In this exercise the relative accuracy of the Hartree-Fock (HF) and density functional (DFT) methods will be examined. The reaction enthalpy at 298 K for the dissociation of diborane (eq 1) will be calculated with these methods and the resulting theoretical values for DH_diss will be compared with experimental values. Over a period of thirty years thermodynamic, kinetic, and mass spectrometric techniques have been used to measure DH_diss and the values obtained have varied from 28 to 59 kcal/mol. In the most recent publication¹ the authors reported the range for DH_diss to be (36.2 - 41.0) +/- 2 kcal/mol at 298 K.

Procedure:

1. BH₃   (See the Tutorial for Hartree-Fock Calculation )



1. Use Spartan '02 to open the bh3.Spartan file in your folder.



2. Use the Hartree-Fock method with the 6-31G* basis set to optimize the geometry. Start from the AM1 geometry.



3. Compute frequencies and print the thermodynamic quantities and vibrational modes to the output file.



4. Save the calculations to the bh3_HF.Spartan file in your folder.



5. Next, open the bh3.Spartan file and use the Density Functional method with theB3LYP/6-31G* basis set to optimize the geometry. Start from the 6-31G* geometry.



6. Compute frequencies and print the thermodynamic quantities and vibrational modes to the output file.



7. Save the calculations to the bh3_DFT.Spartan file in your folder.





2. B₂H₆



1. Use Spartan '02 to build and minimize B₂H₆.



2. Optimize the geometry with the AM1 semi-empirical method and save the results to the b2h6.Spartan file in your folder. Starting with the AM1 geometry, use the Hartree-Fock method with the 3-21G* basis set to optimize the geometry. Finally, start with the 3-21G* geometry and optimize the geometry with Hartree-Fock method and the 6-31G* basis set. Generally, this sequential process is less costly in CPU time than a single-step optimization with Hartree-Fock method and the 6-31G* basis set.



3. In the last optimization step (HF/6-31G*) compute frequencies and print the thermodynamic quantities and vibrational modes to the output file.



4. Save the calculations to the b2h6_HF.Spartan file in your folder.



5. Next, open the b2h6.Spartan file and use the Density Functional method with theB3LYP/6-31G* basis set to optimize the geometry. Start from the 6-31G* geometry.



6. Compute frequencies and print the thermodynamic quantities and vibrational modes to the output file.



7. Save the calculations to the b2h6_DFT.Spartan file in your folder.



3. Calculate DH_diss at 298 K
   
   


1. Calculate the difference in the electonic energy, . Note that the electronic energy computed by the Hartree-Fock and Density Functional methods is in units of hartrees. Use the conversion factor 627.5095 kcal/mol-hartree to express DE_e in units of kcal/mol.



2. Calculate the difference in the zero-point energy, . The Hartree-Fock method calculates vibrational frequencies that are approximately 10% larger than the experimental values. For this reason a scaling factor is applied to the Hartree-Fock vibrational frequencies, zero-point energies,and vibrational energies. When vibrational frequencies are computed with the HF/6-31G(d) method, a scaling factor of 0.9135 is used to correct the zero-point energy and vibrational energy.² Be sure to multiply the Hartree-Fock value for DE₀⁰ by 0.9135. The scaling factors for most density functional methods are near 1.0 ( 0.9804 in the case of B3LYP/6-31G*).



3. Calculate the difference in the vibrational energy, . Be sure to multiply the Hartree-Fock value for DH_v²⁹⁸ by 0.9135.



4. Calculate the difference in the rotational energy, .



5. Calculate the difference in the translatonal energy, .



6. For a constant temperature and constant pressure process, PDV = DnRT and hence .