Chapter 2 Classical Trajectory Methods for Simulation of Laser-Atom and Laser-Molecule Interaction Erik Lötstedt, Tsuyoshi Kato, Katsumi Midorikawa and Kaoru Yamanouchi Abstract The classical trajectory Monte Carlo method applied to the simulation of many-electron atoms and molecules in intense laser fields is reviewed. Two ways to solve the problem of constructing a stable, many-body ground state in classical mechanics are presented: (i) Fermionic molecular mechanics and (ii) interaction via soft-core Coulomb potentials. Five examples of the application of classical trajec- tory methods to the simulation of laser-driven atomic and molecular systems are introduced, ranging from the non-sequential double ionization of He and inner-shell electron ejection in C to the ionization and dissociation dynamics of H 3 + and proton recollision in 15 NH. 2.1 Introduction When a many-electron atom or molecule is exposed to an intense laser field (with a wavelength of typically 800 nm), in general several electrons respond simultaneously to the force of the laser field. Some electrons may individually absorb energy from the laser field, and later transfer part of the absorbed energy to other electrons through the Coulomb interaction. An extreme example of this kind of energy redistribution is the nonsequential double ionization (NSDI) process [1–7]: after field-induced ejection of one electron, the electron is accelerated by the laser field in such a way that it E. Lötstedt (B ) · T. Kato · K. Yamanouchi Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan e-mail: lotstedt@chem.s.u-tokyo.ac.jp T. Kato e-mail: tkato@chem.s.u-tokyo.ac.jp K. Yamanouchi e-mail: kaoru@chem.s.u-tokyo.ac.jp K. Midorikawa RIKEN Center for Advanced Photonics, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan e-mail: kmidori@riken.jp © Springer International Publishing Switzerland 2015 K. Yamanouchi et al. (eds.), Progress in Ultrafast Intense Laser Science XII, Springer Series in Chemical Physics 112, DOI 10.1007/978-3-319-23657-5_2 21