Spin-orbit phase choice

In general they are complex, but they can be chosen real, provided that one includes a choice of phases in the choice of partners 0M. The AMOs (3.1) provide an illustration of this point. The final spin orbitals are aka for fi = 2k and 5 /3 for n = 2k + 1. The corresponding mixing parameters are related by... 

Note that the signs of the off-diagonal matrix elements in Eq. (3.4.37b) depend on the phase choice (i.e., the selected standard order of the spin-orbitals). However, the overall signs of the matrix elements in Eq. (3.4.37b) do not affect the sign or magnitude of the As values which are derived from the square of these matrix elements. 

Finally, some spectroscopic applications for pseudopotentials within SOCI methods are presented in section 3. We focus our attention on applications related to relativistic averaged and spin-orbit pseudopotentials (other effective core potentials applications are presented in chapters 6 and 7 in this book). Due to the large number of theoretical studies carried out so far, we have chosen to illustrate the different SOCI methods and discuss a few results, rather than to present an extensive review of the whole set of pseudopotential spectroscopic applications which would be less informative. Concerning the works not reported here, we refer to the exhaustive and up-to-date bibliography on relativistic molecular studies by Pyykko [21-24]. The choice of an application is made on the basis of its ability to illustrate the performances on both the pseudopotential and the SOCI methods. One has to keep in mind that it is not easy to compare objectively different pseudopotentials in use since this would require the same conditions in calculations (core definition, atomic basis set, SOCI method). The applications are separated into gas phase (section 3.1) and embedded (section 3.2) molecular applications. Even if the main purpose of this chapter is to deal with applications to molecular spectroscopy, it is of great interest to underline the importance of the spin-orbit coupling on the ground state reactivity of open-shell systems. A case study is presented in section 3.1.4. 

The third critical point is the choice of the appropriate electronic structure method to treat the species in gas phase. The change of electronic configuration from the oxidized to the reduced species implies that electronic correlation effects are different and that spin-orbit coupling is likely to contribute differently for the two species. Most studies rely on DFT using either the PBE functional, a hybrid functional, or more recently a meta-functional of the Minnesota M06 family. Changing the functional can yield changes of the gas-phase ionization potential up to an eV. Unfortunately, we cannot compare these DFT values to the most reliable... 

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