# Exercises#

## Chemical shifts#

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

```
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?

## 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.