Published: December 14, 2011 r2011 American Chemical Society 2800 dx.doi.org/10.1021/jp208997r | J. Phys. Chem. A 2012, 116, 2800–2807 ARTICLE pubs.acs.org/JPCA Mixed Quantum-Classical Dynamics in the Adiabatic Representation To Simulate Molecules Driven by Strong Laser Pulses Juan Jos  e Bajo, † Jes us Gonz  alez-V  azquez,* ,†,‡ Ignacio R. Sola, † Jesus Santamaria, † Martin Richter, § Philipp Marquetand, || and Leticia Gonz  alez || † Departamento de Química-Física I, Universidad Complutense de Madrid, 28040 Madrid, Spain ‡ Instituto de Química Física Rocasolano, CSIC, C/Serrano 119, 28006 Madrid Spain § Institut f€ ur Physikalische Chemie, Friedrich-Schiller-Universit € at Jena, Helmholtzweg 4, 07743 Jena, Germany ) Institute of Theoretical Chemistry, University of Vienna, W€ ahringer Strasse 17, A-1090 Wien, Austria 1. INTRODUCTION The development of laser pulses in the femtosecond time domain 1 has allowed the first experimental observation of transition structures that are crucial for understanding chemical reactivity and kinetics. Ultrafast imaging 2 and structural dynamics 3,4 are currently providing a wealth of spectroscopic and structural information concerning the dynamics of molecules in real time. Additionally, as the laser acts on the time scale of the dynamics, ultrashort and strong pulses can be used not only to monitor but also to control the movement of atoms, modifying the yield and rate of chemical reactions 5,6 The use of closed-loop learning techniques has allowed a fast fully experimental ap- proach to control quantum processes in molecules with strong fields. 7,8 However, the experimental observation alone is often not enough to rationalize the outcome of the experiments. In many cases, understanding the underlying processes requires the use of models and theoretical simulations to describe the key aspects of the dynamics. Ideally, to simulate the fast dynamics induced by a strong femtosecond laser pulse, one would solve the time-dependent Schr€ odinger equation (TDSE) for both electrons and nuclei in the presence of the field. However, because the computational effort of quantum simulations scales exponentially with the number of particles, a full quantum description is only possible for small molecules like H 2 + or H 2 . 915 To describe the dynamics of larger systems, it is first necessary to separate the motions of electrons and nuclei, commonly using the BornOppenheimer approximation. In femtochemistry several electronic states are normally involved in the dynamics, so at least the electronic part should be calculated at the quantum level, typically using ab initio methods. It is also necessary to evaluate nonadiabatic terms, correcting part of the BornOppenheimer approximation (although an error remains in the truncation of the electronic wave function to a finite number of states). In contrast, it is possible to treat the nuclear motion using a large number of approaches, from grid-based quantum dynamics techniques, discrete variable representation (DVR) 16,17 or multiconfigura- tional time dependent Hartree (MCTDH) 1820 methods, to mixed quantum classical dynamics (MQCD), 21,22 passing through semiclassical methods like the ab initio multiple spawn- ing (AIMS) 23 or coherent states. 24 In this work, we use the MQCD approximation where the nuclei are assumed to follow classical trajectories obeying Newton equations, and the electronic motion is simulated by solving the TDSE, where the electronic wave function is described as a Special Issue: Femto10: The Madrid Conference on Femtochemistry Received: September 17, 2011 Revised: December 14, 2011 ABSTRACT: The dynamics of molecules under strong laser pulses is characterized by large Stark effects that modify and reshape the electronic potentials, known as laser-induced potentials (LIPs). If the time scale of the interaction is slow enough that the nuclear positions can adapt to these externally driven changes, the dynamics proceeds by adiabatic following, where the nuclei gain very little kinetic energy during the process. In this regime we show that the molecular dynam- ics can be simulated quite accurately by a semiclassical surface- hopping scheme formulated in the adiabatic representation. The nuclear motion is then influenced by the gradients of the laser-modified potentials, and nonadiabatic couplings are seen as transitions between the LIPs. As an example, we simulate the process of adiabatic passage by light induced potentials in Na 2 using the surface- hopping technique both in the diabatic representation based on molecular potentials and in the adiabatic representation based on LIPs, showing how the choice of the representation is crucial in reproducing the results obtained by exact quantum dynamical calculations.