(a) Consider the four normal modes of vibration of a linear molecule AB2 from the standpoint of

(a) Consider the four normal modes of vibration of a linear...

$(a)$ Consider the four normal modes of vibration of a linear molecule $\mathrm{AB}_{2}$ from the standpoint of changing dipole moment and changing polarizability. Which vibrational modes are infrared active, and which are Raman active? (Note the exclusion rule.) $(b)$ Consider the three normal modes of a nonlinear molecule $\mathrm{AB}_{2}$. Which vibrational modes are infrared active, and which are Raman active?

Key Concepts

Normal Modes of Vibration

Normal modes refer to independent patterns of atomic movement about their equilibrium positions in a molecule. Each mode is characterized by a specific frequency and symmetry, and together they describe the complete set of vibrational motions possible. Understanding normal modes is crucial in spectroscopy, as each mode can interact differently with electromagnetic radiation depending on its symmetry characteristics.

Infrared Spectroscopy Selection Rule

In infrared spectroscopy, a vibrational mode is active if it involves a change in the dipole moment of the molecule. This means that for a vibration to absorb infrared radiation, the oscillation must result in a temporary asymmetry in the charge distribution, allowing the molecule to interact with the electric field component of the incident light.

Raman Spectroscopy Selection Rule

Raman spectroscopy is based on inelastic scattering of light, and a vibrational mode is Raman active if it involves a change in the polarizability of the molecule. This rule means that even if a vibration does not change the dipole moment and is therefore infrared inactive, it may still be detected provided it alters the electronic cloud's ability to be distorted by an external electric field.

Molecular Symmetry and the Exclusion Rule

The exclusion rule arises in molecules with a center of inversion, stating that vibrations which are infrared active (those that change the dipole moment) are Raman inactive, and vice versa. This mutually exclusive behavior is a direct consequence of the symmetry properties of the vibrational modes and plays a critical role in determining the spectroscopic activity of different modes in a given molecule.

Molecular Geometry (Linear vs Nonlinear Molecules)

The geometry of a molecule, whether linear or nonlinear, strongly influences its vibrational characteristics and corresponding spectroscopic behavior. Linear molecules have different symmetry elements compared to nonlinear molecules, leading to variations in the number and types of vibrational modes as well as their activity in infrared and Raman spectra. Understanding the role of molecular shape is fundamental in predicting and explaining the observed vibrational spectra.

Transcript

00:02 Okay, so this question not only tells your knowledge on the vibration of a molecule, but also it tells you the knowledge on the valence bond theory and the hybridization of the optos.

00:22 So the first question asks about the molecular shape of the sulfur oxide 3.

00:31 And this basically asks you the geometry of the molecule.

00:37 So we have to use the bonevenous theory and hybridization to solve this question.

00:45 So first, we need to treat the software as a center atoms.

00:50 And we need to write down its electron configurations, which is 3s2 and 3p4.

01:01 It has 6 electrons, it's an outlayer orbital.

01:07 And then we can draw its diagram, right? we have 3s2, you have 3s orbital, and you have 3p orbitals here.

01:21 And that's few electrons.

01:24 You have a pair in the 3s orbital, and you have 4 electrons in the 3p orbital.

01:34 So if you look at this diagram, right, you will find there's only two unfurbed orbitals, p -obitals.

01:45 So theoretically, if you just use the sp orbital to form bonds for sulfur, at most you can form two bonds.

01:54 But looking at s -o -3, definitely there are more than two bonds, right? at least three.

01:59 So this is not enough for forming bonds or doing a hybridization.

02:07 Which means you actually probably need extra dioptos to form bonds.

02:17 There are amosified dioptos.

02:20 So then we can actually find, we can actually know actually the hybridization way is actually dsp3.

02:38 And for the dsp3 hybridization way, the geometry, if you look, check the book, or if you remember, is a this kind of shape, right? it's a double pyramidal.

03:02 And now let's say how to arrange that.

03:08 So suppose, right, we have this kind of structure.

03:13 And there will be, so, and we know that there would be three bonds forming...

Please give Ace some feedback