Example: Excitation energies open shell molecule: CN¶
Calculation of the excitation energies of the open shell molecule CN
$ADFBIN/adf << eor Title excitation energies of CN Atoms C .0000 .0000 .0000 N .0000 .0000 1.1718 End unrestricted charge 0 1 excitations lowest 20 end Basis Type AUG/ADZP End End input eor
In this example, the lowest 20 excitation energies of CN are calculated in a spin-unrestricted TDDFT calculation. In the MO → MO transitions part for the excitations of the output file, the spin of each molecular orbitals are also specified to help assign the spin state of the excited states. The transitions are always from \(\alpha\) spin-orbital to \(\alpha\) spin-orbital or from \(\beta\) spin-orbital to \(\beta\) spin-orbital.
Next the same example for CN is given with the Tamm-Dancoff approximation (TDA) approximation (including TDA in the input). Due to this approximation the calculated excitation energies will not be exactly the same as in the first example.
The third calculation is the calculation of spin-flip excitation energies for CN. Again these energies will not be exactly the same as in the first example. For open-shell molecules, spin-flip transition can result in transition to the ground state with a different Sz value, while the symmetry of the transition density is A1 (\(\Sigma\)+ for linear molecules). The excitation energy of this transition should be zero and this can be used to test the reliability of spin-flip TDDFT. Indeed the calculation of the spin-flip excitation energies of CN shows one value which is close to zero and has a transition density of \(\Sigma\)+ symmetry.
$ADFBIN/adf << eor Title spin-flip excitation energies (TDA) of CN Atoms C .0000 .0000 .0000 N .0000 .0000 1.1718 End unrestricted charge 0 1 excitations lowest 20 end SFTDDFT TDA FORCELDA Basis Type AUG/ADZP End End input eor
Note that the basis set is still far from complete, the ATZ2P is better. For accuracy reasons one may need to increase the numerical quality. If one uses the augmented basis sets for accuracy reasons one could use NumericalQuality Good.