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pseudopotential

pseudopotential

This keyword defines the pseudopotentials used in quantum chemistry calculations. Pseudopotentials can be specified in several flexible ways.

Warning

The pseudopotential keyword includes only the pseudopotential data and does not contain any valence electron basis set information. You must assign the basis set separately using the basis keyword. The valence basis set and core pseudopotential must be consistent — see basis for details.

A typical example: hydrogen (H) is assigned the def2-TZVP basis set. For gold (Au), the valence electrons are described by the def2-TZVP basis set, and the core electrons are represented by the def2-ecp pseudopotential (i.e., Stuttgart-Cologne pseudopotential).

Warning

If you write it incorrectly as shown below, then no pseudopotential will be applied to any element!

Also, keep in mind that the valence basis set and core pseudopotential must be compatible. The following combinations are commonly accepted:

Valence Basis Set Pseudopotential
def2-X def2-ecp
(aug-)cc-X-pp cc-ecp
lanlX lanl-ecp

Using Built-in Pseudopotentials

A collection of important pseudopotentials is provided in the pseudopotential folder located in the same directory as Qbics. The files are named according to their well-known names in the computational chemistry community. For example, pseudopotential/def2-ecp contains the Stuttgart-Cologne pseudopotentials. All file names are in lowercase.

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

Qbics will extract pseudopotential information from pseudopotential/def2-ecp for all atoms for which pseudopotentials are defined.
For example, if your molecule contains only C, H, N, Ce, and F, and the file pseudopotential/sdd includes a pseudopotential only for Ce, then no pseudopotentials will be applied to C, H, N, and F.

Explicit Pseudopotential Definitions

You can also explicitly define your pseudopotentials.
For example, if you want to apply pseudopotentials to Rb and Sr, you can define them as follows:

The analytical expression of the pseudopotential is:


$$V(\mathbf{r}) = V_L(r)+\sum_{l=0}^{L-1}V_l(r)\sum_{m=-l}^{+l}\left|S_{lm}\right\rangle\left\langle S_{lm}\right|$$

$$V_l(r) = \sum_{k=1}^{K}d_{kl}r^{n_{kl}}e^{-\xi_{kl}r^2}$$

The pseudopotential definition follows the standard Gaussian94 format:

  • The definition for each atom ends with four asterisks (****).
  • It begins with the element name (e.g., Rb) followed by a 0. (The 0 currently has no functional meaning.)
  • Next, three parameters are provided: the pseudopotential name, the maximum angular momentum quantum number L, and the number of core electrons.
  • This is followed by the semi-local part (Vl(r), for 0 ≤ l < L, defined by blocks such as s-f POTENTIAL) and the local part (VL(r), defined by f POTENTIAL). Each pseudopotential block has the following structure:
    • A comment line.
    • The contraction degree K.
    • Then, K lines each containing three real numbers: (1) Power nkl; (2) Exponent ξkl; (3) Contraction coefficient dkl.
Hint

Pseudopotentials in Gaussian94 format can be obtained from various external sources.

However, be sure to replace D with E, as D is not recognized by Qbics. Also, remember to insert **** between definitions for different elements.

Using Self-defined Pseudopotential Files

You can also place your explicit pseudopotential definitions in a file, such as /home/zhang/userdef/my-own-pseudopotential. Qbics will automatically read the file if you provide the full file name including the path.

Theoretical Background

Pseudopotentials are widely used in 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. This approach reduces the size of the required basis set and allows the inclusion of relativistic effects at a non-relativistic level.

Input Examples

Some examples are also given in basis.

Example: Using Explicitly Defined Pseudopotentials for Ce(H2O)83+

Below is an example of calculating Ce(H2O)83+ using explicitly defined pseudopotentials for Ce and the standard def2-SVP basis set for Ce, H, and O.

Note that since the pseudopotential accounts for the 47 core electrons of Ce ([Kr]4d104f1), the apparent spin multiplicity is 1, which greatly simplifies the calculation.