pdtm - density transition matrix 
--------------------------------

The ``pdtm`` program calculates matrix elements of one-electron operators between many-electron states, under the density (or transition) matrix formalism. This formalism allows us to express the matrix elements between many-electron states via one-electron matrix elements. The ``pdtm`` program forms these reduced density (or transition) matrices and calculates the reduced matrix elements. The following quantities can be calculated from this program:  

* electron g-factors  
* magnetic dipole and electronic quadrupole hyperfine structure constants :math:`A` and :math:`B`  
* electric :math:`Ek` and magnetic :math:`Mk` multipole transition amplitudes, where :math:`k = 1,2,3` corresponds to the dipole, quadrupole, and octupole transitions  
* nuclear spin independent parity nonconserving PNC amplitude  
* amplitude of the electron interaction with the P-odd nuclear anapole moment AM 
* P, T-odd interaction of the dipole electric dipole moment  
* nucleus magnetic quadrupole moment

This program begins by reading the file ``CONF.INP`` for system parameters and the list of configurations. Next, basis radial orbitals are read from the file ``CONF.DAT``, and radial integrals for all operators are calculated and written to the file ``DTM.INT``. If this file already exists, ``pdtm`` uses it and does not recalculate the radial integrals. 

For the diagonal matrix elements, the list of determinants and eigenvectors corresponding to the state of interest are read from the files ``CONF.DET`` and ``CONF.XIJ``, respectively. For the non-diagonal matrix elements, the initial state is read from the file ``CONF.DET`` and ``CONF.XIJ``, and the final state is read from the files ``CONF1.DET`` and ``CONF1.XIJ``. The results of the diagonal and non-diagonal matrix elements are written to the files ``DM.RES`` and ``TM.RES``, respectively. 

``pdtm`` takes in the input file ``dtm.in``:

.. code-block:: 

    Mode = (DM, TM, Init)                           # DM - density matrix, TM - transition matrix, Init - form DTM.INT
    Levels = level_range_from (level_range_to)      # from level_range_from to level_range_to
    Operators = E1                                  # form final tables of listed operators

The value of ``Mode`` can take the following values:

* ``DM`` - form density matrix and calculate diagonal matrix elements
* ``TM`` - form transition matrix and calculate non-diagonal matrix elements
* ``Init`` - create the file ``DTM.INT``, which is used for ``rpa_dtm`` and ``pol`` programs

The value of ``Levels`` can take in a range of levels depending on whether ``Mode`` was specified as ``DM`` or ``TM``. The following are some examples.

To calculate DM for energy levels 1 to 5, with a table of g-factors:

.. code-block::

    Mode = DM
    Levels = 1 5
    Operators = GF

To calculate TM for energy levels 1 to 4 from ``CONF.XIJ`` to energy levels 4 to 9 from ``CONF1.XIJ``, with tables of :math:`E1` and :math:`M2` reduced matrix elements:

.. code-block::

    Mode = TM
    Levels = 1 5, 4 9
    Operators = E1, M2

The value of ``Operators`` takes in a list of operators to produce a final table for.

.. note::

    ``Levels`` and ``Operators`` is not read if ``Mode == Init``.

.. note::

    Some :math:`3J`-coefficients might be zero in some cases, such as trying to compute :math:`E1` matrix element for  :math:`5s^2\, {}^1S_0 \rightarrow 5s5p\,{}^3P_1`. This will fail if the odd run had :math:`J=0`, :math:`M_J=0`. One needs to re-run CI with :math:`J=1`, :math:`M_J=1`.


Running dtm
~~~~~~~~~~~

To run parallel ``pdtm``, run the command:

.. code-block:: 

    mpirun -n <nprocs> pdtm