Degrees of Freedom (3N where N is the #nu= clei per molecule)
3 coordinates translation motion
3 coordinates rotation m= otion
3n - m (where m is 6 or 5, pending on if = it's non-linear or linear, respectively)
Molecule | vmodes | |
---|---|---|
CO_{2} | 4 | n=3D3; 3n - 5 =3D 3(3) - 5 |
CO | 1 | n=3D2; 3n - 5 =3D 3(2) - 5 |
v =3D stretching =E2=88=86 bond length
=CE=B4 =3D bending =E2=88=86 in bon= d angle
=CF=81_{r} =3D rockin= g =E2=88=86 in angle between group of atoms
=CF=81_{w }=3D wagging =E2=88=86 = in angle between plane of group of atoms
=CF=81_{t } =3D twisting =E2= =88=86 in angle between planes of two groups of atoms_{}
=CF=80 =3D out of plane
s =3D symmetric
as =3D symmetric
d =3D degenerate
ht= tps://chem.libretexts.org/Reference/Reference_Tables/Group_Theory_Tables/Ch= aracter_Tables
https://en.wikipedia.org/wiki/Molecular_symme= try
A rotation about principal axis =3D symmetrical
B rotation about principal axis =3D asymetrical
E & T doubly and triply degenerate
inversion center: g =3D no change in sign, u =3D change in sign w/ respe= ct to inversion.
CO_{2} - cyclic C_{nv} Group ( n-fold proper rotation ax= is Cn )
E, C2, =CF=83 (xz) & =CF=83 (yz)
C2v | E | C2 | =CF=83 (xz) | =CF=83 (yz) | |
---|---|---|---|---|---|
v1 | 1 | 1 | 1 | 1 | a1 |
v2 | 1 | 1 | 1 | 1 | a2 |
v3 | 1 | -1 | -1 | 1 | b2 |
A_{1g}, b_{1g}, e_{u} =3D stretching vibrations<= /p>
b_{2g}, a_{2u}, b_{2u}, e_{u} =3D bendin= g vibrations
s + l
https://en.wikipedia.org/w= iki/Total_angular_momentum_quantum_number
J and branches: P =E2=88=86J =3D -1 Branch, Q - =E2=88=86J =3D 0 Branch,= R - =E2=88=86J =3D 1 Branch