Wavepacket quantum dynamics

The article reviews the use of wavepackets in molecular quantum dynamics. The basic theory concerned with their use in both reactive molecular scattering and photodissociation dynamics is outlined. The great advantage of using wavepackets is that the full S matrix for the scattering problem need not be evaluated, and the numerical effort can be concentrated on those initial molecular quantum states which are of interest. Wavepackets may be used within a time-dependent or a time-independent framework, both are discussed and compared. Some examples of calculations from both reactive scattering and photodissociation theory are given.

[1]  P. Dirac Principles of Quantum Mechanics , 1982 .

[2]  A. R. Edmonds Angular Momentum in Quantum Mechanics , 1957 .

[3]  R. Rubin,et al.  Quantum‐Mechanical Calculation of the Probability of an Exchange Reaction for Constrained Linear Encounters , 1959 .

[4]  R. Wyatt,et al.  Quantum Dynamics of the Collinear (H, H2) Reaction , 1969 .

[5]  W. Miller Coupled Equations and the Minimum Principle for Collisions of an Atom and a Diatomic Molecule, Including Rearrangements , 1969 .

[6]  R. Wyatt,et al.  Dynamics of the Collinear H+H2 Reaction. I. Probability Density and Flux , 1971 .

[7]  M. Karplus,et al.  Theoretical Studies of H + H2 Rotationally Inelastic Scattering , 1972 .

[8]  M. Karplus,et al.  Theoretical studies of H+H2 reactive scattering , 1974 .

[9]  T. Kamal,et al.  Quantum mechanical investigations of the collinear collisions F + H2 and F + D2 using the wavepacket approach , 1975 .

[10]  L. Raff,et al.  Comparison of quantum mechanical and quasiclassical scattering as a function of surface topology , 1976 .

[11]  G. Schatz,et al.  Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. II. Accurate cross sections for H+H2 , 1976 .

[12]  G. Schatz,et al.  Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. I. Theory , 1976 .

[13]  E. Heller,et al.  Time dependent formulation of polyatomic photofragmentation: Application to H3+ , 1978 .

[14]  E. Heller Quantum corrections to classical photodissociation models , 1978 .

[15]  E. Heller Photofragmentation of symmetric triatomic molecules: Time dependent picture , 1978 .

[16]  J. W. Humberston Classical mechanics , 1980, Nature.

[17]  E. Heller The semiclassical way to molecular spectroscopy , 1981 .

[18]  M. Shapiro,et al.  Photofragmentation of triatomic molecules. Theory of angular and state distribution of product fragments , 1981 .

[19]  L. Raff,et al.  Calculation of reaction probabilities and rate coefficients for collinear three‐body exchange reactions using time‐dependent wave packet methods , 1981 .

[20]  M. Feit,et al.  Solution of the Schrödinger equation by a spectral method , 1982 .

[21]  E. Heller,et al.  Exact time‐dependent wave packet propagation: Application to the photodissociation of methyl iodide , 1982 .

[22]  M. Feit,et al.  Solution of the Schrödinger equation by a spectral method II: Vibrational energy levels of triatomic molecules , 1983 .

[23]  R. Kosloff,et al.  A fourier method solution for the time dependent Schrödinger equation as a tool in molecular dynamics , 1983 .

[24]  C. Leforestier Competition between dissociation and exchange processes in a collinear A + BC collision. I. Exact quantum results☆ , 1984 .

[25]  J. R. Esmond,et al.  High resolution absorption cross-section measurements of ozone at 195 K in the wavelength region 240–350 nm , 1984 .

[26]  H. Tal-Ezer,et al.  An accurate and efficient scheme for propagating the time dependent Schrödinger equation , 1984 .

[27]  J. Nee,et al.  Photoabsorption cross section of HF at 107-145 nm , 1985 .

[28]  R. Kosloff,et al.  Absorbing boundaries for wave propagation problems , 1986 .

[29]  Zhang,et al.  Wave-packet solution to the time-dependent arrangement-channel quantum-mechanics equations. , 1986, Physical review. A, General physics.

[30]  D. Kouri,et al.  Close coupling‐wave packet formalism for gas phase nonreactive atom–diatom collisions , 1987 .

[31]  R. Kosloff Time-dependent quantum-mechanical methods for molecular dynamics , 1988 .

[32]  R. Dixon,et al.  Time-dependent quantum dynamics of molecular photofragmentation processes , 1990 .

[33]  D. Neuhauser Bound state eigenfunctions from wave packets: Time→energy resolution , 1990 .

[34]  D. Neuhauser,et al.  A time‐dependent wave packet approach to atom–diatom reactive collision probabilities: Theory and application to the H+H2 (J=0) system , 1990 .

[35]  D. Neuhauser State‐to‐state reactive scattering amplitudes from single‐arrangement propagation with absorbing potentials , 1990 .

[36]  G. G. Balint-Kurti,et al.  Reflection and transmission of waves by a complex potential—a semiclassical Jeffreys–Wentzel–Kramers–Brillouin treatment , 1992 .

[37]  G. G. Balint-Kurti,et al.  Parametrization of complex absorbing potentials for time-dependent quantum dynamics , 1992 .

