Spin-flip excitation energies: SiH₂

Sample directory: adf/SiH2_spinflip/

Calculation of the spin-flip excitation energies of the open shell molecule SiH₂

$ADFBIN/adf << eor
Title spin-flip excitation energies of SiH2
Atoms Zmatrix
 Si 0  0  0
 H  1  0  0  1.5145
 H  1  2  0  1.5145  92.68
End

excitations
  lowest 20
end

unrestricted
charge 0 2

SFTDDFT
FORCEALDA
TDA

Basis
 Type TZ2P
End

End input
eor

In this example, the lowest 20 spin-flip excitation energies of SiH₂ are calculated in a spin-unrestricted TDDFT calculation.

In this case an excited state is used as reference, which means that there can also be a negative excitation energy, which is indeed the case. The electron configuration used in the SCF is (a₁)¹(b₁)¹, with S_z=1, thus a ³B₁ state, which is an excited state. The ¹A₁ state with electron configuration (a₁)² is lower in energy, and is the ground state.

There is also an excited ¹A₁ state with electron configuration (b₁)². The transition from the ground ¹A₁ state to the excited ¹A₁ state is an excitation from the electron configuration (a₁)² to (b₁)². This transition is actually a double excitation, which means that some double excitations can be reached using spin-flip TDDFT with carefully selected reference states.

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. Note that in these spin-flip calculations the transitions are always from α spin-orbital to β or from β spin-orbital to α spin-orbital.

For open-shell molecules, spin-flip transition can result in transition to the ground state with a different S_z value, while the symmetry of the transition density is A1. 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 excition energies of SiH₂ shows one value which is close to zero and has a transition density of A1 symmetry.

The ¹A₁ state with electron configuration (a₁)² can also be used in the calculation of the excitation energies. This is a closed shell configuration, in which case we do not need the spin-flip method.

$ADFBIN/adf << eor
Title excitation energies of SiH2
Atoms Zmatrix
 Si 0  0  0
 H  1  0  0  1.5145
 H  1  2  0  1.5145  92.68
End

excitations
  lowest 20
end

Basis
 Type TZ2P
End

End input
eor

The transition from the ground ¹A₁ state to the excited ¹A₁ state, which is an excitation from the electron configuration (a₁)² to (b₁)², can not be reached in this calculation, since it has mainly double excitation character. Of course, other excited ¹A₁ states can be reached.