Molecular magnetic properties Hamiltonian

In the Hamiltonian conventionally used for derivations of molecular magnetic properties, the applied fields are represented by electromagnetic vector and scalar potentials [1,20] and if desired, canonical transformations are invoked to change the magnetic gauge origin and/or to introduce electric and magnetic fields explicitly into the Hamiltonian, see e.g. refs. [1,20,21]. Here we take as our point of departure the multipolar Hamiltonian derived in ref. [22] without recourse to vector and scalar potentials. 

The magnetic properties of most free radicals can conveniently be represented by parameters describing their interaction with an external magnetic field and the intra-molecular hyperfine interactions, i.e. the parameters g and ax of the Spin-Hamiltonian... 

In this chapter we focus on methodological and computational aspects that are key to accurately modeling the spectroscopic and thermodynamic properties of molecular systems containing actinides within the density functional theory (DFT) framework. Our focus is on properties that require either an accurate relativistic all-electron description or an accurate description of the dynamical behavior of actinide species in an environment at finite temperature, or both. The implementation of the methods and the calculations discussed in this chapter were carried out with the NWChem software suite [1]. In the first two sections we discuss two methods that account for relativistic effects, the ZORA and the X2C Hamiltonian. Section 12.2.1 discusses the implementation of the approximate relativistic ZORA Hamiltonian and its extension to magnetic properties. Section 12.3 focuses on the exact X2C Hamiltonian and the application of this methodology to obtain accurate molecular properties. In Section 12.4 we examine the role of a dynamical environment at finite temperature as well as the presence of other ions on the thermodynamics of hydrolysis and exchange reaction mechanisms. Finally, Section 12.5 discusses the modeling of XAS... 

Having considered the general expressions for first- and second-order molecular properties, we now restrict ourselves to properties associated with the application of static uniform external electric and magnetic fields. For such perturbations, the Hamiltonian operator may be written in the manner (in atomic units)... 

Hund s cases are important because they tell the experimentalist what kind of patterns might be found in a spectrum, how to look for these patterns, and what inferences about quantum number assignments can be drawn from the patterns once they are detected. Hund s cases tell the dynamicist how to construct a reduced dimension picture of intramolecular processes. The reduction in dimensionality is based on the existence of approximate constants of motion, eigenvalues of operators that commute with most of the molecular Hamiltonian [see Sections 9.4.9 and 9.4.10]. Hund s cases, embodied in models of vectors precessing about other vectors, explain how information about molecule frame properties (e.g., a permanent magnetic dipole or an electric dipole transition moment) survives rotational averaging and becomes observable in the laboratory frame (and vice versa). 

In everything we have done so far we have been concentrating on the calculation of the wavefunction associated with the usual molecular Hamiltonian (the non-relativistic, Born-Oppenheimer, electrostatic Hamiltonian) using the variation method. However, many of the most interesting properties of molecules arise from interactions of the molecule with various electric and magnetic fields as well as with other molecules. 

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