basis

This keyword defines the basis functions for quantum chemical calculations and allows flexible definition of basis sets.

Using Built-in Basis Sets

Many important basis sets are provided in the basis directory located in the same path as Qbics. The files are named after the well-known basis sets in the computational chemistry community. For example, basis/cc-pvdz contains the cc-pVDZ basis set. All file names use lowercase letters.

To use them, simply specify the basis set name. It is case-insensitive. For example, to apply def2-TZVP to all atoms:

basis
  def2-TZVP
end

Qbics extracts the basis set information from the file located at basis/def2-tzvp.

Explicit Basis Set Definitions

You can also explicitly define your own basis sets. For example, if your system contains two elements, H and Li, their basis sets can be defined as follows:

basis 
  H     0
  S   3   1.00
        13.0107010             0.19682158E-01
        1.9622572              0.13796524
        0.4445379              0.47831935
  S   1   1.00
        0.12194962             1.0000000
  P   1   1.00
        0.8000000              1.0000000
  ****
  Li     0
  S   5   1.00
        266.27785516           0.64920150325E-02
        40.069783447           0.47747863215E-01
        9.0559944389           0.20268796111
        2.4503009051           0.48606574817
        0.72209571855          0.43626977955
  S   1   1.00
        0.52810884721E-01      1.0000000
  S   1   1.00
        0.20960948798E-01      1.0000000
  P   2   1.00
        1.4500000              0.2586000
        0.3000000              1.0000000
  P   1   1.00
        0.0820000              1.0000000
  ****
end

The analytical expression of a Gaussian basis function is:

$$\chi(\mathbf{r}) = A_{L}(\mathbf{r})\sum_{k=1}^{K} C_k e^{-\alpha_k r_A^2}$$

Here,
• \( A_L(\mathbf{r}) \) is the angular part with angular momentum quantum number \( L \).
• \( K \) is the contraction degree.
• \( \alpha_k \) is the exponent.
• \( C_k \) is the contraction coefficient.
• \( \mathbf{A} \) is the atom position.
.

The basis set definition follows the standard Gaussian94 format:

• Each atom's basis set definition ends with four asterisks (****).
• The definition begins with the element name (e.g., Li) followed by a 0. Currently, the 0 has no functional meaning.
• Each GTO shell is then defined, starting with three values:
  • The angular momentum \( L \), which can be any non-negative integer (e.g., 0, 5) or one of the standard letter notations: S, P, D, F, G, H, or I.
  • The contraction degree \( K \), which must be a positive integer.
  • A real number, currently unused.
  • Following that, each line specifies two real numbers: the exponent \( \alpha_k \) and the contraction coefficient \( C_k \) of each primitive GTO to be contracted.

For more details on basis function expressions, please refer to basinfo.

Using Self-Defined Basis Set Files

You can also store your custom basis set definitions in a file, such as /home/zhang/userdef/my-own-basis. Qbics will automatically read the file if you provide its full path.

basis
  /home/zhang/userdef/my-own-basis
end 

The format can be found in the basis directory.

Defining Different Basis Sets for Different Elements

If you want to assign different basis sets to different elements, start with a line containing the keyword element. Then, list each element followed by its corresponding basis set file name, one per line.
For example:

basis
  element # This indicates that Qbics will assign basis set element by element.
  O aug-cc-pvtz
  C cc-pvtz
  N /home/zhang/userdef/my-own-basis
end

Theoretical Background

Karlsruhe Basis Sets

The Karlsruhe basis sets (def2- series) are a versatile and widely used family in quantum chemistry, known for their balance between accuracy and computational efficiency. They are especially suitable for systems involving heavy elements. For elements with atomic number ≥ Rb, the def2- basis sets include effective core potentials (pseudopotentials), which significantly reduce computational cost while preserving high accuracy in valence electron properties.

In Qbics, the following Karlsruhe basis sets are available:

Here:

• pp: Adds additional polarization functions to both heavy atoms and hydrogen atoms.
• pd: Adds diffuse functions to both heavy atoms and hydrogen atoms.
• ppd: Adds both diffuse functions and additional polarization functions to both heavy atoms and hydrogen atoms.

Dunning Correlation-Consistent Basis Sets

Dunning correlation-consistent basis sets are high-precision basis sets widely used in quantum chemistry, especially for systems with significant electron correlation. These basis sets are designed to ensure consistent treatment of electron correlation across different levels of precision, providing reliable and accurate results.
They are particularly recommended for high-accuracy calculations and for studying excited states.

