
.. include:: autodoc_abbr_options_c.rst

.. index:: basis set; available by family
.. _`sec:basisBuiltIn`:

==========
Basis Sets
==========

Basis sets in |PSIfour| are Gaussian functions (not Slater-type functions or plane waves),
all-electron [no effective core potentials (ECPs)],
and of Gaussian94 format (for ease of export from `EMSL <https://bse.pnl.gov/bse/portal>`_).
Both spherical harmonic (5D/7F) and Cartesian (6D/10F) Gaussian functions are supported,
but their mixtures are not, neither within a basis set (*e.g.*, 6D/7F) nor within a calculation
(*e.g.*, cartesian for the orbital basis and spherical for the fitting basis).
For built-in basis sets, the correct ``spherical``/``cartesian`` value for |globals__puream|
is set internally from the orbital basis.

* :ref:`Specifying basis sets <sec:jobControl>`
* Built-in basis sets by family (below)
* :ref:`Built-in basis sets by element <apdx:basisElement>`
* :ref:`User-Defined basis sets <sec:basisUserDefined>`
* :ref:`Auxiliary bases for built-in orbital basis sets <apdx:basisFamily>`


Tables :ref:`Pople <table:basisPopleOrbital>`,
:ref:`Dunning <table:basisDunningOrbital>`, 
:ref:`Dunning (Douglas-Kroll) <table:basisDunningDK>`, and
:ref:`Other <table:basisOther>` summarize the orbital basis sets available in
|PSIfour|.  These tables are arranged so that columns indicate degree of
augmentation by diffuse functions (generally necessary for anions, excited
states, and noncovalent interactions) and DTQ56 indicate the :math:`X\;=\zeta` levels
available.  Several intermediate levels of diffuse space between the customary
non-augmented and augmented versions have been supplied for each basis set,
including heavy-augmented and Truhlar's [Papajak:2011:10]_ calendar
truncations described in Table :ref:`Months Bases <table:basisMonths>`.  Fitting bases 
in Tables :ref:`JKFIT <table:basisDunningJKFIT>`,
:ref:`RI <table:basisDunningMP2FIT>`, and :ref:`DUAL <table:basisDunningDUAL>`
are available for methods incorporating density-fitting or dual-basis
approximations. JKFIT sets are appropriate for fitting :math:`(oo|`\ -type products,
such as encountered in SCF theory and the electrostatics/exchange terms of SAPT.
RI sets are appropriate for fitting :math:`(ov|`\ -type products, such as encountered in
MP2 and most SAPT terms.  Citations for basis sets can be found in their
definition files at :source:`lib/basis` in the source.  For basis set availability by
element and the default value for keyword |globals__puream|, consult
Appendix :ref:`apdx:basisElement`.

|
|

.. _`table:basisPopleOrbital`:

.. table:: Summary of Pople-style orbital basis sets available in |PSIfour| [#f1]_

    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | no diffuse                     | heavy-augmented                  | augmented                          |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | basis set       | [alias]      | basis set        | [alias]       | basis set         | [alias]        |
    +=================+==============+==================+===============+===================+================+
    | STO-3G          |              |                  |               |                   |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 3-21G           |              |                  |               |                   |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-31G           |              | 6-31+G           |               | 6-31++G           |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-31G(d)        | [6-31G\*]    | 6-31+G(d)        | [6-31+G\*]    | 6-31++G(d)        | [6-31++G\*]    |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-31G(d_p)      | [6-31G\*\*]  | 6-31+G(d_p)      | [6-31+G\*\*]  | 6-31++G(d_p)      | [6-31++G\*\*]  |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G          |              | 6-311+G          |               | 6-311++G          |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(d)       | [6-311G\*]   | 6-311+G(d)       | [6-311+G\*]   | 6-311++G(d)       | [6-311++G\*]   |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(d_p)     | [6-311G\*\*] | 6-311+G(d_p)     | [6-311+G\*\*] | 6-311++G(d_p)     | [6-311++G\*\*] |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(2d)      |              | 6-311+G(2d)      |               | 6-311++G(2d)      |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(2d_p)    |              | 6-311+G(2d_p)    |               | 6-311++G(2d_p)    |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(2d_2p)   |              | 6-311+G(2d_2p)   |               | 6-311++G(2d_2p)   |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(2df)     |              | 6-311+G(2df)     |               | 6-311++G(2df)     |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(2df_p)   |              | 6-311+G(2df_p)   |               | 6-311++G(2df_p)   |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(2df_2p)  |              | 6-311+G(2df_2p)  |               | 6-311++G(2df_2p)  |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(2df_2pd) |              | 6-311+G(2df_2pd) |               | 6-311++G(2df_2pd) |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(3df)     |              | 6-311+G(3df)     |               | 6-311++G(3df)     |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(3df_p)   |              | 6-311+G(3df_p)   |               | 6-311++G(3df_p)   |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(3df_2p)  |              | 6-311+G(3df_2p)  |               | 6-311++G(3df_2p)  |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(3df_2pd) |              | 6-311+G(3df_2pd) |               | 6-311++G(3df_2pd) |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+
    | 6-311G(3df_3pd) |              | 6-311+G(3df_3pd) |               | 6-311++G(3df_3pd) |                |
    +-----------------+--------------+------------------+---------------+-------------------+----------------+

