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Benzyne has long been implicated as an intermediate in nucleophilic aromatic substitution, for example, Although the geometry of benzyne has yet to be conclusively established, the results of a \(^{13} \mathrm{C}\) labeling experiment leave little doubt that two (adjacent) positions on the ring are equivalent: There is a report, albeit controversial, that benzyne has been trapped in a low-temperature matrix and its infrared spectrum recorded. Furthermore, a line in the spectrum at \(2085 \mathrm{cm}^{-1}\) has been assigned to the stretching mode of the incorporated triple bond. Optimize the geometry of benzyne using the HF/6-31G* model and calculate vibrational frequencies. For reference, perform the same calculations on 2 -butyne. Locate the \(\mathrm{C} \equiv \mathrm{C}\) stretching frequency in 2 -butyne and determine an appropriate scaling factor to bring it into agreement with the corresponding experimental frequency \(\left(2240 \mathrm{cm}^{-1}\right) .\) Then identify the vibration corresponding to the triple-bond stretch in benzyne and apply the same scaling factor to this frequency. Finally, plot the calculated infrared spectra of both benzyne and 2-butyne. Does your calculated geometry for benzyne incorporate a fully formed triple bond? Compare with the bond in 2 -butyne as a standard. Locate the vibrational motion in benzyne corresponding to the triple bond stretch. Is the corresponding (scaled) frequency significantly different \(\left(>100 \mathrm{cm}^{-1}\right)\) from the frequency assigned in the experimental investigation? If it is, are you able to locate any frequencies from your calculation that would fit with the assignment of a benzyne mode at \(2085 \mathrm{cm}^{-1} ?\) Elaborate. Does the calculated infrared spectrum provide further evidence for or against the experimental observation? (Hint: Look at the intensity of the triple-bond stretch in 2-butyne.)

Step by step solution

01

Geometry optimization

First, optimize the geometry of benzyne and 2-butyne using the HF/6-31G* model in a computational chemistry software. This will provide us with the optimized molecular structure of both molecules for the next steps.

02

Calculation of vibrational frequencies

Calculate the vibrational frequencies of benzyne and 2-butyne using the optimized geometries obtained in Step 1. The output will include all vibrational frequencies and their corresponding modes.

03

Locate the C鈮�C stretching frequency in 2-butyne

Examine the vibrational frequencies of 2-butyne obtained in Step 2 and identify the frequency corresponding to the C鈮�C stretching mode. Note this value for the next step.

04

Determine the scaling factor

To determine the scaling factor, use the experimental frequency of C鈮�C stretching in 2-butyne (2240 cm鈦宦�) and the calculated value obtained in Step 3. The scaling factor is found using the formula: \(Scaling \ factor = \frac{Experimental \ frequency}{Calculated \ frequency}\)

05

Apply the scaling factor to benzyne

Identify the vibrational mode corresponding to the triple-bond stretch in benzyne from the output in Step 2. Multiply the calculated frequency by the scaling factor obtained in Step 4 to obtain the scaled frequency.

06

Plot the calculated infrared spectra

Using the calculated frequencies obtained in Step 2, plot the infrared spectra of benzyne and 2-butyne. Make sure to indicate intensities and vibrational modes in the plot.

07

Analysis and comparison of results

Now analyze the calculated results and answer the following questions: - Does the calculated geometry of benzyne have a fully formed triple bond? Compare with the bond in 2-butyne as a standard. - Is the calculated (scaled) frequency for benzyne's triple bond stretch significantly different (>100 cm鈦宦�) from the experimental value of 2085 cm鈦宦�? If yes, try to locate any other frequencies that would fit with the assignment of benzyne mode at 2085 cm鈦宦�. - Does the calculated infrared spectrum provide further evidence for or against the experimental observation? Consider the intensity of the triple-bond stretch in 2-butyne as a hint. Based on these analyses, you may determine the likelihood of benzyne participating in the nucleophilic aromatic substitution and its overall geometry.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

HF/6-31G* model

The HF/6-31G* model plays a significant role in theoretical chemistry, especially in computational studies of molecular structures and properties. HF refers to Hartree-Fock, a quantum chemical method used to approximate the behavior of electrons in a molecule. It is a self-consistent field method, meaning it uses an iterative approach to solve the Schr枚dinger equation for electrons moving under the influence of the nuclei in the molecule.

