Chemical frontier molecular orbital

Simple Approaches to Quantifying Chemical Reactivity 3.4.2.1 Frontier Molecular Orbital Theory... 

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. 

Extended Huckel provides the approximate shape and energy ordering of molecular orbitals. It also yields the approximate form of an electron density map. This is the only requirement for many qualitative applications of quantum mechanics calculations, such as Frontier Orbital estimates of chemical reactivity (see Frontier Molecular Orbitals on page 141). 

Frontier molecular orbital (FMO) theory 62) has provided new insights into chemical reactivity. This, and the simplicity of its application, has led to its widespread use, particularly in the treatment of pericyclic reactions 63). An FMO treatment depends on the energy of the highest occupied (HOMO) and lowest unoccupied molecular... 

These relations highlight the fact that the formalism of DFT-based chemical reactivity built by Parr and coworkers, captures the essence of the pre DFT formulation of reactivity under frontier molecular orbital theory (FMO). Berkowitz showed that similar to FMO, DFT could also explain the orientation or stereoselectivity of a reaction [12]. In addition, DFT-based reactivity parameters are augmented by more global terms expressed in the softness. 

This quantity can be viewed as a generalization of Fukui s frontier molecular orbital (MO) concept [25] and plays a key role in linking Frontier MO theory and the HSAB principle. It can be interpreted either as the sensitivity of a system s chemical potential to an external perturbation at a particular point r, or as the change of the electron density p(r) at each point r when the total number of electrons is changed. The former definition has recently been implemented to evaluate this function [26,27] but the derivative of the density with respect to the number of electrons remains by far the most widely used definition. 

Luther, G. W., (1990), The Frontier-Molecular-Orbital Theory Approach in Geochemical Processes", in W. Stumm, Ed., Aquatic Chemical Kinetics, Wiiey-lnterscience, New York, pp. 173-198. 

Fleming 1., Frontier Molecular Orbitals and Organic Chemical Reactions, Wiley, London, 1976, Chapter 4. 

It appears that supported metal catalysts can be used to promote synthetically useful organometallic reactions. The utilization of such reactions can be of practical, economic, and environmental importance to the fine chemical industry. Frontier Molecular Orbital and mechanistic considerations indicate that these reactions, along with hydrogenations and, presumably, oxygenations, take place on the coordinately unsaturated comer atoms present on the surface of these dispersed metal catalysts. 

According to the frontier molecular orbital theory (FMO) of chemical reactivity, the formation of a transition state is due to an interaction between the frontier orbitals, such as HOMO and LUMO of reacting species. In general, the important frontier orbitals for a nucleophile reacting with an electrophile are HOMO (nucleophile) and LUMO (electrophile). 

Richard Bader was among the earliest of workers to realize the importance of electron density in providing an understanding of chemistry. Early on he was led to formulate the first symmetry rule governing a chemical reaction in answer to the question of how the electron density changes in response to a motion of the nuclei. This rule, termed the pseudo- or second-order Jahn-Teller effect, provides the theoretical underpinnings of frontier molecular orbital theory and is still widely used in discussions of reaction mechanisms and molecular geometries. 

The Fukui function or frontier function was introduced by Parr and Yang in 1984 [144], They generously gave it a name associated with the pioneer of frontier molecular orbital theory, who emphasized the roles of the HOMO and LUMO in chemical reactions. In a reaction a change in electron number clearly involves removing electrons from or adding electrons to the HOMO or LUMO, respectively, i.e. the frontier orbitals whose importance was emphasized by Fukui.4 The mathematical expression (below) of the function defines it as the sensitivity of the electron density at various points in a species to a change in the number of electrons in the species. If electrons are added or removed, how much is the electron density... 

Fig. 17. Frontier molecular orbitals of bent and linear nitrile ylides. (Reprinted with permission from the Journal of the American Chemical Society. Copyright by the American Chemical Society.)...

The mechanisms of chemical reactions and the reactivity properties of the molecules involved started to be elucidated through the analysis of the wave functions defining the quantum state of molecular systems,5-7 for instance the Fukui s frontier molecular orbital (FMO) theory8,9 has been very successful in rationalizing organic reactions basically through the analysis of the in- and out-of-phase overlap between the highest occupied molecular orbital (HOMO) of the nucleophile and the lowest unoccupied molecular... 

This chapter considers the oxidation of iodide in seawater by natural oxidants (02, H202, and 03). The oxidation of iodide to iodate is considered slow, yet the six-electron T-IOj redox couple normally used to represent the process (or predict stability) is thermodynamically favorable (2). We will discuss both one- and two-electron-transfer processes with these oxidants, focusing on the first step of electron transfer and using the frontier molecular orbital theory approach in conjunction with available thermodynamic and kinetic data. The analysis shows that the chemical oxidation of I to I03 is not a very important process in seawater, except perhaps at the surface microlayer. 

Fig. (1). Frontier molecular orbitals for ground state CO2. The unit of orbital energy is eV in vacuum (in water, PCM). Reproduced with permission from Ref [20]. 2015 American Chemical Society.

The existence of a charge density presupposes a concomitant set of MOs and Sect 2.3 describes how chemical reactivity can be based on the notion of Frontier Molecular Orbital (FMO) control i.e. the most important orbital interactions are between the HOMO on one species and the LUMO on the other or vice versa. FMO control, together with electrostatic charge control, provides a powerful qualitative basis for interpreting reactivity. The relative energies and compositions of MOs are vital and many computer programs now provide 3-dimensional representations of MOs to facilitate analysis. 

A variety of molecular descriptors have been defined and used proceeding from frontier molecular orbital theory (FMO) of chemical reactivity [42]. This theory is based on the concept of the superdelocalizability, an index characterizing the affinity of occupied and unoccupied orbitals in chemical reactions. A distinction has been made between the electrophilic and the nucleophilic superdelocalizability (or acceptor and donor superdelocalizability), respectively. The former describes the interaction of... 

One way of determining nonbonding interactions between two chemical systems is by computing bond orders [67-68], as well as by Frontier Molecular Orbital (FMO) [69-71] interactions in the transition state. It is well known that FMO can be used to explain the reactivity of a diene and dienophile for cycloaddition reactions [72-74]. There was no noteworthy difference between the... 

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