Hartree-Fock II: Exercise 1

Electronic structure of closed and open-shell molecules

Subexercise 1.

Do single-point HF/def2-TZVP calculations (HF method with basis set def2-TZVP) of the water molecule using

a) The Restricted Hartree-Fock approach (RHF)

b) The Unrestricted Hartree-Fock approach (UHF)

Use the following geometry:

O 1.851878 -0.000000 -2.395014

H 1.851878 0.754858 -1.831412

H 1.851878 -0.754858 -1.831412

Q1. How many iterations does it take the SCF to converge for each calculation?

Q2. Do you get the same energy for RHF and UHF? Why do you think that is?

Q3. In UHF calculations you typically get a spin density that you can plot. Do you get that for the UHF calculation of H2O? Why or Why not?

Subexercise 2. Using atom charges to understand electronic structure.

In this exercise we'll look at carbanions.

The figure above shows the deprotonation reaction of CHR₃ molecules to carbanions and protons. Calculate the deprotonation energies (proton affinities) for the following molecules: R = H, F, Br, CCH and CN and then try to understand your results by analyzing the electronic structure.

The latter could be done in different ways, e.g. analyzing the molecular orbitals or the molecular electrostatic potential but the easiest way is to analyze the trend in atomic charge. As we talked about there are different ways of computing atomic charges. Here we will look at Mulliken charges and Hirshfeld charges.

Optimize your geometries as usual using e.g. HF-3c theory. Then do a single-point HF/def2-TZVP calculation (single-point job means that you do not include the Opt keyword) on the optimized geometry to derive the deprotonation energy and to get the charges from, using this inputfile:

! HF def2-TZVP normalprint tightscf

%output

Print[ P_Basis ] 2

Print[ P_MOs ] 1

Print[ P_Hirshfeld] 1

end

Correlate your deprotonation energies with either Mulliken or Hirshfeld charges. Is there a correlation? Do the charges explain the trend in reaction energies?

Subexercise 3. Spin densities of radicals

Open-shell systems have associated spin densities that can be visualized as an isosurface like orbitals

One can plot spin densities in multiple ways. See e.g. ORCA Input Library - Visualization and printing

Perhaps the easiest is to use a single-point energy ORCA inputfile like this:

! HF def2-SVP normalprint tightscf veryslowconv pal8

#The veryslowconv keyword here aids SCF convergence

%output

Print[ P_Basis ] 2

Print[ P_MOs ] 1

end

If you then go to "Render orbitals" in Chemcraft you can choose to plot the spin density instead of the MOs (Bottom of the orbital table). Use a Countour value of 0.05.

Objective: Calculate the spin densities of the following radicals: CH₃, C(Ph)₃ and TEMPO

Do a HF-3c optimization first (! HF-3c opt ) of each radical and then do a single-point HF/def2-SVP calculation (! HF def2-SVP ) using the inputfile above. The latter might take some time, use the pal8 keyword to submit the job to 8 cores.

RB update:

I have updated the instructions here a little bit. The C(Ph)3 radical is a troublemaker to converge properly.

Use def2-SVP basis set instead of def2-TZVP. def2-TZVP takes too long and def2-SVP gives pretty much identical results.

Submit your calculations using the pal8 keyword otherwise it will take too long.

Use the veryslowconv keyword (even better than the slowconv) keyword so that the SCF will converge easier. For some people's calculations the SCF had not properly converged and Chemcraft then complained that there was no orbital/density information available.

Note that you can check whether the SCF converged in your outputfile by looking for CONVERGED, e.g. grep CONVERGED outputfile.out

If cluster busy-ness prevents you from finishing calculations you are allowed to submit report on Sunday instead.

Q1. Describe the spin densities of each radical and where the unpaired electron is.

Q2. Can you confirm your description by looking at the MOs themselves?

Q3. Does a planar vs. staggered conformation of C(Ph)₃ affect the shape/size of the spin density?

Q4. Why do you not need to specify for these radicals that you want UHF rather than RHF ?

Optional exercise for undergrads (compulsory for postgrads):

Do a single-point calculation on the methyl radical using the ROHF method and keepdens keyword and compare the spin density using ROHF to the UHF calculation.