|
|

.. _`table:basisMonths`:

.. table:: Levels of truncation for diffuse functions in standard basis sets

    +--------------------------+--------------------------------------------------------------------------------------+--------------------------------------------+------------------+------------------+------------------+
    | augmentation level       | angular momenta in the diffuse space [#f4]_                                                                                       | valid basis sets                                       |
    +--------------------------+--------------------------------------------------------------------------------------+--------------------------------------------+------------------+------------------+------------------+
    |                          | Li-Kr main group                                                                     | H & He                                     | D\ :math:`\zeta` | T\ :math:`\zeta` | Q\ :math:`\zeta` |
    +==========================+======================================================================================+============================================+==================+==================+==================+
    | aug-cc-pVXZ              | s, p, :math:`\cdots`, :math:`\ell_{max}-2`, :math:`\ell_{max}-1`, :math:`\ell_{max}` | s, p, :math:`\cdots`, :math:`\ell_{max}-1` |  aDZ             |  aTZ             |  aQZ             |
    +--------------------------+--------------------------------------------------------------------------------------+--------------------------------------------+------------------+------------------+------------------+
    | heavy-aug-cc-pVXZ [#f2]_ | s, p, :math:`\cdots`, :math:`\ell_{max}-2`, :math:`\ell_{max}-1`, :math:`\ell_{max}` |                                            | haDZ             | haTZ             | haQZ             |
    +--------------------------+--------------------------------------------------------------------------------------+--------------------------------------------+------------------+------------------+------------------+
    | jun-cc-pVXZ              | s, p, :math:`\cdots`, :math:`\ell_{max}-2`, :math:`\ell_{max}-1`                     |                                            | jaDZ             | jaTZ             | jaQZ             |
    +--------------------------+--------------------------------------------------------------------------------------+--------------------------------------------+------------------+------------------+------------------+
    | may-cc-pVXZ              | s, p, :math:`\cdots`, :math:`\ell_{max}-2`                                           |                                            |                  | maTZ             | maQZ             |
    +--------------------------+--------------------------------------------------------------------------------------+--------------------------------------------+------------------+------------------+------------------+
    | :math:`\cdots`           | s, p                                                                                 |                                            |                  |                  | aaQZ             |
    +--------------------------+--------------------------------------------------------------------------------------+--------------------------------------------+------------------+------------------+------------------+
    | cc-pVXZ                  |                                                                                      |                                            |   DZ             |   TZ             |               QZ |
    +--------------------------+--------------------------------------------------------------------------------------+--------------------------------------------+------------------+------------------+------------------+


|
|

.. _`table:basisDunningOrbital`:

.. table:: Summary of Dunning orbital basis sets available in |PSIfour|

    +---------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | basis set     | no diffuse | feb | mar | apr | may  | jun   | heavy-aug [#f2]_ | aug   | d-aug |
    +===============+============+=====+=====+=====+======+=======+==================+=======+=======+
    | cc-pVXZ       | DTQ56      | 6   | 56  | Q56 | TQ56 | DTQ56 | DTQ56            | DTQ56 | DTQ56 |
    +---------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pV(X+d)Z   | DTQ56      | 6   | 56  | Q56 | TQ56 | DTQ56 | DTQ56            | DTQ56 | DTQ56 |
    +---------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pCVXZ      | DTQ56      | 6   | 56  | Q56 | TQ56 | DTQ56 | DTQ56            | DTQ56 | DTQ56 |
    +---------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pCV(X+d)Z  | DTQ56      | 6   | 56  | Q56 | TQ56 | DTQ56 | DTQ56            | DTQ56 | DTQ56 |
    +---------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pwCVXZ     | DTQ5       |     | 5   | Q5  | TQ5  | DTQ5  | DTQ5             | DTQ5  | DTQ5  |
    +---------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pwCV(X+d)Z | DTQ5       |     | 5   | Q5  | TQ5  | DTQ5  | DTQ5             | DTQ5  | DTQ5  |
    +---------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+

|
|

.. _`table:basisDunningDK`:

