6D vibrational quantum dynamics: Generalized coordinate discrete variable representation and (a)diabatic contraction

A new discrete variable representation (DVR) in generalized vibrational coordinates is proposed together with a new mixed diabatic/adiabatic contraction technique for the treatment of multidimensional vibrational problems up to high vibrational excitations. Formally based on the equidistant Chebyshev DVR in the grid index the new formulation is particularly suitable for multidimensional minimum energy paths. The new Z-matrix DVR proposed in this paper encompasses usual valence coordinates as well as nonlinear maps of coordinates on optimal nonequidistant grids. The pointwise numerical calculation of all kinetic energy terms avoids the algebraic derivation of specialized analytical forms of the kinetic energy adding to the flexibility of the method. With efficient truncation schemes the generalized DVR allows for a compact representation of the time-dependent wave-packet dynamics in up to six dimensions. Vibrationally adiabatic approaches to the detailed modelling of multidimensional quantum-dynamics usual...

[1]  N. Handy,et al.  Potential Energy Surface and Vibrational−Rotational Energy Levels of Hydrogen Peroxide , 1998 .

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

[3]  R. Meyer,et al.  Internal Rotation and Vibration in CH2=CCl–CH2D , 1969 .

[4]  D. Mayers,et al.  RELATIVISTIC ATOMIC WAVE FUNCTIONS. , 1971 .

[5]  N. Handy,et al.  Efficient calculation of rovibrational eigenstates of sequentially bonded four‐atom molecules , 1993 .

[6]  R. Meyer.  Trigonometric Interpolation Method for One‐Dimensional Quantum‐Mechanical Problems , 1970 .

[7]  M. Mladenović.  Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. II. Nonorthogonal descriptions of internal molecular geometry , 2000 .

[8]  Vladimir A. Mandelshtam,et al.  A low-storage filter diagonalization method for quantum eigenenergy calculation or for spectral analysis of time signals , 1997 .

[9]  R. Meyer,et al.  General Internal Motion of Molecules, Classical and Quantum‐Mechanical Hamiltonian , 1968 .

[10]  J. T. Hougen,et al.  The vibration-rotation problem in triatomic molecules allowing for a large-amplitude bending vibration , 1970 .

[11]  R. Marcus.  Generalization of Activated‐Complex Theory. III. Vibrational Adiabaticity, Separation of Variables, and a Connection with Analytical Mechanics , 1965 .

[12]  T. Carrington,et al.  A general discrete variable method to calculate vibrational energy levels of three‐ and four‐atom molecules , 1993 .

[13]  T. Rizzo,et al.  Rotationally resolved vibrational overtone spectroscopy of hydrogen peroxide at chemically significant energies , 1990 .

[14]  J. Light,et al.  Localized representations for large amplitude molecular vibrations , 1988 .

[15]  W. Miller.  REACTION PATH DYNAMICS FOR POLYATOMIC SYSTEMS , 1983 .

[16]  W. Heisenberg,et al.  Zur Quantentheorie der Molekeln , 1924 .

[17]  D. Papoušek,et al.  Molecular vibrational-rotational spectra , 1982 .

[18]  T. Carrington,et al.  Discrete variable representations of complicated kinetic energy operators , 1994 .

[19]  W. B. Cook,et al.  Torsion-Rotation Energy Levels, Hindering Potential, and Inertial Parameters of the First Excited Vibrational State of the Antisymmetric O-H Stretch in Hydrogen Peroxide , 1995 .

[20]  B. S. Garbow,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[21]  T. Carrington,et al.  Reaction surface Hamiltonian for the dynamics of reactions in polyatomic systems , 1984 .

[22]  L. Hofacker.  Quantentheorie chemischer Reaktionen , 1963 .

[23]  R. L. Redington,et al.  Studies of Hydrogen Peroxide: The Infrared Spectrum and the Internal Rotation Problem , 1962 .

[24]  J. Hirschfelder,et al.  General Collision Theory Treatment for the Rate of Bimolecular, Gas Phase Reactions , 1959 .

