: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 HÃ¼ckel 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