The 6-31G* in the name denotes a specific type of basis set used in these calculations. Basis sets are mathematical functions that describe the electron wavefunctions in the molecule. The '6-31G*' basis set is a split-valence set with polarization functions on non-hydrogen atoms, which means it provides a more detailed and accurate description of the electron distribution, accounting for the shape and orientation of electron clouds. For students tackling this model, it is crucial to understand that the HF/6-31G* model balances computational cost with accuracy, making it suitable for studying a wide variety of molecular systems including benzyne.

Vibrational frequencies calculation

In computational chemistry, calculating vibrational frequencies is integral to understanding molecular vibrations and the predicted spectra of molecules. With the use of software, vibrations are computationally simulated by displacing atoms in a molecule and measuring the force restoring them to equilibrium. This process is based on the optimized geometry and occurs after the molecular structure has been thoroughly examined for the lowest energy configuration.

The output from these calculations includes frequencies, which indicate how often a vibration occurs, and modes, which describe the type of vibration (e.g., stretching, bending). For students, recognizing that each vibrational frequency correlates to a specific motion within the molecule is key. These calculations are crucial for predicting the behavior of molecules under infrared radiation, as different vibrational modes will absorb light at different frequencies. When applied to benzyne and 2-butyne, such calculations allow insights into the presence and characteristics of triple bonds within these structures.

C鈮�C stretching frequency

The C鈮�C stretching frequency is a particular vibrational mode that occurs in molecules with a carbon-carbon triple bond. This vibration involves the movement of two carbon atoms along the axis of the bond, either moving towards or away from each other. The stretching frequency is characteristic of the strength and stiffness of the triple bond and is typically observed in the infrared spectrum.

For students studying chemistry, understanding how the triple bond's stiffness leads to higher vibrational frequencies compared to single or double bonds is crucial. The stretching frequency is of particular interest when comparing theoretical and experimental values, as discrepancies can indicate inaccuracies in computational models or new insights into molecular behavior. As in the benzyne and 2-butyne comparison, such analysis can be central to verifying molecular structures and the nature of bonding within them.

Scaling factor determination

The determination of a scaling factor is an important step in comparing theoretical vibrational frequencies with experimental data. Since calculated vibrational frequencies tend to be higher than those measured experimentally due to approximations in the computational methods, a scaling factor is used to correct them. This factor is obtained by dividing the experimental frequency by the calculated frequency for a vibration known to occur in both the studied molecule and a reference molecule.

The understanding of scaling factors can be simplified for students by equating it to a 'fine-tuning' process, where the calculated data is aligned with empirical evidence to increase its reliability. When applied to benzyne analysis, the scaling factor derived from comparison with 2-butyne's known C鈮�C stretching frequency allows for a more accurate prediction of benzyne鈥檚 vibrational characteristics.

Calculated infrared spectra

The calculated infrared (IR) spectra are the visual representations of a molecule's response to infrared radiation, predicting which frequencies will be absorbed due to molecular vibrations. The spectra are plotted as a graph showing the intensity of absorption versus frequency. Each peak corresponds to a different vibrational mode of the molecule, with the position and height of the peak providing information about the vibration's energy and how strongly it interacts with IR radiation.

Students should understand that by analyzing the calculated IR spectra, scientists can gain insights into the molecular structure and chemical bonding. For the benzyne and 2-butyne example, examining the IR spectra can confirm the presence of the C鈮�C stretch, its bonding environment, and the overall structure of the molecules. The intensity of these peaks, especially that of the triple bond stretch, offers additional evidential support for the assignment of vibrational modes to specific molecular bonds.