Absorption line shape

Pump-probe absorption experiments on the femtosecond time scale generally fall into two effective types, depending on the duration and spectral width of the pump pulse. If tlie pump spectrum is significantly narrower in width than the electronic absorption line shape, transient hole-burning spectroscopy [101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112 and 113] can be perfomied. The second type of experiment, dynamic absorption spectroscopy [57, 114. 115. 116. 117. 118. 119. 120. 121 and 122], can be perfomied if the pump and probe pulses are short compared to tlie period of the vibrational modes that are coupled to the electronic transition. 

Pure 2D absorption line shapes are readily obtained in heteronuclear 2D /-resolved spectra. The incorrect setting of 90° and 180° pulses can, however, cause ghost peaks that can be removed by a phase cycling procedure, appropriately named Exorcycle (Rutar, 1984b). A... 

Loring RA (1990) Statistical mechanical calculation of inhomogeneously broadened absorption line shapes in solution. J Phys Chem 94 513-515... 

The vibrational frequency of the special pair P and the bacteriochlorophyll monomer B have also been extracted from the analysis of the Raman profiles [39,40,42,44,51]. Small s group has extensively performed hole-burning (HB) measurements on mutant and chemically altered RCs of Rb. Sphaeroides [44,45,48-50]. Their results have revealed low-frequency modes that make important contribution to optical features such as the bandwidth of absorption line-shape, as well as to the rate constant of the ET of the RCs. 

We begin by considering the absorption line shape for a liquid. If the light is polarized along lab-fixed axis p, the line shape is given by the Fourier transform... 

It is easiest to formulate this problem in the case of a single high-frequency vibrational mode, or chromophore, so let us consider this situation first. For the absorption line shape, which involves only the ground and excited state of the chromophore, a cmcial element is the 0 —> 1 transition frequency and its dependence on the classical bath coordinates. Second, one needs (in the case of IR spectroscopy) the projection of the transition dipole in the direction p of the electric field axis. This projection can depend on bath coordinates in two ways. 

In Figures 9.8 and 9.9, the absorption line shapes as a function of the detuning from the Fj -Fq resonance are shown. The case of unstructured continua is presented in Figure 9.8, in which the situation is shown when only the IFq) level (the one with the dipole allowed transition to the ground state) is broadened (Fq = 0.05 X 10 a.u.). No detuning 82 = 0) of the center of the strong pulse... 

It is very important, in the theory of quantum relaxation processes, to understand how an atomic or molecular excited state is prepared, and to know under what circumstances it is meaningful to consider the time development of such a compound state. It is obvious, but nevertheless important to say, that an atomic or molecular system in a stationary state cannot be induced to make transitions to other states by small terms in the molecular Hamiltonian. A stationary state will undergo transition to other stationary states only by coupling with the radiation field, so that all time-dependent transitions between stationary states are radiative in nature. However, if the system is prepared in a nonstationary state of the total Hamiltonian, nonradiative transitions will occur. Thus, for example, in the theory of molecular predissociation4 it is not justified to prepare the physical system in a pure Born-Oppenheimer bound state and to force transitions to the manifold of continuum dissociative states. If, on the other hand, the excitation process produces the system in a mixed state consisting of a superposition of eigenstates of the total Hamiltonian, a relaxation process will take place. Provided that the absorption line shape is Lorentzian, the relaxation process will follow an exponential decay. 

Fig. 15. Absorption line shapes for an Alg - > Tlu transition, (a) Coupling due to the rasl vibration. (b) Coupling due to both t2g and al9 vibrational modes. These absorption profiles were calculated by Toyozawa and Inoue (123) invoking the semiclassical approximation.

Interestingly enough, one sees differences between the various variants of Markovian and non-Markovian theories already in static linear absorption spectra. In the regime of second-order perturbation theory in the coupling to the electromagnetic field the linear absorption line-shape / (ui) can be calculated from the Fourier transform of the dipole-dipole correlation function as... 

Figure 1 Experimental and simulated EPR spectra of oxidized CooA at pH 7.4. Experimental conditions temperature, 2 K microwave frequency, 35.106GHz microwave power, 20p,W 100 kHz field modulation amplitude, 0.4 mT time constant, 128 ms scan time, 4 min. Lower traces, in absorption line-shape (due to rapid-passage conditions), are the experimental spectrum (blue) and a digital integration of the simulated spectrum (red). Upper traces in first-derivative lineshape are a digital derivative of the experimental spectrum (blue) and the simulated spectrum (red). Simulation parameters component (a) g = [2.60, 2.268, 1.85], (b) g = [2.47, 2.268, 1.90] Gaussian single-crystal linewidths (half-width at half-maximum) W = [500, 200, 400] MHz. Simulated spectra for (a) and (b) are added in the ratio 2 1 to give the summed spectrum shown...

Absorption line shape can be calculated by sampling the possible values of the energy difference X(r). This assumes that the transition dipole is independent of... 

Tl = (72 = Calculation of the absorption line shape involves running... 

Figure 10. Electronic absorption line shape of N,N -diethyl-p-nitroaniline in several bulk and interfacial systems, calculated by molecular dynamics computer simulation at 300K. (a) The spectrum in bulk water (solid line) and at the water liquid/vapor interface (dashed line), (b) The spectrum in bulk 1,2-dichloroethane (solid line) and at the water/1,2-dichloroethane interface.

The differential absorption information is recovered using phase sensitive detection techniques. The demodulated absorption line shape is shown in Fig. 4. The amount of light absorbed is directly proportional to oxygen concentration. The gas density, n, is related to the peak-to-peak signal amplitude. A/, by Beer s law, which for a weakly absorbing molecule, is given by ... 

A new approach to combining CP with MQ MAS in a 2D NMR experiment has been demonstrated, involving CP from H to the single-quantum coherences of a quadrupolar nucleus.In two separate methods, pure-absorption line shapes have been obtained using a z-filter and a reversed split-ti method. 

To apply the Forster equation, the emission and absorption line shapes must be identical for all donors and acceptors, respectively. However, in many types of condensed-phase media (e.g., glasses, crystals, proteins, surfaces), each of the donors and acceptors lie in a different local environment, which leads to a distribution of static offsets of the excitation energies relative to the average, which persists longer than the time scale for EET. When such inhomogeneous contributions to the line broadening become significant, Forster theory cannot be used in an unmodified form [16, 63]. 

Note that each /5a(s,Sa) is associated with an electronic coupling factor 5a(Sd, Sa) within the ensemble average. The/g° (s, Sa) and fl ° (s, Sd) specify the donor and acceptor densities of states (D.O.S.), as described in Ref. 63. The dependence upon disorder is assumed to introduce a static offset of the origin, as is usually assumed. These D.O.S. represent the emission (absorption) line shape of the donor (acceptor), calculated without disorder (hence the superscript hom ) and without dipole strength. Ns and Na are area normalization constants such that 1/Ns = Jq°° dE/g° (s) and 1/Na = Jo°° d a)j° (E). 

The conducting phase of TMQ /16/. Microwave conductivity experiments, performed at low temperature on the samples used for the pressure experiment, have succeeded in showing an increase by a factor 10 from 300 K down to loo K, /41/. The possibility of susceptibility measurement via low field method is limited by the EPR line broadening occurring at low temperature and under pressure. The spin susceptibility was derived from a fit of the EPR absorption line shape with a Lorentzian curve. The proton relaxation time was measured under pressure at low field lOe- with a pulse spectrometer. Figures... 

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