Randomly oriented molecules

An interesting aspect of two-photon spectroscopy is that some polarization infonnation is obtainable even for randomly oriented molecules in solution by studymg the effect of the relative polarization of die two photons. This is readily done by comparing linearly and circularly polarized light. Transitions to A states will absorb linearly polarized light more strongly than circularly polarized light. The reverse is true of transitions to B ... 

Biochemical EPR samples are almost always collections of randomly oriented molecules (frozen) aqueous solutions in which each paramagnetic molecule points in a different direction. In order to generate simulations of these powder EPR spectra we have to calculate the individual spectrum for many different orientations and then add these all up to obtain the powder pattern. Numerical procedures that generate sufficient spectra to approximate a powder pattern are collectively known as walking the unit sphere algorithms. Here is the basic procedure ... 

This chapter considers the distribution of spin Hamiltonian parameters and their relation to conformational distribution of biomolecular structure. Distribution of a g-value or g-strain leads to an inhomogeneous broadening of the resonance line. Just like the g-value, also the linewidth, W, in general, turns out to be anisotropic, and this has important consequences for powder patterns, that is, for the shape of EPR spectra from randomly oriented molecules. A statistical theory of g-strain is developed, and it is subsequently found that a special case of this theory (the case of full correlation between strain parameters) turns out to properly describe broadening in bioEPR. The possible cause and nature of strain in paramagnetic proteins is discussed. 

Wasserman, E., Snyder, L.C., and Yager, W.A. 1964. ESR of the triplet states of randomly oriented molecules. The Journal of Chemical Physics 41 1763-1772. 

Figure 3.27 shows the Mossbauer spectrum that results from splitting of the 57Fe excited state, a quadrupole doublet, for a sample containing randomly oriented molecules such as found in polycrystalline solids or frozen solutions. The two doublets are separated in energy by the quadrupole splitting, A Eq, defined by the... 

Figure 3.27 Typical Mossbauer spectrum for a sample containing randomly oriented molecules.

The energy transfer efficiency is therefore increased with a larger acceptor extinction coefficient, better spectral overlap between the donor emission and the acceptor absorbance, and higher quantum efficiency of the donor. The orientation term k2 can vary from 0 to 4, and for randomly oriented molecules is 2/3. Random orientation is, in fact, generally assumed when calculating the Ro-... 

ESR spectroscopy (a) J. E. Wertz and J. R. Bolton, in Electron Spin Resonance Elementary Theory and Practical Applications McGraw-Hill, New York, 1972. (b) J. A. Berson, in The Chemistry of the Quinonoid Compounds, Vol. II, S. Patai and Z. Rappoport, Eds., John Wiley Sons, Inc., New York, 1988. (c) W. Gordy, in Theory and Applications of Electron Spin Resonance, Vol. 15, A. Weissberger series Ed., W. West, Ed., John Wiley Sons, Inc., New York, 1980, p. 589. (d) E. Wasseiman, W. A. Yager, and L. C. Snyder, Electron spin resonance (E.S.R.) of the triplet states of randomly oriented molecules, J. Chem. Phys. 1964, 41, 1763. 

Figure 4.16 Polar (r, 6, ) curve for intensity of fluorescence emission from randomly oriented molecules excited by polarized radiation. Polarization direction OZ, propagation direction OX.

A question which may sometimes be asked is this If an enantio-morphous crystal- -that is, one possessing neither planes, nor inversion axes, nor a centre of symmetry—is dissolved in a solvent, does the solution necessarily rotate the plane of polarization of light The answer to this question is, Not necessarily . If the molecules or ions of which the crystal is composed are themselves enantiomorphous, then the solution will be optically active. But it must be remembered that enantiomorphous crystals may be built from non-centrosymmetric molecules which in isolation possess planes of symmetry—these planes of symmetry being ignored in the crystal structure such molecules in solution would not rotate the plane of polarization of light. (A molecule of this type, in isolation, may rotate the plane of polarization of light (see p. 91), but the mass of randomly oriented molecules in a solution would show no net rotation.) An example is sodium chlorate NaC103 the crystals are enantiomorphous and optically active, but the solution of the salt is inactive because the pyramidal chlorate ions (see Fig. 131) possess planes of symmetry. 

The ion at +121 amu, interpreted as originating from oxidized vinyl groups, is now absent. This suggests that the highly oriented molecules are more resistant to oxidation at room temperature than the randomly oriented molecules in the thick film. 

