Spin-Orbit Configuration Interaction Methods

In this chapter, we address the following problem Assume that we have derived a method that gives a good approximation to the treatment of relativistic effects in molecular systems, but that leaves out any explicit references to the spin—that is, a spin-free relativistic approximation. How can we go about getting a reliable estimate of the spin-orbit interaction in the system  

To solve this problem, we have to answer two questions, What and How The first one is concerned with finding an operator that describes the spin-orbit interaction that has been left out of our zeroth-order Hamiltonian, Hq, making the total Hamiltonian 

The form of this operator may be a matter of choice, but we would preferably like to restore the terms dropped in developing Hq from the fully relativistic Hamiltonian. This in turn leads to different operators depending on the approach taken towards Ho. 

The other question is concerned with how to treat these W° operators in a computationally efficient manner in a configuration interaction calculation. Although the operators may differ, the problems inherent in their application are common for many of the choices of zeroth-order method. A further challenge is that spin-orbit energies are of comparable magnitude to the correlation energies for heavy elements. Thus, the two should be treated on a reasonably equal footing. Because most of these methods 

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Comparison of Spin—Orbit Configuration Interaction Methods Employing Relativistic Effective Core Potentials for the Calculation of Zero-Field Splittings of Heavy Atoms with a 2P° Ground State. 

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal enviromnent to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment. 

R. J. Buenker, A. B. Alekseyev, H.-P. Liebermarm, R. Lingott, G. Hirsch. Comparison of spin-orbit configuration interaction methods employing relativistic... 

M. Kleinschmidt, J. Tatchen, C. M. Marian. SPOCK.CI A multireference spin-orbit configuration interaction method for large molecules. /. Chem. Phys., 124 (2006) 124101. 

SPIN-ORBIT CONFIGURATION INTERACTION METHODS with the one-electron and two-electron operators defined by... 

SPIN-ORBIT CONFIGURATION INTERACTION METHODS or even to the entire Af-particle space including the external space. 

Abstract An implementation of a massively parallel spin-orbit configuration interaction (PSOCI) method is described. This is an extension of a conventional Cl method that explicitly includes one-electron spin-orbit operators and certain scalar relativistic effects extracted from relativistic effective core potentials. The performance of the PSOCI code is analyzed on several large-scale computing platforms. 

Keywords f-f transition Multi-reference spin-orbit configuration interaction (MRSOCI) method Transition dipole moment Judd-Ofelt theory Dynamic-coupling model Charge transfer... 

In this paper, the main features of the two-step method are presented and PNC calculations are discussed, both those without accounting for correlation effects (PbF and HgF) and those in which electron correlations are taken into account by a combined method of the second-order perturbation theory (PT2) and configuration interaction (Cl), or PT2/CI [100] (for BaF and YbF), by the relativistic coupled cluster (RCC) method [101, 102] (for TIF, PbO, and HI+), and by the spin-orbit direct-CI method [103, 104, 105] (for PbO). In the ab initio calculations discussed here, the best accuracy of any current method has been attained for the hyperfine constants and P,T-odd parameters regarding the molecules containing heavy atoms. 

Alekseyev AB, Liebermann H-P, Buenker RJ (2003) In Hirao K, Ishikawa M (eds) Spin-orbit multireference configuration interaction method and applications to systems containing heavy atoms. World Scientific, Singapore, pp 65-105... 

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). 

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