Quantum-classical description of rotational diffractive scattering using Bohmian trajectories: Comparison with full quantum wave packet results

We apply the mixed quantum/classical method based on the Bohmian formulation of quantum mechanics [E. Gindensperger, C. Meier, and J. A. Beswick, J. Chem. Phys. 113, 9369 (2000)] to the case of rotational diffractive surface scattering of a diatomic molecule. The rotation as well as the normal translational degree of freedom are treated classically while the two parallel degrees of freedom that account for the diffraction are treated quantum mechanically. The effects of treating some degrees of freedom classically are discussed in detail by comparing our novel approximate method to quantum wave packet results obtained by the multiconfiguration time-dependent Hartree method.

[1]  G. Kroes.  Quantum Dynamics of H2−Surface Scattering: H2+ LiF(001) and H2+ Cu(100) , 1999 .

[2]  J. Tully.  Nonadiabatic molecular dynamics , 1991 .

[3]  S. Adhikari,et al.  Four-dimensional quantum and two-dimensional classical mechanical study of molecule–surface interactions , 2000 .

[4]  M. Ehara,et al.  Multiconfiguration time‐dependent Hartree (MCTDH) study on rotational and diffractive inelastic molecule‐surface scattering , 1996 .

[5]  J. G. Snijders,et al.  Performance of close-coupled wave packet methods for molecule-corrugated surface scattering , 1995 .

[6]  Uwe Manthe,et al.  Full dimensional quantum calculations of the CH4+H→CH3+H2 reaction rate , 2000 .

[7]  M. Beck,et al.  The multiconfiguration time-dependent Hartree (MCTDH) method: A highly efficient algorithm for propa , 1999 .

[8]  D. Kouri,et al.  Close‐coupling wave packet approach to numerically exact molecule–surface scattering calculations , 1986 .

[9]  Quantum dissipation in unbounded systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  P. Dirac.  Note on Exchange Phenomena in the Thomas Atom , 1930, Mathematical Proceedings of the Cambridge Philosophical Society.

[11]  U. Manthe,et al.  Full-dimensional quantum study of the vibrational predissociation of the I2⋯Ne2 cluster , 2001 .

[12]  A. Jansen,et al.  Bond breaking in vibrationally excited methane on transition-metal catalysts , 2000, physics/0003033.

[13]  G. Worth,et al.  Relaxation of a system with a conical intersection coupled to a bath: A benchmark 24-dimensional wave packet study treating the environment explicitly , 1998 .

[14]  G. Kroes,et al.  Scattering of H₂ by LiF(001) studies using a new model potential. I. Prediction of large differences in diffractin of cold beams of para H₂ and normal H₂. , 1995 .

[15]  On the classical limit in atom-surface diffraction , 2001 .

[16]  G. Kroes.  Six-dimensional quantum dynamics of dissociative chemisorption of H2 on metal surfaces , 1999 .

[17]  J. G. Snijders,et al.  PERFORMANCE OF A FULLY CLOSE-COUPLED WAVE PACKET METHOD FOR THE H2+LIF(001) MODEL PROBLEM , 1995 .

[18]  D. Lemoine.  Nonreactive atom/molecule-surface scattering within the finite basis wave packet method , 1996 .

[19]  P. Schleyer.  Encyclopedia of computational chemistry , 1998 .

[20]  G. Worth,et al.  Molecular dynamics of pyrazine after excitation to the S2 electronic state using a realistic 24-mode model Hamiltonian , 1999 .

[21]  G. Wolken.  The diffraction of H2, D2 from solid LiF , 1973 .

[22]  D. Kouri,et al.  Vibrational deactivation of diatomic molecules by collisions with solid surfaces , 1981 .

[23]  Attila Askar,et al.  Quantum fluid dynamics in the Lagrangian representation and applications to photodissociation problems , 1999 .

[24]  H. Meyer,et al.  Rotational and diffractive inelastic scattering of a diatom on a corrugated surface: A multiconfiguration time-dependent Hartree study on N2/LiF(001) , 2001 .

