.. CheMPS2: a spin-adapted implementation of DMRG for ab initio quantum chemistry
   Copyright (C) 2013-2018 Sebastian Wouters

   This program is free software; you can redistribute it and/or modify
   it under the terms of the GNU General Public License as published by
   the Free Software Foundation; either version 2 of the License, or
   (at your option) any later version.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.

   You should have received a copy of the GNU General Public License along
   with this program; if not, write to the Free Software Foundation, Inc.,
   51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

.. index:: Matrix elements
.. index:: psi4
.. index:: pyscf

``CheMPS2::Hamiltonian``
========================

There are several ways to feed matrix elements to CheMPS2. They are explained below in detail. Because CheMPS2 is a spin-adapted code, it can only handle spatial orbitals. It is hence not possible to use different orbitals for :math:`\uparrow` and :math:`\downarrow` electrons.

#. The ``CheMPS2::Hamiltonian`` object is able to read in FCIDUMP files. The ``fcidump`` plugin to `psi4 <http://www.psicode.org/>`_ allows to generate such FCIDUMP files.

#. The ``savehdf`` plugin to `psi4 <http://www.psicode.org/>`_ fills a ``CheMPS2::Hamiltonian`` object, and saves the matrix elements to disk in HDF5 format, taking into account their eightfold permutation symmetry.

#. Users can also generate matrix elements themselves, and feed them to the ``CheMPS2::Hamiltonian`` object.


psi4 ``fcidump`` plugin
-----------------------

The ``CheMPS2::Hamiltonian`` object is able to read in FCIDUMP files:

.. code-block:: c++

    CheMPS2::Hamiltonian::Hamiltonian( const string filename, const int psi4groupnumber )
    
The variable ``filename`` should contain the path to the FCIDUMP file, and the variable ``psi4groupnumber`` should be the group number of the abelian point group with real-valued character table as defined in `psi4 <http://www.psicode.org/>`_. The conversion table is provided here:

 +--------------+----+----+----+----+----+-----+-----+-----+
 | Group name   | c1 | ci | c2 | cs | d2 | c2v | c2h | d2h |
 +--------------+----+----+----+----+----+-----+-----+-----+
 | Group number | 0  | 1  | 2  | 3  | 4  | 5   | 6   | 7   |
 +--------------+----+----+----+----+----+-----+-----+-----+

FCIDUMP files can for example be generated by molpro, or by a plugin to `psi4 <http://www.psicode.org/>`_. The plugin has been tested on `psi4-0.5 <https://github.com/psi4/psi4/releases/tag/0.5>`_ (released February 17, 2016).

To make use of this feature, build `psi4 <http://www.psicode.org/>`_ with the plugin option ``ENABLE_PLUGINS=ON``, and then run:

.. code-block:: bash

    $ cd /mypsi4plugins
    $ psi4 --new-plugin fcidump
    $ cd fcidump

Now, replace the file ``fcidump.cc`` with ``/sourcefolder/chemps2/integrals/psi4plugins/fcidump.cc``. To compile the plugin, run:

.. code-block:: bash

    $ make

An example input file to generate a FCIDUMP file:

.. literalinclude:: N2.fcidump.in

This file (``N2.fcidump.in``) should be placed in the folder ``/mypsi4plugins/fcidump/``. The FCIDUMP file can then be generated with:

.. code-block:: bash

    $ cd /mypsi4plugins/fcidump
    $ psi4 N2.fcidump.in N2.fcidump.out
    $ less N2.CCPVDZ.FCIDUMP

Examples of output generated with this plugin can be found in ``/sourcefolder/chemps2/tests/matrixelements/``.


psi4 ``savehdf`` plugin
-----------------------

The ``CheMPS2::Hamiltonian`` object is able to read in HDF5 files generated by a plugin to `psi4 <http://www.psicode.org/>`_. The plugin has been tested on `psi4-0.5 <https://github.com/psi4/psi4/releases/tag/0.5>`_ (released February 17, 2016). It stores all unique matrix elements (remember that there is eightfold permutation symmetry) in binary form with HDF5.

