Dipole, oscillating molecular

The temporal dynamics of the molecular electric dipole excited by the pulse sequence is shown in Figure 6.5a and b for two distinct values of t. The respective upper frames show the induced dipole oscillation nit) (black dashed line) along with the driving electric field mod(ll ) (gray solid line), the lower frames display... 

His early work on atomic and molecular properties and dispersion energies involved the development and application of ab initio pseudostate techniques for the reliable evaluation of atomic and molecular multipolar properties and dispersion energies for small species.216 This was followed by the development and application of practical constrained dipole oscillator strength (DOSD) techniques, based on a combination of experimental and theoretical input, for the reliable evaluation (errors < 1-2%) of the dominant dipolar... 

That is, the electric field near the molecule, Eq. (5), is a sum of the incident field and the field that results due to the oscillating SP dipole. Similarly, the electric field near the SP dipole, Eq. (6), is the sum of the incident field and the field that results fi"om the oscillating molecular dipole. (Note Gaussian units are being assumed for all electromagnetic variables.)... 

In a perfect tetrahedral geometry, the length of the proton jump is equal 2rQH sin (10472) = 1.6 A, because the rotation is around the oxygen atom, the distance rOH is 1 A and the angle HOH is around 104°. So, this jump is, more exactly, a hindered rotation of the whole molecule, where the moving H atom remains attached to the same molecule. This is what I call a molecular diffusion mechanism due to rotational jumps. Within this picture, the permanent dipole oscillates with librational motions and has a different orientation at each jump, but the molecule remains neutral. 

The effect can be described by classical mechanics in terms of forced vibrations of harmonic oscillators. Here since the molecular polarizability t. changes slightly as Ihe bond distorts, nonlinear effects give rise to dipole oscillations at frequencies other than the imposed frequency. Raman himself seems to have been led to this discovery, at least In part, by his theoretical studies of Ihe vibrations of musical instruments such as the violin. 

Raman scattering arises from the interaction between radiation induced oscillating electric dipoles and molecular vibrational modes. In general, the induced polarisability is not necessarily in the direction of the incident beam, and they are related by a second range tensor, a, thus ... 

We now require an expression for the intensity radiated by the induced oscillating molecular dipole derived above. In SI, the intensity (mean rate of energy flow) of a plane wave is [12]... 

The induced oscillating molecular dipoles p(co,z,t) result in a macroscopic polarization P = Np. According to (3.5), the polarization Ps = P(cos) at the Stokes frequency Raman scattering, is given by... 

Davidson s (Appendix E) algorithms. A two-dimensional real space representation of the resulting transition density matrices is convenient for an analysis and visualization of each electronic transition and the molecular optical response in terms of excited-state charge distribution and motions of electrons and holes (Section IIC). Finally, the computed vertical excitation energies and transition densities may be used to calculate molecular spectroscopic observables such as transition dipoles, oscillator strengths, linear absorption, and static and frequency-dependent nonlinear response (Appendix F). The overall scaling of these computations does not exceed X in time and in memory (A being the... 

In the case of a linear molecule, there are two types of IR-active modes those of symmetry, which are asymmetric stretches involving dipole changes along the axis, and bending modes of II symmetry, for which the dipole oscillation is perpendicular to the molecular axis. In the first of these cases, the so-caUed parallel band shape arises from the A/ = 1 selection rule, so there are P and R branches, but no central Q branch. In the second case, the selection rule is AJ = 0, 1, so there is a Q branch as well. Examples of bands with these shapes are shown in Figure 8.14(a) and (b). Note that even if individual lines are not resolved, the presence or absence of a Q branch easily distinguishes the two symmetry species, as shown in spectra of KrF2[13]. 

The clear derivation of the dispersion energy according to Eqs. (4.32), (4.34) from multipole contributions suggests that it is the macroscopic multipole modes rather than the molecular dipole oscillators of spheres 1 and 2 which undergo fluctuations. This becomes even more obvious if we substitute the macroscopic dielectric permeabilities i(co) and fi2( ) of materials 1 and 2 for the molecular susceptibilities Xi(co) and X2(co) according to the law of Clausius-Mosotti... 

This derivation does not hold for a field that oscillates rapidly with time. In such a field, the induced dipole oscillates and the amplitude of these oscillations depends on the frequency. We can, however, define a frequency-dependent dynamic polarizability, or molecular electric... 

The set of dipole oscillator strengths fno, defined in Eq. (7.69), is often called the dipole oscillator strength distribution (DOSD). Summed over all excited states, bound as well as continuum states, they are related to several other molecular properties, as will be shown in the following. One defines two types of energy-weighted moments of the dipole oscillator strength distribution ... 

Several dipole oscillator strength sums are related to other molecular properties by so-called dipole oscillator strength sum rules. The best known is the Thomas Reiche-Kuhn sum rule that relates the S(0) sum to the number of electrons N of the system, i.e. 

As mentioned before, our discussion is following a classical electrodynamics treatment of the EM fields. Spontaneous emission requires QED for a proper description. However, with some ad hoc assumptions, spontaneous emission can be described in a classical framework. Within this framework, spontaneous emission is understood as the emission of light due to an electrical dipole oscillating at a frequency ty corresponding to the de-excitation from the molecular state n to the ground state 0. To calculate the radiative decay rate yr of an excited molecule within this theory, one has to preliminary calculate the total power emitted by the dipole fid. 

While the energy flux method requires the calculation of a flux through a surface, other equations can be derived that make reference only to quantities defined for the molecule and the nanoparticle. In fact, Prad can be considered as the power emitted by the oscillating molecular dipole and by the oscillating charge density induced in the nanoparticle by the field emitted by the molecule. If the latter is approximated by the dipole term only (fimet.on), Prad is just the power of the light emitted by a total dipole /ton + Pmet.on, i-e. ... 

As the molecular polarizability itself is modulated by internuclear motion at frequency combination frequencies. The molecular dipole oscillating at o)p + [Pg.470]

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