Speaker
Description
FEM calculations have been performed in Cartesian coordinates in the finite element framework FEniCS[1], using the density functional approach for a number of small molecules. In order to aid convergence of the orbitals and total energies a suitable cusp factor
$$ F({\bf r})=1+\sum_{j=1}^{N_A} c_j \exp
\left (-2Z_J r_j
\right)\,\,\,{\rm with} \,\, r_j=\vert {\bf r}-{\bf R}_j\vert\,.
$$
was employed, such that the resulting effective potential is non-singular at all nuclei and where the coefficients $c_i$ are obtained by solving a linear system of equations. The finite element ansatz for the pseudo orbitals leads to a sparse generalized eigenvalue problem of dimension $N$ up to 3.6 $10^6$, which was solved employing thethe Jacobi-Davidson method on a High Performance SMP Machine with 32 CPUs and 512 GB of memory.
The resulting total energies and densities were compared with those obtained using the Gaussian basis set package NWChem[2] and excellent agreement was found.
[1] Martin S. Alnæs, Jan Blechta, Johan Hake, August Jo-
hansson, Benjamin Kehlet, Anders Logg, Chris Richard-
son, Johannes Ring, Marie E. Rognes, and Garth N. Wells.
The fenics project version 1.5. Archive of Numerical Soft-
ware, 3(100), 2015.
[2] M. Valiev, E.J. Bylaska, N. Govind, K. Kowalski, T.P.
Straatsma, H.J.J. Van Dam, D. Wang, J. Nieplocha,
E. Apra, T.L. Windus, and W.A. de Jong. Nwchem: A
comprehensive and scalable open-source solution for large
scale molecular simulations. Computer Physics Communi-
cations, 181(9):1477 – 1489, 2010.
