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Ionization Potentials
The ionization potentials of molecules can be estimated in two different ways: by means of Koopmans theorem or by direct computation of the difference between the molecule and its corresponding cation.
Set up input files to perform geometry optimizations of CH4, NH3, H2O, and FH, as well of its corresponding cations.
Optimize each structure at the RHF (molecules) and UHF (cations) levels using the following basis sets: STO-3G, 4-31G, 6-31G*, and 6-31G**. Estimate the ionization potentials by energy differences and by means of Koopmans theorem. Discuss about your findings and comment on the dependence of the ionization potentials with the basis set
quality.
Compare your results against experiment:
EI/a.u.
CH4
0.529
NH3
0.400
H2O
0.463
FH
0.581
Electron Affinity of Fluorine
Calculate the energy of the fluorine atom using Hartree-Fock and the popular hybrid B3LYP density functional using the following basis sets: aug-cc-pVDZ, aug-cc-pVTZ, and aug-cc-pVQZ.
Repeat the calculations for the fluorine anion. Estimating the electron affinity as the difference in energy of the anion and neutral species is called the &Delta SCF result.
The eigenvalues of the canonical HF equations are usually called orbital energies, because they resemble the energies of a one-electron system in an external field. This relationship is described by the Koopmans theorem. This theorem says that if one picks the ion wave function to be a determinant comprised from the occupied orbitals of the neutral atom
plus the lowest virtual orbital, the difference between the energy for the HF determinant and such ion determinant (which is an approximation to the electron affinity) will be the energy of the lowest virtual
orbital.
The
experimental
electron affinity of fluorine is 3.40 eV. Calculate the electron affinity in accordance with Koopmans theorem, and compare with the &Delta SCF and experimental values for the all the different basis sets.
What kind of effects are neglected in these two approximations to the electron affinity?
If an orbital energy corresponds to the energy necessary to delete one electron from the system (taken with opposite sign), then the total electronic energy of the system (i.e., the energy necessary to delete all electrons) equals the sum of the orbital energies. Is this true? Discuss.
Repeat the calculations using the non-hybrid BLYP density functional method. Comment on your results.
FH Bond Dissociation
In this assignment we will compute the dissociation curve for FH at the RHF and UHF levels of theory.
Set up an input file for FH with a bond length of 4.0 angstroms.
Run a RHF/6-31G* single-point calculation.
Use GaussView to visualize the Highest Occupied Molecular Orbital (HOMO) and describe it. In order to visualize an orbital with GaussView do the following:
1. Open the checkpoint (*.chk) file.
2. Go to the "Results" menu and choose the "Surface" option.
3. In "Cube Actions" select "New Cube". Then choose the kind of cube file you want to generate (Molecular Orbital in this case). Choose the appropriate molecular orbital
and
grid
size.
4. After generating the cube file, now select an isodensity value of 0.005 and generate the surface by clicking on "New Surface".
Repeat the previous step but using the results of a UHF/6-31G** calculation. Is the HOMO different than in the RHF case?
Calculate the UHF/6-31G** energy at bond lengths of 0.9005 (optimized), 1.0, 1.5, 2.0, and 3.0 angstroms.
Plot the spin expectation value < > as a function of the bond length.
In what fragments does the FH molecule dissociate in UHF and RHF? Hint: Compare the energy of FH with a large internuclear distance (100 angstroms or so) with the sum of the energies for different combinations of H(+,0,-) and F(+,0,-).
Estimate the bond energy for FH in RHF and UHF.
When one goes from the equilibrium geometry towards the dissociation limit, the point where the UHF curve starts to be lower than the RHF curve is called critical point (or bifurcation). Propose a way to estimate the critical point using only UHF characteristics (energy, derivatives of energy, spin operators expectation values).
Calculate, at the RHF and UHE levels, the energy of the FH dimer with an intermolecular distance of 300 angstroms, and compare with the values obtained for twice the energy of a single molecule. The capability of giving a physically right result for this test is called size consistency.
Hyperfine Couplings in Carbon Trifluoride
In this assignment we will use the unrestricted Hartree-Fock formalism to study the electronic structure of the carbon trifluoride radical, CF3.
Set up input files to perform geometry optimizations of CF3 (C3v symmetry) at the UHF level using the 6-31G, 6-31G(d), 6-31+G(d), 6-311G, 6-311G(d), and 6-311+G(d) basis sets. Report the optimized C-F bond length and F-C-F angle for all basis sets used.
Describe the spin density of CF3 at the UHF/6-31G level. How does it change as one adds polarization or diffuse functions? How does it change upon going to a triple-zeta quality basis set? How would you expect the spin density to look had the calculations been performed with the ROHF formalism? In order to visualize the spin density (the
difference between the alpha and beta spin densities at every point) with GaussView do the following:
1. Open the checkpoint (* *.chk) file.
2. Go to the "Results" menu and choose the "Surface" option.
3. In "Cube Actions" select "New Cube". Then choose the kind of cube file you want to generate (Spin Density in this case). Choose the appropriate grid size.
4. After generating the cube file, use the default isodensity value and generate the surface by clicking on "New Surface". You should see something similar to the image below.
Collect the principal values of the hyperfine coupling matrices and compare against experimental results from EPR measurements (in MHz). Discuss about the basis set influence on the computed values.
Tx
T,
T2
C
-92.2
-39.1
131.3
F
-158.2
-177.9
336.2
Now perform optimization of the planar configuration of CF3 (D3h symmetry). Compute the inversion barrier and comment on the basis set dependence of the barrier.

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