The use of neural networks for fitting potential energy surfaces:: A comparative case study for the H3+ molecule

The fitting of ab initio electronic energies of polyatomic molecules for different nuclear configurations is an active field in quantum chemistry and is an important step in the study of chemical reaction dynamics and for the determination of rovibrational spectra. The choice of a good-fitting function and the decision as to which geometries are relevant for the problem remains a matter of feeling as a large number of ab initio points of good quality usually involves prohibitively large amounts of CPU times. More recently, the use of neural networks has drawn some attention for fitting potential energy surfaces (PES). Neural networks are generic function approximators for any required accuracy and are therefore well suited for fitting many-dimensional PES. In this work we present a comparative study for the ground state PES of the H3(+) molecule obtained fitting state-of-the-art ab initio points. The PES is obtained using both a neural network and a polynomial function in Morse-type symmetry-adapted coordinates. The quality of the surfaces is asserted by computing the associated rovibrational spectra. The resulting energies are compared with known experimental results. (C) 2003 Wiley Periodicals, Inc.