Dipole rotational waves

The principle of FMW involves the heating of both the solvent and the matrix by wave/matter interactions. The microwave energy is converted into heat by two mechanisms dipole rotation and ionic conductance. The heating is, therefore, selective with only polar or moderately polar compounds susceptible. Due to the use of low microwave energy the structure of target molecules remains intact. 

A. E. Kondo, V. M. Blokker, and W. J. Meath,/. Chem. Phys., 96, 2544 (1992). Permanent Dipole Moments and Two-Colour Multi-Photon Resonances in the Two-Level Molecule Rotating Wave Approximation Versus Exact Results. 

Here, [in is the transition dipole moment for the transition between V22 and Vn. In the adiabatic approximation (see, e.g.. Ret. [Stenholm 1994]), the coupled bare potentials V22 and V33 can be replaced by uncoupled adiabatic potentials. Using the rotating-wave approximation, the dynamics of the system is then described by the Schrodinger equation... 

The total Hamiltonian describing the energies of the systems, electromagnetic field and interactions, in the electric dipole and RWA (rotating-wave approximation) approximations [21], is composed of four terms... 

We assume that the molecule has no permanent dipole moment, that is, VaaiR) = Rn>(R) — 0- Moreover, we assume the Condon approximation fiab(R) = nba(R) = constant. Non-Condon terms would introduce interesting new effects, particularly if n(R) has a node. However, that is beyond the scope of the current treatment. We transform the representation to a rotating frame and adopt the rotating-wave approximation. Then... 

ABSTRACT We present a dynamical scheme for biological systems. We use methods and techniques of quantum field theory since our analysis is at a microscopic molecular level. Davydov solitons on biomolecular chains and coherent electric dipole waves are described as collective dynamical modes. Electric polarization waves predicted by Frohlich are identified with the Goldstone massless modes of the theory with spontaneous breakdown of the dipole-rotational symmetry. Self-organization, dissipativity, and stability of biological systems appear as observable manifestations of the microscopic quantum dynamics. 

The transition electric dipole moment in eqn [57] can be developed by invoking the Born-Oppenheimer approximation to express the total molecular wave function as a product of electronic and vibrational parts. (Rotational wave functions do not have to be included here since eqn [57] refers to an isotropic system. That is, the equation is a result of a rotational average which is equivalent to a summation over all the rotational states involved in the transition.) A general molecular state can now be expressed as the product of vibrational and electronic parts. Assuming that the initial and final electronic states are the ground state jcg). 

Applying the electric dipole and rotating-wave approximation, the equations of motion for the density matrix elements ay of the three-level system are [34],... 

In the interaction picture, with the rotating-wave and electric-dipole approximations, the interaction Hamiltonian can be written as... 

Q3. The interaction Hamiltonian in the rotating wave and dipole moment approximations for the three-level system is... 

The Y functions are the rotational wave functions (spherical harmonic functions) and = ix r, 6, (p) is the dipole moment operator of the molecule in the Born-Oppenheimer approximation. The selection rules that result are ... 

As with diatomic molecules, the principal selection rule is that a permanent dipole moment is required for a molecule to produce a microwave spectrum. Linear polyatomic molecules have rotational wave functions exactly like those of diatomic molecules, so their rotational selection rules and spectra are the same as those of diatomic molecules. A symmetric linear molecule such as acetylene (ethyne) has no permanent dipole moment, and does not have a microwave spectrum. The fact that N2O has a microwave spectrum establishes the fact that it is NNO, not NON. Spherical top molecules such as CCI4 and SFe are so symmetrical that they cannot have a nonzero permanent dipole moment, and they have no microwave spectrum. A symmetric top molecule with a permanent dipole moment will have a microwave spectrum. A microwave spectrum is always observed for an asymmetric top molecule, because it has so little symmetry that it must have a nonzero permanent dipole moment. 

Because of point 2, rotational microwave and millimetre wave spectroscopy are powerllil techniques for determining dipole moments. However, the direction of the dipole moment cannot be determined. In the case of 0=C=S, for which /r = 0.715 21 0.000 20 D [(2.3857 0.0007) x 10 ° C m], a simple electronegativity argument leads to the correct conclusion - that the oxygen end of the molecule is the negative end of the dipole. However, in CO, the value of 0.112 D (3.74 x 10 C m) is so small that only accurate electronic stmcture calculations can be relied upon to conclude correctly that the carbon end is the negative one. 

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