A variety of computational methods are available for modeling molecular structures and chemical reactivity. These computational models, as they are sometimes called, include the ab initio Hartree-Fock , configuration interaction, Møller-Plesset, density functional, and semi-empirical methods. The basis functions used in semi-empirical calculations are generally Slater-type orbitals (STOs). The other methods employ Gaussian-type functions. Typically, the method and set of basis functions used in a calculation are indicated with the notation

If the single-point energy is calculated with a method or basis set that differs from the method or basis set used in the geometry optimization, then this difference is noted with the expression



For example MP2/6-31G*//RHF/6-31G* means that the molecular geometry was optimized with the restricted (closed-shell) Hartree-Fock method and the 6-31G* basis set but the electronic energy for the optimized geometry was calculated at the Møller-Plesset 2 level with the 6-31G* basis set.^1,2

    In this exercise we will evaluate the accuracy with which the PM3 semi-empirical, the ab initio Hartree-Fock, and B3LYP density functional methods model the equilibrium geometries of the cis and trans isomer of FNNF and predict the difference in the conformational energies.

Procedure:

1. Build a model of the cis isomer of FNNF. Optimize the geometry with the PM3 semi-empirical method and save the results to the fnnf_cis_PM3.Spartan file in your (username) folder. Click the button on the toolbar at the top of the Spartan '10 window and then highlight the fluorine and nitrogen atoms. The FN bond length will appear at the bottom of the window. Print a hard copy of this page and record the value in the table below. Obtain and record the NN bond length in a similar manner. Click the button and then highlight the fluorine and two nitrogen atoms. The value of the FNN bond angle will appear at the bottom of the window. Record the value of the FNN bond angle in the table. Save your work to a new file named fnnf_cis_HF.Spartan in your (username) folder.
   
   Open the fnnf_cis_HF.Spartan file in the Spartan '10 window if it is not already open. Use the Hartree-Fock method with the 6-31G* basis set to optimize the geometry of the cis isomer of FNNF. See the Tutorial for Hartree-Fock Calculation. Obtain and record the FN bond length, the NN bond length, and the FNN bond angle. Save your work to a new file named fnnf_cis_DF.Spartan in your (username) folder.
   
   Open the fnnf_cis_DF.Spartan file in the Spartan '10 window. Optimize the geometry of the cis isomer with the B3LYP density functional method and the 6-31G* basis set. See the Tutorial for Density Functional Calculation. Obtain and record the bond lengths and angle.
   
   Cis Isomer
   

   	F-N (Å)	N-N (Å)	F-N-N (º)
   PM3
   HF/6-31G*
   B3LYP/6-31G*
   Exp3	1.384 +/- 0.01	1.214 +/- 0.005	114.5 +/- 0.5

   
   
   






2. Build a model of the trans isomer of FNNF. Optimize the geometry with the PM3 semi-empirical method and save the results to the fnnf_trans_PM3.Spartan file in your (username)1` folder. Obtain and record the FN bond length, the NN bond length, and the FNN bond angle in the table below. Save your work to a new file named fnnf_trans_HF.Spartan in your (username) folder.
   
   Open the fnnf_trans_HF.Spartan file in the Spartan '10 window. Use the Hartree-Fock method with the 6-31G* basis set to optimize the geometry of the trans isomer of FNNF. Obtain and record the bond lengths and angle. Save your work to a new file named fnnf_trans_DF.Spartan in your (username) folder.
   
   Open the fnnf_trans_DF.Spartan file in the Spartan '10 window. Optimize the geometry of the cis isomer with the B3LYP density functional method and the 6-31G* basis set. Obtain and record the bond lengths and angle.
   
   Trans Isomer
   

   	F-N (Å)	N-N (Å)	F-N-N (º)
   PM3
   HF/6-31G*
   B3LYP/6-31G*
   Exp4	1.396 +/- 0.008	1.231 +/- 0.01	105.5 +/- 0.7

   
   
   





3. Determine the trans/cis energy difference, ΔE, for each model. To find DE for the PM3 model take the difference between the heats of formation of the trans and cis isomers. The heats of formation are found in the "Output" files. For the Hartree-Fock and density funcational methods ΔE equals the difference between the electronic energy of the trans isomer and the electronic energy of cis isomer. The electronic energies, E(HF) and E(DFT), are reported in hartree. Use the conversion factor 627.5095 Kcal/mol-hartree to express ΔE in units of Kcal/mol or 2625.4997 kJ/mol-hartree to express ΔE in units of kJ/mol. In this approximation the difference in the zero-point energies of the two isomers, roughly -0.2 Kcal/mol, is omitted.
   
   DE = E(trans) - E(cis)
   

   	PM3	HF/6-31G*	B3LYP/6-31G*	Exp5
   DE (Kcal/mol)				3.05 +/- 0.4