Spin deviation operator

The diagonalization of is normally accomplished by a transformation from angular momentum operators to spin deviation operators (Holstein and Pri-makoff, 1940). A spin deviation at the ith site of one quantum of angular momentum is created and annihilated by operators a i and a,- respectively... 

The Amsterdam Density Functional (ADF) method [118,119] was used for calculations of some transactinide compounds. In a modem version of the method, the Hamiltonian contains relativistic corrections already in the zeroth order and is called the zero-order regular approximation (ZORA) [120]. Recently, the spin-orbit operator was included in the ZORA Fock operator [121]. The ZORA method uses analytical basis fimctions, and gives reliable geometries and bonding descriptions. For elements with a very large SO splitting, like 114, ZORA can deviate from the 4-component DFT results due to an improper description of the pi/2 spinors [117]. Another one-component quasirelativistic scheme [122] applied to the calculations of dimers of elements 111 and 114[116,117]isa modification of the ZORA method. 

The expansion coefficients and exponents Df and df. are obtained by least-squares fitting such that the weighted deviation between the original form of the radial part of the spin-orbit operator and the potential representation is minimized. 

Because the convenience of the one-electron formalism is retained, DFT methods can easily take into account the scalar relativistic effects and spin-orbit effects, via either perturbation or variational methods. The retention of the one-electron picture provides a convenient means of analyzing the effects of relativity on specific orbitals of a molecule. Spin-unrestricted Hartree-Fock (UHF) calculations usually suffer from spin contamination, particularly in systems that have low-lying excited states (such as metal-containing systems). By contrast, in spin-unrestricted Kohn-Sham (UKS) DFT calculations the spin-contamination problem is generally less significant for many open-shell systems (39). For example, for transition metal methyl complexes, the deviation of the calculated UKS expectation values S (S = spin angular momentum operator) from the contamination-free theoretical values are all less than 5% (32). 

The calculated splitting of the 2H(2)11/2 levels in Er3+ [295] (and Nd3+ [296]) compounds is always smaller than experimental splitting. An empirical correction has been proposed which includes a multiplying factor for the fourth-order diagonal reduced CF matrix element (2H(2) C4 2H(2)). The correction is efficient for 2H(2)n/2 and 2H(2)9/2 and for those levels which are coupled to them by spin-orbit interaction, such as 4I9/2, 4F9/2 and 4Gn/2. With the multiplying factor 1.717, the mean deviation in fitting 58 levels of Cs2NaErCl6 was decreased by 18% [35]. This correction has approximately the same effect as the g40 A operator of the correlation CF. 

---