.. tip:: All input files can be downloaded: :download:`Files `. pseudopotential =============== .. contents:: :local: This keyword defines the pseudopotentials used for quantum chemistry calculations. You can define pseudopotentials in several flexible ways. .. WARNING:: ``pseudopotential`` **only** contains pseudopotential and does not contain any valence electron basis set information. You must assign basis sets in ``basis``. The valence basis and core pseudopotential **must match**. See :doc:`basis`. Below is a typical example. H is represented by a def2-TZVP basis set. For Au, the valence electrons are represented by a def2-TZVP basis set, and core electrons are repesented by def2-ecp, i.e. Stuggart-Cologne pseudopotential. .. code-block:: bash :linenos: basis def2-TZVP end pseudopotential def2-ecp end # The Karlsruhe basis sets for Au was developed with Stuggart-Cologne pseudopotential. mol Au 0. 0. 0. # SDD+def2-TZVP H 0. 0. 1. # def2-TZVP end .. warning:: If you write it in this **WRONG** way: .. code-block:: bash :linenos: # A wrong input! basis def2-TZVP end mol Au 0. 0. 0. H 0. 0. 1. end Then, **NO** pseudopotential is applied for any element! Also, keep in mind that the valence basis and core pseudopotential **must match**. The following combinations are usually accepted: .. list-table:: :widths: 8 8 :header-rows: 1 * - Valence Basis Set - Pseudopotential * - def2-X - def2-ecp * - (aug-)cc-X-pp - cc-ecp * - lanlX - lanl-ecp Using Built-in Pseudopotentials -------------------------------- A lot of important pseudopotentials have been provided in a folder ``pseudopotential`` in the same path of Qbics. The files are named after their names well-known in computational chemistry community. For example, ``pseudopotential/def2-ecp`` contains the Stuggart-Cologne pseudopotentials. All files are named in small cases. To use them, simple write down the basis set name. It is case-insensitive. For example, to use def2-ecp: .. code-block:: bash :linenos: pseudopotential def2-ecp end Qbics will extract pseudopotential information from ``pseudopotential/def2-ecp`` for all atoms that **have pseudopotentials**. For example, you molecule contains only C, H, N, Ce, and F. Since in ``pseudopotential/sdd``, there is only pseudopotential for Ce, then for C, H, N, and F, no pseudopotentials are applied. Explicit Pseudopotential Definitions ------------------------------------- You can also explicitly define your pseudopotentials. For example, you want to apply pseudopotentials for Rb and Sr, then their pseudopotentials can be defined in this way: .. code-block:: bash :linenos: pseudopotential RB 0 RB-ECP 3 28 f POTENTIAL 1 2 3.84311400 -12.31690000 s-f POTENTIAL 3 2 5.03655100 89.50019800 2 1.97084900 0.49376100 2 3.84311400 12.31690000 p-f POTENTIAL 3 2 4.25834100 58.56897400 2 1.47070900 0.43179100 2 3.84311400 12.31690000 d-f POTENTIAL 3 2 3.02312700 26.22489800 2 0.65038300 0.96283900 2 3.84311400 12.31690000 **** SR 0 SR-ECP 3 28 f POTENTIAL 1 2 4.63397500 -15.80599200 s-f POTENTIAL 3 2 7.40007400 135.47943000 2 3.60637900 17.53446300 2 4.63397500 15.80599200 p-f POTENTIAL 3 2 6.48486800 88.35970900 2 3.28805300 15.39437200 2 4.63397500 15.80599200 d-f POTENTIAL 3 2 4.62284100 29.88898700 2 2.24690400 6.65941400 2 4.63397500 15.80599200 **** end The analyitcal expression of pseudopotential is: .. math:: V(\mathbf{r}) = V_L(r)+\sum_{l=0}^{L-1}V_l(r)\sum_{m=-l}^{+l}\left|S_{lm}\right\rangle\left\langle S_{lm}\right| .. math:: V_l(r) = \sum_{k=1}^{K}d_{kl}r^{n_{kl}}e^{-\xi_{kl}r^2} The pseudopotential definition is of standard Gaussian94 format: - The definition of the pseudopotential for each atom ends with 4 