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13.1 Scalar relativistic effects

Scalar-relativistic effects can be included explicitly, either by means of the Pauli, the Douglas-Kroll-Hess, or eXact-2-Component Hamiltonians. In the first case, the effects are evaluated to first order in perturbation theory (including the mass-velocity and Darwin terms) by setting


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 2nd-order Douglas-Kroll-Hess Hamiltonian, one has to specify


at the beginning of the input (note that the order can range from 2 to 99). 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

dkho=2         !activate 2nd-order Douglas-Kroll-Hess tretament
geometry={cu}  !geometry
basis=vtz-dk   !special DK basis set (mandatory!)
hf             !Hartree-Fock
e_rhf=energy   !Total relativistic energy

To use the eXact-2-Component (X2C) Hamiltonian, one has to specify


In this case the DK contracted basis sets can also be used, but special X2C contracted basis sets are prefered, e.g., vtz-x2c. These will be available soon. 2017-12-12