Fischer theory

Constant segment density models. We begin this discussion by reconsideration of the constant segment density model so as to be able to demonstrate later that this approach leads to the same result as is predicted by the Fischer theory. 

Abstract The wave function of Coulson and Fischer is examined within the context of recent developments in quantum chemistry. It is argued that the Coulson-Fischer ansatz establishes a third way in quantum chemistry, which should not be confused with the traditional molecular orbital and valence bond formalisms. The Coulson-Fischer theory is compared with modern valence bond approaches and also modern multireference correlation methods. Because of the non-orthogonality problem which arises when wave functions are constructed from arbitrary orbital products, the application of the Coulson-Fischer method to larger molecules necessitates the introduction of approximation schemes. It is shown that the use of hierarchical orthogonality restrictions has advantages, combining a picture of molecular electronic structure which is an accord with simple, but nevertheless empirical, ideas and concepts, with a level of computational complexity which renders praetieal applications to larger molecules tractable. An open collaborative virtual environment is proposed to foster further development. 

Keywords Coulson-Fischer wave function Coulson-Fischer analysis Coulson-Fischer theory Modern valence bond theory Multireference correlation problem Collaborative virtual environment... 

We submit that the Coulson-Fischer ansatz affords a third way in quantum chemistry that is distinct from the traditional valence bond and molecular orbital theories. In the next two sections, we very briefly survey the current state of the art in valence bond theory and in the multireference correlation problem based on the molecular orbital theory, before considering the Coulson-Fischer theory in more detail in Section 6. 

Evidence for this renaissance is seen in the number of monographs [53-55], edited volumes [56-58] and review articles [52, 59, 60, 62, 63, 61, 64-69] on valence bond theory published in recent years. These works display a rich variety of theoretical machinery inspired by the valence bond picture of molecular structure. Some of the methodologies - particularly in the so-called modern valence bond theories introduced by Gerratt and Lipscomb [70,71] under the name spin-coupled wave functions and developed by Gerratt [72,73] and his collaborators [68,74-86] over the past 40 years - exploit the Coulson-Fischer ansatz. As we have seen in Section 3 and will consider further in Section 6, the Coulson-Fischer theory presents a third way of constructing approximate molecular wave functions which combine many of the advantages of both molecular orbital theory and valence bond theory. 

Here we are proposing the creation of an open collaborative virtual environment for the development of the Coulson-Fischer method for molecular wave functions. To this end we have created web pages at http //quantumsystems.googlepages.com/ cve theCoulson-Fischertheory, which is intended to form an element of a collaborative virtual environment for the further advancement of the Coulson-Fischer theory. In his recently published report, Karadakov [52] expresses his view that... 

The generalised valence bond (GVB) method, developed by Goddard in 1970, is one of the simplest and oldest valence bond methods that use flexible orbitals in a general way. The generalised Coulson-Fischer theory for the hydrogen molecule mentioned above is used to describe every electron pair in a molecule. The orbitals for each electron pair are expanded in terms of the full basis set and are non-orthogonal. Orbitals from different pairs are forced to be orthogonal. This condition simplifies the calculations but may lead to some difficulties [160,161],... 

The generalization of a Coulson-Fischer type wave function to the molecular case with an arbitrary size basis set is known as Spin Coupled Valence Bond (SCVB) theory. ... 

A number of reaction pathways have been proposed for the Fischer indolization reaction. The mechanism proposed by Robinson and Robinson in 1918, which was extended by Allen and Wilson in 1943 and interpreted in light of modem electronic theory by Carlin and Fischer in 1948 is now generally accepted. The mechanism consists of three stages (I) hydrazone-ene-hydrazine equilibrium (II) formation of the new C-C bond via a [3,3]-sigmatropic rearrangement (III) generation of the indole nucleus by loss of... 

The problem of molecular recognition has attracted biologically oriented chemists since Emil Fischer s lock-and-key theory l0). Within the last two decades, many model compounds have been developed micelle-forming detergents11, modified cyclodextrins 12), many kinds of crown-type compounds13) including podands, coronands, cryptands, and spherands. Very extensive studies using these compounds have, however, not been made from a point of view of whether or not shape similarity affects the discrimination. 

Fischer-type carbene complexes, generally characterized by the formula (CO)5M=C(X)R (M=Cr, Mo, W X=7r-donor substitutent, R=alkyl, aryl or unsaturated alkenyl and alkynyl), have been known now for about 40 years. They have been widely used in synthetic reactions [37,51-58] and show a very good reactivity especially in cycloaddition reactions [59-64]. As described above, Fischer-type carbene complexes are characterized by a formal metal-carbon double bond to a low-valent transition metal which is usually stabilized by 7r-acceptor substituents such as CO, PPh3 or Cp. The electronic structure of the metal-carbene bond is of great interest because it determines the reactivity of the complex [65-68]. Several theoretical studies have addressed this problem by means of semiempirical [69-73], Hartree-Fock (HF) [74-79] and post-HF [80-83] calculations and lately also by density functional theory (DFT) calculations [67, 84-94]. Often these studies also compared Fischer-type and... 