asterisks, i.e. ``****``. - The definition starts with the element name like ``Rb`` and a ``0``. Currently ``0`` has no meaning. - Then, three parameters are given: pseudopotential name, maximum angular momentum :math:`L`, and number of core electrons. - Then, the semi-local part (:math:`V_l(r) (0\le l < L)`, defined by ``s-f POTENTIAL``, etc.) and the local one (:math:`V_L(r)`, defined by ``f POTENTIAL``) are listed. Each pseudopotential has the form : * The first line is a comment. * The contraction degree :math:`K`. * Then, each line defines the power :math:`n_{kl}` , the exponent :math:`\xi_{kl}`, and the contraction coefficient :math:`d_{kl}`. They are 3 real numbers. .. hint:: Pseudopotentials in Gaussian94 format can be obtained from: - https://www.basissetexchange.org/ - https://www.cosmologic-services.de/basis-sets/basissets.php - https://www.tc.uni-koeln.de/PP/clickpse.en.html But, remember to replace ``D`` to ``E`` since the former is not recognized by Qbics. Also, add ``****`` between elements. Using Self-defined Pseudopotential Files ------------------------------------------ You can also put your explicit pseudopotential definitions into some files, say ``/home/zhang/userdef/my-own-pseudopotential``. Qbics will automatically read it if you give explicit file name including path. .. code-block:: bash :linenos: pseudopotential /home/zhang/userdef/my-own-pseudopotential end Theoretical Background ------------------------- Pseudopotential is widely used in the fields of quantum chemistry, atomic physics, solid state physics, and computational materials science. The basic idea is to replace the influence of the nucleus and core electrons on the valence electrons with an effective potential. It can reduce the size of the basis set and also include relativistic effects on a non-relativistic level. Input Examples ------------------------- Some examples are also given in :doc:`basis`. Example: Using Explicitly Defined Pseudopotentials for Ce(H\ :sub:`2`\ O)\ :sub:`8`\ :sup:`3+` ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Below is an example of calculating Ce(H\ :sub:`2`\ O)\ :sub:`8`\ :sup:`3+` using explicitly defined pseudopotentials for Ce and standard def2-svp for Ce, H, and O. Note that, since the pseudopotential has been applied to describe 47 core electrons of Ce ([Kr]4d\ :sup:`10`\ 4f\ :sup:`1`), the apparant spin multiplicity is ``1``, greatly simplifying the calculation. .. code-block:: bash :linenos: :caption: pseudopotential-1.inp basis def2-svp end pseudopotential Ce 0 ECP47MWB 4 47 G-Komponente 1 2 1.000000 0.000000 S-G 2 2 3.522200 95.842155 2 1.761100 -3.775040 P-G 2 2 3.017700 68.092779 2 1.508900 -0.966756 D-G 2 2 2.144300 36.381848 2 1.072200 0.190447 F-G 1 2 4.278500 -40.585328 **** end grimmedisp type bj end scf charge +3 spin2p1 1 end mol Ce -0.0000088 0.0000037 -0.0006635 O 1.8174770 -1.1442674 -1.3565307 O 2.0940885 0.4762325 1.3551096 O 0.4762019 -2.0941013 1.3550928 O -1.1442759 -1.8174502 -1.3565612 O -1.8174735 1.1443092 -1.3565265 O -2.0941079 -0.4762528 1.3550846 O 1.1442883 1.8174686 -1.3565204 O -0.4762411 2.0940836 1.3551277 H -2.7384080 -1.1961061 1.2400375 H -2.4318208 0.0300465 2.1143243 H -1.6982474 1.7415082 -2.1154550 H -2.7821029 1.0904008 -1.2419254 H 0.0300785 2.4317909 2.1143563 H -1.1960900 2.7383918 1.2400978 H 2.7383924 1.1960849 1.2400788 H 2.4317951 -0.0300811 2.1143427 H 1.6982634 -1.7414504 -2.1154737 H 2.7821042 -1.0903611 -1.2419111 H -1.0903471 -2.7820826 -1.2419964 H -1.7414853 -1.6982065 -2.1154789 H 1.7415073 1.6982406 -2.1154327 H 1.0903589 2.7820987 -1.2419353 H 1.1960541 -2.7384032 1.2400470 H -0.0301159 -2.4318311 2.1143124 end task energy b3lyp end