Relativistic Effects

The following approaches to treat relativistic effects are available in DALTON:

ECP

The Effective Core Potential approach of Pitzer and Winter [102] is available for single-point calculations by asking for ECP as the basis set for the chosen element. So far, only a limited set of elements is covered by the basis set library. See the rsp_ecp example in the test-suite. The corresponding spin-orbit operators are not implemented.

Douglas-Kroll

The Douglas-Kroll scalar relativistic one-electron integrals are available by adding the .DOUGLAS-KROLL keyword

**DALTON INPUT
.DOUGLAS-KROLL
.RUN WAVE FUNCTIONS
....

See also the energy_douglaskroll example in the test suite.

NOTE: Exact analytical gradients and Hessians are not available at the moment, the approximate gradient and Hessians does, however, give fairly accurate geometries. For this approach, only basis sets should be used where the contraction coefficients were optimized including the Douglas-Kroll operators. DALTON currently provides: DK-Pol (relativistic version of Sadlej's POL basis sets), raf-r for some heavy elements, and the relativistically recontracted correlation-consistent basis sets of Dunning (cc-pVXZ-DK, X=D,T,Q,5). The combination with property operators should be done with care, e.g. the standard magnetic property operators are not suitable in this case.

Spin-orbit Mean-Field

The spin-orbit mean-field approach can be used for either replacing the Breit-Pauli spin-orbit operator, or as an operator with suitable relativistic corrections in combination with the Douglas-Kroll approach. It is based on an effective one-electron operator, where the two-electron terms are summed in a way comparable to the Fock operator [103]. As all multi-center integrals are neglected, this scheme is very fast, avoids the storage of the two-electron spin-orbit integrals, and can therefore be used for large systems.

.....
**INTEGRALS    
.MNF-SO    replaces     .SPIN-ORBIT             
.....

For properties, the same substitution should be made, in the case of special components, X1SPNORB labels are replaced by X1MNF-SO and so on, whereas the two-electron terms will be skipped completely. For calculating phosphorescence with the quadratic response scheme, .PHOSPHORESENCE should be just replaced by .MNFPHO which takes care of choosing the appropriate integrals.

NOTE:

The choice between the Breit-Pauli or Douglas-Kroll mean-field operator is done by (not) providing the .DOUGLAS-KROLL keyword. It is therefore not possible to combine e.g. non-relativistic wave-functions with the Douglas-Kroll spin-orbit integrals.

In the present implementation, the mean-field approach works only for basis sets with a generalized contraction scheme such as the ANO basis sets, raf-r, or cc-pVXZ(-DK). For other types of basis sets, the program might work without a crash, but it will most likely provide erroneous results.