In the early days of this blog, I asked Am I HOMO- and LUMO-phobic?
Molecular orbitals are beautiful intuitive concepts that are extremely valuable for qualitative understanding. However, they do not exist, i.e., there is no way to measure one, even in principle.
Furthermore, for typical organic molecules used in organic photonics and electronics the one-electron energies associated with these orbitals usually do not give reliable estimates of physically observable energies [associated with true many-body states] such as the ionisation energy, electron affinity, optical energy gap....
I was pleased to see that the above issues are nicely explained and quantified in a recent paper
Reassessing the use of one-electron energetics in the design and characterization of organic photovoltaics
Brett M. Savoie, Nicholas E. Jackson, Tobin J. Marks, and Mark A. Ratner
We present results showing that common approximations employed in the design and characterization of organic photovoltaic (OPV) materials can lead to significant errors in widely adopted design rules. First, we assess the validity of the common practice of using HOMO and LUMO energies in place of formal redox potentials to characterize organic semiconductors. We trace the formal justification for this practice and survey its limits in a way that should be useful for those entering the field. We find that while the HOMO and LUMO energies represent useful descriptive approximations, they are too quantitatively inaccurate for predictive material design. Second, we show that the excitonic nature of common organic semiconductors makes it paramount to distinguish between the optical and electronic bandgaps for materials design. Our analysis shows that the usefulness of the “LUMO–LUMO Offset” as a design parameter for exciton dissociation is directly tied to the accuracy of the one-electron approximation. In particular, our results suggest that the use of the “LUMO–LUMO Offset” as a measure of the driving force for exciton dissociation leads to a systematic overestimation that should be cautiously avoided.
Some of these issues were also highlighted in earlier work, led by my UQ colleague Ben Powell, but not referenced.
I disagree with your comment. Its true, the wave function, cannot be measured. But the square of the wave function and thus the "molecular orbital density" can be easily reconstructed from photoemission experiments.
ReplyDeleteThe such measured orbitals, especially the HOMO and LUMO agree very well with DFT calculations.
What we can learn? We can improve the calculations. Despite DFT (and other codes) get HOMO and LUMO and other orbitals right, sometimes the energetic order of the measured orbitals is different. They are many more interesting aspects of orbital mapping, e.g. the substrate - molecule interaction, which changes the measured shape of the orbital. ....
http://www.sciencemag.org/content/326/5953/702.short
I stand by my claim.
DeleteARPES does not measure the density of a molecular orbital [a fictional quantity that is defined by Hartree-Fock theory]. ARPES measures the one-electron spectral density [a many-body quantity]. If the correlations are weak this quantity will be approximately given by a Hartree-Fock calculation. For some molecules in the ground state HOMOs may have some similarity to what one is seeing in an experiment probing ground state properties.
However, the excited states of many molecules relevant to organic photonics [particularly near conical intersections] have a multi-determinal character and a single HOMO will be a poor representation of the one-electron spectral density.
Furthermore, the Kohn-Sham orbitals in DFT do not represent anything physical. They are merely a calculational device. By some fortunate and poorly understood cancellation of errors they sometimes resemble Hartree-Fock orbitals and the results of some experiments.
I must agree with Max. Please see Phys. Rev. Lett. 107, 086101 (2011). In this paper the authors claim to have measured not only the amplitude of the HOMO and LUMO of an organic molecule, but also the gradient of each MO using specially prepared STM tips.
ReplyDeleteSaying that MOs do not exist in molecules is equivalent to saying that Bloch waves don't exist in metals. I agree that correlation effects are important in molecules, but one should remember that usually a single determinant state over a set of appropriate MOs already captures the vast majority of the wavefunction. In other words, the overlap of the single determinant state and the true wavefunction is close to unity.
The real problem is one of energy scales. The fact that accurate excitation energies cannot be derived from one-electron energies does not imply much about the validity of the MO picture. If the single determinant state already captures 99% of the total energy of the states, but the excitation energies are within the final 1%, they definitely require explicit treatment of correlation effects.
In the paper on photovoltaics linked above I think the most important question is whether trends in energies on the order of 0.1 eV should even be preserved between gas phase, solution, and solid state. Even if accurate gas phase excitation energies are achievable, how well do they correlate with device performance? In a field where reproducibility is a SERIOUS issue, I have to question the use of ab-initio techniques on the whole.
My response it much the same as to Max above.
DeleteJust because authors claim to have measured something does not mean that is what they have actually measured.
HOMO's and LUMO's are not physical observables. They may resemble the one-electron spectral density in certain situations, but that does not mean they are "real" by my definition.
For similar reasons I would say that Bloch states do not exist. They are a very useful theoretical construct and in the limit of weak correlations will correspond to most of the spectral weight associated with peaks in the one-electron spectral density. However, once the correlations are strong they are not one sees in a photoemission experiment.
I agree with your concern about trying to relate gas phase DFT level calculations to performance of photovoltaic devices.
http://condensedconcepts.blogspot.com.au/2010/07/opv-cell-efficiency-is-emergent.html
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