The VMFCI method: A flexible tool for solving the molecular vibration problem

The present article introduces a general variational scheme to find approximate solutions of the spectral problem for the molecular vibration Hamiltonian. It is called the “vibrational mean field configuration interaction” (VMFCI) method, and consists in performing vibrational configuration interactions (VCI) for selected modes in the mean field of the others. The same partition of modes can be iterated until self‐consistency, generalizing the vibrational self‐consistent field (VSCF) method. As in contracted‐mode methods, a hierarchy of partitions can be built to ultimately contract all the modes together. So, the VMFCI method extends the traditional variational approaches and can be included in existing vibrational codes based on the latter approaches. The flexibility and efficiency of this new method are demonstrated on several molecules of atmospheric interest. © 2006 Wiley Periodicals, Inc. J Comput Chem 27: 627–640, 2006

[1]  Vincenzo Barone,et al.  Accurate vibrational spectra of large molecules by density functional computations beyond the harmonic approximation: the case of uracil and 2-thiouracil , 2004 .

[2]  E. Sibert,et al.  A nine-dimensional perturbative treatment of the vibrations of methane and its isotopomers , 1999 .

[3]  D. L. Gray,et al.  The anharmonic force field and equilibrium structure of methane , 1979 .

[4]  Clovis Darrigan,et al.  New parallel software (P_Anhar) for anharmonic vibrational calculations: Application to (CH3Li)2 , 2005, J. Comput. Chem..

[5]  Joel M. Bowman,et al.  Variational calculations of rovibrational energies of CH4 and isotopomers in full dimensionality using an ab initio potential , 1999 .

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

[7]  Joel M. Bowman,et al.  Variational Calculations of Rotational−Vibrational Energies of CH4 and Isotopomers Using an Adjusted ab Initio Potential , 2000 .

[8]  M. Ratner,et al.  A semiclassical self-consistent field (SC SCF) approximation for eigenvalues of coupled-vibration systems , 1979 .

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

[10]  N. Handy,et al.  The variational method for the calculation of RO-vibrational energy levels , 1986 .

[11]  T. Carrington,et al.  Discrete‐Variable Representations and their Utilization , 2007 .

[12]  P. Cassam-Chenaï,et al.  Electronic and vibronic dipole moments of CH2D , 1995 .

[13]  D. Schwenke Towards accurate ab initio predictions of the vibrational spectrum of methane. , 2002, Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.

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

[15]  Vincenzo Barone,et al.  Anharmonic vibrational properties by a fully automated second-order perturbative approach. , 2005, The Journal of chemical physics.

[16]  P. Cassam-Chenaï Ab initio predictions for the Q-branch of the methane vibrational ground state , 2003 .

[17]  P. Fleurat‐Lessard,et al.  The vibrational energies of ozone up to the dissociation threshold: Dynamics calculations on an accurate potential energy surface , 2002 .

[18]  T. Carrington,et al.  Using simply contracted basis functions with the Lanczos algorithm to calculate vibrational spectra , 2004 .

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

[20]  Rudolf Burcl,et al.  On the representation of potential energy surfaces of polyatomic molecules in normal coordinates: II. Parameterisation of the force field , 2003 .

[21]  E. Venuti,et al.  High dimensional anharmonic potential energy surfaces: The case of methane , 1999 .

[22]  N. Matsunaga,et al.  Degenerate perturbation theory corrections for the vibrational self-consistent field approximation: Method and applications , 2002 .

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

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

[25]  Hua-Gen Yu Converged quantum dynamics calculations of vibrational energies of CH4 and CH3D using an ab initio potential. , 2004, The Journal of chemical physics.

[26]  J. Tennyson The calculation of the vibration-rotation energies of triatomic molecules using scattering coordinates , 1986 .

[27]  P. Taylor,et al.  An Accurate ab initio Quartic Force Field and Vibrational Frequencies for CH4 and Isotopomers , 1995 .

[28]  L. Wiesenfeld The Vibron Model for Methane: Stretch–Bend Interactions , 1997 .

[29]  Harry Partridge,et al.  The determination of an accurate isotope dependent potential energy surface for water from extensive ab initio calculations and experimental data , 1997 .

[30]  Jean-Paul Champion,et al.  The High Resolution Infrared Spectrum of CH3D in the Region 900–1700 cm−1 , 1997 .

[31]  L. Halonen Internal coordinate Hamiltonian model for Fermi resonances and local modes in methane , 1997 .

[32]  J. Light,et al.  Iterative solutions with energy selected bases for highly excited vibrations of tetra-atomic molecules. , 2004, The Journal of chemical physics.

[33]  Cheng‐Lung Chen,et al.  Variational calculations of rotational–vibrational energy levels of water , 1985 .

[34]  T. Carrington,et al.  How to choose one-dimensional basis functions so that a very efficient multidimensional basis may be extracted from a direct product of the one-dimensional functions: energy levels of coupled systems with as many as 16 coordinates. , 2005, The Journal of chemical physics.

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

[36]  M. Ratner,et al.  A vibrational eigenfunction of a protein: Anharmonic coupled-mode ground and fundamental excited states of BPTI , 1997 .

[37]  G. Chaban,et al.  Ab initio calculation of anharmonic vibrational states of polyatomic systems: Electronic structure combined with vibrational self-consistent field , 1999 .