Douglas-Kroll-Hess transformation relativistic effects

The transformed Hamiltonians that we have derived allow us to calculate intrinsic molecular properties, such as geometries and harmonic frequencies. We would like to be able to calculate response properties as well, with wave functions derived from the transformed Hamiltonian. If we used a method such as the Douglas-Kroll-Hess method, it would be tempting to simply evaluate the property using the nonrelativistic property operators and the transformed wave function. As we saw in section 15.3, the property operators can have a relativistic correction, and for properties sensitive to the environment close to the nuclei where the relativistic effects are strong, these corrections are likely to be significant. To ensure that we do not omit important effects, we must derive a transformed property operator, starting from the Dirac form of the property operator. 

We could of course proceed as we did for the Douglas-Kroll transformation and use a transformation that depends only on the nuclear potential. This would remove the awkwardness of having 1 /r,y in the denominator, but we still have the product of c f(2mc — Vi) with 1 /r,-y to deal with. If we are only interested in spin-free relativistic effects, we could neglect the transformation of the electron-electron interaction, as we did in the Douglas-Kroll-Hess approximation. This approximation yields the Hamiltonian... 

General two-component methods have been discussed in various chapters of the first part of this book, for instance in chapter 11 on Two-Component Methods and the Generalised Douglas-Kroll Transformation by Wolf, Reiher and Hess [165], in chapter 12 by Kutzelnigg on Perturbation Theory of Relativistic Effects [166] and in chapter 13 by Sundholm on Perturbation Theory Based on Quasi-Relativistic Hamiltonians [167]. 

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