Example: Spin-flip excitation energies: SiH2¶
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 \((a_1)^1\) \((b_1)^1\), with \(S_z=1\), thus a \(^3 B_1\) state, which is an excited state. The \(^1 A_1\) state with electron configuration \((a_1)^2\) is lower in energy, and is the ground state.
There is also an excited 1A1 state with electron configuration \((b_1)^2\). The transition from the ground 1A1 state to the excited 1A1 state is an excitation from the electron configuration \((a_1)^2\) to \((b_1)^2\). 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 Sz 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 excitation 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 \((a_1)^2\) 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 \(^1 A_1\) state to the excited \(^1 A_1\) state, which is an excitation from the electron configuration \((a_1)^2\) to \((b_1)^2\), can not be reached in this calculation, since it has mainly double excitation character. Of course, other excited \(^1 A_1\) states can be reached.