Dipole moments coupled systems

Since the proton tautomerism of naphthazarin [13] or 9-hydroxy-phenalenone [6] can be investigated precisely in an isolated system, it is intriguing to see how these tautomeric molecules behave as dielectrics in the solid state. Incidentally, if the tautomers keep the centrosymmetry during the tautomerization process, the dielectric response cannot be detected, because the changing directions of the dipole moments coupled with the tautomerization, even though they invert, cancel. 

Infrared and Raman spectroscopy each probe vibrational motion, but respond to a different manifestation of it. Infrared spectroscopy is sensitive to a change in the dipole moment as a function of the vibrational motion, whereas Raman spectroscopy probes the change in polarizability as the molecule undergoes vibrations. Resonance Raman spectroscopy also couples to excited electronic states, and can yield fiirtlier infomiation regarding the identity of the vibration. Raman and IR spectroscopy are often complementary, both in the type of systems tliat can be studied, as well as the infomiation obtained. 

As a consequence, field methods, which consist of computing the energy or dipole moment of the system for external electric field of different amplitudes and then evaluating their first, second derivatives with respect to the field amplitude numerically, cannot be applied. Similarly, procedures such as the coupled-perturbed Hartree-Fock (CPHF) or time-dependent Hartree-Fock (TDHF) approaches which determine the first-order response of the density matrix with respect to the perturbation cannot be applied due to the breakdown of periodicity. 

The potential energy curves (Fig. 1), the non-adiabatic coupling, transition dipole moments and other system parameters are same as those used in our previous work (18,19,23,27). The excited states 1 B(0 ) and 2 B( rio) are non-adiabatically coupled and their potential energy curves cross at R = 6.08 a.u. The ground 0 X( Eo) state is optically coupled to both the and the 2 R( nJ) states with the transition dipole moment /ioi = 0.25/xo2-The results to be presented are for the cw field e(t) = A Yll=o cos (w - u pfi)t described earlier. However, for IBr, we have shown (18) that similar selectivity and yield may be obtained using Gaussian pulses too. 

As the isoquinoline molecule reorients in the order listed above, the absorption of infrared radiation by the in-plane vibrational modes would be expected to increase, while that of the out-of-plane modes would be predicted to decrease (in accordance with the surface selection rule as described above). In the flat orientation there is no component of the dipole moment perpendicular to the surface for the in-plane modes, and under the surface selection rule these modes will not be able to absorb any of the incident radiation. However, as mentioned above, infrared active modes (and in some cases infrared forbidden transitions) can still be observed due to field-induced vibronic coupled infrared absorption (16-20). We have determined that this type of interaction is present in this particular system. 

An ordered monolayer of molecules having a large dynamical dipole moment must not be regarded as an ensemble of individual oscillators but a strongly coupled system, the vibrational excitations being collective modes (phonons) for which the wavevector q is a good quantum number. The dispersion of the mode for CO/Cu(100) in the c(2 x 2) structure has been measured by off-specular EELS, while the infrared radiation of course only excites the q = 0 mode. 

Dispersion forces (instantaneous-dipole - induced-dipole interactions) even in atoms and molecules having no permanent dipole moment, the continuous movement of electrons results, at any instant, in a small dipole moments, which fluctuatingly polarize the electronic system of the neighboring atoms or molecules. This coupling causes the electronic movements to be synchronized in such... 

Now, let us consider a system where an achiral molecule (A) and a chiral molecule (C) have a fixed mutual orientation. An electronic transition of the achiral molecule from the ground state z(0> to the excited state Aa, higher in energy by E0a, has a zero-order (non-perturbed) electric dipole moment po0 and an orthogonal magnetic dipole moment ma0. These moments are increased in the molecular pair (A -C) by first-order dynamic coupling as ... 

The last term in Eq. (1) describes the coupling to the laser field which has the form (t) = 00(t)0(r — t) sin2(7rt/r) cos(flt), where 0 is the amplitude, r the duration, and the center frequency of the pulse. The dipole moment vector is oriented in the plane of the molecule da0 are the respective matrix elements. Here, we will focus on the excitation of the stretching vibration which in our coordinate system is mostly polarized along the x axis. Thus, we will take into account only the x component of the dipole moment, assuming that the laser field is polarized accordingly [10],... 

In order for the induced dipole moment, ft, to transform as a vector, the spherical harmonics describing the various orientations have to be coupled in an appropriate way. We write the induced dipole components of a system of two molecules of arbitrary symmetry, according to [141]... 

The dipole moment is the total dipole of the sample, p = Y.i Pi The correlation function describes the response of the system to the weakly coupled radiation field. The effects of the field are modeled by the response of the individual atoms or molecules unaffected by the weak coupling. The Hamiltonian describes the interaction of the field and matter (first-order perturbatiuon theory). The correlation function describes how the perturbed system approaches equilibrium. 

The generalization to the control of the dynamics of a molecule with n electronic states is straightforward. For the purpose of deducing the control conditions we will examine the extreme case in which every possible pair of these electronic states is connected via the radiation field and a nonzero transition dipole moment. If the molecule is coupled to a radiation field that is a superposition of individual fields, each of which is resonant with a dipole allowed transition between two surfaces, the density operator of the system can be represented in the form... 

The above relations define the conditions for concurrent control of population and energy transfers between all of the states of the system that are connected by dipole allowed transitions. It is unlikely that a situation that complicated will ever be encountered. In the n-state molecule language, typically, not all pairs of states of the molecule are connected with nonzero transition dipole moments. In the skeleton spectrum language, there is usually only a small subset of dipole coupled doorway states. In both cases, of course, when only some pairs of states are coupled with nonzero transition dipole moments, the appropriate control conditions are simplified. 

An important advantage in phosphorus systems is the fact that 31P, which is the only natural isotope, has a spin of and can be easily measured by NMR. Its characteristic chemical shifts 8 (p.p.m.) and its H and 13C coupling constants J (Hz) have influenced the development of the heterocyclic chemistry of phosphorus more than any other physical methods such as IR, UV, MS, dipole moment measurement and others. 

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