CHEMISTRY 158b, FALL, 2008, SECOND GRADED EXERCISE
NAME:______
In this exercise, due on 24 Nov., you will apply the theory of quantum mechanical and methods of molecular modeling to a diatomic molecule and the polyatomic molecule whose microwave spectrum you analyzed in the first graded exercise.
Your diatomic molecule is ______
Your polyatomic molecule is ______
I) Qualitative Molecular Orbital theory of your diatomic molecule.
The instructor developed a qualitative approach to MO theory in class. This simple but instructive model uses valence orbitals and the orbital energies. You will apply this approach to your diatomic molecule. Note that the valence shell of all elements in the second row of the periodic table includes 2s and 2p orbitals. Those in the third row include 3s, 3p, and 3d orbitals. If the qualitative approach yields two equally convincing models for your molecule, work out the details for each case.
A) Develop a MO diagram for your molecule.
B) Predict the electronic configuration and term symbol of your molecule in its ground electronic state. The term symbol includes the spin multiplicity, 2S + 1. You will need it for the ab initio calculations that follow.
C) Support your configuration with a succinct argument. If two configurations are likely, discuss both.
D) Analyze the occupied molecular orbitals.
E) Discuss the bonding in your molecule as informed by your model. Do 3d orbitals play a role?
II) Hartree-Fock Ab Initio Calculations on your molecule.
A) Use Version ’06 of Spartan for your calculations. The instructor will demonstrate its use in class. Draw the structure in the Expert mode and calculate the structure with the minimum electronic energy. Use the Hartree-Fock method with a 3-21G* basis set. (Select 3-21G from the menu of basis sets.) Note that you must provide the charge and multiplicity of your molecule. If you predicted two configurations in Part I, perform a separate calculation for each multiplicity.
B) Perform separate calculations for the two atomic species produced upon dissociation of your diatomic molecule.
C) Compare the molecular orbitals predicted in Part I with those generated above. Spartan performs an all-electron calculation and uses a split basis set so it generates many MO’s with multiple terms. You will have to locate the MO’s that correspond with those predicted in Part I. Hint: start with the HOMO.
D) If your qualitative model predicts two configurations, which one is indicated to be stabler by Spartan? Perform the following calculatons on the stabler species.
E) Obtain values for the following quantities from the results of your Spartan calculations: re in Ångstrom, De (the bond dissociation energy) in kJ/mol, and the first ionization energy in eV. Compare these results with the literature values. The JANAF Thermochemical Tables and the NIST Web sites whose links are provided in MolData are comprehensive, critically reviewed sources of data.
F) Although Spartan calculates the vibrational frequency, it is instructive to obtain this result manually. To this end, perform a series of Hartree-Fock calculations using the “Energy” rather than “Equilibrium Geometry” calculation method. The alternate method solves the Schroedinger equation for a fixed geometry. For each calculation, set r to a value within 1-2 milliÅngstrom of re. You will generate a set of energies corresponding to r equal to, less than, and greater than re. If r is sufficiently close to re, the energies will depend quadratically on r-re. Hence, fit the electronic energy to (r – re)2. The slope of this fit is k/2. Select the isotopomer with the highest natural abundance, e.g. 12C16O for carbon monoxide, and calculate its vibrational frequency in cm-1. Compare your result with the value from the literature.
G) You will find that the Hartree-Fock value of De compares poorly with the experimental result. The large error reflects the neglect of correlation energy. Density functional theory (DFT) provides an excellent cost-effective means of handling correlation. Repeat the calculations with DFT as the method, B3LYP as the functional, and a 6-31G* basis set. If you are adventurous, use the somewhat better functional of Donald Truhlar by entering EXCHANGE=M06 as a keyword. Recalculate De. How does the DFT result compare with experiment?
III) Molecular Modeling on Your Polyatomic Molecule.
In the first graded exercise, you were assigned the low resolution microwave spectrum of a polar conformer of a polyatomic molecule and obtained a value of B + C for this conformer. In this part of the exercise, you will identify the conformation with the aid of molecular modeling. When the microwave data were measured, molecular modeling was in its infancy and spectroscopists used bond lengths and bond angles from small molecules in the analysis of their spectra. Today molecular modeling has matured to the point that it has replaced the previous empirical approach.
One can perform this portion of the exercise with quantum mechanics. However, these calculations scale as N(electrons)4 and can consume days of computer time. Fortunately, molecular mechanics, a classical method, yields excellent results for uncharged organic molecules and runs with a remarkable reduction in computer time. In effect, molecular mechanics treats a molecule as a set of balls, springs, partial charges, and van der Waals radii. The parameters used in this method are generated by exhaustive ab initio calculations on a carefully selected set of test molecules. Molecular mechanics is heavily used in the determination of the three-dimensional structure of proteins from NMR data.
A) Use the Organic drawing utility of Spartan to draw the structure of your molecule. In this case, pay close attention to the bond order. If your structure has an aromatic ring, let Spartan insert it. Be sure to draw the correct isomer.
B) Minimize the energy of your structure with the method of Molecular Mechanics and the Merck Molecular Force Field (MMFF). Provide MOMENTS as a keyword in the Options box. This keyword will generate the rotational constants A, B, and C in cm-1.
In Step B you have generated the structure and energy of a conformer but not necessarily the global minimum. All minimization methods adjust the structure to find the closest minimum and not necessarily that with the lowest energy. This is not an issue with diatomic and small polyatomic molecules such as water where there is only one global minimum. However, polyatomic molecules have many structural parameters and a very complicated, multidimensional potential energy surface with many minima. In the next step, you will search conformational space and find all the low-energy conformers with your covalent structure.
C) Perform an additional set of calculations using the result from Part B as a seed. In this case, the calculation method will be Conformer Distribution rather than Equilibrium Geometry. The software will create a molecular spreadsheet. After completion of the calculation, delete the molecule on the screen and read in the results. You will note a new file has appeared with the same file name but the new, required file has a modified extension.
Once you have loaded the file with the structures, load the molecular spreadsheet by clicking on Spreadsheet under Display. The spreadsheet will have one row per conformation. Display the relative energies by clicking at the top of a blank column and then on the Add button. Select rel. E (energy relative to the global minimum) from the options and kJ/mol as the units. After the energies have been added, sort the structures in order of energy by clicking on the Sort button. To display a structure on the screen, click on its row in the spreadsheet.
By comparing the calculated values of B + C with the the value of extracted from the microwave spectrum of your conformer, determine its three-dimensional structure. The rotational constants are stored in the full output which you can access by clicking on Output under Display. Is your conformer the global minimum?
A comment on the energies generated in molecular mechanics is in order. The energy differs from zero if the bond lengths and bond angles do not match those in the test set of molecules and the molecule has van der Waals and Coulombic interactions between atoms separated by three or bonds. The three-dimensional structure of a complex polyatomic molecule is a tradeoff of many factors. The size of lone electron pairs versus bonded pairs is important but only one of many factors. Molecular mechanics considers all of them.
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