By a detailed and laborious analysis, Teller showed that excepting linear molecules there are always first-order terms in an expansion of the matrix elements of the Hamiltonian in terms of symmetry-lowering ( in the language of group theory : non-totally symmetric ) normal modes.
42.
The most important linear molecule with more than three atoms is acetylene ( H " Ca " C " H ), in which each of its carbon atoms is considered to be a central atom with a single bond to one hydrogen and a triple bond to the other carbon atom.
43.
As described by the VSEPR model, the five valence electron pairs on the central atom form a trigonal bipyramid in which the three lone pairs occupy the less crowded equatorial positions and the two bonded atoms occupy the two axial positions at the opposite ends of an axis, forming a linear molecule.
44.
In the high temperature limit, it is traditional to correct for the missing nuclear spin states by dividing the rotational partition function by a factor \ sigma = 2 with \ sigma known as the rotational symmetry number which is 2 for linear molecules with a center of symmetry and 1 for linear molecules without.
45.
In the high temperature limit, it is traditional to correct for the missing nuclear spin states by dividing the rotational partition function by a factor \ sigma = 2 with \ sigma known as the rotational symmetry number which is 2 for linear molecules with a center of symmetry and 1 for linear molecules without.
46.
For linear molecules there are only 2 rotational degrees of freedom, because the rotation parallel to the symmetry axis corresponds to a spin of atoms which we didn't count in the composition of the degrees of freedom in terms of the atoms ( so, the book keeping of the degrees of freedom will then yield 3n-5 vibrational degrees of freedom ).
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