In Qbics, the following Dunning correlation-consistent basis sets are available:

Here:

• aug: Adds diffuse functions to both heavy atoms and hydrogen atoms.
• c: Adds tight basis functions to describe core electrons.
• wc: Adds even tighter core functions for improved treatment of core electron correlation.

Dunning Correlation-Consistent Basis Sets with Pseudopotentials

Dunning correlation-consistent basis sets with pseudopotentials simplify calculations for heavy elements by replacing core electrons with pseudopotentials. This approach significantly reduces computational cost while maintaining high accuracy for valence electron interactions.

In Qbics, the following Dunning correlation-consistent basis sets with pseudopotentials are available:

Pople Basis Sets

Pople basis sets are widely used in quantum chemical calculations to describe the electronic structure of molecules. They offer an effective balance between computational efficiency and accuracy, particularly for molecules containing elements from hydrogen (H) to calcium (Ca).

The following Pople basis sets are available in Qbics:

Here:

• (d): Adds one set of d functions to heavy atoms.
• (d,p): Adds one set of d functions to heavy atoms and one set of p functions to hydrogen atoms.
• +: Adds s and p diffuse functions to heavy atoms.
• ++: Adds s and p diffuse functions to heavy atoms and s diffuse functions to hydrogen atoms.
• (2df,p): Adds two sets of d functions and one set of f functions to heavy atoms, and two sets of p functions to hydrogen atoms.

STO-nG Basis Sets

In STO-nG basis sets, each atomic orbital is represented using a single-zeta basis, where n Gaussian functions approximate a Slater-type orbital. This approach offers a compact and computationally efficient representation of atomic wavefunctions.

The following STO-nG basis sets are available in Qbics:

Los Alamos National Laboratory Pseudopotentials

The Los Alamos National Laboratory (LANL) basis sets are designed to simplify quantum chemistry calculations involving heavy elements. For all elements with atomic number ≥ 11 (i.e., sodium and heavier), effective core potentials (pseudopotentials) are used to replace core electrons, reducing computational cost while maintaining accuracy.

The following LANL basis sets are available in Qbics:

Here:

• +: Adds d diffuse functions.
• d or f: Adds d or f polarization functions.

Input Examples

Some examples are also provided in the pseudopotential section.

Example: CuH with cc-pVDZ and cc-pVDZ-PP

Below is a calculation example for CuH using both an all-electron correlation-consistent basis set and a correlation-consistent basis set with a pseudopotential. The first example uses the all-electron basis set:

# All electrons for CuH.
basis
    cc-pvdz
end

mol
   Cu     -0.00000000     -0.00000000     -0.23939021
    H      0.00000000      0.00000000      1.23939021
end

task
    opt b3lyp
end

The output is shown below:
The number of electrons is 30, and the optimized bond length is 1.48 Å.

SCF Structure:
 # of electrons:       30
 # of alpha electrons: 15
 # of beta electrons:  15

Now, we use the pseudopotential version:

# Pseudopotentials for Cu, all-electrons for H.
basis
    element
    Cu cc-pvdz-pp
    H  cc-pvdz
end

pseudopotential
   cc-ecp
end

mol
   Cu     -0.00000000     -0.00000000     -0.23939021
    H      0.00000000      0.00000000      1.23939021
end

task
    opt b3lyp
end

The output is shown below:
The number of electrons is 20; 10 core electrons of Cu (corresponding to the Ne core) are replaced by a pseudopotential. The optimized bond length is 1.46 Å.

SCF Structure:
 # of electrons:       20
 # of alpha electrons: 10
 # of beta electrons:  10

Example: AuH with Karlsruhe Basis Set

This example demonstrates how to calculate AuH using a Karlsruhe basis set:

basis
    def2-TZVP
end

pseudopotential
   def2-ecp # If there are elements >= Rb, this must be used!
end

mol
   Au     0. 0. 0.
    H     0. 0. 1.5
end

task
    opt b3lyp
end

Example: AgI with LANL Basis Set

This example demonstrates how to optimize the structure of AgI using a LANL basis set:

basis
   lanl2dz 
end

pseudopotential
    lanl-ecp # For LANL basis set, this should always be set.
end

mol
   Ag     0. 0. 0.
    I     0. 0. 1.5
end

task
    opt b3lyp
end

The output is as follows:
The number of electrons is 26, meaning that 74 electrons were replaced by pseudopotentials. The optimized bond length is 2.65 Å.

SCF Structure:
 # of electrons:       26
 # of alpha electrons: 13
 # of beta electrons:  13

The number of electrons is 26, so 74 electrons were replaced by pseudopotential. The optimized structure has a bond length of 2.65 Angstrom.