basinfo

This keyword specifies the implementation details of the basis functions.

Options

Theoretical Background

Angular Type of Basis Functions

The analytical form 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 position of the atom.

The angular part \( A_L(\mathbf{r}) \) has two forms:

• Cartesian: expressed as \( x_A^l y_A^m z_A^n \).
• spherical: given by a real solid spherical harmonic function.

Spherical basis sets are more compact and efficient for quantum chemical calculations.

Ghost Atoms

In quantum chemistry, ghost atoms are atoms that have basis functions but no nuclei or electrons. They are commonly used in basis set superposition error (BSSE) calculations to evaluate the interaction between two molecules. Ghost atoms help eliminate the artificial interaction caused by overlapping basis functions.

Although BSSE can be calculated manually using the ghost option, this is usually unnecessary. Qbics handles it automatically through energy decomposition analysis (EDA).

Input Examples

Example: GeH₃F-NCH with Ghost Atoms

For the complex GeH₃F-NCH, calculate the energy with HCN treated as a ghost molecule at the B3LYP/def2-SVP level of theory.

basis
    def2-svp
end

basinfo
    ghost 6-8 # The indices of HCN.
end

scf
    charge  0
    spin2p1 1
    type    R
end

mol
   Ge      0.00000000      0.00221863     -0.79935317
    H      0.00000000      1.48645043     -0.40384625
    H      1.28514604     -0.74161126     -0.40477816
    H     -1.28514603     -0.74161126     -0.40477816
    F      0.00000000      0.00108752     -2.56116087
    C      0.00000000     -0.00225138      3.35662076
    H      0.00000000     -0.00220444      4.43604901
    N      0.00000000     -0.00207825      2.20326200    
end

task
    energy b3lyp
end

The ghost keyword indicates that atoms 6, 7, and 8 (i.e., C, H, and N) are treated as ghost atoms.

In the output, you can see:

# of ghost atoms: 3
 Indices: 6 7 8
 Sum of ghost atom electrons: 14

...    

SCF Structure:
 # of electrons:       44
 # of alpha electrons: 22
 # of beta electrons:  22
 2S+1:                 1

The ghost atoms are listed, and the total number of electrons is 44 — exactly matching the electron count of GeH₃F, confirming that HCN is treated as a ghost molecule.