Exercises#

Functional dependence#

Consider methanol:

ch3oh = '''
C       0.6627602692    -0.0195253241    -0.0000000000
O      -0.7482324502     0.1217146925     0.0000000000
H       1.0282229693    -0.5397922417    -0.8872632580
H       1.0282229693    -0.5397922417     0.8872632580
H       1.0781531801     0.9835591659    -0.0000000000
H      -1.1253011321    -0.7605402778     0.0000000000
'''

Calculate the valence spectra using TDHF and TDDFT with the following functionals:

  • BLYP

  • B3LYP

  • BHandHLYP

Plot and analyze the resulting spectra:

  • How do the absolute energies compare?

    • Compare this to the HOMO-LUMO gaps

  • Calculate a reference spectra using ADC(2)

    • Which lower-level method is closest?

Charge-transfer#

Consider the ethylene-tetrafluoroethylene dimer from this famous paper, using an approximate dimer constructed from these monomers:

c2h4 = """
C        0.6655087212      0.0000000000      0.0000000000                 
C       -0.6655087212      0.0000000000      0.0000000000                 
H        1.2112231877      0.9379948213      0.0000000000                 
H        1.2112231877     -0.9379948213      0.0000000000                 
H       -1.2112231877      0.9379948213      0.0000000000                 
H       -1.2112231877     -0.9379948213      0.0000000000   
"""

c2f4 = """
C        0.6665934397      0.0000000000      0.0000000000                 
C       -0.6665934397     -0.0000000000      0.0000000000                 
F        1.3499511337      1.1743643195      0.0000000000                 
F        1.3499511337     -1.1743643195      0.0000000000                 
F       -1.3499511337      1.1743643195      0.0000000000                 
F       -1.3499511337     -1.1743643195      0.0000000000   
"""

Calculate the distance dependence of TDHF and TDDFT (BLYP, B3LYP, BHandHLYP) to reproduce the erroneous results presented in the original article. See if you can correct this using the estimation presented in there, with:

\[ E_{\textrm{CT}}(r) \approx \textrm{IP}_A + \textrm{EA}_B - 1/R. \]

Triplet instability#

Consider the triplet instabilities discussed in this article, and reproduce the results for ethene.

Consider different functionals and RPA as well as TDA, with ADC(2) for reference calculations.

Solutions#

To be added.