Static electric field molecular magnetic properties

Effects of a Static Electric Field on Molecular Magnetic Properties Employing the CTOCD Method Shielding Polarizabilities of CO, H20, and CH4 Compounds... 

Molecular Magnetic Properties in the Presence of a Static Electric Field. 

We shall briefly review some definitions to compute molecular magnetic properties in the presence of a static electric field, L e., hypermagnetizabilities and shielding polarizabilities, Zafr and a1. ... 

Perturbation theory has been used to define molecular magnetic properties up to fourth order. The invariance of the response tensors in a gauge transformation of the vector potential has been analyzed, and its connections with the conditions for charge and current conservations have been discussed. The quantum mechanical definition of electron current density in the presence of static electric and magnetic fields has been employed to provide relationships for magnetic... 

The quantum theory of molecular collisions in external fields described in this chapter is based on the solutions of the time-independent Schrodinger equation. The scattering formalism considered here can be used to calculate the collision properties of molecules in the presence of static electric or magnetic fields as well as in nonresonant AC fields. In the latter case, the time-dependent problem can be reduced to the time-independent one by means of the Floquet theory, discussed in the previous section. We will consider elastic or inelastic but chemically nonreac-tive collisions of molecules in an external field. The extension of the formalism to reactive scattering problems for molecules in external fields has been described in Ref. [12]. 

Of special interest to us are the properties related to the external application of uniform static electric and magnetic fields, which we will denote by F and B, respectively. To second order, the energy of a closed-shell molecular system may be written as... 

Liquid crystals are generally characterized by the strong correlation between molecules, which respond cooperatively to external perturbations. That strong molecular reorientation (or director reorientation) can be easily induced by a static electric or magnetic field is a well-known phenomenon. The same effect induced by optical fields was, however, only studied recently. " Unusually large nonlinear optical effects based on the optical-field-induced molecular reorientation have been observed in nematic liquid-crystal films under the illumination of one or more cw laser beams. In these cases, both the static and dynamical properties of this field-induced molecular motion are found to obey the Ericksen-Leslie continuum theory, which describe the collective molecular reorientation by the rotation of a director (average molecular orientation). 

In its broadest sense, spectroscopy is concerned with interactions between light and matter. Since light consists of electromagnetic waves, this chapter begins with classical and quantum mechanical treatments of molecules subjected to static (time-independent) electric fields. Our discussion identifies the molecular properties that control interactions with electric fields the electric multipole moments and the electric polarizability. Time-dependent electromagnetic waves are then described classically using vector and scalar potentials for the associated electric and magnetic fields E and B, and the classical Hamiltonian is obtained for a molecule in the presence of these potentials. Quantum mechanical time-dependent perturbation theory is finally used to extract probabilities of transitions between molecular states. This powerful formalism not only covers the full array of multipole interactions that can cause spectroscopic transitions, but also reveals the hierarchies of multiphoton transitions that can occur. This chapter thus establishes a framework for multiphoton spectroscopies (e.g., Raman spectroscopy and coherent anti-Stokes Raman spectroscopy, which are discussed in Chapters 10 and 11) as well as for the one-photon spectroscopies that are described in most of this book. 

The next natural objects are neutral atoms or molecules. The wave properties of atoms and molecules, and various types of their interaction with matter and electromagnetic fields (from static to optical) make it possible to implement atom and molecular optics. It is precisely the great variety of methods for exerting an effect on an atom (or molecule) possessing a static electrical or magnetic moment, a quadrupole... 

Terms of higher order in the field amplitudes or in the multipole expansion are indicated by. . . The other two tensors in (1) are the electric polarizability ax and the magnetizability The linear response tensors in (1) are molecular properties, amenable to ab initio computations, and the tensor elements are functions of the frequency m of the applied fields. Because of the time derivatives of the fields involved with the mixed electric-magnetic polarizabilities, chiroptical effects vanish as a> goes to zero (however, f has a nonzero static limit). Away from resonances, the OR parameter is given by [32]... 

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)... 

Another set of fundamental properties of metal clusters involves their response to static external electric and magnetic fields. Transition metal clusters embedded in matrices have been extensively studied with these techniques. [143] Unfortunately, the size distribution of the particles is broad in these experiments and interactions with the matrix can introduce changes in the properties of the metal aggregates. This is also true for metal clusters stabilized by ligands, as will be discussed in Section 2.4.5.3. The study of clusters in molecular beams overcomes these difficulties. This powerful approach, when combined with mass spectrome-tric detection, allows the investigation of mass selected free clusters. The main disadvantage is that since the particle densities are quite low, most of the standard spectroscopic techniques cannot be used. 

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