Calculations using Gaussian software at TD-B3LYP 6311G (d) give a lower energy HOMO to LUMO+1 transition than the HOMO to LUMO. The molecule under study is an uncharged closed shell heteroaromatic. There must be a simple explanation but its been a hell of a long time since I read any Molecular Spectroscopy. Anyone out there got a simple non-mathematical explanation? Much appreciated.
Although the interpretation of an excitation is done using transitions between orbitals, the excitation energy is not just equal to the orbital energy difference, but additional terms (two electron integrals) play an important role. Furthermore, while the ground state is usually well represented by a single Slater-determinant, the excited state often consists of several determinants. Thus depending on the mixture of configurations, the size of the two electron-terms and the orbital energy differences, the excited state which consists mainly of the HOMO to LUMO transition is not necessarily the lowest in energy.
I think the non-mathematical reason is that, although we think and do the interpretation using an independent particle model, reality is more complex.
Best regards
Christof
Although the interpretation of an excitation is done using transitions between orbitals, the excitation energy is not just equal to the orbital energy difference, but additional terms (two electron integrals) play an important role. Furthermore, while the ground state is usually well represented by a single Slater-determinant, the excited state often consists of several determinants. Thus depending on the mixture of configurations, the size of the two electron-terms and the orbital energy differences, the excited state which consists mainly of the HOMO to LUMO transition is not necessarily the lowest in energy.
I think the non-mathematical reason is that, although we think and do the interpretation using an independent particle model, reality is more complex.
Best regards
Christof
It does seem so counter intuitive though, but thanks for the input!
In some Quantum Chemistry softwares, the ordering of MOs is done base on symmetry(symetry adapted molecular orbitals). This can sometimes not coincide with energy ordering. In such a situation you have to manually order the orbitals.
It could also be that your calculation has not converged. do you have a frequency analysis? check just to make sure before considering the former option.
The energies of the unoccupied orbitals aren't very meaningful, since were one of the orbitals 'occupied', the mean field experienced by the other electrons would be different. This in turn would results in a different total electron density which may stabilise one KS orbitals relative to another, and so the energy ordering of unoccupied orbitals would not be expected to correspond with the energy ordering of the excited states. Also, Christof makes a good point about excited states often having significant multiconfigurational character, and so interpreting excited states in terms of transitions betweens a single pair of KS orbitals is often not valid.
Best wishes,
Andy
It is simply because the excited determinants constitute the basis for the subseqent configuration interactions. The excited states are spanned by more than one determinent. A typical case is naphtalene, for which the state based mostly on HOMO>LUMO excitation is higher in energy than the state that is spanned by two major contributions from HOMO>LUMO+1 and HOMO-1>LUMO.
Interaction between them is enough to lower the energy of the state below the one of the HOMO>LUMO state.
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