### Speaker

Prof.
Quang Huy TRAN
(IFPEN)

### Description

Many applications of quantum chemistry involve ab initio simulations. These are feasible thanks to well-known approximations to the Schrödinger equation, such as Hartree-Fock’s or Density Functional Theory. More than 70 softwares are available to chemists in this field, the most common ones being VASP, Gaussian and ABINIT. A key difference between them lies in the basis functions selected to express the molecular orbitals. One of the newcomers, the massively parallel program BigDFT, uses wavelet bases for performance considerations.
To better capture the cusp singularities of the orbitals in the all-electron calculations without increasing the complexity of BigDFT, we suggest enriching the wavelet basis by Gaussian functions centered at each nucleus position. To optimize the construction of additional Gaussian functions, we rely on a combination of a posteriori error estimates and the greedy algorithm. We adapt the ideas from Maday and his co-authors to establish that the dual norm of the residue can serve as an effective estimate for the energy decrease between the pure-wavelet solution and the augmented-basis solution. Furthermore, in a similar spirit with reduced-basis techniques, we recommend the greedy algorithm for building an incremental sequence of additional Gaussian functions.
As a proof of concept to this strategy, we investigate a one-dimensional model of Schrödinger type with delta potentials, which represents a system of one electron and several nuclei of known charges and positions. Due to the small number of additional degrees of freedom, wavelet-Gaussian mixed bases exhibit a significant gain in accuracy while having a low computational cost. This testifies to the interest of this approach.

### Primary author

Prof.
Quang Huy TRAN
(IFPEN)