Solution of atomic Hartree–Fock equations with the P version of the finite element method

The Hartree–Fock equations for atoms are solved with the p version of the finite element method, which differs from the traditional finite element method in using high order, hierarchic polynomials as basis functions. Recursion formulas are developed for the analytical evaluation of integrals, which are crucial in reducing the computation time and maintaining the accuracy of the solution. A hierarchic computational approach is used where the solution at a certain level is used to start the calculation at the next level. Results are presented for closed and open shell atoms taken from various columns of the periodic table that show excellent agreement with accurate numerical calculations.

[1]  C. Fischer,et al.  Spline algorithms for continuum functions , 1989 .

[2]  Dietmar Kolb,et al.  Accurate Hartree-Fock-Slater calculations on small diatomic molecules with the finite-element method , 1988 .

[3]  Richard A. Friesner,et al.  Solution of self-consistent field electronic structure equations by a pseudospectral method , 1985 .

[4]  Finite element methods in quantum mechanics , 1987 .

[5]  R. Metzger,et al.  Piecewise polynomial configuration interaction natural orbital study of 1 s2 helium , 1979 .

[6]  D. J. Paddon,et al.  Multigrid Methods for Integral and Differential Equations. , 1987 .

[7]  S. Iwata,et al.  Promotion of the proton transfer reaction by the intermolecular stretching mode: Application of the two‐dimensional finite element method to the nuclear Schrödinger equation , 1988 .

[8]  S. Vinitsky,et al.  Hydrogen atom H and H_{2}^{+} molecule in strong magnetic fields , 1980 .

[9]  Levin,et al.  Finite-element solution of the Schrödinger equation for the helium ground state. , 1985, Physical review. A, General physics.

[10]  M. Strayer,et al.  Relativistic Theory of Fermions and Classical Fields on a Collocation Lattice , 1987 .

[11]  H+2 correlation diagram from finite element calculations , 1985 .

[12]  T. Gilbert,et al.  Spline representation. I. Linear spline bases for atomic calculations , 1974 .

[13]  J. Gillis,et al.  Methods in Computational Physics , 1964 .

[14]  Ivo Babuška,et al.  The p-Version of the Finite Element Method for Parabolic Equations. Part 1 , 1981 .

[15]  Richard A. Friesner,et al.  Solution of the Hartree–Fock equations by a pseudospectral method: Application to diatomic molecules , 1986 .

[16]  White,et al.  Finite-element method for electronic structure. , 1989, Physical review. B, Condensed matter.

[17]  J. Gázquez,et al.  Piecewise polynomial electronic wavefunctions , 1977 .

[18]  J. Simons,et al.  The Hartree-Fock Method for Atoms , 1979 .

[19]  T. Gilbert,et al.  Spline bases for atomic calculations , 1976 .

[20]  P. M. Hunt,et al.  Application of finite element and boundary integral methods in molecular collision theory. I. Introduction and model calculations , 1988 .

[21]  M. Ablowitz,et al.  A comparison between finite element methods and spectral methods as applied to bound state problems , 1980 .

[22]  Johnson,et al.  Computation of second-order many-body corrections in relativistic atomic systems. , 1986, Physical review letters.

[23]  Heinemann,et al.  Solution of the Hartree-Fock-Slater equations for diatomic molecules by the finite-element method. , 1988, Physical review. A, General physics.