Computation of vibrational energy levels and eigenstates of fluoroform using the multiconfiguration time-dependent Hartree method.

A theoretical study of the vibrational spectrum of the CHF(3) molecule is carried out with the aid of the multiconfiguration time-dependent Hartree (MCTDH) algorithm. In order to obtain the eigenvalues and the eigenstates, recent developments in the MCTDH improved relaxation method in a block form are exploited. Around 80 eigenvalues are reported, which are converged with a very high accuracy. The results obtained with our study are compared with those of a previous work using the wave operator sorting algorithm approach. The present investigation exemplifies the robustness and the accuracy of the improved relaxation method.

[1]  T. Carrington,et al.  A finite basis representation Lanczos calculation of the bend energy levels of methane , 2003 .

[2]  K. Szalewicz,et al.  Water trimer torsional spectrum from accurate ab initio and semiempirical potentials. , 2008, The Journal of chemical physics.

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

[4]  H. Meyer,et al.  A study of the mode-selective trans--cis isomerization in HONO using ab initio methodology. , 2004, The Journal of chemical physics.

[5]  Hans-Dieter Meyer,et al.  Intramolecular vibrational energy redistribution in toluene: a nine-dimensional quantum mechanical study using the MCTDH algorithm , 2004 .

[6]  Hua-Gen Yu,et al.  A rigorous full-dimensional quantum dynamics calculation of the vibrational energies of H3O-2. , 2006, The Journal of chemical physics.

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

[8]  H. Meyer,et al.  Time-dependent wave packet study on trans-cis isomerization of HONO driven by an external field. , 2007, The Journal of chemical physics.

[9]  Hans-Dieter Meyer,et al.  Theoretical investigation of highly excited vibrational states in DFCO: calculation of the out-of-plane bending states and simulation of the intramolecular vibrational energy redistribution. , 2007, The Journal of chemical physics.

[10]  D. Bégué,et al.  A comparison of two methods for selecting vibrational configuration interaction spaces on a heptatomic system: ethylene oxide. , 2007, The Journal of chemical physics.

[11]  T. Carrington,et al.  Improving the calculation of rovibrational spectra of five-atom molecules with three identical atoms by using a C3upsilonG6 symmetry-adapted grid: applied to CH3D and CHD3. , 2005, The Journal of chemical physics.

[12]  R. Wyatt,et al.  Toward ab Initio Intramolecular Dynamics , 1995 .

[13]  M. Quack,et al.  Tridiagonal Fermi resonance structure in the IR spectrum of the excited CH chromophore in CF3H , 1984 .

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

[15]  K. Kawaguchi,et al.  Measurement and Analysis of the ν4 Band of Fluoroform and Its Molecular Constants , 1981 .

[16]  H. Meyer,et al.  Theoretical investigation of intramolecular vibrational energy redistribution in highly excited HFCO. , 2006, The Journal of chemical physics.

[17]  P. Cassam-Chenaï,et al.  Alternative perturbation method for the molecular vibration-rotation problem , 2003 .

[18]  Xavier Chapuisat,et al.  A harmonic adiabatic approximation to calculate highly excited vibrational levels of "floppy molecules" , 2001 .

[19]  T. Carrington,et al.  Contracted basis Lanczos methods for computing numerically exact rovibrational levels of methane. , 2004, The Journal of chemical physics.

[20]  E. Davidson The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices , 1975 .

[21]  Hua-Gen Yu An exact variational method to calculate vibrational energies of five atom molecules beyond the normal mode approach , 2002 .

[22]  G. Herzberg Infrared and raman spectra , 1964 .

[23]  H. Bürger,et al.  Schwingungsspektren und kraftkonstanten symmetrischer kreisel—III: Die IR-spektren von HCF3 und DCF3 , 1971 .

[24]  S. Ramesh,et al.  A study of the vibrations of fluoroform with a sixth order nine-dimensional potential: a combined perturbative-variational approach , 2005 .

[25]  G. Guelachvili,et al.  Fluoroform: The polyad at 8–9 μm , 1984 .

[26]  John Z. H. Zhang,et al.  Quantum reactive scattering with a deep well: Time‐dependent calculation for H+O2 reaction and bound state characterization for HO2 , 1994 .

[27]  F. Stoeckel,et al.  Highly excited vibrational states of CHF3 and CHD3 in the range of the vs=5 CH chromophore , 1986 .

