GF method

Abstract: Neutron inelastic scattering (NIS) and ultraviolet resonance Raman scattering (RRS) experimental data have been obtained from purine nucleic base samples, i.e., adenine, C8-deuterated adenine, and a (N9, C6-amino) - deuterated species. The two types of spectra have made it possible to carry out complete theoretical assignments of the vibrational modes of adenine and its derivatives. Normal mode wavenumbers as well as atomic displacements have been calculated by the Wilson GF method, using a valence force field and a non-redundant set of internal coordinates

Abstract: The GF method for obtaining accurate many‐electron wavefunctions was described in a previous paper. In this paper, some of the properties of this method are explored, and it is shown that the Hellmann–Feynman, Koopmans', and Brillouin's theorems apply to GF wavefunctions. Calculations are reported on Li2, CH4, and CH3 in order to demonstrate some aspects of the method.

Abstract: A systematic study of the sugar pucker characteristic vibration modes as a function of its geometrical conformations, has been performed. The present investigation is based on the Wilson GF method and a non-redundant valence force field. The calculated results allow to assign the modes arising mainly from the sugar motions and present in quasi whole vibrational spectra related to the right or left-handed double-helices (i.e., 1050 cm−1,960 cm−1 and 890 cm−1). Moreover, the conformation dependent modes as those at 860 cm−1 and around 810 cm−1 (A form) as well as the one located around 830 cm−1 (B form) are interpreted by the present investigation. The possibility of the interaction of the latter modes with the phosphate group motions along the DNA double-helical chains are also discussed.

Abstract: The chapter summarizes important concepts from the theory of molecular vibrations of which normal coordinate analysis is a part. Section 2 describes how molecular vibrations or, more precisely, harmonic oscillators are treated in classical mechanics and how normal coordinates are defined. The quantum mechanics of coupled harmonic oscillators, which is based on normal coordinates, is developed in section 3, together with the selection rules for infrared and Raman spectroscopy. It is followed by excursions into some applications of symmetry concepts and into the domain of real molecules where harmonic oscillators are satisfactory approximations at best (anharmonicity and large-amplitude internal motions). Section 4 introduces the commonly used internal and symmetry coordinates, the transformations between them and the Cartesian and normal coordinates, Wilson's GF method of normal coordinate analysis, and discusses redundant sets of internal coordinates. A short survey of force fields past and present (central, valence, and Urey-Bradley force fields and force fields from semiempirical and ab initio calculations) is given in section 5. The invariance of internal coordinates, the transformation from internal to Cartesian coordinates, and some aspects of redundant coordinates are detailed in appendices. Keywords: anharmonicity; Cartesian coordinates; force constant; force field; harmonic oscillator; internal coordinates; molecular vibrations; normal coordinate analysis; potential energy distribution; quantum mechanics; redundant coordinates; relative intensity; symmetry coordinates; vibrational energy levels; vibrational wave functions; vibrational frequencies; vibrational selection rules