8-node Isoparametric Element And Parallel Computing In Quantum Chemistry

The finite element method (FEM) is a famous technique to solve different problems in engineering science. Since 1970, FEM has been applied to solve quantum chemistry problems such as the electronic structure of atoms or diatomic molecules to obtain wave functions and total energies.In order to reach the accurate results with a very small number of grid points, A finite element method with 8-node isoparametric element is presented to solving two-dimensional quantum chemistry problems for ground state energies of diatomic molecules in this paper. The FEM is the main program, meanwhile generalized Jacbi and a parallel subspace iteration method with modal transfer is developed to solve the generalized eigenvalue problem.Based on the numerical examples for BH, LiH, Li2, N2 and CO are given to show the simplification and efficiency of the finite element method with 8-node isoparametric element. Compare with other FEM, this method can achieve the same accurate results, using fewer grid nodes. A parallel subspace iteration method with modal transfer is employed to compute molecular orbits and orbital energies. An implementation of this method on a cluster of micromputers is discussed. Numerical results for BH and LiH are presented to demonstrate the effectiveness of this method.