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11 Relativistic effects and pseudopotentials

Scalar-relativistic effects can be included explicitly, either by means of the Pauli or the Douglas-Kroll Hamiltonian. In the former case, the effects are evaluated to first order perturbation theory (including the mass-velocity and Darwin terms) by setting

gexpec,rel

at the beginning of the input. The relativistic contributions are stored by the program within the variable erel. An example is ***,Cu ground state

! Pauli Hamiltonian

gexpec,rel !compute relativistic correction using perturbation theory geometry=cu !geometry basis=vtz !basis set hf !Hartree-Fock calculation e_rhf=energy+erel !store total relativistic energy in variable e_rhf

To use the Douglas-Kroll Hamiltonian, one has to specify

dkroll=1

at the beginning of the input. The relativistic contributions are then included as part of the total energies. In this case the example reads ***,Cu ground state

! Douglas-Kroll-Hess Hamiltonian

dkroll=1 !activate Douglas-Kroll tretament geometry=cu !geometry basis=vtz-dk !special DK basis set hf !Hartree-Fock e_rhf=energy !Total relativistic energy

An implicit treatment of scalar-relativistic effects is possible with pseudopotentials (ECPs). In that case, one has to specify ECP parameters and basis sets within basis blocks:

basis={...
ecp,atom,ecpname
spd..,atom,basisname
...}

Often, it is even sufficient to specify a ECP basis-set keyword like

basis=vtz-PP

and this will automatically select the given basis set and the associated pseudopotential. In this case the input for the copper atom calculation could be ***,Cu ground state

! ECP

geometry=cu !geometry basis=vtz-pp !special pseudo potential basis set; this also selects the ECP hf !HF e_rhf=energy !Total energy. This does not include contributions from the core !orbitals that are included in the ECP.

For a list of available ECPs, ECP basis sets, and corresponding keywords, see
http://www.theochem.uni-stuttgart.de/pseudopotentials/index.en.html

Spin-orbit splittings can be calculated by setting up (and diagonalizing) spin-orbit matrices between scalar-relativistic states. The latter have to be calculated and stored within CI calculations:

{ci;...;save,record1.file}
...
{ci;...;save,recordn.file}

In all-electron calculations, one proceeds with the calculation of SO integrals

lsint

(For ECP calculation, this is not needed.)

Generating and processing of SO matrices is done with

{ci;hlsmat,keyword3,record1.file,..,recordn.file}

where keyword3 is ls or ecp for all-electron or ECP calculations, respectively.

An example input with ECPs is ***,Br geometry=br basis=vtz-pp rhf;wf,sym=5 multi;wf,sym=2;wf,sym=3;wf,sym=5 !2P states, state averaged ci;wf,sym=2;save,5101.2 !2Px state ci;wf,sym=3;save,5102.2 !2Py state ci;wf,sym=5;save,5103.2 !2Pz state ci;hlsmat,ls,5101.2,5102.2,5103.2 !compute and diagonalize SO matrix

The corresponding input for an all-electron calculation is

***,Br dkroll=1 geometry=br basis=vtz-dk rhf;wf,sym=5 multi;wf,sym=2;wf,sym=3;wf,sym=5 !2P states, state averaged lsint !Compute spin-orbit 2-electron integrals ci;wf,sym=2;save,6101.2 !2Px state ci;wf,sym=3;save,6102.2 !2Py state ci;wf,sym=5;save,6103.2 !2Pz state ci;hlsmat,ls,6101.2,6102.2,6103.2 !compute and diagonalize SO matrix

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