[25]  P. Taylor,et al.  AN ACCURATE AB-INITIO QUARTIC FORCE-FIELD FOR FORMALDEHYDE AND ITS ISOTOPOMERS , 1993 .

[26]  Nicholas C. Handy,et al.  The vibrational energy levels of ammonia , 1999 .

[27]  A. S. Dickinson,et al.  Calculation of Matrix Elements for One‐Dimensional Quantum‐Mechanical Problems , 1968 .

[28]  S. Chu,et al.  Generalized Fourier-grid Hamiltonian approach to the Dirac equation: variational solution without basis set , 1991 .

[29]  T. Rizzo,et al.  Vibrational overtone spectroscopy of the 4νOH+νOH’ combination level of HOOH via sequential local mode–local mode excitation , 1992 .

[30]  William F. Polik,et al.  Pure vibrational spectroscopy of S0 formaldehyde by dispersed fluorescence , 1996 .

[31]  Z. Bačić.  Accurate calculation and assignment of highly excited vibrational levels of floppy triatomic molecules in a basis of adiabatic vibrational eigenstates , 1991 .

[32]  Tucker Carrington,et al.  The triatomic Eckart-frame kinetic energy operator in bond coordinates , 1997 .

[33]  M. Quack,et al.  Specific Rate Constants of Unimolecular Processes II. Adiabatic Channel Model , 1974 .

[34]  P. Giguère.  The Infra‐Red Spectrum of Hydrogen Peroxide , 1950 .

[35]  L. R. Zumwalt,et al.  The Infra‐Red Bands of Hydrogen Peroxide at λ9720 and the Structure and Torsional Oscillation of Hydrogen Peroxide , 1941 .

[36]  M. Mladenović.  Rovibrational Hamiltonians for general polyatomic molecules in spherical polar parametrization. I. Orthogonal representations , 2000 .

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

[38]  J. Light,et al.  Adiabatic approximation and nonadiabatic corrections in the discrete variable representation: Highly excited vibrational states of triatomic molecules , 1987 .

[39]  D. Luckhaus,et al.  Experimental and theoretical vibrational overtone spectra of vCH=3, 4, 5, and 6 in formaldehyde (H2CO) , 1996 .

[40]  J. W. C. Johns,et al.  Torsion-vibration interaction in H2O2: First high-resolution observation of ν3☆ , 1992 .

[41]  Benjamin Fehrensen,et al.  Inversion Tunneling in Aniline from High Resolution Infrared Spectroscopy and an Adiabatic Reaction Path Hamiltonian Approach , 1999 .

[42]  B. Kuhn,et al.  A new six-dimensional analytical potential up to chemically significant energies for the electronic ground state of hydrogen peroxide , 1999 .

[43]  F. Crim,et al.  Vibrational overtone predissociation spectroscopy of hydrogen peroxide , 1985 .

[44]  D. Luckhaus,et al.  The rovibrational spectrum of hydroxylamine: A combined high resolution experimental and theoretical study , 1997 .

[45]  Tucker Carrington,et al.  Reaction surface description of intramolecular hydrogen atom transfer in malonaldehyde , 1986 .

[46]  John C. Light,et al.  Theoretical Methods for Rovibrational States of Floppy Molecules , 1989 .

[47]  T. Rizzo,et al.  Unimolecular reactions near threshold: The overtone vibration initiated decomposition of HOOH (5νOH) , 1986 .

[48]  V. Špirko,et al.  Anharmonic potential function and effective geometries for the NH3 molecule , 1989 .

[49]  N. Handy,et al.  THE VIBRATIONS OF FORMALDEHYDE , 1995 .

[50]  M. Quack,et al.  Sequence structure in the high-resolution infrared spectrum of trifluoropropyne , 1982 .

[51]  R. Meyer.  Flexible models for intramolecular motion, a versatile treatment and its application to glyoxal☆ , 1979 .

[52]  Tucker Carrington,et al.  Adiabatic approach to the coupling between local‐ and normal‐like modes , 1987 .

[53]  J. Reilly,et al.  High resolution vibrational overtone spectroscopy of hydrogen peroxide in the Δv=4 region , 1989 .

