Spin-orbit coupling pseudopotential

Naveh, D., Kronik, L., Tiago, M.L. and Chelikowsky J.R. (2007) Real-space pseudopotential method for spin-orbit coupling within density functional theory. Physical Review B - Condensed Matter, 76, 153407-1-153407-4. 

Parameters of energy-consistent ab initio pseudopotentials and corresponding valence basis sets are available for almost all elements of the periodic table [93,94,117,190-192,194-201]. A compilation of parameters for the use within the MOLPRO program system also exists on the internet under the address http //www.theochem.uni-stuttgart.de. Special care has to be taken when spin-orbit coupling is included in calculations with small-core PPs some SO operators are constructed (similar to the large-core case) for a fully variational two-component treatment, whereas in some cases effective valence SO operators are defined. The latter have to be applied in SO-CI calculations for the valence electrons, in which the semi-core shells (outside the PP core) are frozen in their scalar-relativistic form. 

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. 

Gathering the experience of the previously discussed examples, we can say that the theoretical study of spectroscopic properties of transition metal complexes is far from being simple. Relativistic pseudopotentials (AREP and SOREP) were shown to be efficient and accurate tools to tackle this problem. From the methodological point of view, recently developed effective Hamiltonian SOCI methods that can treat correlation and spin-orbit coupling on the same footing exist (see section 2.2.5), and efforts have to be invested in applying... 

Abstract During the past decade the method of model core potential has undergone a period of dynamic development and applications, which ranged from atomic to protein-scale studies. Incorporation of the relativistic effects became the centre of the model core potential development and the accuracy and applicability of this method were greatly increased. A breakthrough on this front of research was the development of the model core potential that can account for the spin-orbit coupling effect. In the present chapter we review the theoretical foundations of the pseudopotential approach to the molecular electronic structure. We then provide an overview of the model core potential method as well as its development and applications in the first decade of this century. A perspective on the future of this method is also given. 

The CG method was first used by Kahn et al. (1978) for the uranium atom to obtain appropriate all-electron reference data for the generation of an ab initio pseudopotential which includes the major relativistic corrections except spin-orbit coupling. The latter... 

W i) is an integral operator with kernel W p, p ) and V p, p ) is the Fourier-transformed external potential. Hess s code has been implemented in several program codes like TURBOMOLE or MOLCAS3. Most of the applications are carried out scalar (one-component) without spin-orbit coupling and usually the two-electron operator is chosen as the simple Coulomb operator. This scheme (extended to spin-orbit coupling it necessary) leads to very accurate molecular properties for even the heaviest elements. A large number of applications in the chemistry of heavy elements are carried out by using either the scalar relativistic pseudopotential or density functional approximations. The pseudopotentials most widely used are linear... 

DK Douglas-Kroll MVD mass-velocity-I-Darwin NRPP nonrelativistic pseudopotential ARPP scalar relativistic pseudopotential SOPP spin-orbit coupled relativistic pseudopotential. The difference between DF and DK is mainly due to spin-orbit coupling,... 

The electronic structure of the molecule, formed by two very heavy atoms , will be considerably influenced by relativistic effects, as are the mass-velocity correction, the Darwin correction, and also the spin-orbit coupling see a recent review on relativistic quantum chemistry [1] see also two earlier reviews (primarily concerned with Au) [2, 3] and three related reviews of Pyykkb [4 to 6]. In the Pt2 case, two main routes were used 1) Relativistic effective potentials (REP) or pseudopotentials were introduced into SCF theory [7 to 10] for details, see below and a review on effective potentials in molecular quantum chemistry [11]. 2) The SCF-Xa-Dirac Scattered Wave (DSW) method was used, which treats relativistic... 

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