Abstract
We have applied a basis set of distributed Gaussian functions within the S-matrix version of the Kohn variational method to scattering problems involving deep potential energy wells. The Gaussian positions and widths are tailored to the potential using the procedure of Bačić and Light (1986 J. Chem. Phys. 85 4594) which has previously been applied to bound-state problems. The placement procedure is shown to be very efficient and gives scattering wavefunctions and observables in agreement with direct numerical solutions. We demonstrate the basis function placement method with applications to hydrogen atom–hydrogen atom scattering and antihydrogen atom–hydrogen atom scattering.
Highlights
Variational approaches to quantum scattering have a long history and many versions have been devised
Variational methods have been used for a diverse range of scattering problems including ones with deep potential energy wells and/or high collision energies, for example H + H2 reactive scattering [4], electron–molecule elastic and inelastic scattering [5,6,7], positron-H2 scattering [8], antihydrogen–H2 scattering [9] and nuclear scattering [10]
The successful application of a variational method to a given quantum scattering problem requires the choice of a suitable basis set
Summary
Variational approaches to quantum scattering have a long history and many versions have been devised. The successful application of a variational method to a given quantum scattering problem requires the choice of a suitable basis set. A simple variational method was developed by Miller et al: the S-matrix Kohn variational principle (SKVP) [11, 12] Applying variational methods to these problems can lead to difficulties if conventional translational basis sets such as Slater or spaced Gaussians are used. In this work we apply a distributed Gaussian basis set within the SKVP to problems involving highly oscillatory scattering wavefunctions.
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