As described in Scalar relativistic Hamiltonians

The X2C module in PSI4 supports different combinations of basis set. By default, if the input file specifies only BASIS, then the X2C module will solve the modified Dirac equation in an uncontracted basis and then recontract the X2C Hamiltonian in the original basis. Alternatively, the user can use BASIS_RELATIVISTIC to specify a different basis set to solve the modified Dirac equation.

set {

basis cc-pvdz-dk

basis_relativistic cc-pvtz-dk

relativistic x2c

}

Is there any literature on comparing about the accuracy in the above two ways of building auxiliary basis set (de-contraction/triple zeta basis set)? I can do some benchmark on my own, but if there is any published result would be more convenient.

Thank you very much

It’s not really a question of an auxiliary basis set; rather the issue is that when you run a relativistic calculation, the core orbitals can change significantly. If you use a basis set that has already been designed for a relativistic method (like the -dk basis sets in the above example), you should be in the clear.

I am not familiar with the theories. The manual puts

```
BASIS_RELATIVISTIC
Auxiliary basis set for solving Dirac equation in X2C and DKH calculations. Defaults to decontracted orbital basis.
```

I guess some matrix elements in two-component methods require auxiliary basis set to compute (maybe I am wrong)

The input

```
molecule {
H
F 1 0.92
}
set {
scf_type pk
basis cc-pvdz-dk
relativistic x2c
}
energy('hf')
```

leads to

`Total Energy = -100.1054542650154673`

and

```
molecule {
H
F 1 0.92
}
set {
scf_type pk
basis cc-pvdz-dk
basis_relativistic cc-pvtz-dk
relativistic x2c
}
energy('hf')
```

leads to

`Total Energy = -100.0916326054318688`

and

```
molecule {
H
F 1 0.92
}
set {
scf_type pk
basis cc-pvdz-dk
basis_relativistic cc-pvtz-dk-decon
relativistic x2c
}
energy('hf')
```

leads to

` Total Energy = -100.0968526836019947`

and

```
molecule {
H
F 1 0.92
}
set {
scf_type pk
basis cc-pvdz-dk
basis_relativistic cc-pvqz-dk-decon
relativistic x2c
}
energy('hf')
```

leads to

` Total Energy = -100.1083697741510719`

and

```
molecule {
H
F 1 0.92
}
set {
scf_type pk
basis cc-pvdz-dk
basis_relativistic cc-pv5z-dk-decon
relativistic x2c
}
energy('hf')
```

leads to

` Total Energy = -100.1069842160752756`

(all in `PSI4 1.6.1`

)

So there is a question about what is the best choice for `basis_relativistic`

(balancing accuracy and efficiency, maybe decontract the basis is fine. I would like to see some benchmark literature on it)