Douglas-Kroll-Hess Property Transformation

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. 

It is even possible to define a free-particle transformation from which we could continue to develop a matrix Douglas-Kroll-Hess or Barysz-Sadlej-Snijders approximation. But with the matrix formalism we now have available, there is the opportunity to take a different approach, one that centers around the properties of the matrix X. 

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