# Basis Sets

Basis sets in PSI4 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). 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 PUREAM is set internally from the orbital basis.

- Built-In Basis Sets
- Specifying basis sets
- Built-in basis sets by family
- Built-in basis sets by element
- User-Defined basis sets
- Auxiliary bases for built-in orbital basis sets

## Built-In Basis Sets

A wide range of orbital basis sets are built into PSI4. These are summarized in Tables Pople, Dunning, Dunning (Douglas-Kroll), Karlsruhe, Jensen, and Other in Appendix Basis Sets by Family. 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 \(X\;=\zeta\) 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 Months Bases. Fitting bases in Tables JKFIT, RI, and DUAL are available for methods incorporating density-fitting or dual-basis approximations. JKFIT sets are appropriate for fitting \((oo|\)-type products, such as encountered in SCF theory and the electrostatics/exchange terms of SAPT. RI sets are appropriate for fitting \((ov|\)-type products, such as encountered in MP2 and most SAPT terms. Citations for basis sets can be found in their definition files at psi4/psi4/share/psi4/basis in the source. For basis set availability by element and the default value for keyword PUREAM, consult Appendix Basis Sets by Element.

PSI4 uses the angular momentum convention below that, consistent with EMSL, skips the letter `J`. Note that Gaussian94 convention is not to skip this letter. Another portion of the G94 format, labeling angular momentum with `L=l` syntax is not presently implemented, though this is coming.

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    L:    0123456789...
    Psi4: SPDFGHIKLM...
    G94:  SPDFGHIJKL...

## Mixing Basis Sets

While the above syntax will suffice for specifying basis sets in most cases, the user may need to assign basis sets to specific atoms. To achieve this, a basis “block” can be used. We use a snippet from the mints2 sample input file, which performs a benzene SCF computation, to demonstrate this feature.

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    basis {
       assign DZ
       assign C 3-21G
       assign H1 sto-3g
       assign C1 sto-3g
    }

The first line in this block assigns the DZ basis set to all atoms for the primary/orbital basis. The next line then assigns 3-21G to all carbon atoms, leaving the hydrogens with the DZ basis set. On the third line, the hydrogen atoms which have been specifically labelled as `H1` are given the STO-3G basis set, leaving the unlabelled hydrogen atoms with the DZ basis set. Likewise, the fourth line assigns the STO-3G basis set to just the carbon atoms labelled `C1`. This bizarre example was constructed to demonstrate the syntax, but the flexibility of the basis set specification is advantageous, for example, when selectively omitting diffuse functions to make computations more tractable.

In the above example the basis sets have been assigned asymmetrically, reducing the effective symmetry from \(D_{6h}\) to \(C_{2v}\); PSI4 will detect this automatically and run in the appropriate point group.

Basis blocks can also be named, e.g., `basis optional_basis_name {...}` and the basis defined by it later applied to another molecule.

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    # sets basis keyword
    basis mybas {
        assign aug-cc-pvtz
        assign f cc-pvtz
    }

    # re-sets basis keyword
    set basis aug-cc-pvtz

    molecule hf {
        H
        F 1 1.0
    }

    molecule h2o {
        O
        H 1 1.0
        H 1 1.0 2 90.0
    }

    # runs HF and H2O with aug-cc-pvtz
    energy('hf', molecule=hf)
    energy('hf', molecule=h2o)

    # re-re-sets basis keyword
    set basis mybas

    # runs HF with cc-pvtz on F and aug-cc-pvtz on H
    energy('hf', molecule=hf)

    # runs H2O with aug-cc-pvtz, effectively
    energy('hf', molecule=h2o)

Finally, we note that the `basis {...}` block may also be used for defining basis sets, as detailed in User-Defined Basis Sets.

Calculations requesting density fitting (on by default for many methods) require auxiliary fitting basis set(s) in addition to the primary orbital one associated with the BASIS keyword. When most popular basis sets are being used, including Dunning and Pople-style, the SCF, DF-MP2, and SAPT codes will chose the appropriate auxiliary basis set automatically according to Auxiliary Basis Sets, unless instructed otherwise by setting the auxiliary basis set in the input. Should needed elements be missing from the best auxiliary basis or should the orbital basis be unknown to PSI4, the auxiliary basis will fall back on def2 quad-zeta fitting bases. Note that if BASIS is known to be larger than quad-zeta, PSI4 will not attempt to fall back on the def2 fitting bases.