[54]  Quantum-classical reaction path/surface model for chemical reactions. III. The reaction H2+OH→H2O+H , 1990 .

[55]  F. Gatti,et al.  Fully coupled 6D calculations of the ammonia vibration-inversion-tunneling states with a split Hamiltonian pseudospectral approach , 1999 .

[56]  D. Luckhaus,et al.  Intramolecular energy transfer and vibrational redistribution in chiral molecules: experiment and theory , 1994 .

[57]  T. Carrington,et al.  Calculation of vibrational (J=0) excitation energies and band intensities of formaldehyde using the recursive residue generation method , 1996 .

[58]  Dong H. Zhang,et al.  Exact full‐dimensional bound state calculations for (HF)2, (DF)2, and HFDF , 1995 .

[59]  Darin C. Burleigh,et al.  An accurate quartic force field for formaldehyde , 1996 .

[60]  Lawrence B. Harding,et al.  Vibrational energy levels of formaldehyde , 1985 .

[61]  A study of the ground electronic state of hydrogen peroxide , 1989 .

[62]  Baer,et al.  Phase space approach for optimizing grid representations: The mapped Fourier method. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[63]  A. Viel,et al.  Six-dimensional calculation of the vibrational spectrum of the HFCO molecule , 2000 .

[64]  D. Luckhaus,et al.  An experimental and theoretical study of the vibrationally mediated photodissociation of hydroxylamine , 1999 .

[65]  T. Srinivasan,et al.  A Raman study of H2O2 and D2O2 vapor , 1974 .

[66]  J. W. C. Johns,et al.  The far infrared spectrum of H2O2. First observation of the staggering of the levels and determination of the cis barrier , 1989 .

[67]  N. Handy,et al.  The vibrational–rotational energy levels of silanone , 1999 .

[68]  D. Luckhaus,et al.  Spectrum and dynamics of the CH chromophore in CD2HF. I. Vibrational Hamiltonian and analysis of rovibrational spectra , 1992 .

[69]  John E. Adams,et al.  Reaction path Hamiltonian for polyatomic molecules , 1980 .

[70]  D. O. Harris,et al.  Calculation of Matrix Elements for One‐Dimensional Quantum‐Mechanical Problems and the Application to Anharmonic Oscillators , 1965 .

[71]  K. Wiberg,et al.  AB INITIO CBS-QCI CALCULATIONS OF THE INVERSION MODE OF AMMONIA , 1997 .

[72]  Ronnie Kosloff,et al.  MAPPED FOURIER METHODS FOR LONG-RANGE MOLECULES : APPLICATION TO PERTURBATIONS IN THE RB2(0U+) PHOTOASSOCIATION SPECTRUM , 1999 .

[73]  Benjamin Fehrensen,et al.  Mode selective stereomutation tunnelling in hydrogen peroxide isotopomers , 1999 .

[74]  Tucker Carrington,et al.  The discrete variable representation of a triatomic Hamiltonian in bond length–bond angle coordinates , 1992 .

[75]  T. Carrington,et al.  Vibrational energy levels of formaldehyde calculated from an internal coordinate hamiltonian using the Lanczos algorithm , 1993 .

[76]  Donald E. Jennings,et al.  High-resolution infrared spectrum of hydrogen peroxide: The ν6 fundamental band , 1986 .

[77]  D. Luckhaus.  The rovibrational dynamics of hydroxylamine , 1997 .

[78]  M. Mladenović,et al.  Theoretical study of the rovibrational energy spectrum and the numbers and densities of bound vibrational states for the system HCO + /HOC + , 1998 .

[79]  G. D. Billing.  The reaction-volume Hamiltonian for polyatomic three-centre reactions: the classical Hamiltonian , 1996 .

[80]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .

[81]  P. Bunker.  Carbon suboxide as a semirigid bender , 1980 .

[82]  L. Schriver,et al.  The 7.9-μm Band of Hydrogen Peroxide: Line Positions and Intensities , 1995 .

[83]  P. Taylor,et al.  An accurate ab initio quartic force field for ammonia , 1992 .