.. table:: Summary of Dunning Douglas-Kroll orbital basis sets available in |PSIfour|

    +------------------+------------+-----+-----+-----+-----+-----+------------------+--------+-------+
    | basis set        | no diffuse | feb | mar | apr | may | jun | heavy-aug [#f2]_ | aug    | d-aug |
    +==================+============+=====+=====+=====+=====+=====+==================+========+=======+
    | cc-pVXZ-DK       | DTQ5       |     |     |     |     |     | DTQ5             | DTQ5   |       |
    +------------------+------------+-----+-----+-----+-----+-----+------------------+--------+-------+
    | cc-pV(X+d)Z-DK   |            |     |     |     |     |     |                  |        |       |
    +------------------+------------+-----+-----+-----+-----+-----+------------------+--------+-------+
    | cc-pCVXZ-DK      | DTQ5       |     |     |     |     |     | DTQ5             | DTQ5   |       |
    +------------------+------------+-----+-----+-----+-----+-----+------------------+--------+-------+
    | cc-pCV(X+d)Z-DK  |            |     |     |     |     |     |                  |        |       |
    +------------------+------------+-----+-----+-----+-----+-----+------------------+--------+-------+
    | cc-pwCVXZ-DK     | --TQ5      |     |     |     |     |     | --TQ5            | --TQ5  |       |
    +------------------+------------+-----+-----+-----+-----+-----+------------------+--------+-------+
    | cc-pwCV(X+d)Z-DK |            |     |     |     |     |     |                  |        |       |
    +------------------+------------+-----+-----+-----+-----+-----+------------------+--------+-------+

|
|

.. _`table:basisDunningJKFIT`:

.. table:: Summary of Dunning JK-fitting basis sets available in |PSIfour|

    +------------------------+------------+-----+-----+-----+-----+-----+------------------+------+-------+
    | basis set              | no diffuse | feb | mar | apr | may | jun | heavy-aug [#f2]_ | aug  | d-aug |
    +========================+============+=====+=====+=====+=====+=====+==================+======+=======+
    | cc-pVXZ-JKFIT [#f3]_   | DTQ5       |     | 5   | Q5  | TQ5 | DTQ5| DTQ5             | DTQ5 |       |
    +------------------------+------------+-----+-----+-----+-----+-----+------------------+------+-------+
    | cc-pV(X+d)Z-JKFIT      | DTQ5       |     | 5   | Q5  | TQ5 | DTQ5| DTQ5             | DTQ5 |       |
    +------------------------+------------+-----+-----+-----+-----+-----+------------------+------+-------+
    | cc-pCVXZ-JKFIT [#f3]_  |            |     |     |     |     |     |                  |      |       |
    +------------------------+------------+-----+-----+-----+-----+-----+------------------+------+-------+
    | cc-pCV(X+d)Z-JKFIT     |            |     |     |     |     |     |                  |      |       |
    +------------------------+------------+-----+-----+-----+-----+-----+------------------+------+-------+
    | cc-pwCVXZ-JKFIT [#f3]_ |            |     |     |     |     |     |                  |      |       |
    +------------------------+------------+-----+-----+-----+-----+-----+------------------+------+-------+
    | cc-pwCV(X+d)Z-JKFIT    |            |     |     |     |     |     |                  |      |       |
    +------------------------+------------+-----+-----+-----+-----+-----+------------------+------+-------+

|
|

.. _`table:basisDunningMP2FIT`:

.. table:: Summary of Dunning MP2-fitting basis sets available in |PSIfour|

    +------------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | basis set        | no diffuse | feb | mar | apr | may  | jun   | heavy-aug [#f2]_ | aug   | d-aug |
    +==================+============+=====+=====+=====+======+=======+==================+=======+=======+
    | cc-pVXZ-RI       | DTQ56      | 6   | 56  | Q56 | TQ56 | DTQ56 | DTQ56            | DTQ56 |       |
    +------------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pV(X+d)Z-RI   | DTQ56      | 6   | 56  | Q56 | TQ56 | DTQ56 | DTQ56            | DTQ56 |       |
    +------------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pCVXZ-RI      |            |     |     |     |      |       |                  |       |       |
    +------------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pCV(X+d)Z-RI  |            |     |     |     |      |       |                  |       |       |
    +------------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pwCVXZ-RI     | DTQ5       |     | 5   | Q5  | TQ5  | DTQ5  | DTQ5             | DTQ5  |       |
    +------------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+
    | cc-pwCV(X+d)Z-RI | DTQ5       |     | 5   | Q5  | TQ5  | DTQ5  | DTQ5             | DTQ5  |       |
    +------------------+------------+-----+-----+-----+------+-------+------------------+-------+-------+

|
|

.. _`table:basisDunningDUAL`:

.. table:: Summary of Dunning dual-basis helper basis sets available in |PSIfour|

    +----------------------+------------+-----+-----+-----+-----+-----+------------------+-----+-------+
    | basis set            | no diffuse | feb | mar | apr | may | jun | heavy-aug [#f2]_ | aug | d-aug |
    +======================+============+=====+=====+=====+=====+=====+==================+=====+=======+
    | cc-pVXZ-DUAL         | TQ         |     |     |     |     |     | TQ               | DTQ |       |
    +----------------------+------------+-----+-----+-----+-----+-----+------------------+-----+-------+
    | cc-pV(X+d)Z-DUAL     |            |     |     |     |     |     |                  |     |       |
    +----------------------+------------+-----+-----+-----+-----+-----+------------------+-----+-------+
    | cc-pCVXZ-DUAL        |            |     |     |     |     |     |                  |     |       |
    +----------------------+------------+-----+-----+-----+-----+-----+------------------+-----+-------+
    | cc-pCV(X+d)Z-DUAL    |            |     |     |     |     |     |                  |     |       |
    +----------------------+------------+-----+-----+-----+-----+-----+------------------+-----+-------+
    | cc-pwCVXZ-DUAL       |            |     |     |     |     |     |                  |     |       |
    +----------------------+------------+-----+-----+-----+-----+-----+------------------+-----+-------+
    | cc-pwCV(X+d)Z-DUAL   |            |     |     |     |     |     |                  |     |       |
    +----------------------+------------+-----+-----+-----+-----+-----+------------------+-----+-------+

|
|

.. _`table:basisOther`:

.. table:: Summary of other orbital basis sets available in |PSIfour|

    +--------------+-------------+----------------+
    | Karlsruhe                  | other          |
    +--------------+-------------+----------------+
    | no diffuse   | augmented   |                |
    +==============+=============+================+
    | def2-SV(P)   |             | DZP            |
    +--------------+-------------+----------------+
    | def2-SVP     | def2-SVPD   | TZ2P           |
    +--------------+-------------+----------------+
    | def2-TZVP    | def2-TZVPD  | TZ2PF          |
    +--------------+-------------+----------------+
    | def2-TZVPP   | def2-TZVPPD | Sadlej-LPol-ds |
    +--------------+-------------+----------------+
    | def2-QZVP    | def2-QZVPD  | Sadlej-LPol-dl |
    +--------------+-------------+----------------+
    | def2-QZVPP   | def2-QZVPPD | Sadlej-LPol-fs |
    +--------------+-------------+----------------+
    |              |             | Sadlej-LPol-fl |
    +--------------+-------------+----------------+

|
|

.. rubric:: Footnotes

.. [#f1] Absolutely no commas are allowed in basis set specification. Use the underscore character instead.
.. [#f2] The heavy-aug-cc-\ *stub* and jul-cc-\ *stub* basis sets are identical.
.. [#f3] The JKFIT basis sets are designed in the cc-\ *stub*\ (X+d)Z 
         framework that includes an additional set of
         *d*-fuctions for second-row *p*-block elements. Identical basis sets
         with the cc-\ *stub*\ XZ-JKFIT label are provided for convenience.
.. [#f4] D\ :math:`\zeta` has :math:`\ell_{max}=2` or d.
         T\ :math:`\zeta` has :math:`\ell_{max}=3` or f.
         Q\ :math:`\zeta` has :math:`\ell_{max}=4` or g, *etc*.

