Page 161 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

146 M. DEFRANCESCHI ET AL.
Nuclear attraction, electron-electron repulsion and exchange terms. Using the Eqs. 6 and
7, these contributions are respectively written in terms of the quantity Wij(q) previously
defined in Eq. 11 :

and

The detailed expression for is then :

The momentum space equivalent of the total energy E, is :

3. Principles for numerical resolutions

Because of the terms and explicit solutions to Eq. 3 cannot be obtained in
position space. In such cases approximate solutions are usually expressed as truncated
linear combinations of basis functions (LCAO expressions). In spite of its successes, the
LCAO approximation experiences various difficulties (truncation limits, nature of the
basis functions, etc.) hard to estimate and which are not entirely controllable [51].