Automatic generation of potential energy and property surfaces of polyatomic molecules in normal coordinates.

A procedure for the automatic construction of Born-Oppenheimer (BO) potential energy and molecular property surfaces in rectilinear normal coordinates is presented and its suitability and accuracy when combined with vibrational structure calculations are assessed. The procedure relies on a hierarchical n-mode representation of the BO potential energy or molecular property surface, where the n-mode term of the sequence of potentials/molecular properties includes only the couplings between n or less vibrational degrees of freedom. Each n-mode cut of the energy/molecular property surface is first evaluated in a grid of points with ab initio electronic structure methods. The ab initio data are then spline interpolated and a subsequent polynomial fitting provides an analytical semiglobal representation for use in vibrational structure programs. The implementation of the procedure is outlined and the accuracy of the method is tested on water and difluoromethane. Strategies for improving the proposed algorithm are also discussed.

[1]  K. Hirao,et al.  A new analytic form of ab initio potential energy function: An application to H2O , 2002 .

[2]  O. Christiansen.  Response theory for vibrational wave functions. , 2005, The Journal of chemical physics.

[3]  Ove Christiansen,et al.  INVITED ARTICLE www.rsc.org/pccp | Physical Chemistry Chemical Physics , 2006 .

[4]  N. Handy,et al.  Extensions and tests of “multimode”: a code to obtain accurate vibration/rotation energies of many-mode molecules , 1998 .

[5]  J. Tennyson,et al.  High-Accuracy ab Initio Rotation-Vibration Transitions for Water , 2003, Science.

[6]  R. Hanson,et al.  Shock tube measurements of rate coefficients of elementary gas reactions , 1979 .

[7]  M. Ratner,et al.  MOLLER-PLESSET PERTURBATION THEORY APPLIED TO VIBRATIONAL PROBLEMS , 1996 .

[8]  R. Benny Gerber,et al.  Vibrational wave functions and spectroscopy of (H2O)n, n=2,3,4,5: Vibrational self‐consistent field with correlation corrections , 1996 .

[9]  J. Morcillo,et al.  Infra-red intensities in CH2F2, CH2Cl2 and CF2Cl2☆ , 1966 .

[10]  Jacob Kongsted,et al.  Automatic generation of force fields and property surfaces for use in variational vibrational calculations of anharmonic vibrational energies and zero-point vibrational averaged properties. , 2006, The Journal of chemical physics.

[11]  Satoshi Maeda,et al.  A new method for constructing multidimensional potential energy surfaces by a polar coordinate interpolation technique , 2003 .

[12]  Richard Dawes,et al.  Interpolating moving least-squares methods for fitting potential energy surfaces: computing high-density potential energy surface data from low-density ab initio data points. , 2007, The Journal of chemical physics.

[13]  S. Kondo,et al.  Infrared intensities and Coriolis interactions in methylene fluoride , 1980 .

[14]  J. Light,et al.  Generalized discrete variable approximation in quantum mechanics , 1985 .

[15]  Mark A. Ratner,et al.  Self‐Consistent‐Field Methods for Vibrational Excitations in Polyatomic Systems , 2007 .

[16]  R. Bartlett,et al.  A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples , 1982 .

[17]  Joel M. Bowman,et al.  Self‐consistent field energies and wavefunctions for coupled oscillators , 1978 .

[18]  K. Hirao,et al.  Highly accurate potential-energy and dipole moment surfaces for vibrational state calculations of methane. , 2006, The Journal of chemical physics.

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

[20]  Isao Suzuki,et al.  Vibration-rotation spectra and molecular force field of methylene fluoride and methylene fluoride-d2 , 1973 .

[21]  J. Light,et al.  On distributed Gaussian bases for simple model multidimensional vibrational problems , 1986 .

[22]  M. Gordon,et al.  Direct Vibrational Self-Consistent Field Method: Applications to H2O and H2CO , 2000 .

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

[24]  D. Lide.  The Microwave Spectrum and Structure of Methylene Fluoride1 , 1952 .

[25]  E. Hirota.  Anharmonic potential function and equilibrium structure of methylene fluoride , 1978 .

[26]  Johannes Neugebauer,et al.  Fundamental vibrational frequencies of small polyatomic molecules from density-functional calculations and vibrational perturbation theory , 2003 .

[27]  Joel M. Bowman,et al.  The self-consistent-field approach to polyatomic vibrations , 1986 .

[28]  A. Müller,et al.  A study on the GVFF of CHF3, CH2F2, and CH3F , 1978 .

[29]  G. Scoles,et al.  Transition dipole moment measurements for the υ9 band of difluoromethane using Rabi oscillations , 1988 .

