Relativistic Quantum Chemical Calculations in Practice

The case studies discussed in the preceding sections show that the accuracy of molecular spectra of heavy element compounds is, qualitatively speaking, governed by relativistic and electron-correlation effects. The numerous methods, which are in practical use in quantum chemistry and whose foundations have been elaborated in chapter 8, require a lot of experience in order to produce sound results. Fortunately, there exist two excellent books, which present the wealth of computational methods with a thorough analysis of their capabilities, to which we may refer the reader [1156,1157]. 

Relativity affects the N-electron wave function through the proper choice of the many-electron Hamiltonian. On the other hand, electron correlation is considered through a multi-determinantal ansatz for the N-electron wave function (or through a suitable choice of an approximate exchange- orrelation functional in a DFT framework). It is desirable to somehow systematize the many different options from which one can choose in actual calculations. Mainly three different methodological branches emerge in a deliberately oversimplified picture  

CASPT2 calculation. Spin-orbit interaction, when necessary, can be included a posteriori as a perturbation. This intrinsically one-component formalism allows one to treat molecules of extended size compared to the four-component approach. As an alternative to CASSCF/CASPT2, truncated MRCI calculations can be envisaged. Limitations arise at the horizon when spin-orbit splitting of atomic one-electron shells starts to become large. Then, a spin-averaged orbital picture will no longer be sufficient. It can be expected that this will be the case for the heavy open-shell p-block elements Bi, Po, and At. 

Of course, this second branch also accommodates DPT methods with approximate contemporary functionals. Again, approximate relativistic Hamiltonians such as the DKH or the ZORA Hamiltonian will do a good job. This holds true for the second-order DKH2 Hamiltonian, but one may always choose the fourth-order DKH4 Hamiltonian, which is still a uniquely defined operator (i.e., it is independent of the parametrization chosen for the unitary transformation). The fact that the lowest-order Hamiltonians in the regular approximation and in the DKH scheme work so well is also the reason why ZORA and DKH2 Hamiltonians yield similarly good results [1161]. Both Hamiltonians are now well established and heavily used in actual calculations. Needless to say, these all-electron methods are mandatory when effects of the core electrons become decisive (as, for instance, in MoRbauer spectroscopy). 

Although computational methods are under constant development in relativistic quantum chemistry, it can be expected that the principles given above will endure for all time. This holds even more true for the theory of relativistic quantum chemistry derived in this book. 

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