Molecular power spectrum

Fig. 37. The translational power spectrum as predicted by molecular dynamics simulation ol liquid water (from Ref. 3>)...

There are many experiments which determine only specific frequency components of the power spectra. For example, a measurement of the diffusion coefficient yields the zero frequency component of the power spectrum of the velocity autocorrelation function. Likewise, all other static coefficients are related to autocorrelation functions through the zero frequency component of the corresponding power spectra. On the other hand, measurements or relaxation times of molecular internal degrees of freedom provide information about finite frequency components of power spectra. For example, vibrational and nuclear spin relaxation times yield finite frequency components of power spectra which in the former case is the vibrational resonance frequency,28,29 and in the latter case is the Larmour precessional frequency.8 Experiments which probe a range of frequencies contribute much more to our understanding of the dynamics and structure of the liquid state than those which probe single frequency components. 

Figure 13.2 Molecular structure and absorption and fluorescence spectra of 1R125 in methanol, along with the laser power spectrum before shaping (dashed line). (Taken from Fig. 2, Ref. [41].)...

When there are more than one species present in a sample, each contributes to give a correlation function which is a sum of exponentials and a power spectrum which is a sum of Lorentzians. The intensity of each component in the composite function is proportional to the product of the molecular weight and the concentration in (w/v) units, assuming the refractive index increments of each component are identical. Two basic approaches are available to extract the particle distribution from the QLLS data. 

Static lattice simulation methods predict the tendency of polymers to avoid the strict regularity of a crystal by finding several lattice structures with similar energies but that vary in their chain-setting angle and cell vectors. The readiness with which the polymer sublattice in doped systems lowers its symmetry is echoed in both the defective static lattice simulations and the molecular dynamics treatment of lattice motions. In the former we observed the wide ranging response of the chains to even a small displacement of a dopant ion as described in Sections 5.3.2, 5.3.4, 5.4.2. and 5.6.3 while the dopant s power spectrum calculated in the course of the MD lattice simulations in Section 6.1 testifies to the important host-dopant interactions in potassium-doped polyacetylene. 

Example I The low-resolution (LR) positive-ion ESI mass spectrum and the charge-deconvoluted molecular weight spectrum inset) of bovine serum albumin (BSA) as obtained from a quadrupole ion trap instrument are compared below (Fig. 12.24). In case of such high-mass ions the resolving power of a quadrupole ion trap is insufficient to separate different cationization products of equal charge state. Nonetheless, charge deconvolution reveals that ion series A belongs to the noncovalent BSA dimer, while series B results from the monomer [26]. 

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