[38]  S. Gray Wave packet dynamics of resonance decay: An iterative equation approach with application to HCO→H+CO , 1992 .

[39]  R. Dixon,et al.  Grid methods for solving the Schrödinger equation and time dependent quantum dynamics of molecular photofragmentation and reactive scattering processes , 1992 .

[40]  D. Neuhauser Reactive scattering with absorbing potentials in general coordinate systems , 1992 .

[41]  D. Hoffman,et al.  Time-to-energy transform of wavepackets using absorbing potentials. Time-independent wavepacket-Schrödinger and wavepacket-Lippmann—Schwinger equations , 1993 .

[42]  Wei Zhu,et al.  A general time-to-energy transform of wavepackets. Time-independent wavepacket-Schrödinger and wavepacket-Lippmann—Schwinger equations , 1993 .

[43]  A. Kummel,et al.  State-resolved photodissociation of nitrous oxide , 1993 .

[44]  Hoffman,et al.  Time-dependent wave-packet forms of Schrödinger and Lippmann-Schwinger equations. , 1994, Physical review letters.

[45]  S. Gray,et al.  Classical Hamiltonian structures in wave packet dynamics , 1994 .

[46]  Wei Zhu,et al.  Variational principles for the time‐independent wave‐packet‐Schrödinger and wave‐packet‐Lippmann–Schwinger equations , 1994 .

[47]  Gillian C. Lynch,et al.  Ab Initio chemical kinetics: Converged quantal reaction rate constants for the D + H2 system , 1994 .

[48]  Wei Zhu,et al.  Further analysis of solutions to the time-independent wave packet equations for quantum dynamics: General initial wave packets , 1994 .

[49]  B. Jackson Time-dependent wave packet approach to quantum reactive scattering. , 1995, Annual review of physical chemistry.

[50]  J. Light,et al.  Artificial boundary inhomogeneity method for quantum scattering solutions in an Lt2 basis , 1995 .

[51]  D. Kouri,et al.  General Derivation of the Time-Independent Wavepacket Schrödinger and Lippmann-Schwinger Equations , 1995 .

[52]  V. Mandelshtam,et al.  Spectral projection approach to the quantum scattering calculations , 1995 .

[53]  V. Mandelshtam,et al.  A simple recursion polynomial expansion of the Green’s function with absorbing boundary conditions. Application to the reactive scattering , 1995 .

[54]  D. Manolopoulos,et al.  Symplectic integrators tailored to the time‐dependent Schrödinger equation , 1996 .

[55]  Hua Guo,et al.  EXTRACTION OF RESONANCES VIA WAVE PACKET PROPAGATION IN CHEBYSHEV ORDER DOMAIN : COLLINEAR H + H2 SCATTERING , 1996 .

[56]  J. Zhang,et al.  An experimental study of HF photodissociation: Spin–orbit branching ratio and infrared alignment , 1996 .

[57]  R. Wyatt,et al.  Dynamics of molecules and chemical reactions , 1996 .

[58]  Hua Guo,et al.  Evolution of quantum system in order domain of Chebyshev operator , 1996 .

[59]  D. Neuhauser,et al.  PERFORMANCE OF A TIME-INDEPENDENT SCATTERING WAVE PACKET TECHNIQUE USING REAL OPERATORS AND WAVE FUNCTIONS , 1996 .

[60]  Youhong Huang,et al.  Further analysis of solutions to the time‐independent wave packet equations of quantum dynamics. II. Scattering as a continuous function of energy using finite, discrete approximate Hamiltonians , 1996 .

[61]  D. Kouri,et al.  State-to-state time-dependent wavepacket approach to reactivescattering: State-resolved cross-sections forD+H2(v=1, j=1,m)→H+DH(v,j) , 1997 .

[62]  E. Baerends,et al.  Six-dimensional quantum dynamics of dissociative chemisorption of (v=0, j=0) H2 on Cu(100). , 1997 .

[63]  D. Hoffman,et al.  A time-independent wavepacket approach to the ( t, t')-method for treating time-dependent Hamiltonian systems , 1997 .

[64]  S. Gray,et al.  Flux analysis for calculating reaction probabilities with real wave packets , 1998 .

[65]  S. Gray,et al.  Quantum dynamics with real wave packets, including application to three-dimensional (J=0) D + H2 → HD + H reactive scattering , 1998 .

[66]  G. Schatz,et al.  Helicity decoupled quantum dynamics and capture model cross sections and rate constants for O(1D) + H2 → OH + H , 1999 .

[67]  T. Seideman,et al.  Quantum mechanical study of photodissociation of oriented ClNO(S1) , 1999 .

[68]  Alex Brown,et al.  Spin–orbit branching in the photodissociation of HF and DF. I. A time-dependent wave packet study for excitation from v=0 , 2000 .

[69]  T. Martínez,et al.  Ab Initio Multiple Spawning: Photochemistry from First Principles Quantum Molecular Dynamics , 2000 .

[70]  Alex Brown,et al.  Spin–orbit branching in the photodissociation of HF and DF. II. A time-dependent wave packet study of vibrationally mediated photodissociation , 2000 .