[28]  Christophe Iung,et al.  A quantum dynamical study of CH overtones in fluoroform. I. A nine‐dimensional ab initio surface, vibrational spectra and dynamics , 1995 .

[29]  R. Wyatt,et al.  Quantum dynamics of overtone relaxation in benzene. V. CH(v=3) dynamics computed with a new ab initio force field , 1993 .

[30]  D. Clary,et al.  Calculation of the energy levels of weakly bound molecular trimers: Application to (H2)3 , 2002 .

[31]  Donald G Truhlar,et al.  Calculation of converged rovibrational energies and partition function for methane using vibrational-rotational configuration interaction. , 2004, The Journal of chemical physics.

[32]  Hans-Dieter Meyer,et al.  Calculation and selective population of vibrational levels with the Multiconfiguration Time-Dependent Hartree (MCTDH) algorithm , 2006 .

[33]  H. Meyer,et al.  Intramolecular vibrational energy redistribution in the highly excited fluoroform molecule: a quantum mechanical study using the multiconfiguration time-dependent Hartree algorithm. , 2004, The Journal of chemical physics.

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

[35]  D. Schwenke,et al.  Vibrational energy levels for CH4 from an ab initio potential. , 2001, Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.

[36]  D. Lauvergnat,et al.  Quantum study of the internal rotation of methanol in full dimensionality (1+11D): a harmonic adiabatic approximation , 2003 .

[37]  T. Carrington,et al.  A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schrödinger equation in nine dimensions , 2003 .

[38]  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 .

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

[40]  M. Quack,et al.  OVERTONE INTENSITIES AND DIPOLE MOMENT SURFACES FOR THE ISOLATED CH CHROMOPHORE IN CHD3 AND CHF3 : EXPERIMENT AND AB INITIO THEORY , 1990 .

[41]  Ronnie Kosloff,et al.  A direct relaxation method for calculating eigenfunctions and eigenvalues of the Schrödinger equation on a grid , 1986 .

[42]  Hua-Gen Yu Full-dimensional quantum calculations of vibrational spectra of six-atom molecules. I. Theory and numerical results. , 2004, The Journal of chemical physics.

[43]  Daniel Neuhauser,et al.  Extraction, through filter‐diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short‐time segment of a signal. I. Theory and application to a quantum‐dynamics model , 1995 .

[44]  William Klemperer,et al.  Encyclopedia of Chemical Physics and Physical Chemistry , 2003 .

[45]  R. Zare,et al.  Tridiagonal Fermi resonance structure in the vibrational spectrum of the CH chromophore in CHF3. II. Visible spectra , 1987 .

[46]  Hans-Dieter Meyer,et al.  Efficiently computing bound-state spectra: A hybrid approach of the multi-configuration time-dependent Hartree and filter-diagonalization methods , 2001 .

[47]  C. Leforestier,et al.  Calculation of highly excited vibrational levels: a prediagonalized Davidson scheme , 2002 .

[48]  M. Beck,et al.  A hybrid approach of the multi-configuration time-dependent Hartree and filter-diagonalisation methods for computing bound-state spectra. Application to HO2 , 2001 .

[49]  A quantum dynamical study of CH overtones in fluoroform. II. Eigenstate analysis of the vCH=1 and vCH=2 regions , 1997 .

[50]  J. Kauppinen,et al.  High-resolution infrared spectrum of the v 3 and v 6 bands of HCF3 and of their hot bands , 1979 .

[51]  J. Reilly,et al.  The vibrational overtone spectrum of fluoroform in the Δν=4 CH stretching region , 1994 .

[52]  J. S. Wong,et al.  Coupling of CH stretching and bending vibrations in trihalomethanes , 1987 .

[53]  S. Ramesh,et al.  Combined perturbative-variational investigation of the vibrations of CHBr(3) and CDBr(3). , 2004, The Journal of chemical physics.

[54]  R. Wyatt,et al.  Quasiclassical dynamics of benzene overtone relaxation on an ab initio force field. I. Energy flow and survival probabilities in planar benzene for CH(v=2,3) , 1998 .

[55]  W. Miller,et al.  Theories of intramolecular vibrational energy transfer , 1991 .

[56]  V. Mandelshtam,et al.  Spectral Analysis of Time Correlation Function for a Dissipative Dynamical System Using Filter Diagonalization: Application to Calculation of Unimolecular Decay Rates , 1997 .

