Molecular orbital lowest-energy

The results of the modeling smdy of the chain transfer chemistry have been published elsewhere. Quinone diimines are predicted to be more than two orders of magnimde more reactive toward free radicals than the corresponding PPD. The reactivity of a radical with another molecule should be related to the Lowest Unoccupied Molecular Orbital (LUMO) energy of that molecule. The reaction of a radical with a PPD differs from the reaction of a radical with QDI. 

A Hiickel molecular orbital calculation for the cyclopentadiene system can be carried out as illustrated in Chapter 5. As is shown in Figure 5.20, the Frost-Musulin diagram places the five molecular orbitals at energies of a + 2/3, a + 0.618/3 (2), and a — 1.618/3 (2). Because the cyclopentadienyl anion has six electrons, only the three lowest energy levels are populated and are the orbitals interacting with those on the iron. Figure 21.15 shows the orbitals of the cyclopentadienyl anion. 

AMI semi-empirical and B3LYP/6-31G(d)/AMl density functional theory (DFT) computational studies were performed with the purpose of determining which variously substituted 1,3,4-oxadiazoles would participate in Diels-Alder reactions as dienes and under what conditions. Also, bond orders for 1,3,4-oxadiazole and its 2,5-diacetyl, 2,5-dimethyl, 2,5-di(trifluoromethyl), and 2,5-di(methoxycarbonyl) derivatives were calculated <1998JMT153>. The AMI method was also used to evaluate the electronic properties of 2,5-bis[5-(4,5,6,7-tetrahydrobenzo[A thien-2-yl)thien-2-yl]-l,3,4-oxadiazole 8. The experimentally determined redox potentials were compared with the calculated highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) energies. The performance of the available parameters from AMI was verified with other semi-empirical calculations (PM3, MNDO) as well as by ab initio methods <1998CEJ2211>. 

In the simplest frozen orbital approach, both IE and EA values can be approximated as the negative of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, respectively, following the Koopmans theorem. A better way is to calculate the energies of the system and its cationic and anionic counterparts separately and then estimate fx and 17 from Equations 12.4 and 12.5, respectively. 

In addition to the above prescriptions, many other quantities such as solution phase ionization potentials (IPs) [15], nuclear magnetic resonance (NMR) chemical shifts and IR absorption frequencies [16-18], charge decompositions [19], lowest unoccupied molecular orbital (LUMO) energies [20-23], IPs [24], redox potentials [25], high-performance liquid chromatography (HPLC) [26], solid-state syntheses [27], Ke values [28], isoelectrophilic windows [29], and the harmonic oscillator models of the aromaticity (HOMA) index [30], have been proposed in the literature to understand the electrophilic and nucleophilic characteristics of chemical systems. 

Fig. 5-3. Electron energy levels in an isolated adsorbate particle and an adsorbent solid metal M = metal R = isolated particle LUMO = lowest unoccupied molecular orbital (lowest vacant electron level) HOMO = highest occupied molecular orbital (highest occupied electron level).

In accordance with theoretical predictions (90), the concerted pathway for 1,3-dipolar cycloaddition is replaced by a two-step mechanism when two requirements are satisfied. One of the criteria involves an extremely large difference in the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energies of the reaction partners. The other factor involves a pronounced steric hindrance at one termini of the 1,3-dipole (190). The first case of a stepwise... 

The slightly lower lowest unoccupied molecular orbital (LUMO) energy of pyrido[3,4-r71pyridazine 5 compared to its isomer [2,3-r7] 6, calculated by the AMI method <1985JA3902>, explained the shorter time required for the pyrido[3,4-r7j-pyridazine to complete the [4+2] cycloaddition reaction with cyclic enamines of different ring sizes <1995M211, 2001ARK21>. 

Table 13.1 Example of two chemicals with similar predicted properties [octanol-water partition coefficient (logPQ/w) and lowest unoccupied molecular orbital (LUMO) energy] and similar acute aquatic toxicity (LC50) values to the fathead minnow [6].

An attempt to generate an amino-aryl carbene 154 from the alkylated phenanthridinium salt 153 (Equation 78) <2006TL531> was unsuccessful due to steric interactions. The actual reaction with a variety of strong, sterically hindered bases/nucleophiles is shown (Equations 79-81). The mesityllithium products proved that a carbene intermediate is not possible. Unlike /-butyl alcohol and hexamethyldisilazane, trimethylbenzene, the conjugate acid of mesityllithium, is not prone to carbene insertion reactions. Electronically this is explained by the planar nature of 153 which serves to lower the lowest unoccupied molecular orbital (LUMO) energy of the iminium moiety. 

From now on, we will always represent molecular orbitals in energy order—the highest-energy MO at the top (usually an antibonding MO) and the lowest in energy (usually a bonding MO and the one in which the electrons are most stable) at the bottom. We suggest you do the same. 

Butadiene has two Jt bonds and so four electrons in the n system. Which molecular orbitals are these electrons in Since each molecular orbital can hold two electrons, only the two molecular orbitals lowest in energy are filled. Let s have a closer look at these orbitals. In, the lowest-energy bonding orbital, the electrons are spread out over all four carbon atoms (above and below the plane) in one continuous orbital. There is bonding between all the atoms. The other two electrons are in 2. This orbital has bonding interactions between carbon atoms 1 and 2, and also between 3 and 4 but an antibonding interaction between carbons 2 and 3. Overall, in both the occupied Jt orbitals there are... 

The difference between the amount of energy we expect to get out on hydrogenation (360 kj mol-1) and what is observed (208 kj mol-1) is about 150 kj mol-1. This represents a crude measure of just how extra stable benzene really is relative to what it would be like with three localized double bonds. In order to understand the origin of this stabilization, we must look at the molecular orbitals. We can think of the Jt molecular orbitals of benzene as resulting from the combination of the six p orbitals. We have already encountered the molecular orbital lowest in energy with all the orbitals combining in-phase. 

The electronic structure of microcrystalline silicon of one-dimensional (1-D), 2-D, and 3-D clusters were calculated using the Discrete-Variational (DV)-Xa Molecular-Orbital method. The calculated results are discussed with respect to the effect of the size and the number of dimensions on the energy levels of molecular orbitals. The energy-gap (Eg) between the highest-occupied molecular orbital (HOMO) and the lowest-unoccupied molecular orbital (LUMO) decreases with the increase of cluster size amd the number of dimensions. It is found that including silicon 3d orbitals as basis sets decreases the Eg value. The results show that the components of silicon 3d orbitals in the unoccupied levels near LUMO are over 50 per cent. The calculated results predict that the Eg value will be close to the band gap of crystalline silicon when a 3-D cluster contadns more than 1000 silicon atoms with a diameter of 4nm. 

The standard potentials f/R,oo, which hold for Oox = red in Eq. (21) or y = 1/2 in Eq. (22), depend directly on the chemical nature of the compound. Consequently, they are linked to the corresponding electronic energy levels derived from the molecular orbital (MO) theory. A linear dependency between [/r,oo and the corresponding eigenvalue coefficients for the lowest unoccupied molecular orbital (LUMO) or highest occupied molecular orbital (HOMO) energy levels was found... 

Energy of lowest unoccupied molecular orbital, r) Energy gap. Ionization potential, from relationship given in ref. [8]. Ionization potential, from relationship given in ref. [9]. u) stable to distortion [10]. 

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