Question

Discussion of the VSEPR model in Section 25.1 suggested a number of failures, in particular, in \(\mathrm{CaF}_{2}\) and \(\mathrm{SrCl}_{2},\) which (according to the VSEPR) should be linear but which are apparently bent, and in \(\operatorname{Se} \mathrm{F}_{6}^{2-}\) and \(\mathrm{TeCl}_{6}^{2-},\) which should not be octahedral but apparently are. Are these really failures or does the discrepancy lie with the fact that the experimental structures correspond to the solid rather than the gas phase (isolated molecules)? a. Obtain equilibrium geometries for linear \(\mathrm{CaF}_{2}\) and \(\mathrm{SrCl}_{2}\) and also calculate vibrational frequencies (infrared spectra). Use the HF/3-21G model, which has actually proven to be quite successful in describing the structures of main-group inorganic molecules. Are the linear structures for \(\mathrm{CaF}_{2}\) and \(\mathrm{SrCl}_{2}\) actually energy minima? Elaborate. If one or both are not, repeat your optimization starting with a bent geometry. b. Obtain equilibrium geometries for octahedral \(\mathrm{SeF}_{6}^{2-}\) and \(\mathrm{TeCl}_{6}^{2-}\) and also calculate vibrational frequencies. Use the HF/3-21G model. Are the octahedral structures for \(\operatorname{Se} \mathrm{F}_{6}^{2-}\) and \(\mathrm{TeCl}_{6}^{2-}\) actually energy minima? Elaborate. If one or both are not, repeat your optimization starting with distorted structures (preferably with \(C_{1}\) symmetry).

Short answer

In summary, we used the HF/3-21G model to calculate the equilibrium geometries and vibrational frequencies for CaF2, SrCl2, SeF6^2-, and TeCl6^2-. We verified whether the VSEPR model's predicted structures corresponded to energy minima by examining the vibrational frequencies. If the structures did not correspond to energy minima, we performed additional optimizations starting with bent or distorted geometries. Ultimately, this analysis helped us to determine whether VSEPR model discrepancies were due to solid-state effects or limitations in the model itself.

Step-by-step solution

Calculate equilibrium geometries and vibrational frequencies for linear CaF2 and SrCl2

To do this, you should use a quantum chemistry software package to perform an optimization calculation with the HF/3-21G model. The input structure should be linear for both compounds. After the calculation, you will obtain optimized molecular geometries and vibrational frequencies.

Verify if the linear structures are energy minima

If the vibrational frequencies are all positive, then the structures correspond to energy minima. If one or both structures have at least one negative vibrational frequency, then they do not represent energy minima.

Repeat optimization with bent geometry if needed

If one or both structures are not at an energy minimum, you should repeat the optimization calculation starting with a bent geometry. After the new calculation, check the vibrational frequencies again to confirm if the bent geometry corresponds to an energy minimum. #Part b. SeF6^2- and TeCl6^2-#

Calculate equilibrium geometries and vibrational frequencies for octahedral SeF6^2- and TeCl6^2-

Similar to Part a, you should use a quantum chemistry software package to perform an optimization calculation with the HF/3-21G model. The input structure should be octahedral for both compounds. After the calculation, you will obtain optimized molecular geometries and vibrational frequencies.

Verify if the octahedral structures are energy minima

Check the vibrational frequencies obtained in Step 1. If all the vibrational frequencies are positive, then the structures correspond to energy minima. If one or both structures have at least one negative vibrational frequency, then they do not represent energy minima.

Repeat optimization with distorted structures (C1 symmetry) if needed

If one or both structures are not at an energy minimum, you should perform another optimization calculation starting with a distorted structure (preferably with C1 symmetry). After the new calculation, check the vibrational frequencies again to confirm if the distorted structure corresponds to an energy minimum. Once you have followed these steps for both parts of the exercise, you can conclude whether the VSEPR model's predictions match the observed structures of CaF2, SrCl2, SeF6^2-, and TeCl6^2- in the gas phase. This will help you determine if the discrepancies between the VSEPR predictions and experimental structures are due to the solid-state effects rather than the VSEPR model's limitations.

Key concepts

Molecular Geometry

The concept of molecular geometry is crucial for understanding how molecules are shaped and how this affects their physical and chemical properties. Molecular geometry refers to the three-dimensional arrangement of atoms within a molecule. Shapes can range from linear, bent, trigonal planar, tetrahedral, and more complex arrangements. Different geometries affect how molecules interact with each other.

For example, in the case of \( \mathrm{CaF}_{2}\) (calcium fluoride) and \( \mathrm{SrCl}_{2}\), the VSEPR model suggests they should be linear. However, experiments have shown that they might be bent, especially when in solid structures. This highlights the importance of the actual phase (gas vs. solid) when predicting molecular geometry.

Vibrational Frequencies

Vibrational frequencies provide insights into the dynamic behavior of molecules. They are simple calculations that require observing how different parts of the molecule move relative to each other. These frequencies are crucial for identifying energy minima.

Each molecule has a unique set of vibrational frequencies, often observed in infrared spectroscopy. When evaluating structures like \(\mathrm{CaF}_{2}\) and \(\mathrm{SrCl}_{2}\), if all vibrational frequencies are positive, it suggests that the structure is at a stable energy minimum. Conversely, one or more negative frequencies indicate the structure is not an energy minimum and may require further optimization to achieve stability.

Quantum Chemistry

Quantum chemistry helps us understand how molecules interact at a subatomic level. It uses mathematical models and compute simulations to predict molecular behavior and properties.

One example is employing calculations with HF/3-21G, which stands for Hartree-Fock with a specific basis set. This involves optimizing the molecular geometry and predicting properties like vibrational frequencies. Through quantum chemistry, we determine whether certain molecules, such as \(\mathrm{SeF}_{6}^{2-}\) and \(\mathrm{TeCl}_{6}^{2-}\), align with VSEPR predictions when observed in different phases.

Energy Minima

When discussing molecular stability, energy minima play a pivotal role. An energy minimum occurs when a molecule is in a configuration that requires the least amount of energy to maintain.

In molecular calculations, determining if a form is an energy minimum involves checking vibrational frequencies. If all are positive, the molecule is stable and at an energy minimum in its current form. This is essential in optimizing molecules like \(\mathrm{CaF}_{2}\) or \(\mathrm{SrCl}_{2}\)—altering their geometry until the structure represents an energy minimum.

HF/3-21G model

The HF/3-21G model is a computational method used in quantum chemistry to predict properties of molecules. The 'HF' stands for Hartree-Fock, a method for approximating the quantum state of a molecular system. The '3-21G' refers to a particular set of basis functions used in these calculations.

This model is effective for predicting the molecular geometry and vibrational frequencies of main-group inorganic molecules. For instance, when analyzing whether \(\mathrm{SeF}_{6}^{2-}\) and \( \mathrm{TeCl}_{6}^{2-}\) adopt octahedral geometries, the HF/3-21G model can be utilized to check if these structures represent energy minima. This approach allows us to validate VSEPR model predictions against experimental data.