:orphan: .. _atomic_huckel_start: Extended Huckel start ===================== Background ---------- The basis theory is given here: :cite:`Hoffman1963`. The present development was further motivated by :cite:`Norman2012`. The particularity of the present approach is that it employs pre-calculated atomic fragments. A start guess is generated by solving the following general eigenvalue problem .. math:: H\mathbf{c} = S\mathbf{c}\varepsilon where :math:`S` is the overlap matrix in terms of pre-calculated atomic orbitals. The Hamiltonian matrix is defined as .. math:: H_{ij} = \left\{\begin{array}{lcl}\epsilon_i;&\quad&i=j\\KS_{ij};&\quad&i\ne j\end{array}\right. where :math:`K` is the Wolfsberg-Helmholtz constant. The default value is 1.75, but it can be changed with the keyword :ref:`SCF_.HUCPAR`. Example ------- .. image:: LuF3.png :scale: 50 :alt: alternate text We consider a Kohn-Sham calculation of the closed-shell :math:`LuF_3` molecule using the PBE functional. We start from the molecular input file `LuF3.xyz` .. literalinclude:: LuF3.xyz and the menu file `PBE.inp` .. literalinclude:: PBE.inp Unfortunately, and curiously, this calculation does not converge .. literalinclude:: PBE_LuF3.out We therefore try the extended Hückel method for a better start guess. The input file `PBEhuc.inp` reads .. literalinclude:: PBEhuc.inp In addition to the keyword :ref:`SCF_.AD HOC` file names for the Lu and F atomic types are given, followed by orbital strings specifying what atomic orbitals to select (see :ref:`orbital_strings` for the syntax). The calculation now converges in 20 iterations .. literalinclude:: PBEhuc_LuF3.out