One-dimensional tunneling calculations in the imaginary-frequency, rectilinear saddle-point normal mode.

We present tunneling calculations using the reaction path Hamiltonian in the zero-curvature approximation and a one-dimensional Hamiltonian in the imaginary-frequency, rectilinear normal mode of a saddle point, neglecting the vibrational angular momentum terms. This latter Hamiltonian was recently introduced and applied to the tunneling splitting in full-dimensional malonaldeyde [Y. Wang et al., J. Chem. Phys. 128, 224314 (2008)]. The results using the latter method are shown to be much more accurate than those using the former one for the ground-state tunneling splittings for H and D-transfer in malonaldehyde and for the D+H(2) reaction in three dimensions for zero total angular momentum.

[1]  N. Handy,et al.  The vibrational levels of ammonia. , 2002, Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.

[2]  Joel M Bowman,et al.  Full-dimensional quantum calculations of ground-state tunneling splitting of malonaldehyde using an accurate ab initio potential energy surface. , 2008, The Journal of chemical physics.

[3]  D. Truhlar,et al.  Reaction‐path potential and vibrational frequencies in terms of curvilinear internal coordinates , 1995 .

[4]  U. Manthe,et al.  Accurate potential energy surface and quantum reaction rate calculations for the H+CH4-->H2+CH3 reaction. , 2006, The Journal of chemical physics.

[5]  W. Miller,et al.  Quantum mechanical reaction probabilities via a discrete variable representation-absorbing boundary condition Green's function , 1992 .

[6]  W. Miller,et al.  Calculation of the cumulative reaction probability via a discrete variable representation with absorbing boundary conditions , 1992 .

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

[8]  K. Fukui.  Formulation of the reaction coordinate , 1970 .

[9]  Michael E. Coltrin,et al.  A new tunneling path for reactions such as H+H2→H2+H , 1977 .

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

[11]  K. Hirao,et al.  Tunneling splitting in polyatomic molecules: Application to malonaldehyde , 2003 .

[12]  W. Miller,et al.  A semiclassical tunneling model for use in classical trajectory simulations , 1989 .

[13]  K. Hirao,et al.  Generation of full-dimensional potential energy surface of intramolecular hydrogen atom transfer in malonaldehyde and tunneling dynamics , 2001 .

[14]  S. Carter,et al.  Full dimensional calculations of vibrational energies of H3O+ and D3O+. , 2002, Spectrochimica acta. Part A, Molecular and biomolecular spectroscopy.

[15]  E. C. Kemble.  The Fundamental Principles Of Quantum Mechanics , 1937 .

[16]  K. Hirao,et al.  Simple and accurate method to evaluate tunneling splitting in polyatomic molecules. , 2003, The Journal of chemical physics.

[17]  Uwe Manthe,et al.  The ground state tunneling splitting and the zero point energy of malonaldehyde: a quantum Monte Carlo determination. , 2007, The Journal of chemical physics.

[18]  Kazuhiro Ishida,et al.  The intrinsic reaction coordinate. An ab initio calculation for HNC→HCN and H−+CH4→CH4+H− , 1977 .

[19]  C. Horowitz,et al.  Functional representation of Liu and Siegbahn’s accurate ab initio potential energy calculations for H+H2 , 1978 .

[20]  Joel M. Bowman,et al.  Reduced dimensionality theory of quantum reactive scattering , 1991 .

[21]  C. Tautermann,et al.  The optimal tunneling path for the proton transfer in malonaldehyde , 2002 .

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