Mat-1.3656 Seminar on
numerical analysis and computational science
Monday, Jan 27, 2014, room M233 at 14.15, Eirola & Stenberg
Susi Lehtola, Aalto", Department of Applied Physics
Completeness-optimization of basis sets for electronic structure calculations
Quantum chemistry is all about solving the Schrödinger equation for
electrons in atoms and molecules. Most calculations in quantum
chemistry are performed using finite basis sets, with which the
integro-differential Schrödinger equation can be written as an
algebraic one that is suitable for computer implementation.
The spherical symmetry of atoms is maintained to a large extent in
molecules, which is the main motivation for the linear combination of
atomic orbital (LCAO) basis sets. Out of LCAO basis sets, Gaussian
basis sets are most often used. With them, calculations can be
performed not only within the mean-field Hartree-Fock or Kohn-Sham
density-functional theory methods, but also more elaborate methods that
try to capture the instantaneous interactions between the electrons.
The parametrization of basis sets is traditionally a highly elaborate
task, which relies on energy optimization of the basis functions.
However, the convergence of the energy does not guarantee
convergence for all properties, such as nuclear magnetic shielding
constants, or the dipole moment of molecules, which probe other features
of the electronic wave function.
The main focus of this talk is the discussion of the recently suggested
method of completeness-optimization of basis sets [1]. In the procedure
the connection between the goodness of a basis set and the energy is
forgotten. Instead, full attention is given to the mathematical
completeness of the function space, which is then optimized to
reproduce the wanted property. This makes the generation of
computationally efficient basis sets extremely simple, even for
computationally difficult properties [1-3].
[1] P. Manninen and J. Vaara, J. Comput. Chem. 27, 434 (2006).
[2] J. Lehtola, P. Manninen, M. Hakala, and K. Hämäläinen, J. Chem.
Phys. 137 (2012), 104105.
[3] S. Lehtola, P. Manninen, M. Hakala and K. Hämäläinen, J. Chem.
Phys. 138 (2013), 044109.