The fitting of potential energy and transition moment functions using neural networks: transition probabilities in OH (A2Σ+→X2Π)

Abstract We have studied the performance of the back-propagation neural network with different architectures and activation functions to fit potential energy curves and dipolar transition moment functions of the OH molecule from the ab initio data points of Bauschlicher and Langhoff [J. Chem. Phys. 87 (1987) 4665]. The neural network fittings are tested in different moments of the training process by computing the vibrational levels, the transition probabilities between A 2 Σ + and X 2 Π electronic states, and the radiative lifetimes. The results from the neural network fittings are then compared with experimental values, previous results calculated by Bauschlicher and Langhoff and the ones obtained by using of extended Rydberg function fitting.

[1]  D. Levy,et al.  The microwave spectrum of the OH X2Π radical in the ground and vibrationally-excited (ν ≤ 6) levels , 1979 .

[2]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[3]  S. Langhoff,et al.  Radiative lifetimes and dipole moments of the A 2Σ+, B 2Σ+, and C 2Σ+ states of OH , 1982 .

[4]  Eduardo D. Sontag.  Sigmoids Distinguish More Efficiently Than Heavisides , 1989, Neural Computation.

[5]  Raúl Rojas,et al.  Neural Networks - A Systematic Introduction , 1996 .

[6]  Martin Fodslette Møller,et al.  A scaled conjugate gradient algorithm for fast supervised learning , 1993, Neural Networks.

[7]  J. A. Coxon.  The A2Σ+-X2Πi system of OD: Determination of molecular constants by the direct two-state fit approach , 1975 .

[8]  S Suhai,et al.  Neural-network analysis of the vibrational spectra of N-acetyl L-alanyl N'-methyl amide conformational states. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  F. V. Prudente,et al.  Discrete variable representation and negative imaginary potential to study metastable states and photodissociation processes. Application to diatomic and triatomic molecules , 1997 .

[10]  Richard P. Brent,et al.  Fast training algorithms for multilayer neural nets , 1991, IEEE Trans. Neural Networks.

[11]  J. Murrell,et al.  Molecular Potential Energy Functions , 1985 .

[12]  Steven D. Brown,et al.  Neural network models of potential energy surfaces , 1995 .

[13]  D. Crosley,et al.  Transition probabilities in the A 2Σ+−X 2Πi electronic system of OH , 1998 .

[14]  H. Rabitz,et al.  A general method for constructing multidimensional molecular potential energy surfaces from ab initio calculations , 1996 .

[15]  Michihiko Sugawara,et al.  Numerical solution of the Schrödinger equation by neural network and genetic algorithm , 2001 .

[16]  D. Colbert,et al.  A novel discrete variable representation for quantum mechanical reactive scattering via the S-matrix Kohn method , 1992 .

[17]  D. Fotiadis,et al.  Artificial neural network methods in quantum mechanics , 1997, quant-ph/9705029.

[18]  Harold A. Scheraga,et al.  Description of the potential energy surface of the water dimer with an artificial neural network , 1997 .

[19]  Antônio de Pádua Braga,et al.  Artificial neural network applied for predicting rainbow trajectories in atomic and molecular classical collisions , 1997 .

[20]  J. Michael Finlan,et al.  New alternative to the Dunham potential for diatomic molecules , 1973 .

[21]  William H. Press,et al.  Numerical recipes , 1990 .

[22]  Tucker Carrington,et al.  A general framework for discrete variable representation basis sets , 2002 .

[23]  A. Varandas,et al.  Calculation of the asymptotic interaction and modelling of the potential energy curves of OH and OH , 1995 .

[24]  J. J. Soares Neto,et al.  The fitting of potential energy surfaces using neural networks: Application to the study of vibrational levels of H3+ , 1998 .

[25]  G. Nyman,et al.  A generalized discrete variable representation approach to interpolating or fitting potential energy surfaces , 2000 .

