Quantum mechanics bending vibrations

Scaled quantum mechanics computations of vibrational spectra of small molecules, including thiirane, were performed by Katsyuba and Vandyukova <2003CPL658>. With 13 scaling factors, applied to B3LYP force fields, they were able to compute stretching and bending frequencies for 26 molecules with a total standatd deviation of about 11 cm for 6-31G and 6-31-l-G basis sets. The latter basis set was recommended for Raman spectra. 

The emerging picture is one in which the quantum-mechanical equivalents of the constants of motion for the two valence electrons in these atoms are like those associated with the near-rigid rotations, bending vibrations, and stretching vibrations we normally associate with linear triatomic molecules. These new results bring into question the range of validity of the nearly-independent-particle model, the quantum-mechanical counterpart of Bohr s planetary model, for atoms with more than one valence electron. 

In this section, we will present a mathematical description of the BCRLM. We will define the classical and quantum mechanical Hamiltonian for the translational, vibrational, tumbling, and bending degrees of freedom for the system. After expanding the scattering wavefunction in... 

Vibrational spectroscopy of molecules depends on quantum mechanics, which requires well-defined frequencies and atomic displacements known as the normal modes of vibrations of the molecules. A linear molecule with N atoms has 3N-5 normal modes, and a nonlinear molecule has 3N-6 normal modes of vibrations. Several types of motions leads to normal modes such as (i) stretching motion between two bonded atoms, (ii) bending motion between three atoms connected by two bonds, and (iii) out-of-plane deformation modes take place with changes from a planar structure to a nonplanar one. 

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