Spin-orbital coupling response theory calculation

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

RESPONSE THEORY AND CALCULATIONS OF SPIN-ORBIT COUPLING PHENOMENA IN MOLECULES... 

Table 3 Spin-orbit coupling matrix elements between singlet and triplet states form second order response theory calculations on H20++ (10-6 au). A 6ai, 3b2, 3bj, la2 active space B 4ai, 2b2, 2bi active space. From Ref. [55],...

Apart from primary structural and energetic data, which can be extracted directly from four-component calculations, molecular properties, which connect measured and calculated quantities, are sought and obtained from response theory. In a pilot study, Visscher et al. (1997) used the four-component random-phase approximation for the calculation of frequency-dependent dipole polarizabilities for water, tin tetrahydride and the mercury atom. They demonstrated that for the mercury atom the frequency-dependent polarizability (in contrast with the static polarizability) cannot be well described by methods which treat relativistic effects as a perturbation. Thus, the varia-tionally stable one-component Douglas-Kroll-Hess method (Hess 1986) works better than perturbation theory, but differences to the four-component approach appear close to spin-forbidden transitions, where spin-orbit coupling, which the four-component approach implicitly takes care of, becomes important. Obviously, the random-phase approximation suffers from the lack of higher-order electron correlation. 

We will deal only with computational procedures that are normal for molecnles encoimtered in organic photochemistry. These methods depend heavily on the assumption that the spin-orbit conpling term is only a minor perturbation. In snch an instance, it is common to not include small relativistic terms such as spin-orbit coupling in the Hamiltonian from the beginning bnt to include them as an afterthought after an ordinary nonrelativistic calculation. This is usually done nsing pertnrbation theory or response theory. 

P. Agren, 0. Vahtras, B. Minaev, Response theory and calculations of spin-orbit coupling phenomena in molecules, Adv. Quantum Chem. 27 (1996) 71-162. 

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