[30]  P. Jørgensen,et al.  Frequency-dependent first hyperpolarizabilities using coupled cluster quadratic response theory , 1997 .

[31]  S. Irle,et al.  Direct ab initio variational calculation of vibrational energies of the H2O⋯Cl− complex and resolution of experimental differences , 2000 .

[32]  G. Chaban,et al.  Ab initio calculations of anharmonic vibrational spectroscopy for hydrogen fluoride (HF)n (n = 3, 4) and mixed hydrogen fluoride/water (HF)n(H2O)n (n = 1, 2, 4) clusters. , 2002, Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.

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

[34]  Joel M. Bowman,et al.  On using potential, gradient, and Hessian data in least squares fits of potentials: Application and tests for H2O , 2002 .

[35]  Joel M. Bowman,et al.  Investigations of self-consistent field, scf ci and virtual stateconfiguration interaction vibrational energies for a model three-mode system , 1982 .

[36]  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 .

[37]  Weitao Yang,et al.  The collocation method for bound solutions of the Schrödinger equation , 1988 .

[38]  Ove Christiansen,et al.  A second quantization formulation of multimode dynamics. , 2004, The Journal of chemical physics.

[39]  Lazar' Mateevich Sverdlov,et al.  Vibrational spectra of polyatomic molecules , 1974 .

[40]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[41]  Guntram Rauhut,et al.  Accurate calculation of anharmonic vibrational frequencies of medium sized molecules using local coupled cluster methods. , 2007, The Journal of chemical physics.

[42]  Per Jensen,et al.  Computational molecular spectroscopy , 2000, Nature Reviews Methods Primers.

[43]  Kimihiko Hirao,et al.  Ab initio potential energy surface for vibrational state calculations of H2CO , 2003 .

[44]  Sergei Manzhos,et al.  Using neural networks to represent potential surfaces as sums of products. , 2006, The Journal of chemical physics.

[45]  M. Head‐Gordon,et al.  A fifth-order perturbation comparison of electron correlation theories , 1989 .

[46]  Sergei Manzhos,et al.  A random-sampling high dimensional model representation neural network for building potential energy surfaces. , 2006, The Journal of chemical physics.

[47]  E. Hirota,et al.  Microwave spectrum of methylene fluoride centrifugal distortion and molecular structure , 1970 .

[48]  G. Rauhut.  Efficient calculation of potential energy surfaces for the generation of vibrational wave functions. , 2004, The Journal of chemical physics.

[49]  Ove Christiansen,et al.  Møller–Plesset perturbation theory for vibrational wave functions , 2003 .

[50]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[51]  J. Kongsted,et al.  Linear response functions for a vibrational configuration interaction state. , 2006, The Journal of chemical physics.

[52]  D. Benoit,et al.  Fast vibrational self-consistent field calculations through a reduced mode-mode coupling scheme. , 2004, The Journal of chemical physics.

[53]  V. Barone,et al.  Coriolis couplings in variational computations of vibrational spectra beyond the harmonic approximation: implementation and validation , 2004 .

[54]  S. Carter,et al.  MULTIMODE: A code to calculate rovibrational energies of polyatomic molecules , 2003 .

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

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

[57]  Ove Christiansen,et al.  Vibrational coupled cluster theory. , 2004, The Journal of chemical physics.

[58]  B. Braams,et al.  On using low-order Hermite interpolation in `direct dynamics' calculations of vibrational energies using the code `MULTIMODE' , 2001 .

[59]  S. Saëki,et al.  Infrared absorption intensities of methylene fluoride , 1976 .

[60]  H. Koch,et al.  Integral-direct coupled cluster calculations of frequency-dependent polarizabilities, transition probabilities and excited-state properties , 1998 .

[61]  Hans-Dieter Meyer,et al.  Product representation of potential energy surfaces. II , 1996 .

[62]  Nicholas C. Handy,et al.  On the representation of potential energy surfaces of polyatomic molecules in normal coordinates , 2002 .

[63]  Fred A. Hamprecht,et al.  Development and assessment of new exchange-correlation functionals , 1998 .

[64]  E. Bright Wilson,et al.  Book Reviews: Molecular Vibrations. The Theory of Infrared and Raman Vibrational Spectra , 1955 .

[65]  N. Handy,et al.  A theoretical determination of the rovibrational energy levels of the water molecule , 1987 .

[66]  W. Green,et al.  Anharmonic vibrational properties of CH2F2 : A comparison of theory and experiment , 1991 .

[67]  D. Tannor,et al.  Introduction to Quantum Mechanics: A Time-Dependent Perspective , 2006 .