.. tip::
    All input files can be downloaded: :download:`Files <https://zhjun-sci.com/qbics/input_library/keywords-basinfo.tar.gz>`.

basinfo
==============

.. contents::
   :local:

This keyword defines the implementation details of basis functions.

Options
------------

.. option:: angular_type

   .. list-table::
      :stub-columns: 1
      :widths: 5 20
   
      * - Value
        - ``Cartesian``. Will use Cartesian basis sets, i.e., 6\ *d*/10\ *f*/15\ *g*.
      * - 
        - ``spherical``. Will use the spherical basis sets, i.e., 5\ *d*/7\ *f*/9\ *g*.
      * - Default
        - ``spherical``
      
   Determine whether to use spherical or Cartesian GTO basis set. Usually, there is **NO** need to use Cartesian GTO basis sets except for test purpose.

.. option:: linear_dependence

   .. list-table::
      :stub-columns: 1
      :widths: 5 20
   
      * - Value
        - A real number
      * - Default
        - ``1.E-8``
   
   Assign the threshold that admits the linear dependence of the basis set. It should be a positive real number. When linear dependence is detected, Qbics will stop the calculation and raises an error. 

   Linear dependence occurs when:
   
   #. There are identical basis functions for the same nuclear;
   #. Two nuclei of the same element are too close;
   #. There are many diffuse basis functions for a large molecule.

.. option:: ghost

   .. list-table::
      :stub-columns: 1
      :widths: 5 20
   
      * - Value
        - Atom range
      * - Default
        - None
   
   Assigning "ghost atoms" means that those atoms defined in ``mol ... end`` have basis functions, but nuclear and electrons disappear. This is often used for some special purposes, like basis set superposition error (BSSE) calculations, although Qbics can automatically do this. 

Theoretical Background
-------------------------

Angular Type of Basis Functions
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

The analyitcal expression of Gaussian basis function is: 

.. math::
  
  \chi(\mathbf{r}) = A_{L}(\mathbf{r})\sum_{k=1}^{K} C_k e^{-\alpha_k r_{A}^2}

Here, :math:`A_{L}(\mathbf{r})` is the angular part with angular momentum quantum number :math:`L`, :math:`K` is the contraction degree, :math:`\alpha_k` is the exponent, :math:`C_k` is the contraction coefficient, and :math:`\mathbf{A}` is the atom position.
    
The angular part :math:`A_{L}(\mathbf{r})` has 2 forms: one is ``Cartesian``, of the form :math:`x_A^{l_x}y_A^{l_y}z_A^{l_z}`,  and ``spherical``, of a real solid spherical harmonic function. The spherical basis sets are more efficient and compact for quantum chemical calculations.

Ghost Atoms
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

In quantum chemistry, ghost atoms are atoms that have basis functions but no nuclear and electrons. They are often used in basis set superposition error (BSSE) calculations, where the interaction between two molecules is calculated. The ghost atoms are used to remove the interaction between the basis functions of the two molecules. 

One can use ``ghost`` option to calculate BSSE manually, but this is unnecessary. Qbics can automatically handle this by :doc:`eda`.

Input Examples
--------------------

Example: GeH\ :sub:`3`\ F-NCH with Ghost Atoms
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

For the complex GeH\ :sub:`3`\ F-NCH, calculate the energy that HCN is the ghost molecule at B3LYP/def2-SVP level of theory:

.. code-block:: bash
    :linenos:
    :caption: basinfo-1.inp

    basis
        def2-svp
    end
    
    basinfo
        ghost 6-8 # The indices of HCN.
    end
    
    scf
        charge  0
        spin2p1 1
        type    R
    end
    
    mol
       Ge      0.00000000      0.00221863     -0.79935317
        H      0.00000000      1.48645043     -0.40384625
        H      1.28514604     -0.74161126     -0.40477816
        H     -1.28514603     -0.74161126     -0.40477816
        F      0.00000000      0.00108752     -2.56116087
        C      0.00000000     -0.00225138      3.35662076
        H      0.00000000     -0.00220444      4.43604901
        N      0.00000000     -0.00207825      2.20326200    
    end
    
    task
        energy b3lyp
    end
    
The ``ghost`` keyword indicates that atom 6,7,8, i.e., C,H,N are ghost ones. 

.. figure:: figs/basinfo-1.jpg

In the output, you can see:

.. code-block:: bash
    :linenos:
    :caption: basinfo-1.out

    # of ghost atoms: 3
     Indices: 6 7 8
     Sum of ghost atom electrons: 14

    ...
    
    SCF Structure:
     # of electrons:       44
     # of alpha electrons: 22
     # of beta electrons:  22
     2S+1:                 1
    
The ghost atoms are listed. Also, the number of electrons are only ``44``, which is exactly the number of electrons for GeH\ :sub:`3`\ F only.