Perturbations electromagnetic radiation

Poul Jorgensen [13] has been involved in developing such so-called response theories for perturbations that may be time dependent (e.g. as in the interaction of light s electromagnetic radiation). 

Tlie problem of particular interest in physics and chemistry is concerned with the interaction of electromagnetic radiation, and light in particular, with matter. The electric field of the radiation can directly perturb an atomic or molecular system. Then, as in the Stark effect, the energy of interaction - the perturbation - is given by... 

Abstract This review reports on the study of the interplay between magnetic coupling and spin transition in 2,2 -bipyrimidine (bpym)-bridged iron(II) dinuclear compounds. The coexistence of both phenomena has been observed in [Fe(bpym)(NCS)2]2(bpym), [Fe(bpym)(NCSe)2]2(bpym) and [Fe(bt)(NCS)2]2(bpym) (bpym = 2,2 -bipyrimidine, bt = 2,2 -bithiazoline) by the action of external physical perturbations such as heat, pressure or electromagnetic radiation. The competition between magnetic exchange and spin crossover has been studied in [Fe(bpym)(NCS)2]2(bpym) at 0.63 GPa. LIESST experiments carried out on [Fe(bpym)(NCSe)2]2(bpym) and [Fe(bt)(NCS)2]2(bpym) at 4.2 K have shown that it is possible to generate dinuclear molecules with different spin states in this class of compounds. A special feature of the spin crossover process in the dinuclear compounds studied so far is the plateau in the spin transition curve. Up to now, it has not been possible to explore with a microscopic physical method the nature of the species... 

Even at the highest fields, the NMR experiment would not be practicable if mechanisms did not exist to restore the Boltzmann equilibrium that is perturbed as the result of the absorption of electromagnetic radiation in making an NMR measurement. These mechanisms are known by the general term of relaxation and are not confined to NMR spectroscopy. Because of the small magnitude of the Boltzmann excess in the NMR experiment, relaxation is more critical and more important in NMR than in other forms of spectroscopy. 

I. The Perturbation Describing Interactions With Electromagnetic Radiation... 

On absorption or emission of radiation, a system goes from one stationary state to another under the influence of incident electromagnetic radiation. It is therefore, necessary to investigate how a system is disturbed or perturbed so that a transition is induced. 

Transition probabilities. The interaction of quantum systems with light may be studied with the help of Schrodinger s time-dependent perturbation theory. A molecular complex may be in an initial state i), an eigenstate of the unperturbed Hamiltonian, Jfo I ) = E 10- If the system is irradiated by electromagnetic radiation of frequency v = co/2nc, transitions to other quantum states /) of the complex occur if the frequency is sufficiently close to Bohr s frequency condition,... 

We shall apply the time-dependent perturbation theory of the last section to a system exposed to electromagnetic radiation. Before doing so, we review the classical wave theory of light.2... 

Absorption of electromagnetic radiation by monatomic gases leads either to production of atoms in excited states or, if the wavelength is short enough, to ionization. Absorption lines have widths which depend on the following factors1 (a) the temperature, i.e. there will be a Doppler effect which will broaden the line if the absorbing atoms are in motion (b) an intrinsic factor dependent on the nature of the electronic state and on the extent of perturbations by other states ... 

Van der Waals interactions between identical solid particles are always attractive [7]. However, if the Hamaker constant of the suspending fluid is intermediate between the Hamaker constants of two different particles, the van der Waals interactions will be repulsive [9]. Moreover, in view of the finite speed of propagation of electromagnetic radiation, the response of a molecule to perturbations in the electric field deriving from another nearby molecule is not instantaneous. Retardation effects are observable at separation distances as small as 1 or 2 nm, and they become prominent at larger distances (>10 nm) [50]. Gregory [50] has proposed a simple expression for describing retarded van der Waals interactions between flat plates ... 

Spectroscopy is concerned with the observation of transitions between stationary states of a system, with the accompanying absorption or emission of electromagnetic radiation. In this section we consider the theory of transition probabilities, using time-dependent perturbation theory, and the selection rules for transitions, particularly those relevant for rotational spectroscopy. 

As promised at the end of section 6.11.1 we now consider a specific example of the time-dependent perturbation introduced in equations (6.263) and (6.272). The radiation density for electromagnetic radiation with unit dielectric constant and magnetic permeability is given by [5, 72]... 

In most of the examples described in this book, the rotational angular momentum is coupled to other angular momenta within the molecule, and the selection rules for transitions are more complicated than for the simplest example described above. Spherical tensor methods, however, offer a powerftd way of determining selection rules and transition intensities. Let us consider, as an example, rotational transitions in a good case (a) molecule. The perturbation due to the oscillating electric component of the electromagnetic radiation, interacting with the permanent electric dipole moment of the molecule, is represented by the operator... 

The first theoretical model of optical activity was proposed by Drude in 1896. It postulates that charged particles (i.e., electrons), if present in a dissymmetric environment, are constrained to move in a helical path. Optical activity was a physical consequence of the interaction between electromagnetic radiation and the helical electronic field. Early theoretical attempts to combine molecular geometric models, such as the tetrahedral carbon atom, with the physical model of Drude were based on the use of coupled oscillators and molecular polarizabilities to explain optical activity. All subsequent quantum mechanical approaches were, and still are, based on perturbation theory. Most theoretical treatments are really semiclassical because quantum theories require so many simplifications and assumptions that their practical applications are limited to the point that there is still no comprehensive theory that allows for the predetermination of the sign and magnitude of molecular optical activity. 

In order to obtain a theoretical expression for the oscillator strength, perturbation theory may be used to treat the interaction between electromagnetic radiation and the molecule. Since an oscillating field is a perturbation that varies in time, time-dependent perturbation theory has to be used. Thus, the Hamiltonian of the perturbed system is = 0) +... 

Perturbation. The sample is now irradiated with a pulse of plane-polarised rf radiation at the Larmor frequency. Plane polarised electromagnetic radiation consists of electric and magnetic fields oscillating in fixed planes perpendicular to each other and to the direction of the radiation. The nuclear spin packets which are already in thermal... 

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