[57]  E. Hylleraas,et al.  Numerische Berechnung der 2S-Terme von Ortho- und Par-Helium , 1930 .

[58]  Oriol Vendrell,et al.  Full dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. II. Infrared spectrum and vibrational dynamics. , 2007, The Journal of chemical physics.

[59]  Ove Christiansen,et al.  Vibrational excitation energies from vibrational coupled cluster response theory. , 2007, The Journal of chemical physics.

[60]  H. J. Bernstein,et al.  Rotation‐Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths. I. The Spectrum of Fluoroform (CHF3) from 2.4μ to 0.7μ , 1948 .

[61]  D. Romanini,et al.  Vibrational overtone spectroscopy of the 41 band of CHF3 , 1996 .

[62]  M. Beck,et al.  Extracting accurate bound-state spectra from approximate wave packet propagation using the filter-diagonalization method , 1998 .

[63]  T. Carrington,et al.  Variational quantum approaches for computing vibrational energies of polyatomic molecules , 2008 .

[64]  N. Handy,et al.  An Improved Anharmonic Potential for CHF3 , 1996 .

[65]  R. Kirk,et al.  The general harmonic force field of fluoroform , 1975 .

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

[67]  R. Wyatt,et al.  Wave operator and artificial intelligence contraction algorithms in quantum dynamics: Application to CD3H and C6H6 , 1993 .

[68]  Martin Quack,et al.  Spectra and Dynamics of Coupled Vibrations in Polyatomic Molecules , 1990 .

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

[70]  R. Wyatt,et al.  Time‐dependent quantum mechanical study of intramolecular vibrational energy redistribution in benzene , 1993 .

[71]  T. Rizzo,et al.  VIBRATIONAL OVERTONE SPECTRA OF JET-COOLED CF3H BY INFRARED-LASER ASSISTED PHOTOFRAGMENT SPECTROSCOPY , 1995 .

[72]  E. Sibert,et al.  Theoretical studies of the potential surface and vibrational spectroscopy of CH3OH and its deuterated analogs. , 2005, The Journal of chemical physics.

[73]  N. Handy,et al.  Vibrational levels of methanol calculated by the reaction path version of MULTIMODE, using an ab initio, full-dimensional potential. , 2007, The journal of physical chemistry. A.

[74]  J. Watson Simplification of the molecular vibration-rotation hamiltonian , 2002 .

[75]  C. Iung,et al.  Calculation of specific, highly excited vibrational states based on a Davidson scheme: application to HFCO. , 2005, The Journal of chemical physics.

[76]  H. Meyer,et al.  Time-dependent wave packet study on trans-cis isomerization of HONO. , 2004, The Journal of chemical physics.

[77]  R. Saykally,et al.  Determination of a flexible (12D) water dimer potential via direct inversion of spectroscopic data , 2002 .

[78]  Guntram Rauhut,et al.  Configuration selection as a route towards efficient vibrational configuration interaction calculations. , 2007, The Journal of chemical physics.

[79]  Oriol Vendrell,et al.  Full-dimensional (15-dimensional) quantum-dynamical simulation of the protonated water dimer. I. Hamiltonian setup and analysis of the ground vibrational state. , 2007, The Journal of chemical physics.

[80]  R. Wyatt,et al.  Quantum dynamics of overtone relaxation in benzene. II. 16 mode model for relaxation from CH(v=3) , 1992 .

[81]  P. Cassam-Chenaï,et al.  The VMFCI method: A flexible tool for solving the molecular vibration problem , 2006, J. Comput. Chem..

[82]  Thomas Elsaesser,et al.  Ultrafast vibrational dynamics of hydrogen bonds in the condensed phase. , 2004, Chemical reviews.

[83]  K. Lehmann,et al.  INTRAMOLECULAR DYNAMICS FROM EIGENSTATE-RESOLVED INFRARED SPECTRA , 1995 .

[84]  C. Leforestier,et al.  CALCULATION OF SELECTED HIGHLY EXCITED VIBRATIONAL STATES OF POLYATOMIC MOLECULES BY THE DAVIDSON ALGORITHM , 2003 .

[85]  J. MacDonald,et al.  Successive Approximations by the Rayleigh-Ritz Variation Method , 1933 .

[86]  M. Quack,et al.  The wave packet motion and intramolecular vibrational redistribution in CHX3 molecules under infrared multiphoton excitation , 1991 .