Why the values of the HOMO-LUMO gap is different for ground-state geometry obtained from DFT and first excited state geometry obtained from TD DFT. What they signify physically?
In the ground state, all states above the HOMO are unoccupied and thus LUMO is truly the Lowest Unoccupied Molecular Orbital. In the excited states, the initially occupied states may lose their electrons and thus become (temporarily) unoccupied and some of the unoccupied states can gain electrons. In this context, an excited state configuration does not have a well-defined HOMO-LUMO gap. This is one reason for the difference, you asked.
As for the physical significance of the HOMO-LUMO gap, it does bear many valuable information. A large gap usually means the system is chemically very stable with rigid ionic bonds. A smaller gap can be a signature that the system is chemically reactive (one example is radicals). Also depending on the size of the HOMO-LUMO gap, different optical properties can be realized.
Please have a look at the question on RG similar to yours. Please refer the link for more details
https://www.researchgate.net/post/Why_is_the_excitation_energy_of_organic_molecules_calculated_from_TDDFT_much_lower_than_HOMO-LUMO_gap_Can_anyone_provide_any_formula_in_TDDFT
According to
Tatiana Korona added an answer February 4, 2015
The picture of an excited state created from the ground state by the excitation from HOMO-k to LUMO+n is not valid.
I hope this helps
Regards,
Karthick
Why would they be the same? You do a DFT calculation for two different geometries, so each of them has its own electronic ground state and unique ground state density, so typically also the HOMO-LUMO gap will be different.
It depends on your system to which extend their difference means anything. If the first excited state is localized, the HOMO-LUMO gap is a good approximation to the true excitation energy and TDDFT with the usual LDA and GGA (or better, SAOP) should give you a descent result. This picture gets increasingly destroyed by mixing HF exchange without range separation. So, the HOMO-LUMO gap gives you an approximation to the first optical excitation energy at that particular geometry.
The gap at your excited state geometry (geo_1) should typically be smaller than at the ground state geometry (geo_0), because it becomes easier to excite an electron. You can also show this using that E_1 ≈ E_0 + gap. The definition of first excited state geometry (=geo_1) is that you minimised E_1 w.r.t the geometry, so E_1(geo_1) < E_1(geo_0), with geo_0 the ground state geometry. Since E_0(geo_0) < E_0(geo_1) and E_0 < E_1, gap(geo_0) > gap(geo_1).
Dear Mallikarjun
I recommend this article to solve your doubts, it helped me a while ago.
Article Mind the gap!
Kind regards.
HOMO stands for "Highest Occupied Molecular Orbital", and LUMO stands for "Lowest Unoccupied Molecular Orbital". Don't be confused though, because the LUMO is higher in energy than the HOMO.
Of the orbitals that have electrons, the HOMO is the highest in energy, and of the orbitals that don't, the LUMO is the lowest in energy. That means they are closest in energy out of all orbitals in the molecule.
Due to the energies of these orbitals being the closest of any orbitals of different energy levels, the HOMO-LUMO gap is where the most likely excitations can occur. Hence, it is the most important energy gap to consider.
Excitations becomes easier as the HOMO-LUMO gap converges, such as for large aromatic systems (like tetracene or benzo[a]pyrene), or for transition-metal complexes (that is why they tend to be colored).
The larger the aromatic system is, the smaller the HOMO-LUMO gap!
When you have a large aromatic system in particular, small HOMO-LUMO gaps lead to mobile π electrons since it is easy for the electron to jump to a higher energy level that is close in energy.
The greater the mobility of the π electrons in large conjugated pi orbital systems, the greater the distribution of the energy throughout the molecule, stabilizing it.
In molecules, the Kohn-Sham gap (HOMO-LUMO orbital energy difference) is a very good approximation for the first excitation energy. However, if you want to study the nature of an excitation, you should perform a TDDFT calculation and figure out which are the MOs actually involved in the electronic transition of interest. Further TDDFT geometry optimization can provide you the energy of the relaxed system in the excited state. Logically, the energy of a local minimum on an adiabatic excited-state potential energy surface will be lower than the vertical excitation energy.
HOMO-LUMO gap: The definition is E(LUMO) minus E(HOMO), obviously it must be a positive value. When talking about the gap of molecular systems, if there is no prerequisite, most cases refer to this kind of gap. Moreover， you should also know that HOMO_LUMO can not be determined via experiment menthods as it is not a real physical quantity. It can be used for the prediction of reaction site
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