Giuseppe Zerbi

Normal Coordinate Calculations as a Tool for Vibrational Assignments. I. Fundamental Vibrations of Simple Aliphatic Amines

Fundamental frequencies, normal coordinates, and force constants were calculated using an Overlay technique for CH3NH2, CD3NH2, CH3ND2, CD3ND2, (CH3)2NH, (CH3)2ND, (CH3)3N, and (CD3)3N. Both valence and Urey–Bradley force fields were adopted. The vibrational assignments previously reported on all these molecules have been partly confirmed and partly modified. The usefulness and limitations of normal coordinate calculations in problems of vibrational assignments is discussed.

Dispersion Curves and Frequency Distribution of Polymers: Single Chain Model

A general method for the calculation of dispersion curves for any single polymer chain in terms of internal coordinates is proposed. The method is immediately applicable to electronic computers. Dispersion curves and the corresponding frequency distributions have been obtained for polyethylene and deuterated polyethylene, hexagonal polyoxymethylene, and deutero derivative and orthorhombic polyoxymethylene. Spectroscoptically active fundamentals have been calculated and the normal modes described in terms of a valence force field. Experimental data from vibrational spectroscopy and inelastic neutron scattering have been compared and discussed in terms of that predicted by calculations.

A generalization of GF method to crystal vibrations

Abstract A hermitian dynamical matrix in terms of Cartesian displacement coordinates is derived starting from a harmonic force constant matrix expressed in terms of the Wilsons internal displacement coordinates. The method accounts both for inter- and intramolecular coupling. The frequency spectrum can be obtained from the dynamical matrix without directly solving the secular equation by the application of Deans negative eigenvalues theorem.

Fundamental frequencies and molecular configuration of biphenyl—II Normal coordinates

Abstract Both a modified Urey—Bradley Force Field and a Simplified Valence Force Field have been refined through a least square technique on the fundamental frequencies of biphenyl-d0 and biphenyl-d10 determined in a previous paper. A critical analysis of the obtained results is discussed. The description of the normal modes is obtained from Potential Energy Distribution and from atomic displacements. The problem of vibrations localized in ortho, meta and para position is discussed together with the problem of ortho hydrogen interaction. The results seem to indicate that the extent of delocalization of π-bonds across the inter-ring Cue5f8C bond (conjugation), if it exists, it must be very small.

Molecular Vibrations of High Polymers

Abstract The discussion in the present review is restricted to the spectroscopic problems of polymeric systems in their ideal molecular and crystalline states. Relaxation of the strict theoretical conclusions for approaching the true physical nature of polymers and their practical applications will be discussed in more detail in another article.

Symmetry coordinates in molecular vibrations

Symmetry coordinates which factor G and F matrices are usually constructed by hand through the Wigner operator. A simple method is described here which provides a systemof coordinates which factor the same matrices to the maximum extent allowed by the symmetry of the molecule. Thecoordinates are closer to the normal ones than the usual Wigner type symmetry coordinates and may be obtained equally well for molecules or polymers.

Vibrational Analysis of Random Polymers

The frequency distributions of some isotopically random polymers are calculated by applying Deans negative eigenvalue theorem. It is shown that the results of calculation are in good agreement with the infrared spectra of polymers of cis‐CHDu2009=u2009CHD and trans‐CHDu2009=u2009CHD, giving strong confirmation to the previous view that the polymerization by a Ziegler‐type catalyst occurs with the cis opening of the double bond. The spectra of copolymers of CH2u2009=u2009CH2, CHDu2009=u2009CD2, and CD2u2009=u2009CD2 are also discussed. The effects of randomness and deuterium content on the frequency distribution are studied.

Redundant coordinates in the harmonic approximation

Abstract This paper discusses the problem of redundant coordinates in the harmonic approximation. It is shown that, as long as only small vibrations are considered, the possible redundancy relations among the coordinates are always linear. It is further shown that the constant K which is usually called intramolecular tension, does not enter the equations of motion in the case of small vibrations.

Low‐Frequency Vibrations of Crystalline Biphenyl

The spectrum of inelastically scattered slow neutrons has been obtained for polycrystalline biphenyl. Whereas translational modes account for the broad general features of the whole spectrum, the fine structure observed can be interpreted in terms of librational and q‐independent internal modes. The six theoretically predicted librations have been assigned. Moreover, one has good reasons to believe that the torsional internal mode, practically inactive in infrared and Raman, occurs in the INS spectrum at about 70 cm—1.

Force Constants and Normal Vibrations of the Propargyl Halides

Several modifications of a Urey—Bradley field combined with a valence force field have been used for the calculation of the normal coordinates of the propargyl halides CH2X–C≡C–H (X=F, Cl, Br, I). The force constants obtained by a least‐squares method have been compared in terms of the structural changes introduced by the halogen atom. A kinetic effect seems to account for the splitting of the –C≡C–H in‐plane and out‐of‐plane bending modes.