! HF def2-TZVP ROHF Keepdens

Note that the spin density for a ROHF calculation can not be plotted using the Chemcraft orbital rendering procedure. It requires use of the orca_plot program to create a spindens-Cube file. See details here:

https://sites.google.com/site/orcainputlibrary/printing-and-visualization

Q5. Is there some difference?

Q6. What if you use a countour value of 0.01 instead? What do you see ?

Q7. EPR experiments on the methyl radical have been carried out and they show hyperfine couplings involving hydrogens. Is this experimental observation in agreement with the UHF and/or ROHF spin density?

Subexercise 4. HF on HF

By now you are probably getting fed up with the limited accuracy of Hartree-Fock. Let's drive the message home but also show that there is hope ahead.

A Hartree-Fock calculation of the diatomic hydrogen fluoride is no exception. The experimental homolytic bond dissociation energy (BDE) is known to be 141.2 kcal/mol. To make things simple we will use the experimental H-F bond length of 0.9171 Angstrom and just do single-point energy calculations. No optimizations!

We are going to use the large aug-cc-pVQZ basis set which should be large enough to have a negligible basis set error. (or you can do your own basis set study.) With a negligible basis set error present, the difference between the experimental BDE and the Hartree-Fock-calculated BDE should be almost entirely due to the error of the Hartree-Fock method (and not the basis set expansion), plus neglect of some hopefully small contributions due to zero-point energy and thermal effects.

Q1. What is the calculated BDE when using the Hartree-Fock method and the large aug-cc-pVQZ basis set?

Q2. How large is the error ? Is this acceptable?

As has been mentioned, nobody really uses the Hartree-Fock method on its own due to huge errors like this. Still Hartree-Fock theory is a vital first approximation towards more accurate methods. We will talk about these different methods and theories in later lectures. But let's explore the accuracy of some of these methods now: a) the group of post-Hartree-Fock methods and b) the group of DFT methods

Post-HF methods include (in order of increasing complexity): MP2, SCS-MP2, CCSD, CCSD(T)

DFT methods include (in order of increasing complexity): LDA, BLYP, PBE, B3LYP, PW6B95

Calculate the BDE of hydrogen fluoride with these methods.

Note. As we have talked about, Hartree-Fock method is exact for 1-electron systems like the hydrogen atom (only has a basis set error due to the use of a specific basis set).

We have not yet talked about post-HF methods like MP2, CCSD etc. but they work by first calculating the Hartree-Fock energy and then calculate electron correlation energy by computing the electron correlation energy of pairs of electrons.

Total post-HF energy = : E^Hartree-Fock + E^correlation

A 1-electron system has no electron pairs so if you try a CCSD calculation on the H atom, ORCA will probably complain since there are no pairs to calculate. The correlation energy of a 1-electron system is thus 0.

Since you want to calculate the Bond Dissociation Energy of Hydrogen-Fluoride using the CCSD method for example, you of course need the CCSD energy of all species: H,F and HF. For the H atom in this case you simply use the energy of the Hartree-Fock step (where correlation energy is 0) while you use the actual CCSD energy for F atom and HF molecule. The Hartree-Fock energy in a post-HF job can always be found after the line in the output:

* SUCCESS *

* SCF CONVERGED AFTER 8 CYCLES *

*****************************************************

----------------

TOTAL SCF ENERGY

----------------

Total Energy : -0.49994832 Eh -13.60429 eV

-----------------

Q3. Does the method error decrease?

Q4. Are we getting acceptable accuracy with these methods?

Q5. Do any of these DFT methods give acceptable accuracy?

Optional exercise for undergrads (compulsory for postgrads):

The experimental BDE is determined as the reaction enthalpy at 298.15K.

Q6. How big is the zero-point energy and thermal contribution to the bond dissociation energy?

You can determine this to a good approximation by performing an OPT+FREQ job using the B3LYP DFT method and the def2-TZVP basis set. Note that geometry optimizations and frequency calculations are almost never performed at the post-HF level (too expensive and unnecessary).

Q7. Does inclusion of the zero-point energy and thermal contribution (enthalpy correction) matter for chemical accuracy (usually defined to be equal to an error of 1 kcal/mol) or can it be ignored (in this case)?