Frontier analysis

Inflation-linked bonds also have different behavioural characteristics to other assets. They form a distinct asset class offering portfolio diversification benefits. This can be demonstrated using efficient frontier analysis. However, we should bear in mind what has already been said in the... 

Efficient frontiers also invariably place Treasury bills as the risk-free asset. T-bills may be risk-free from a creditworthiness point of view, bnt it is not tenable that a three-month nominal asset is a risk-free instrn-ment for someone with, say, a 30-year savings horizon. If you are investing for 30 years, over which time you are interested in your prospective real returns, then a 30-year linker (to be held to maturity) is your riskfree asset, almost by definition. 100% invested in that bond becomes the lowest risk portfolio on yonr frontier. Efficient frontier analysis starts to lose its impact once this premise is accepted, not least because you do not have a large data sample of consecutive, nonoverlapping 30-year periods (for any asset) to produce robust analysis. ... 

Use frontier orbital analysis to decide whether the dimeriza... 

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

Other reactions are controlled kinetically, and the most stable product is not the major one observed. In these cases, you must look at the reactant side of the reaction coordinate to discover factors determining the outcome. Klopman and Salem developed an analysis of reactivity in terms of two factors an electrostatic interaction approximated by atomic charges and a Frontier orbital interaction. Fleming s book provides an excellent introduction to these ideas. 

Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new product (or intermediate in a multistep reaction) is formed. PMO theory incorporates the concept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. These orbitals are the highest filled oihital of one reactant (the HOMO, highest occupied molecular oihital) and the lowest unfilled (LUMO, lowest unoccupied molecular oihital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

Frontier orbital theory also provides the basic framework for analysis of the effect that the symmetiy of orbitals has upon reactivity. One of the basic tenets of MO theory is that the symmetries of two orbitals must match to permit a strong interaction between them. This symmetry requirement, when used in the context of frontier orbital theory, can be a very powerful tool for predicting reactivity. As an example, let us examine the approach of an allyl cation and an ethylene molecule and ask whether the following reaction is likely to occur. 

The positively charged allyl cation would be expected to be the electron acceptor in any initial interaction with ethylene. Therefore, to consider this reaction in terms of frontier orbital theory, the question we need to answer is, do the ethylene HOMO and allyl cation LUMO interact favorably as the reactants approach one another The orbitals that are involved are shown in Fig. 1.27. If we analyze a symmetrical approach, which would be necessary for the simultaneous formation of the two new bonds, we see that the symmetries of the two orbitals do not match. Any bonding interaction developing at one end would be canceled by an antibonding interaction at the other end. The conclusion that is drawn from this analysis is that this particular reaction process is not favorable. We would need to consider other modes of approach to analyze the problem more thoroughly, but this analysis indicates that simultaneous (concerted) bond formation between ethylene and an allyl cation to form a cyclopentyl cation is not possible. 

A more complete analysis of interacting molecules would examine all of the involved MOs in a similar wty. A correlation diagram would be constructed to determine which reactant orbital is transformed into wfiich product orbital. Reactions which permit smooth transformation of the reactant orbitals to product orbitals without intervention of high-energy transition states or intermediates can be identified in this way. If no such transformation is possible, a much higher activation energy is likely since the absence of a smooth transformation implies that bonds must be broken before they can be reformed. This treatment is more complete than the frontier orbital treatment because it focuses attention not only on the reactants but also on the products. We will describe this method of analysis in more detail in Chapter 11. The qualitative approach that has been described here is a useful and simple wty to apply MO theory to reactivity problems, and we will employ it in subsequent chapters to problems in reactivity that are best described in MO terms. I... 

A similar analysis of the 1,5-sigmatropic shift of hydrogen leads to the opposite conclusion. The relevant frontier orbitals in this case are the hydrogen Is orbital and ij/j of the pentadienyl radical. The suprafacial mode is allowed whereas the antarafacial mode is forbidden. The suprafacial shift corresponds to a favorable six-membered ring. 

