Boltzmann population

NH in its v = 1 vibrational level and in a high rotational level (e.g. J> 30) prepared by laser excitation of vibrationally cold NH in v = 0 having high J (due to nahiral Boltzmann populations), see figure B3.T3 and... 

Miller an d Rich assumed th at cyclosporin A an d its MeHrn t an alogs share a common hioactive con formation. fheir molecular mech an ics calculation s found such a conformation, fh e Boltzmann population of th e proposed hioactive conformation correlates with the immunosuppressive activities of the compounds. 

B. Averaging Over Equilibrium Boltzmann Population of Initial States... 

If state n in Figure 2.2(a) is populated in excess of its Boltzmann population by absorption, the species M in this state will decay to the lower state until the Boltzmann population is regained. The decay is a first-order process, so that... 

If the spectrum is observed in emission it is the rotational populations in the upper state which determine relative intensities. They may or may not be equilibrium Boltzmann populations, depending on the conditions under which the molecule got into the upper state. 

Depending on the method of pumping, the population of may be achieved by — Sq or S2 — Sq absorption processes, labelled 1 and 2 in Figure 9.18, or both. Following either process collisional relaxation to the lower vibrational levels of is rapid by process 3 or 4 for example the vibrational-rotational relaxation of process 3 takes of the order of 10 ps. Following relaxation the distribution among the levels of is that corresponding to thermal equilibrium, that is, there is a Boltzmann population (Equation 2.11). 

The rotational temperature is defined as the temperature that describes the Boltzmann population distribution among rotational levels. For example, for a diatomic molecule, this is the temperature in Equation (5.15). Since collisions are not so efficient in producing rotational cooling as for translational cooling, rotational temperatures are rather higher, typically about 10 K. 

Figure 4.2 Energy levels and populations for an IS system in which nuclei I and S are not directly coupled with each other. This forms the basis of the nuclear Overhauser enhancement effect. Nucleus S is subjected to irradiation, and nucleus I is observed, (a) Population at thermal equilibrium (Boltzmann population).

The temperature dependence of the observable is obtained by assuming a Boltzmann population of the vibrational levels, so that... 

An advanced subject in the theory of quadrupole splitting is the fact that the quadrupole splitting can become temperature dependent. At the heart of this effect is the change in Boltzmann populations of electronically nearly degenerate many-electron states with temperature. 

FIGURE 4.1 Boltzmann population of a doublet as a function of temperature. The lower and the higher level of the doublet have population n0 and n1 respectively, and they are separated by an energy difference of 0.3 cnr1. 

Biomolecular spectroscopy on frozen samples at cryogenic temperatures has the distinct disadvantage that the biomolecules are in a state that is not particularly physiological. Recall that EPR spectroscopy is done at low temperatures to sharpen-up spectra by slowing down relaxation, to increase amplitude by increasing Boltzmann population differences, and to decrease diamagnetic absorption of microwaves by changing from water to ice. Certain S = 1/2 systems, notably radicals and a few mononuclear metal ions, have sufficiently slow relaxation, and sufficiently limited spectral anisotropy to allow their EPR detection in the liquid phase at ambient temperatures, be it in aqueous samples of reduced size. 

The ratio of the intensity of anti-Stokes and Stokes lines is primarily determined by the Boltzmann population of the excited vibrational states. For mid-IR frequencies this fractional population is very low (seIO-4 at 2000cm-1). As a result, Raman spectra are usually taken from the Stokes side of the Rayleigh line as these are generally very much more intense and are not broadened by emissions from hot states. 

In the quantum mechanical formulation of electron transfer (Atkins, 1984 Closs et al, 1986) as a radiationless transition, the rate of ET is described as the product of the electronic coupling term J2 and the Frank-Condon factor FC, which is weighted with the Boltzmann population of the vibrational energy levels. But Marcus and Sutin (1985) have pointed out that, in the high-temperature limit, this treatment yields the semiclassical expression (9). 

Now taking into account the Boltzmann population distribution, Nf/Ni =... 

Although exit channel effects are capable of producing a range of non-Boltzmann population distributions, the wavelength dependence of the kinetic energy provides an indication that nonthermal activation is responsible for the fast component of the desorption signal. The activation mechanism responsible for this desorption process is not determined from these experiments, but will be re-addressed in section 4.6. 

Oxidized Fe2S2 ferredoxins, containing two equivalent iron atoms, with J = 400 cm , show sharper NMR lines with respect to the monomeric iron model provided by oxidized rubredoxin (107-109), due to the decreased Boltzmann population of the paramagnetic excited states. For reduced ferredoxins (Si = 5/2, S2 = 2), with J = 200 cm , the ground state is paramagnetic (S = 1/2) (110). A smaller decrease in linewidth is expected. However, the fast electron relaxation rates of the iron(II) ion cause both ions to relax faster, and the linewidths in the dimer are sharp. 

The energy separation between the non-degenerate and degenerate states can be assessed by fitting the MCD intensity as a function of 1/T at a discrete wavelength to a Boltzmann population distribution for a two level system. 

Europium also does not modify the mantle thermoluminescence perceptibly. There are no sharp emission lines in the red due to a conceivable luminescence of a quasi-stationary concentration of Uo built up by the flame, in contradistinction to cathodo-luminescence. It must be remembered that the Boltzmann population of this state is only 4.10 even at 2000 K. 

Proper treatment of dipole moments (or other properties) in flexible molecules thus involves evaluating Boltzmann populations (see discussion in Chapter 14). This is beyond our present scope and coverage will be limited to assessing the performance of different models with regard to their ability to reproduce the change in dipole moment with change in conformer. Data are presented in Table 10-7, with the usual series of theoretical models surveyed. 

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