Quantum chemistry, open-shell molecules

In addition to the intrinsic challenge to theory posed by open-shell systems, a considerable amount of motivation for studying them also stems from pragmatic considerations. First, the reactive nature of radicals makes them extraordinarily difficult to study in the laboratory, and the presence of several low-lying excited states tends to make their electronic spectroscopy complicated. In fact, it has even been stated that the assistance of quantum chemistry is absolutely necessary to properly interpret many experimental studies of these systems [99]. The importance of open-shell molecules is obvious in areas that include... 

So far, we have encountered the spin density as a variable both in the description of electronic structures of open-shell character and in the analysis of local quantities such as local spins or bond orders. For an accurate treatment of open-shell molecules, spin-spin interactions and chemical bonding, reliable spin densities are thus mandatory. However, the determination of rehable spin density distributions can be a difficult task in quantum chemistry [199, 200]. Examples of such difficult cases are iron nitrosyl complexes containing salen or porphyrin ligands for which DFT spin densities considerably depend on the approximate exchange-correlation functional [87,199]. 

The principal developer of the code has been Frank Neese, first at the Max Planck Institute for Bioinorganic Chemistry in Miilheim and then at the University of Bonn. In the words of the program s author, ORCA is a flexible, efficient and easy-to-use general purpose tool for quantum chemistry with specific emphasis on spectroscopic properties of open-shell molecules. It features a wide variety of standard quantum chemical methods ranging from semiempirical methods to DFT to single- and multireference correlated ab initio methods. It can also treat environmental and relativistic effects. An abbreviated list of program s features includes ... 

Eqs. (l)-(3), (13), and (19) define the spin-free CGWB-AIMP relativistic Hamiltonian of a molecule. It can be utilised in any standard wavefunction based or Density Functional Theory based method of nonrelativistic Quantum Chemistry. It would work with all-electron basis sets, but it is expected to be used with valence-only basis sets, which are the last ingredient of practical CGWB-AIMP calculations. The valence basis sets are obtained in atomic CGWB-AIMP calculations, via variational principle, by minimisation of the total valence energy, usually in open-shell restricted Hartree-Fock calculations. In this way, optimisation of valence basis sets is the same problem as optimisation of all-electron basis sets, it faces the same difficulties and all the experience already gathered in the latter is applicable to the former. 

A key development in quantum chemistry has been the computation of accurate self-consistent-field wave functions for many diatomic and polyatomic molecules. The principles of molecular SCF calculations are essentially the same as for atomic SCF calculations (Section 11.1). We shall restrict ourselves to closed-shell configurations. For open shells, the formulas are more complicated. 

Abstract In this chapter we examine some basic concepts of quantum chemistry to give a solid foundation for the other chapters. We do not pretend to review all the basics of quantum mechanics but rather focus on some specific topics that are central in the theoretical description of magnetic phenomena in molecules and extended systems. First, we will shortly review the Slater-Condon rules for the matrix elements between Slater determinants, then we will extensively discuss the generation of spin functions. Perturbation theory and effective Hamiltonians are fundamental tools for understanding and to capture the complex physics of open shell systems in simpler concepts. Therefore, the last three sections of this introductory chapter are dedicated to standard Rayleigh-Schrddinger perturbation theory, quasi-degenerate perturbation theory and the construction of effective Hamiltonians. 

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