Vibrational-Rotational Spectroscopy

Vocabulary flashcards covering the principles of ro-vibrational spectroscopy, selection rules, spectral branches, vibration-rotation interaction, and the method of combination differences.

Ro-vibrational spectroscopy

The study of transitions in gas-phase molecules that involve simultaneous changes in both vibrational and rotational energy states.

$$\Delta v = \pm 1$$

The vibrational selection rule for fundamental transitions in simple diatomic linear molecules like CO.

$$\Delta J = \pm 1$$

The rotational selection rule for simple diatomic linear molecules, indicating that pure vibrational transitions ($\Delta J = 0$) are forbidden.

P-branch

A series of peaks in the ro-vibrational spectrum where $\Delta J = -1$, resulting in lower wavenumbers relative to the center ($\text{Vibration} - \text{Rotation}$).

R-branch

A series of peaks in the ro-vibrational spectrum where $\Delta J = +1$, resulting in higher wavenumbers relative to the center ($\text{Vibration} + \text{Rotation}$).

Null gap

The empty space at the exact vibrational frequency ($\nu_0$) in a diatomic ro-vibrational spectrum caused by the forbidden $\Delta J = 0$ transition.

$$P(J'')$$

A transition label indicating the rotational level of the lower state is $J''$ and moves to state $J'' - 1$ (e.g., $P(1)$ is $J'' = 1 \rightarrow J' = 0$).

$$R(J'')$$

A transition label indicating the rotational level of the lower state is $J''$ and moves to state $J'' + 1$ (e.g., $R(0)$ is $J'' = 0 \rightarrow J' = 1$).

Vibration-Rotation Interaction

A physical complication where the rotational constant ($B$) is not constant because it depends on the vibrational state ($v$) and average bond length ($r$).

$$B \propto 1/r^2$$

The relationship stating the rotational constant is inversely proportional to the square of the bond length; as vibration increases bond length (r_1 > r_0), the constant decreases (B_1 < B_0).

R-branch Compression

A spectral effect of vibration-rotation interaction where line spacing decreases (lines bunch together) as $J$ increases.

P-branch Dilation

A spectral effect of vibration-rotation interaction where line spacing increases (lines spread apart) as $J$ increases.

Combination Differences

An analytical method used to isolate rotational constants ($B_0$ and $B_1$) by choosing pairs of spectral lines that share a common upper or lower state.

$$\Delta_2 F''(J) = 4B_0(J + 1/2)$$

The expression for ground state combination differences derived from $R(J-1) - P(J+1)$, where the gradient of the plot against $(J + 1/2)$ is $4B_0$.

$$\Delta_2 F'(J) = 4B_1(J + 1/2)$$

The expression for excited state combination differences derived from $R(J) - P(J)$, where the gradient of the plot against $(J + 1/2)$ is $4B_1$.

Parallel Modes (Stretches)

Vibrational motion along the bond axis in linear polyatomic molecules (like HCN) where selection rules result in only P and R branches ($\Delta J = \pm 1$).

Perpendicular Modes (Bends)

Vibrational motion at right angles to the bond axis in linear polyatomic molecules that allows $\Delta J = 0$ transitions.

Q-branch

An intense spike in the center of the spectrum for perpendicular vibrational modes where all $\Delta J = 0$ transitions occur at nearly the same frequency.

$$3n-5$$

The formula used to determine the degrees of vibrational freedom for linear polyatomic molecules.

$$3n-6$$

The formula used to determine the degrees of vibrational freedom for non-linear molecules.

Non-Linear Ro-vibrational Spectrum

A complex spectrum characterized by a dense forest of overlapping lines due to three independent rotational constants ($A$, $B$, and $C$).