[26]  P. H. Acioli,et al.  Estimating correlation energy of diatomic molecules and atoms with neural networks , 1997, Journal of Computational Chemistry.

[27]  I. Kiss,et al.  Artificial Neural Network Approach to Predict the Solubility of C60 in Various Solvents , 2000 .

[28]  Lionel M. Raff,et al.  Quasiclassical trajectory studies using 3D spline interpolation of ab initio surfaces , 1975 .

[29]  Paul G. Mezey,et al.  Potential Energy Hypersurfaces , 1987 .

[30]  Mark N. Gibbs,et al.  Combining ab initio computations, neural networks, and diffusion Monte Carlo: An efficient method to treat weakly bound molecules , 1996 .

[31]  J. A. Coxon.  Optimum molecular constants and term values for the X2Π(ν ≤ 5) and A2Σ+(ν ≤ 3) states of OH , 1980 .

[32]  D. Yarkony.  A theoretical treatment of the predissociation of the individual rovibronic levels of OH/OD(A 2Σ+) , 1992 .

[33]  S. Langhoff,et al.  Theoretical determination of the radiative lifetime of the A 2Σ+ state of OH , 1987 .

[34]  L. Kułak,et al.  Neural network solution of the Schrödinger equation for a two-dimensional harmonic oscillator , 1993 .

[35]  P. Jensen,et al.  The development of a new Morse-oscillator based rotation-vibration Hamiltonian for H3+ , 1985 .

[36]  Michael A. Collins,et al.  Molecular potential-energy surfaces for chemical reaction dynamics , 2002 .

[37]  V. Barone,et al.  Representation of potential energy surfaces by discrete polynomials: proton transfer in malonaldehyde , 2000 .

[38]  M. Yoshimine,et al.  Ab initio study of the X2Π and A2Σ+ states of OH. I. Potential curves and properties , 1974 .

[39]  Bobby G. Sumpter,et al.  Theory and Applications of Neural Computing in Chemical Science , 1994 .

[40]  Włodzisław Duch,et al.  Neural networks as tools to solve problems in physics and chemistry , 1994 .

[41]  Harold A. Scheraga,et al.  A polarizable force field for water using an artificial neural network , 2002 .

[42]  Dmitrii E. Makarov,et al.  FITTING POTENTIAL-ENERGY SURFACES : A SEARCH IN THE FUNCTION SPACE BY DIRECTED GENETIC PROGRAMMING , 1998 .

[43]  S. Canuto,et al.  Efficient estimation of second virial coefficients of fused hard-sphere molecules by an artificial neural network , 2001 .

[44]  C. M. Roach,et al.  Fast curve fitting using neural networks , 1992 .

[45]  D. Donaldson,et al.  A two-laser pulse-and-probe study of T-R, V energy transfer collisions of H+NO at 0.95 and 2.2 eV , 1985 .

[46]  Donald J. Kouri,et al.  Distributed approximating functional fit of the H3 ab initio potential-energy data of Liu and Siegbahn , 1997 .

[47]  Alfonso Niño,et al.  Neural Modeling of Torsional Potential Hypersurfaces in Non-rigid Molecules , 1998, Comput. Chem..

[48]  J. J. Soares Neto,et al.  The fitting of potential energy surfaces using neural networks. Application to the study of the photodissociation processes , 1998 .

[49]  D. W. Noid,et al.  Potential energy surfaces for macromolecules. A neural network technique , 1992 .

[50]  Thomas B. Blank,et al.  Adaptive, global, extended Kalman filters for training feedforward neural networks , 1994 .

[51]  I. Shavitt,et al.  Calculation and fitting of potential energy and dipole moment surfaces for the water molecule: Fully ab initio determination of vibrational transition energies and band intensities , 1997 .

[52]  J. Muckerman.  Some useful discrete variable representations for problems in time-dependent and time-independent quantum mechanics , 1990 .

[53]  D. Crosley,et al.  Calculated rotational transition probabilities for the A−X system of OH , 1980 .