To make use of this feature, build `psi4 <http://www.psicode.org/>`_ with the plugin option ``ENABLE_PLUGINS=ON``, and then run:

.. code-block:: bash

    $ cd /mypsi4plugins
    $ psi4 --new-plugin savehdf
    $ cd savehdf

Now, replace the file ``savehdf.cc`` with ``/sourcefolder/chemps2/integrals/psi4plugins/savehdf.cc``. To compile the plugin, the Makefile should be adjusted. Change the line

.. code-block:: bash

    $(CXX) $(LDFLAGS) -o $@ $^ $(CXXDEFS)

to

.. code-block:: bash

    $(CXX) $(LDFLAGS) -o $@ $^ $(CXXDEFS) -lchemps2

Remember to add the library and include paths to the Makefile as well, if ``libchemps2`` is not installed in a standard location. For debian/sid, the HDF5 headers are located in the folder ``/usr/include/hdf5/serial/``. It might be necessary to add it to the ``INCLUDES`` variable in the Makefile.
To compile the plugin, run:

.. code-block:: bash

    $ make

An example input file to use the ``savehdf`` plugin:

.. literalinclude:: N2.savehdf.in

This file (``N2.savehdf.in``) should be placed in the folder ``/mypsi4plugins/savehdf/``. The matrix elements can then be saved to disk in binary form with HDF5 by running:

.. code-block:: bash

    $ cd /mypsi4plugins/savehdf
    $ psi4 N2.savehdf.in N2.savehdf.out
    $ ls *.h5

The plugin generates three files:

.. code-block:: bash

    /mypsi4plugins/CheMPS2_Ham_parent.h5
    /mypsi4plugins/CheMPS2_Ham_Tmat.h5
    /mypsi4plugins/CheMPS2_Ham_Vmat.h5

which allow to create an instance of the ``CheMPS2::Hamiltonian`` object:

.. code-block:: c++

    CheMPS2::Hamiltonian::Hamiltonian( const bool fileh5, const string main_file, const string file_tmat, const string file_vmat )

The variable ``fileh5`` should be ``true``, and the three strings should contain the paths to the three files listed above, in the same respective order.

.. _chemps2_psi4irrepconventions:

Custom matrix elements
----------------------

It is also possible to create a ``CheMPS2::Hamiltonian`` object with your own matrix elements. Please consult the ``CheMPS2::Hamiltonian`` class in the `doxygen html output <http://sebwouters.github.io/CheMPS2/doxygen/index.html>`_, and more specifically the functions:

.. code-block:: c++

    CheMPS2::Hamiltonian::Hamiltonian( const int Norbitals, const int nGroup, const int * OrbIrreps )
    void CheMPS2::Hamiltonian::setEconst( const double val )
    void CheMPS2::Hamiltonian::setTmat( const int index1, const int index2, const double val )
    void CheMPS2::Hamiltonian::setVmat( const int index1, const int index2, const int index3, const int index4, const double val )

The variable ``Norbitals`` should be the total number of orbitals in the active space. The variable ``nGroup`` should be the group number of the abelian point group with real-valued character table as defined in `psi4 <http://www.psicode.org/>`_. The array ``OrbIrreps`` of length ``Norbitals`` contains for each orbital its irreducible representation number as defined in `psi4 <http://www.psicode.org/>`_. The conversion table is provided here:

 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+
 | Group / Irreps | 0   | 1   | 2   | 3   | 4   | 5   | 6   | 7   |
 +================+=====+=====+=====+=====+=====+=====+=====+=====+
 | 0: c1          | A   |     |     |     |     |     |     |     |
 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+
 | 1: ci          | Ag  | Au  |     |     |     |     |     |     |
 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+
 | 2: c2          | A   | B   |     |     |     |     |     |     |
 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+
 | 3: cs          | A'  | A'' |     |     |     |     |     |     |
 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+
 | 4: d2          | A   | B1  | B2  | B3  |     |     |     |     |
 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+
 | 5: c2v         | A1  | A2  | B1  | B2  |     |     |     |     |
 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+
 | 6: c2h         | Ag  | Bg  | Au  | Bu  |     |     |     |     |
 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+
 | 7: d2h         | Ag  | B1g | B2g | B3g | Au  | B1u | B2u | B3u |
 +----------------+-----+-----+-----+-----+-----+-----+-----+-----+

Two important remarks:

#. On creation of the ``CheMPS2::Hamiltonian`` object, every matrix element is set to zero.
#. Physics notation is used for the two-electron integrals in CheMPS2: :math:`V_{ij;kl} = ( ik \mid jl )` or ``CheMPS2::Hamiltonian::setVmat( i, j, k, l, (ik|jl) )``.