Normalized Molecular Moment Structure

Molnar SP, King JW. Theory and applications of the integrated molecular transform and the normalized molecular moment structure descriptors QSAR and QSPR paradigms. Int J Quantum Chem 2001 85 662-675. 

F or the characterization of the charge distribution in a molecule, the numerically unitary integrated molecular transform (FTm), its analogous electronic (FTe) and charge (FTC) transforms, and the normalized molecular moment (Mn), its analogous electronic (AQ and charge (Mc) moment, have been developed as molecular structure descriptors [45,46]. Those descriptors have been applied successfully for the development of QSAR models for various physicochemical, pharmacological, and thermodynamic properties of compounds. 

The set of molecular data required for statistical thermodynamic calculations includes molecular mass, structural parameters for determination of a point group, a symmetry number a and calculation of a product of principal moments of inertia IA IB Ic, as well as 3n - 6 frequencies of normal vibrations for an n-atomic molecule. 

The second problem of interest is to find normal vibrational frequencies and integral intensities for spectral lines that are active in infrared absorption spectra. In this instance, we can consider the molecular orientations, to be already specified. Further, it is of no significance whether the orientational structure eRj results from energy minimization for static dipole-dipole interactions or from the competition of any other interactions (e.g. adsorption potentials). For non-polar molecules (iij = 0), the vectors eRy describe dipole moment orientations for dipole transitions. 

Analysis of the rotational fine structure of IR bands yields the moments of inertia 7°, 7°, and 7 . From these, the molecular structure can be fitted. (It may be necessary to assign spectra of isotopically substituted species in order to have sufficient data for a structural determination.) Such structures are subject to the usual errors due to zero-point vibrations. Values of moments of inertia determined from IR work are less accurate than those obtained from microwave work. However, the pure-rotation spectra of many polyatomic molecules cannot be observed because the molecules have no permanent electric dipole moment in contrast, all polyatomic molecules have IR-active vibration-rotation bands, from which the rotational constants and structure can be determined. For example, the structure of the nonpolar molecule ethylene, CH2=CH2, was determined from IR study of the normal species and of CD2=CD2 to be8... 

The study of oriented polymers with polarized infrared radiation is an equally important tool in the detailed analysis of the vibrational spectrum, since it permits us, within certain restrictions, to determine the orientation (with respect to the molecular structure) of the transition moment for a given normal mode. This makes it possible, as we shall see, not only to classify bands in the spectrum but to establish their origin. Although polarizers are available with commercial spectrometers, their use has not yet become as general as would be desirable. Some comments... 

The structure and tilt angle of the molecules relative to the surface normal were determined by their FTIR spectra. In helical peptides, the transition moment of amide-I band lies nearly parallel to the helix axis and that of amide-II perpendicular. Since transition moments, which lie parallel to the gold surface, cannot be detected in grazing angle FTIR, the ratio between the intensities of the amide-I band (1,665 cm-1) and amide-II band (1,550 cm-1) indicates to what extend the molecules in the monolayer are oriented perpendicular to the gold surface. Based on the FTIR spectra it was possible to calculate the tilt angle, namely the angle between the molecular axis and the surface normal. The frequencies of amide-I and amide-II vibrations indicate that the monolayer is indeed in an a helix form (Fig. 2a). 

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