Diacyl peroxides undergo thermal and photochemical decomposition to give radical intermediates (for a recent review, see Hiatt, 1971). Mechanistically the reactions are well understood as a result of the many investigations of products and kinetics of thermal decomposition (reviewed by DeTar, 1967 Cubbon, 1970). Not surprisingly, therefore, one of the earliest reports of CIDNP concerned the thermal decomposition of benzoyl peroxide (Bargon et al., 1967 Bargon and Fischer, 1967) and peroxide decompositions have been used more widely than any other class of reaction in testing theories of the phenomenon. 

The first example of chemically induced multiplet polarization was observed on treatment of a solution of n-butyl bromide and n-butyl lithium in hexane with a little ether to initiate reaction by depolymerizing the organometallic compound (Ward and Lawler, 1967). Polarization (E/A) of the protons on carbon atoms 1 and 2 in the 1-butene produced was observed and taken as evidence of the correctness of an earlier suggestion (Bryce-Smith, 1956) that radical intermediates are involved in this elimination. Similar observations were made in the reaction of t-butyl lithium with n-butyl bromide when both 1-butene and isobutene were found to be polarized. The observations were particularly significant because multiplet polarization could not be explained by the electron-nuclear cross-relaxation theory of CIDNP then being advanced to explain net polarization (Lawler, 1967 Bargon and Fischer, 1967). 

Equation 4 renders the YBG equation solvable. However, as did Fischer and Methfessel we shall further simplify the theory by making the van der Waals structureless fluid approximation (g = 0,sa ) In the Integral Involving the long-ranged continuous force u. The YBG equation thus becomes... 

In particular, the reactions of electrophilically activated benzonitrile A-oxides with 3-methylenephthalimidines with formation of 2-isoxazolines and oximes and the cycloaddition between alkynyl metal(O) Fischer carbenes and nitrones leading to 4-isoxazolines have been investigated by density functional theory methods <06JOC9319 06JOC6178>. 

Allen und Wilson 4) fiihrten die E. FiscHERsche Indolsynthese mit Phenylhydrazin durch, in dem der dem Benzolkern benachbarte Stickssoff einen UberschuB an 15N enthielt. Der gesamte UberschuB an 15N wurde im erhaltenen 2-Phenyl-indol gefunden, wie es nach der Theorie von Robinson und Robinson 171) und den Versuchen von E. Fischer 79) mit asymmetrischem Methylphenylhydrazin zu erwarten war. 

Cheng, J., Gong, X.-Q., Hu, P Lok, C. M Ellis, P and French, S. 2008. A quantitative determination of reaction mechanisms from density functional theory calculations Fischer-Tropsch synthesis on flat and stepped cobalt surfaces. J. Catal. 254 285-95. 

The earliest theory, advanced by Fischer and Tropsch in 1926 (84), proposed that the reaction proceeded via formation of intermediate metal carbides which react on the catalyst surface to form methylene groups. It was then suggested that these methylene groups polymerize on the surface to form hydrocarbon chains, which desorb as saturated and unsaturated hydrocarbons. In 1939 Craxford and Rideal expanded the carbide theory, proposing (85), for cobalt-based catalysts, the following reaction sequence ... 

Subsequent studies have failed to support the carbide theory, and it is now generally accepted that carbides of the type proposed by Craxford play little or no part in the Fischer-Tropsch synthesis (86, 87). It has, however, recently been suggested, by analogy with the mechanism proposed for the Haber synthesis of ammonia, that carbides formed by dissociative absorption of carbon monoxide would be expected to be readily hydrogenated and could therefore be of importance in Fischer-Tropsch synthesis over heterogeneous catalyst (88). 

Also, in 1890 Fischer had proven that the reduction of fructose with sodium amalgam yields a mixture of mannitol and sorbitol and pointed out that this conformed with the van t HofF-Le Bel theory (19). It seems, therefore, that the idea of asymmetric induction was clearly in a state of incubation prior to his publication of the relative configurations of the sugars in 1891. 

Key words Dotz reaction, benzannulation, Fischer carbene complexes, reaction mechanism, density functional theory... 

Geison, "Scientific Change." J. S. Fruton, "Contrasts in Scientific Style Emil Fischer and Franz Hofmeister, Their Research Schools and Their Theories of Protein Structure," Proceedings of the American Philosophical Society 129 (1985) 313370 also see, Fruton, "The Liebig Research Group, a Reappraisal," ibid., 132 (1988) 166 Holmes, "Complementarity," 121164 and J. B. Morrell, "The Chemist Breeders ... 

Fruton, Joseph S. "Contrasts in Scientific Style Emil Fischer and Franz Hofmeister Their Research Schools and Their Theories of Protein Structure." Proceedings of the American Philosophical Society 129 (1985) 313370. 

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