8 May 1998 Ž . Chemical Physics Letters 287 1998 585–589 The fitting of potential energy surfaces using neural networks. Application to the study of the photodissociation processes Frederico V. Prudente ) , J.J. Soares Neto Departamento de Fısica, UniÕersidade de Brasılia, CP 04455, 70910-900 Brasılia, DF, Brazil ´ ´ ´ Received 16 December 1997; in final form 25 February 1998 Abstract A back-propagation neural network is utilized to fit potential energy surfaces and the transition dipole moment of the HCl q ion, using the ab initio electronic energies calculated by Pradhan, Kirby and Dalgarno. These surfaces are used in the study of the photodissociation process. The photodissociation cross section is calculated utilizing the equally spaced discrete variable representation and the negative imaginary potential method. q 1998 Elsevier Science B.V. All rights reserved. 1. Introduction Photodissociation of molecules induced by photon absorption allows a detailed study of molecular dy- namics such as the breaking of bonds, internal en- ergy transfer and radiationless transitions. To obtain an accurate photodissociation cross section, it is necessary to attain the accurate ground and excited- state potential energy surfaces and transition dipole moment. The obtainment of potential energy surfaces Ž . Ž . PES and dipole moment functions DMF consists . of two parts: i the ab initio calculation of the electronic structure for a set of nuclear configura- . tions; and ii the fitting of these points to define the potential energy surface over the whole nuclear con- figuration space. There are two methods of doing this fitting. The use of a power series in an appropriate coordinate system to describe the surfaces, for example, the ) Corresponding author. E-mail:fred@fis.unb.br. wx bond order potential 1 , the Simons–Parr–Finlan Ž . wx SPF expansion 2 and the Morse functions expan- wx sion 3 . The main difficulty, in this case, is obtain- ing the best set of coefficients for the expansion to fit the surfaces. The second class of procedures interpolates the ab initio points using local functions wx such as the cubic spline 4 . The spline interpolation is an accurate method for the fitting of one-dimen- sional PES and DMF. However, the interpolation error in the spline grows rapidly with increasing dimension. For a system with more than about four degrees of freedom the scheme becomes impractical wx 5 , even for more sophisticated versions of polyno- wx mial splines 6 . An alternative to these methods is the multilayer w x neural network 7,8 . It has been used in a variety of applications in chemistry and physics. To interpolate a PES and a DMF, a neural network does not need to know a priori the shape of the surface and utilizes a small set of ab initio points. The outcome of the interpolation is smooth, continuous and includes all features of the surface. Other features are: the ex- pressions for the PES and DMF are relatively simple 0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. Ž . PII: S0009-2614 98 00207-3