Exercises#

Chemical shifts#

Calculate the chemical shift between the two -CH\(_2\) and -CF\(_2\) ionization energies, \(1s \rightarrow \pi^{\ast}\) core-excitation energies (XAS), and \(\pi \rightarrow 1s\) core-decay energies (XES) of 1,1-difluoroethene. How do the chemical shifts of the different spectroscopies compare, and what do you think is the reason for any (dis)similarlities?

Geometry:

c2h2f2 = '''
C       0.0000000000     0.0000000000     1.3836545197
C       0.0000000000     0.0000000000     0.0624718520
H       0.9374006976     0.0000000000     1.9085904157
H      -0.9374006976     0.0000000000     1.9085904157
F       1.0780878284     0.0000000000    -0.6951077256
F      -1.0780878284     0.0000000000    -0.6941077256
'''

Basis set augmentation#

Consider the ionization energy of neon, as calculated with \(\Delta\)SCF: using a 6-31G* basis set, add a single s-function at a time with different exponents. Plotting the resulting IE as a function of the exponent, where is the resulting IE closest to experiment? What does this tell you?

Ground-state model for XAS#

Starting with the ground-state model used to calculate X-ray emission spectra, adapt this to instead consider X-ray absorption spectra of 1,1-difluoroethene (energies from \(\epsilon_c - \epsilon_v\), intensities from \(| \langle \psi_c | \hat{\mu} | \psi_v \rangle |^2\)). How does the absolute energies compare to experiment? What about relative features?

The Tamm-Dancoff approximation#

Adapt the full-space versus CVS-space comparison of X-ray absorption spectra calculated with TDDFT to one using the Tamm-Dancoff approximation. How does the full- versus CVS-space solutions compare? How does the TDA results compare to the full (RPA) results?

Ideas#

  • Visualizing relacation: look at MOs, NTOs, and A/D of water@6-311+G* [ADC(1) and ADC(2)]

    • UV/vis and XAS, final states should be roughly simular

    • Connect to the discussion on relaxation

  • Assigning XAS and XES features of some interesting system

    • MOs, NTOs, …

  • Look at polarization dependence

  • Study how the region above the IE changes with more and more diffuse basis functions

Solutions#

Chemical shift#

To be added, using results obtained with 6-31G*:

  • Koopmans’ theorem:

  • IE (\(\Delta\)MP2):

  • XAS (CVS-ADC(2)):

  • XES (ADC(2)):

Basis set augmentation#

To be added, comparing to a discussion on the Z+1 approximation. Provide reference.

Ground-state model for XAS#

To be added, considering this with HF and B3LYP, using a 6-311+G* basis set.

The Tamm-Dancoff approximation#

To be added.