[71]  J. M. Teule,et al.  State-to-state photodynamics of nitrous oxide and the effect of long-range interaction on the alignment of O(1D2) , 2000 .

[72]  G. Schatz,et al.  Probing the effect of the H2 rotational state in O(1D)+H2→OH+H: Theoretical dynamics including nonadiabatic effects and a crossed molecular beam study , 2000 .

[73]  S. Althorpe Quantum wavepacket method for state-to-state reactive cross sections , 2001 .

[74]  Alex Brown,et al.  Photodissociation of HOBr. Part II. Calculation of photodissociation cross-sections and photofragment quantum state distributions for the first two UV absorption bands , 2001 .

[75]  S. Gray,et al.  Quantum mechanical calculation of reaction probabilities and branching ratios for the O( D)+HD OH(OD)+D(H) reaction on the X A' and 1 A" adiabatic potential energy surfaces. , 2001 .

[76]  O. Vasyutinskii,et al.  Vector correlations and alignment parameters in the photodissociation of HF and DF , 2002 .

[77]  S. Gray,et al.  Sinc wave packets: New form of wave packet for time-dependent quantum mechanical reactive scattering calculations , 2003 .

[78]  G. Worth,et al.  Quantum molecular dynamics: propagating wavepackets and density operators using the multiconfiguration time-dependent Hartree method , 2003 .

[79]  O. Vasyutinskii,et al.  Spin-Polarized Hydrogen Atoms from Molecular Photodissociation , 2003, Science.

[80]  G. G. Balint-Kurti Wavepacket Theory of Photodissociation and Reactive Scattering , 2004 .

[81]  S. Althorpe The plane wave packet approach to quantum scattering theory , 2004 .

[82]  O. Vasyutinskii,et al.  Photofragment angular momentum distribution beyond the axial recoil approximation: the role of molecular axis rotation. , 2005 .

[83]  Alex Brown,et al.  Ab initio potential energy surfaces, total absorption cross sections, and product quantum state distributions for the low-lying electronic states of N2O , 2005 .

[84]  Alex Brown Photodissociation of HI and DI: polarization of atomic photofragments. , 2004, The Journal of chemical physics.

[85]  G. G. Balint-Kurti,et al.  Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics. , 2005, The Journal of chemical physics.

[86]  Hua Guo,et al.  Quantum statistical and wave packet studies of insertion reactions of S(1D) with H2, HD, and D2. , 2005, The Journal of chemical physics.

[87]  R. Schinke,et al.  The photodissociation of ozone in the Hartley band: a theoretical analysis. , 2005, The Journal of chemical physics.

[88]  Sean C. Smith,et al.  State-to-state reactive differential cross sections for the H+H2-->H2+H reaction on five different potential energy surfaces employing a new quantum wavepacket computer code: DIFFREALWAVE. , 2006, The Journal of chemical physics.

[89]  V. Batista,et al.  Matching-pursuit/split-operator-Fourier-transform simulations of excited-state nonadiabatic quantum dynamics in pyrazine. , 2006, The Journal of chemical physics.

[90]  Keli Han,et al.  The time-dependent quantum wave packet approach to the electronically nonadiabatic processes in chemical reactions , 2006 .

[91]  R. Schinke,et al.  Comment on "Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics" [J. Chem. Phys. 123, 014306 (2005)]. , 2007, The Journal of chemical physics.

[92]  Stephen K. Gray,et al.  DIFFREALWAVE: A parallel real wavepacket code for the quantum mechanical calculation of reactive state-to-state differential cross sections in atom plus diatom collisions , 2008, Comput. Phys. Commun..

[93]  G. G. Balint-Kurti Time-dependent and time-independent wavepacket approaches to reactive scattering and photodissociation dynamics , 2008 .

[94]  S. Iyengar,et al.  Hydrogen tunneling in an enzyme active site: a quantum wavepacket dynamical perspective. , 2008, The journal of physical chemistry. B.

[95]  S. Iyengar Computing vibrational properties in hydrogen‐bonded systems using quantum wavepacket ab initio molecular dynamics , 2009 .

[96]  B. A. Lindquist,et al.  Photodynamics in complex environments: ab initio multiple spawning quantum mechanical/molecular mechanical dynamics. , 2009, The journal of physical chemistry. B.

[97]  Keli Han,et al.  Nonadiabatic effects in the H + H2 exchange reaction: accurate quantum dynamics calculations at a state-to-state level. , 2009, The Journal of chemical physics.

[98]  J. Brédas,et al.  Quantum Dynamics of the Excited State Intramolecular Proton Transfer in 2-(2'-Hydroxyphenyl)-Benzothiazole , 2009 .

[99]  O. Vasyutinskii,et al.  Vector correlation analysis for inelastic and reactive collisions between partners possessing spin and orbital angular momentum. , 2009, The journal of physical chemistry. A.

[100]  Sean C. Smith,et al.  The dynamics of the H(+) + D(2) reaction: a comparison of quantum mechanical wavepacket, quasi-classical and statistical-quasi-classical results. , 2010, Physical chemistry chemical physics : PCCP.