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pseudopotential

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 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.

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:

# 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:

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:

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:

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:

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

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

The pseudopotential definition 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 \(L\), and number of core electrons.

• Then, the semi-local part (\(V_l(r) (0\le l < L)\), defined by s-f POTENTIAL, etc.) and the local one (\(V_L(r)\), defined by f POTENTIAL) are listed. Each pseudopotential has the form :

  • The first line is a comment.

  • The contraction degree \(K\).

  • Then, each line defines the power \(n_{kl}\) , the exponent \(\xi_{kl}\), and the contraction coefficient \(d_{kl}\). 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.

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 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 standard def2-svp for Ce, H, and O.

Note that, since the pseudopotential has been applied to describe 47 core electrons of Ce ([Kr]4d¹⁰4f¹), the apparant spin multiplicity is 1, greatly simplifying the calculation.

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