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For a linear molecule, analysis of the rotational spectrum provides values for the rotational constant [notes 2] and the moment of inertia of the molecule, and, knowing the atomic masses, can be used to determine the bond length directly. For diatomic molecules this process is straightforward.
Clar's rule states that for a benzenoid polycyclic aromatic hydrocarbon (i.e. one with only hexagonal rings), the resonance structure with the largest number of disjoint aromatic π-sextets is the most important to characterize its chemical and physical properties. Such a resonance structure is called a Clar structure. In other words, a ...
Example of a linear molecule. N atoms in a molecule have 3N degrees of freedom which constitute translations, rotations, and vibrations.For non-linear molecules, there are 3 degrees of freedom for translational (motion along the x, y, and z directions) and 3 degrees of freedom for rotational motion (rotations in R x, R y, and R z directions) for each atom.
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.
Like ordinary Raman spectroscopy, resonance Raman is compatible with samples in water, which has a very weak scattering intensity and little contribution to spectra. However, the need for an excitation laser with a wavelength matching that of an electronic transition in the analyte of interest somewhat limits the applicability of the method. [8]
In CO 2, the bending vibration ν 2 (667 cm −1) has symmetry Π u.The first excited state of ν 2 is denoted 01 1 0 (no excitation in the ν 1 mode (symmetric stretch), one quantum of excitation in the ν 2 bending mode with angular momentum about the molecular axis equal to ±1, no excitation in the ν 3 mode (asymmetric stretch)) and clearly transforms according to the irreducible ...
(2) The PARENT and CHOOSE operations determine the optimal set of NBOs corresponding to a specific resonance structure. Additionally, CHOOSE is able to eliminate identical resonance structures. (3) A user may then call SELECT to select the structure that best matches to the true molecular structure.
where an are the approximations to the motion expanded in a complete basis set, E comes from the kinetic energy term, and Γ comes from the elastic energy term. The order of the matrices is ~10^3 for good approximations. Equation (5) determines the resonance frequencies from the elastic moduli. [3]