expanded up to the quadrupole. Only the monopole term of the Krieger-Li-Iafrate exchange potential is currently implemented. As in any nontrivial optimization problem, convergence to the optimal many-electron state (i.e., the ground state) is not automatically guaranteed.

Running time:
Execution time depends on the size of the propagated orbitals and the number of time-steps.