Four-component configuration interaction

There is normally interaction with more than one magnetic nucleus. Consider, for example, the methyl radical. Each proton may be in either of two spin states, a and jS, so that there are four possible resultant magnetic spin-states ,a,a ,a,jS a,j8,j8 j8,j8,)3. The spectrum therefore has four components, and since the configurations ,a,j8 and a,j3,j8 may each be achieved in three ways whereas the other two configurations are unique, the relative intensities of the absorptions are 1 3 3 1. The resulting spectrum is shown in Fig. 1 the radical was generated by the interaction of t-butyl hydroperoxide with titanous ion (Section IID) and the hyperfine splitting constant, —the separation of the mid-points of... 

Accounting for relativistic effects in computational organotin studies becomes complicated, because Hartree-Fock (HF), density functional theory (DFT), and post-HF methods such as n-th order Mpller-Plesset perturbation (MPn), coupled cluster (CC), and quadratic configuration interaction (QCI) methods are non-relativistic. Relativistic effects can be incorporated in quantum chemical methods with Dirac-Hartree-Fock theory, which is based on the four-component Dirac equation. " Unformnately the four-component Flamiltonian in the all-electron relativistic Dirac-Fock method makes calculations time consuming, with calculations becoming 100 times more expensive. The four-component Dirac equation can be approximated by a two-component form, as seen in the Douglas-Kroll (DK) Hamiltonian or by the zero-order regular approximation To address the electron cor-... 

Mochizuki and Okamoto applied the Dirac program for the estimation of stabilities of trivalent actinide elements and water or ammine complexes (Mochizuki and Okamoto 2002). Mochizuki and Tatewaki (2002) also carried out the electronic structure calculation on the hexa-hydrated ions of curium and gadolinium. They used the Dirac program and also predicted the fluorescence transition energy using the Complete Open-Shell Configuration Interaction (COSCI) method. Even the hexa-hydrate curium ion needs 2,108 basis functions for the fully relativistic four-component calculation. 

For more details on configuration interaction methods that include spin-orbit coupling we refer to the reviews by Marian [796,797] and by Hess, Marian and Peyerimhoff [767]. Finally, we also mention that the four-component coupled-cluster approaches discussed in section 8.9 have two-component relatives (see Refs. [798,799] for examples). 

T. Heig, H. J. A. Jensen, J. Olsen, L. Visscher. The Generalized Active Space Concept for the Relativistic Treatment of Electron Carre- lation. Ill Large-scale configuration interaction and four-component multi-canfiguration self-consistent field methods with application to UO2. J. Chem. Phys., 124 (2006) 104106. 

S. Knecht, H. J. A. Jensen, T. Heig. Large-scale parallel configuration interaction. 11. Two- and four-component double-group general active space implementation with appUcation to BiH. /. Chem. Phys., 132 (2010) 014108. 

Several groups have developed four-component methods for the calculation of polyatomic molecules in the last decade. While several codes for DHF calculations exist by now, " programs for calculations on polyatomic molecules including correlation by means of ab initio techniques appeared only very recently. They feature relativistic multi-reference configuration interaction, second-order M0ller-Plesset coupled-cluster methods. ... 

Low-Lying Excited States of Lanthanide Diatomics Studied by Four-Component Relativistic Configuration Interaction Methods... 

Y. Wasada-Tsutsui, Y. Watanabe, and H. Tatewaki, Electronic structures and bonding of CeF a frozen-core four-component relativistic configuration interaction study, J. Phys. Chem. Alll, 8877-8883 (2007). 

H. Tatewaki, Y. Watanabe, S. Yamamoto, and E. Miyoshi, Electronic structure of the GdF molecule by frozen-core four-component relativistic configuration interaction calculations, J. Chem. Phys. 125,044309 (9 pages) (2006). 

S. Yamamoto, H. Tatewaki, and T. Saue, Dipole allowed transitions in GdF A four-component relativistic general open-shell configuration interaction study, J. Chem. Phys. 129, 44505 ( 8 pages) (2008). 

S. Yamamoto and H. Tatewaki, and H. Moriyama, Electronic spectra of EuF studied by a four-component relativistic configuration interaction method, Theor. Chem. Acc. 131,1230 (9 pages) (2012). 

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