Accuracies for uncontracted vs larger-zeta auxillary basis in two-component calculations

1

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

2

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.

3

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)