I have shown that, in simple systems, Patterson functions can give us valuable clues about distances, even when we know nothing about phases (see Chapter 6, Section III.C). Diffraction from the randomly oriented molecules in a solution or powder would give a spherically averaged diffraction pattern, from which we can compute a spherically averaged Patterson map. Is this map interpretable ... 

The most comprehensive information obtained from a Mossbauer spectrum is contained in Bint that depends on the magnetic hyperfine tensor A and, through (S), on the ZFS, the electronic g tensor (and exchange couplings when we consider polynuclear systems). For samples containing randomly oriented molecules, such as poly crystalline powders or molecules in frozen solution, the Mossbauer spectrum depends on the orientation of the molecule relative to the direction of the applied field,4 6 which is fixed in the laboratory and is generally either parallel or perpendicular to the direction of Mossbauer radiation. As a consequence, the spectrum is a powder average from which we have to extract the various tensor quantities of... 

We restrict our discussion to the case of isotropic dilute solutions of randomly oriented molecules, e.g. liquid solutions or amorphous solid solutions. (In practice, the vast majority of VCD experiments are carried out using liquids at room temperature.)... 

Fig 6. Schematic diagram of polarization measurements of a. Completely uniaxially oriented molecules, b. Two-dimensional system with partially oriented molecules, and c. Three-dimensional system with randomly oriented molecules. Axis of chromophoric group of the molecule lies along the double-headed arrows. The intensities of the incident exciting light and the fluorescence emission are represented by and //, respectively. The vertical and horizontal components of // are represented by J and /j respectively... 

Kottis and Lefebvre (322) have suggested that if polarized light is used to excite randomly oriented molecules to the triplet state, observation of the changes in the AMg = +1 ESR spectrum can reveal the correlation of the polarization properties of the excitation with the principal axis system of the triplet zero-field tensor. Such photoselection experiments have been carried out successfully by Lhotse and coworkers (323) and El-Sayed and Siegel (324) on a number of aromatic systems. Piette and collaborators (325) have studied the effect of metal complexation on the zero-field parameters and lifetimes of the phosphorescent triplet of aromatic-metal complexes with similar photoselection technique. The changes in... 

Spectra of samples in the liquid state (Fig. 2.6-lB) are given by molecules which may have any orientation with respect to the beam of the spectrometer. Like in gases, flexible molecules in a liquid may assume any of the possible conformations. Some bands are broad, since they are the sum of spectra due to different complexes of interacting molecules. In the low frequency region spectra often show wings due to hindered translational and rotational motions of randomly oriented molecules in associates. These are analogous to the lattice vibrations in molecular crystals, which, however, give rise to sharp and well-defined bands. The depolarization ratio p of a Raman spectrum of molecules in the liquid state (Eqs. 2.4-11... 13) characterizes the symmetry of the vibrations, i.e., it allows to differ between totally symmetric and all other vibrations (see Sec. 2.7.3.4). 

Practical measurements involve averaging over a large ensemble of molecules. For randomly oriented molecules, as in a solution or a polycrystaUine powder, k eja) ) = die recoil fraction becomes... 

Because of our reliance here on ESR results, it is perhaps worthwhile to briefly summarize their benefits and limitations The spectra of randomly-oriented molecules (the general case) in matrices can provide the total spin (S), the g tensor components, the hyperfine tensor components with magnetic nuclei, and sometimes... 

A first step towards the consideration of free, randomly oriented molecules (or microcrystals) is the superposition of S(A) with S(—A) ... 

Here, we discuss the polarization of fluorescence emission. The spatial orientations of emitting fluorophores determine the polarization of photons emitted. This relationship is the basis of fluorescence depolarization experiments as illustrated in Fig. 4a. When a sample of randomly oriented molecules (e.g., proteins... 

Most linear optical phenomena such as refraction, absorption and Rayleigh scattering are described by the first term in Eq. (1) where is the linear susceptibility tensor. The higher order terms and susceptibilities are responsible for nonlinear optical effects. The second-order susceptibility tensor T underlies SFG, whereas and BioCARS arises within As we are concerned with optical effects of randomly oriented molecules in fluids, we need to consider unweighted orientational averages of the susceptibility tensors in Eq. (1). We will show that the symmetries of the corresponding isotropic components and correspond to time-even pseudoscalars the hallmark of chiral observables [2]. 

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