The same conclusions are drawn by analysis of the frontier orbitals involved in cycloadditions. For the most common case of the Diels-Alder reaction, which involves dienophiles with electron-attracting substituents, the frontier orbitals are l/2 of the diene (which is the HOMO) and n of the dienophile (which is the LUMO). Reaction occurs by interaction of the HOMO and LUMO, which can be seen from the illustration below to be allowed. 

A theoretical study based on PM3 frontier molecular orbital (FMO) and potential energy surface (PES) analysis at the RHF/6-31-I-G level was performed to examine the reaction of l-amino-2-ethoxycarbonylpyridinium mesitylenesulfonate and acrylonitrile in the presence of Hiinig s base leading to the formation of 3-cyano-4-hydroxy-l,2-dihydropyrido[l,2-ft]pyridazi-nium inner salt (54) (99JOC9001). The calculations indicated that both the... 

Fig. 3.26 Frontier molecular orbital analysis for the Simmons-Smith cyclopropanation. [Dargel, T.K. Koch, W.J. Chem. Soc., Perkin Trans. 1996, 2, 877. Reproduced by pemiission of The Royal Society of Chemistry]...

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Fukui at Kyoto Imperial University in Japan introduced a simplified version. According to Fukui, we need to consider only two molecular orbitals, called the frontier orbitals. These frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In ground-state 1,3,5-hexa-triene, for example, 1//3 is the HOMO and excited-stale 1,3,5-hexatriene, however, 5 is the LUMO. 

The total synthesis of palytoxin (1) is a landmark scientific achievement. It not only extended the frontiers of target-oriented synthesis in terms of the size and complexity of the molecules, but also led to new discoveries and developments in the areas of synthetic methodology and conformational analysis. Among the most useful synthetic developments to emerge from this synthesis include the refinement of the NiCh/CrC -mediated coupling reaction between iodoolefins and aldehydes, the improvements and modifications of Suzuki s palladium-catalyzed diene synthesis, and the synthesis of A-acyl vinylogous ureas. 

The symposium upon which this volume is based was organized at a turning point in nitrosamine research. Almost all types of commercial products have been tested for volatile nitrosamines, and there have been a number of outstanding accomplishments of combined university-gov-emment-private industry actions to lower or eliminate volatile nitrosamines in those products found to be contaminated. However, there is still a major gap of knowledge with regard to compounds that are not amenable to analysis by gas chromatography, and this is clearly a frontier of current research. There are also many important questions regarding chemistry, mechanism of action, and relation to human disease whose answers lie in the future of research in this field. 

DNA analysis has become an invaluable tool having very many practical applications that aim to open new frontiers in science. The sequencing of the human genome will provide information that could be applied to the study of genetic disorders as well as complications affecting the behaviour of humans at molecular level. 

Somorjai GA. 1992. The frontiers of surface-structure analysis. Surf Interface Anal 19 493-507. 

In a, P-unsaturated carbonyl compounds and related electron-deficient alkenes and alkynes, there exist two electrophilic sites and both are prone to be attacked by nucleophiles. However, the conjugated site is considerably softer compared with the unconjugated site, based on the Frontier Molecular Orbital analysis.27 Consequently, softer nucleophiles predominantly react with a, (i-unsaturated carbonyl compounds through conjugate addition (or Michael addition). Water is a hard solvent. This property of water has two significant implications for conjugate addition reactions (1) Such reactions can tolerate water since the nucleophiles and the electrophiles are softer whereas water is hard and (2) water will not compete with nucleophiles significantly in such... 

When ene-nitrile oxidoisoquinolium betaine 131 was heated as a dilute solution in toluene to 120 °C (Scheme 1.15), near quantitative conversion to the cycloadduct 133, resulting from the undesired regioselectivity, was observed. While the near complete conversion to cycloadduct 133 of oxidoisoquinolinium betaine 131 indeed demonstrated complete avoidance of the conjugate addition pathway in favor of cycloaddition, initial production of undesired isomeric cycloadduct 133 (instead of 136) was disappointing. Notably, cycloadduct 133 is expected to be less kinetically favored based on frontier molecular orbital (FMO) analysis (assuming dipole HOMO-controlled cycloaddition) of the putative transition state. This result stands in contrast to the cycloaddition of nitroalkene oxidoisoquinolinium betaine... 

---