The same basis “block” syntax can be used to specify basis sets other than that used to define orbitals. For example,

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    set df_basis_mp2 cc-pvdz-ri

     or

    df_basis_mp2 {
       assign cc-pVDZ-RI
    }

are both equivalent ways to set the auxiliary basis set for density fitted MP2 computations. To assign the aug-cc-pVDZ-RI to carbon atoms, the following command is used:

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    df_basis_mp2 {
       assign C aug-cc-pVDZ-RI
    }

## Decontracted Basis Sets

Decontraction of the basis set can be useful in certain situations. In order to decontract a given basis set, simply add “-decon” to the name of the primary basis set (e.g. decontract).

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    set basis cc-pvdz-decon

Obviously this will add significantly to the computational cost of any given calculation, however it can be useful when checking the basis set dependence of a particular calculated property or in certain situations where a large basis set is critical. Currently it is recommended that a decontracted basis is always used when performing relativistic calculations using the X2C Hamiltonian.

## User-Defined Basis Sets

Note

No recompile of the PSI program is necessary for changes made to files in `$PSIDATADIR`, including those described below.

There are three routes by which a basis set in G94 format can be introduced to PSI4’s notice.

(1) Install new basis set file into PSI4 basis library.

Copy the basis set definitions for all elements into a blank file. Exclamation points denote comments. As the first line of the file, add the word `spherical` or `cartesian` to indicate whether the basis set will run in (5D/7F) or (6D/10F).

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    cartesian
    ****
    H     0
    S   3   1.00
          3.42525091             0.15432897
          0.62391373             0.53532814
          0.16885540             0.44463454
    ****
    O     0
    S   3   1.00
        130.7093200              0.15432897
         23.8088610              0.53532814
          6.4436083              0.44463454
    SP   3   1.00
          5.0331513             -0.09996723             0.15591627
          1.1695961              0.39951283             0.60768372
          0.3803890              0.70011547             0.39195739
    ****

Name the file with the name of the basis set and a `.gbs` extension, after applying the following transformations.

- All letters lowercase
- Replace all `*` with `s`
- Replace all `+` with `p`
- Replace all `(` `)` `,` with `_` (underscores replace parentheses and commas)

For example, basis 6-31++G** is stored in psi4/psi4/share/psi4/basis/6-31ppgss.gbs, and cc-pV(D+d)Z is stored in psi4/psi4/share/psi4/basis/cc-pv_dpd_z.gbs. Only one basis set may be specified per file. Copy the new basis set file into psi4/psi4/share/psi4/basis. Request the new basis set in an input file in the usual manner.

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    set basis new_basis_name

(2) Use new basis set file in arbitrary location.

Prepare a basis set file exactly as above. Append the directory containing the basis set file to the environment variable `PSIPATH`.

Request the new basis set in an input file in the usual manner.

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    set basis new_basis_name

(3) Include new basis set in input file.

Construct for a basis set a section like the one below that includes `[basis name]`, PUREAM value, and element basis set specifications. Hash signs denote comments. This format is exactly like the stand-alone basis file except for the addition of the basis name in brackets.

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    [ sto-3g ]
    cartesian
    ****
    H     0
    S   3   1.00
          3.42525091             0.15432897
          0.62391373             0.53532814
          0.16885540             0.44463454
    ****
    O     0
    S   3   1.00
        130.7093200              0.15432897
         23.8088610              0.53532814
          6.4436083              0.44463454
    SP   3   1.00
          5.0331513             -0.09996723             0.15591627
          1.1695961              0.39951283             0.60768372
          0.3803890              0.70011547             0.39195739
    ****

Copy the section into a PSI4 input file and surround it with the command `basis {...}`, as shown below. Multiple basis sets can be specified by adding additional sections within the surrounding brackets. Use `assign` statements to actually request the basis set. This `basis {...}` section replaces the usual `set basis XXX` line. In a more complex input, if the user needs to call the user-defined basis by name, this can be achieved using the syntax `basis mybas {...}`, and then the basis can be recalled later as `set basis mybas`. To use a custom basis set as described in this section, it must be defined prior to its use in a function that performs a computation.

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    basis {

    # assign basset to all atoms and addl to hydrogens
    assign basset
    assign H addl

    # basis set section like in snippet above goes here
    [basset]
    ...

    # additional basis set sections follow
    [addl]
    ...
    }

The test case mints2 provides a complete example of user-specified basis sets.

## Inputting effective core potentials (ECPs)

For ECP containing basis sets, all of the above mechanisms may still be used to input the basis set; simply place the ECP definitions (in G94 format) in the same file or input section as the orbital basis definition. Because the ECP appears in the same section as the orbital basis, it will be parsed automatically and the number of core electrons the ECP represents will be detected, so no further input is required to use a core potential. See Effective core potentials (ECPs) for more information about using ECPs and the Def2-TZVP basis set definition for an example of their input syntax.