Molecular eigenstates frequency

The state s is not really a physically accessible state, since in order to prepare the molecule initially in radiation with particular coherence between different frequencies which correspond to all the observed spectral lines from the molecular states which contain this zeroth order state initial state cj>0. The molecular eigenstates should then have unit quantum yields at very low pressure, a result which is not inconsistent with experimental extrapolations to zero pressure. This small molecule limit is depicted schematically in Fig. 4a. 

The fluorescence oscillates in time with frequency 2t>. Of course, since we neglected the radiative width, it seems to oscillate forever. If we reintroduce this width, realizing that each molecular eigenstate in this symmetric case gets y/2, we have... 

Holme and Hutchinson suggest tuning two, or several, lasers to nearly degenerate molecular eigenstates. By adjusting the strength of the field at each frequency, they are able to combine these two molecular eigenstates with arbitrary coefficients, and thereby prepare a desired superposition state. These workers have focused on applications to local mode overtones, where field-free evolution would lead to relaxation into an intramolecular bath. 

The most commonly used experimental techniques probe molecules in the frequency domain rather than in the time domain. As emphasized recently (1) the increased level of detail provided by frequency-domain methods produces a more complete picture of the vibrational energy redistribution process, invalidating frequently made claims that time domain techniques, being more direct, are somehow superior. The molecular eigenstate spectra provided by high-resolution experiments currently provide the most complete picture of molecular dynamics. Of course, the frequency-domain and time-domain viewpoints are complementary and we frequently obtain enhanced understanding by considering both viewpoints. 

Often the frequencies twi and virtual level is close to a real molecular eigenstate, which greatly enhances the transition probability. It is therefore generally advantageous to excite the final level / by two different photons with a>i + u>2 = (Ef - Ei)/h rather than by two photons out of the same laser with 2co = Ef — , )/h. 

Owing to the coherence, we need to consider the macroscopic evolution of the field in a medium that shows a macroscopic polarization induced by the field-matter interaction. This will be done in three steps. First, the polarization induced by an arbitrary field will be calculated and expanded in power series in the field, the coefficients of the expansion being the material susceptibilities (frequency domain) or response function (time domain) of wth-order. Nonlinear Raman effects appear at third order in this expansion. Second, the perturbation theory derivation of the third-order nonlinear susceptibility in terms of molecular eigenstates and transition moments will be outlined, leading to a connection with the spontaneous Raman scattering tensor components. Last, the interaction of the initial field distribution with the created polarization will be evaluated and the signal expression obtained for the relevant techniques of Table 1. 

Atomic and Molecular Energy Levels. Absorption and emission of electromagnetic radiation can occur by any of several mechanisms. Those important in spectroscopy are resonant interactions in which the photon energy matches the energy difference between discrete stationary energy states (eigenstates) of an atomic or molecular system = hv. This is known as the Bohr frequency condition. Transitions between... 

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,... 

Owing to the fact that the state vectors are not eigenstates of the unperturbed molecular Hamiltonian, the linear differential equations for the parameters will be coupled. A Fourier transformation leads to matrix equations in the frequency domain to be solved for the Fourier amplitudes. Tliese matrix equations are often solved with iterative techniques due to their large sizes. 

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