[25]  Eric R. Bittner,et al.  Integrating the quantum Hamilton–Jacobi equations by wavefront expansion and phase space analysis , 2000 .

[26]  Haobin Wang,et al.  Basis set approach to the quantum dissipative dynamics: Application of the multiconfiguration time-dependent Hartree method to the spin-boson problem , 2000 .

[27]  Hans-Dieter Meyer,et al.  An efficient and robust integration scheme for the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method , 1997 .

[28]  G. Wolken.  Collision of a diatomic molecule with a solid surface , 1973 .

[29]  G. Kroes,et al.  Calculations on rotationally and diffractionally inelastic molecule‐surface scattering for arbitrary angles of incidence: A new wave packet technique , 1994 .

[30]  D. Kouri,et al.  Molecule–corrugated surface collisions: Converged close coupling wave packet and quasiclassical trajectory calculations for N2 scattering from corrugated lattices , 1993 .

[31]  C Brooksby,et al.  Quantum backreaction through the Bohmian particle. , 2001, Physical review letters.

[32]  H. Meyer,et al.  Calculation of H+H2 and H+D2 reaction probabilities within the multiconfiguration time-dependent Hartree approach employing an adiabatic correction scheme , 1998 .

[33]  E. Baerends,et al.  Six-dimensional quantum dynamics of dissociation of rotationally excited H2 on Cu(100) , 1998 .

[34]  R. Wyatt,et al.  Quantum trajectory analysis of multimode subsystem-bath dynamics. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  D. Lemoine.  THE FINITE BASIS REPRESENTATION AS THE PRIMARY SPACE IN MULTIDIMENSIONAL PSEUDOSPECTRAL SCHEMES , 1994 .

[36]  U. Manthe,et al.  Wave‐packet dynamics within the multiconfiguration Hartree framework: General aspects and application to NOCl , 1992 .

[37]  U. Manthe,et al.  The multi-configurational time-dependent Hartree approach , 1990 .

[38]  E. Baerends,et al.  Rotational Effects in Six-Dimensional Quantum Dynamics for Reaction of H2 on Cu (100). , 1999 .

[39]  Herschel Rabitz,et al.  Multidimensional wave packet dynamics within the fluid dynamical formulation of the Schrodinger equation , 1998 .

[40]  P. Holland.  The Quantum Theory of Motion , 1993 .

[41]  R. Wyatt.  Quantum wave packet dynamics with trajectories: Application to reactive scattering , 1999 .

[42]  Robert E. Wyatt,et al.  Electronic transitions with quantum trajectories. II , 2001 .

[43]  F. Borondo,et al.  Causal trajectories description of atom diffraction by surfaces , 2000 .

[44]  G. D. Billing.  Quantum dressed classical mechanics , 2001 .

[45]  Robert E. Wyatt.  Quantum wavepacket dynamics with trajectories: wavefunction synthesis along quantum paths , 1999 .

[46]  Application of Quantum-Dressed Classical Mechanics: Molecule Surface Scattering † , 2001 .

[47]  G. Wolken.  Rotational transitions in molecule--solid scattering , 1975 .

[48]  Robert E. Wyatt,et al.  Quantum wave packet dynamics with trajectories: Implementation with distributed approximating functionals , 2000 .

[49]  C. Meier,et al.  Mixing quantum and classical dynamics using Bohmian trajectories , 2000 .

[50]  H. Meyer,et al.  Time‐dependent calculation of reactive flux employing complex absorbing potentials: General aspects and application within the multiconfiguration time‐dependent Hartree wave approach , 1996 .

[51]  A. Jansen,et al.  Ten-dimensional wave packet simulations of methane scattering , 1998, physics/0106025.

[52]  Energy distribution analysis of the wavepacket simulations of CH4 and CD4 scattering , 2000, physics/0003031.

[53]  G. D. Billing,et al.  Classical Path Method in Inelastic and Reactive Scattering , 1994 .