Highest occupied molecular orbital calculations

Frontier Orbital theory supplies an additional assumption to this calculation. It considers only the interactions between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). These orbitals have the smallest energy separation, leading to a small denominator in the Klopman-Salem equation. The Frontier orbitals are generally diffuse, so the numerator in the equation has large terms. 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

A CASSCF calculation is requested in Gaussian with the CASSCF keyword, which requires two integer arguments the number of electrons and the number of orbitals in the active space. The active space is defined assuming that the electrons come from as many of the highest occupied molecular orbitals as are needed to obtain the specified number of electrons any remaining required orbitals are taken from the lowest virtual orbitals. 

Next, examine the equilibrium structure of acetamide (see also Chapter 16, Problem 8). Are the two NH protons in different chemical environments If so, would you expect interconversion to be easy or difficult Calculate the barrier to interconversion (via acetamide rotation transition state). Rationalize your result. Hint Examine the highest-occupied molecular orbital (HOMO) for both acetamide and its rotation transition state. Does the molecule incorporate a n bond. If so, is it disrupted upon rotation ... 

Table 1 Calculation of some molecular-based descriptors for BOA, DIMBOA and MBOA. Physicochemical descriptor like logP (partition coefficient between octanol and water) constitutional descriptors like the number of a specified atoms or bonds (number of carbons, hydrogens, oxygens, nitrogens, single and aromatic bonds, the total number of atoms and bonds) and molecular weight quantum-mechanical descriptors like HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest Unoccupied Molecular Orbital).

The half-wave redox potentials can be satisfactorily correlated to the energy of the highest occupied molecular orbitals in quinocyclopropenes 118—125 by calculations according to the simple HMO model7S ... 

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>. 

Fig. 6. HOMO (left) and second highest occupied molecular orbital, sHOMO (right) of la predicted by DFT calculations. Hydrogen atoms and axial oxygens are not shown for clarity. From Ref. (27).

In the course of investigation of reactivity of the mesoionic compound 44 (Scheme 2) the question arose if this bicyclic system participates in Diels-Alder reactions as an electron-rich or an electron-poor component <1999T13703>. The energy level of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) orbitals were calculated by PM3 method. Comparison of these values with those of two different dienophiles (dimethyl acetylenedicarboxylate (DMAD) and 1,1-diethylamino-l-propyne) suggested that a faster cycloaddition can be expected with the electron-rich ynamine, that is, the Diels-Alder reaction of inverse electron demand is preferred. The experimental results seemed to support this assumption. 

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. 

The redox potentials can be determined by electrochemical measurements or by theoretical calculations using the energy levels of the LUMO (lowest unoccupied molecular orbital) and the HOMO (highest occupied molecular orbital). 

As the logarithm of 1-octanol-water partition coefficient (log P) describes the hydrophobicity of molecules and the retention of solutes in RP-HPLC depends on the hydrophobicity, a strong correlation can be expected between the log V value and the retention of solutes in RP-HPLC. Besides log P, a considerable number of physicochemical parameters have been tested for their capacity to predict retention in RP-HPLC. Thus, Snyder s polarity index, fraction of positively and negatively charged surface area, molecular bulkiness, nonpolar surface area, electron donor and acceptor capacity, various ster-ical parameters, and the energy of highest occupied molecular orbit have all been included in QSRR calculations. 

The above stability order is supported by the results of ab initio calculations, where a correlation has been established between the oxidation limits of these anions and the energy level of their highest occupied molecular orbital (HOMO). However, the gapping discrepancies that exist between intrinsic and solution stability limits remain to be explained. 

The UV Vis spectrum of 34 features a broad band centered at 363 nm, E— 17,400mol cm . As indicated by a time-dependent DFT calculation, electronic excitations from the Highest Occupied Molecular Orbital (HOMO), HOMO-1 and HOMO-2 to the LUMO are the major contributors to this broad band. 

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