Molecular orbitals HOMO

Energies op the Lowest Empty (LEMO) and Three Highest (HOMO) Molecular Orbitals of Cytosine Calculated by Different All-Valence or All-Electron Methods... 

Under photochemical conditions, the electrocyclic ring closing of butadienes always proceeds by the disrotatory pathway, which is the opposite of the result under thermal conditions. The FMOs make the stereochemical result easy to understand. Under photochemical conditions, an electron is promoted from the HOMO i]ii to the LUMO 1//7, so i//i becomes the HOMO. Molecular orbital i//i has an antibonding interaction between the termini of the 77 system in the conrotatory TS but a bonding interaction between the termini of the 77 system in the disrotatory TS, so the reaction proceeds in a disrotatory fashion. 

Within a molecular orbital approximation, the electron is ejected from the highest occupied molecular orbital (HOMO). Molecular orbital calculations at various levels of sophistication describe the highest occupied MOs of most yhdes as being strongly localized on tlie ylidic carbon. Exceptions to this are found for example in cyclopentadienide derivatives, where the orbital of corresponding symmetry is the HOMO-1 (IE2). In terms of reactivity, the low first ionization potentials of ylides reflect high oxidizabihty, high proton affinity, and basicity. UV photoelectron spectra in conjunction with detailed molecular orbital calculations for each individual ylide structure have made possible a rationalization of the different substituent and heteroatom effects. 

In summary, there are two essentially different chemical bonding interactions that cause an adsorbate to be adsorbed in low or high coordination. The interaction with doubly occupied HOMO molecular orbitals of a type tends to direct the adsorbate to low-coordination sites. The interaction with it symmetric adsorbate orbitals tends to direct the adsorbate to high-coordination sites. The stronger the interaction with the d-valence electrons and the higher the electron occupation, the relatively stronger the atop driving interaction becomes. 

Figure 2c shows the electronic structure of graphene described by a simple tight-binding Hamiltonian the electronic wavefunctions from different atoms overlap. However, such an overlap between the Pz(it) orbital and the Px and Py orbitals is zero by symmetry. Thus, the Pz electrons form the 71 band, and they can be treated independently from the other valence electrons. The two sub-lattices lead to the formation of two bands, n and Jt, which intersect at the corners of the Brillouin zone. This yields the conical energy spectrum (Dirac cone, inset in Fig. 2c) near the points K and K, which are called Dirac points. The bottom cone (equivalent to the HOMO molecular orbital) is fully occupied, while the top cone (equivalent to the LUMO molecular orbital) is empty. The Fermi level Ep is chosen as the zero-energy reference and lies at the Dirac point. Consequently, graphene is a special semimetal or zero-band-gap semicondutor, whose intrinsic Fermi surface is reduced to the six points at the corners of the two-dimensional Brillouin zone. 

Knowledge of molecular orbitals, particularly of the HOMO Highest Occupied Molecular Orbital) and the LUMO Lowest Unoccupied Molecular Orbital), imparts a better understanding of reactions Figure 2-125b). Different colors e.g., red and blue) are used to distinguish between the parts of the orbital that have opposite signs of the wavefunction. 

Figure 2-125. Different isovalue-based surfaces of phenylalanine a) isoelectronic density b) molecular orbitals (HOMO-LUMO) c) isopotential surface and d) isosurface of the electron cryo-microscopic volume of the ribosome of Escherichia coii.

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

HOMO and LLMO, also known as Frontier orbitals, are important in in tcrprcLitig results of a calculation (see Frontier Molecular Orbitals on page 141). You can use these m olecular orbiLals to comptiLe the lowest excited electronic singlet state of molecules and the ground states of radicals. 

Frori tier Orbital theory supplies an additional asstim piion to ih is calculation. It considers on ly the interactions between the h ighest occupied molecular orbital (HOMO) and the lowest unoccupied rn olecular orbital (I.UMO). These orbitals h ave th e sin a 1 lest energy separation, lead in g to a sin all den oin in a tor in th e Klopinan -.Salem ct uation, fhe Hronticr orbitals are generally diffuse, so the numerator in the equation has large terms. 

If the mini her of electrons, N, is even, yon can haven dosed shell (as shown ) where the occupied orbitals each contain two electron s. For an odd n nrn her of electron s, at least on e orbital rn ust be singly occupied. In the example, three orbitals are occupied by-electron s and two orbitals arc nn occupied. Th e h ighest occupied nioleciilar orbital (HOMO is t[r), and the lowest unoccupied molecular orbital (LUMO) is The example above is a singlet, a state oh total spin S=0. Exciting one electron from the HOMO to the LUMO orbital would give one ol the I ollowing excited states ... 

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

I he electron density distribution of individual molecular orbitals may also be determined and plotted. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are often of particular interest as these are the orbitals most cimimonly involved in chemical reactions. As an illustration, the HOMO and LUMO for Jonnamide are displayed in Figures 2.12 and 2.13 (colour plate section) as surface pictures. 

These absorptions are ascribed to n-n transitions, that is, transitions of an electron from the highest occupied n molecular orbital (HOMO) to the lowest unoccupied n molecular orbital (LUMO). One can decide which orbitals are the HOMO and LUMO by filling electrons into the molecular energy level diagram from the bottom up, two electrons to each molecular orbital. The number of electrons is the number of sp carbon atoms contributing to the n system of a neuhal polyalkene, two for each double bond. In ethylene, there is only one occupied MO and one unoccupied MO. The occupied orbital in ethylene is p below the energy level represented by ot, and the unoccupied orbital is p above it. The separation between the only possibilities for the HOMO and LUMO is 2.00p. 

As is true for all orbitals a ti orbital may contain a maximum of two electrons Ethylene has two ti electrons and these occupy the bonding ti molecular orbital which is the HOMO The antibondmg ti molecular orbital is vacant and is the LUMO... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

HOMO (Section 10 13) Highest occupied molecular orbital (the orbital of highest energy that contains at least one of a molecule s electrons)... 

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