Treat the hexatriene molecule using the particle-in-a-box model. (a) Assume that

Question

Treat the hexatriene molecule using the particle-in-a-box model.

(a) Assume that the electrons are free to move along the length of the conjugated polyene backbone of the molecule (along the length of the C=C–C=C–C=C region). Use 1.54 A? as the length of the C–C bond and 1.35 A? as the length of a C=C bond. Evaluate:

(b) the energy of the highest filled energy level (HOMO)

(c) the energy of the lowest filled energy level (LUMO)

(d) and the difference in energy between the HOMO and LUMO levels.

(e) What wavelength of light corresponds to the HOMO–LUMO energy gap?

(f) Based on your experience with a MO picture for the ? electrons in conjugated molecules, indicate how you would expect the structure of the molecule to change when it absorbs a photon.

Explanation / Answer

HOMO stands for highest occupied molecular orbital. LUMO stands for lowest unoccupied molecular orbital. The energy difference between the HOMO and LUMO is termed the HOMO-LUMO gap. HOMO and LUMO are sometimes referred to as frontier orbitals.[1]

Each molecular orbital has a calculated energy level. Chemists sort the molecular orbitals (MOs) by energy levels. Chemists assume that the electrons will occupy the lowest energy level MOs first. For example, if a molecule has enough electrons to fill 15 MOs, the 15 MOs with the lowest energy levels will be occupied. The 15th MO on the list would be called the "highest occupied molecular orbital" (HOMO) and the 16th MO on the list would be the "lowest unoccupied molecular orbital" (LUMO). The difference in the HOMO's energy level and the LUMO's energy level is called the band gap. The band gap can sometimes serve as a measure of the excitability of the molecule: the smaller the energy, the more easily a molecule's electrons will be excited. For example, this can help predict whether a substance will have luminescence.

B)Normally HOMO, LUMO difference will be high, but HOMO energy level is increasing while we add/ substitute electron donating groups. For this I know little bit of reason that is Band gap will reduce (that means: HOMO, LUMO level will be contract) when the electron density increases.

C)Any system will show the same trend unless there is non-innocence involved. The reasoning is based on simple MO theory rationale. Unfortunately I don't know of any text book which helps rationalize +1 and -I effects from a MO theory point of view. It can be done quite easily and it will help explain these situations where you try to interpret MO theory aspects e.g. HOMO/LUMO with empirical phenomena like -I and +I.

D) In HOMO/LUMO formation, a molecule has to obey “ Body Center Conservation Rule” which means that whether a system is split or unsplit, its energy has to be conserved . So, HOMO/LUMO energies will vary.

HOMO/LOMU concept of formation/ nonformation of an adduct between LA-LB as follows with a brief explanation as:

[i]A Lewis base[LB] has an electron pair in HOMO of suitable symmetry which overlaps with the LUMO of Lewis acid[LA]. Smaller the energy difference between the two, the stronger will be the bond and stabler will be the adduct because the MO of the adduct thus formed has quite lower energy energy than those of HOMO and LUMO of the LA and LB respectively.

[ii] Suppose HOMO of LB is higher in energy than LUMO of LA.Then they overlap with each other only to a VERY SMALL EXTENT. In such a case, the MO of the adduct formed by this very small overlap of HOMO and LUMO of the LB and LA respectively will have ONLY A LITTLE ENERGY DIFFERENCE from that of LUMO of the LA. Either the adduct may not form at all or if formed, will be unstable.

I now take established cases: MOD of transition metal complexes. Though there are present over six types of diagrams, but only 3 for octahedral complexes will suffice.

Though diagrams are a bit difficult to understand, but I simplify them for you wrt to HOMO/LUMO.

To determine the HOMO and the LUMO levels of the molecule, go into the listing of the molecular energy levels,

14 -9.514529e-02 2.000000e+00
15 9.514485e-02 6.417571e-44
From the occupations, we see that level 14 is the Highest Occupied Molecular Orbital (HOMO), while level 15 is the Lowest Unoccupied Molecular Orbital (LUMO). The energy of the levels are given relative to the Fermi level and in units of Hartree.

The energy of the Fermi level is listed in the beginning of the file.

# Fermi level = -1.219381e-01 #
# Number of electrons = 30.000000 #
From these values, we can evaluate the absolute HOMO and LUMO energies

EHOMO=-5.91eV
ELUMO=-0.73eV

E) Its energy would be lower, so it's wavelength, often denoted by ?, would be higher. Retinol absorbs purple light, corresponding to about 400nm. Retinal absorbs bluelight corresponding to about 450nm. As the HOMO/LUMO energy gap decreases,the wavelength of the absorbed color increases.

The energy difference between the HOMO and LUMO or HOMO-LUMO gap is generally the lowest energy electronic excitation that is possible in a molecule. The energy of the HOMO-LUMO gap can tell us about what wavelengths the compound can absorb. Or alternatively, measuring the wavelengths a compound absorbs in the lab can be used as a measure of the HOMO-LUMO gap.

Finally, for most molecules (that are not extremely symmetric) there are no degenerate molecular orbitals (MOs with the same energy). Thus the MOs are a series of single orbitals of increasing energy. Since most stable molecules have an even number of electrons (closed shell), nearly all molecules will have all their electrons paired in molecular orbitals.

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