Mechanism molecular orbital treatment

Several molecular orbital treatments of dibenzothiophene have appeared, the object in general being twofold. First, to derive a model which will account for the positional electrophilic reactivity observed for dibenzothiophene, and second, as a result of such a model, to formulate an accurate quantum mechanical model for the sulfur atom and empirical... 

When the quantum mechanical equations are examined it is found that the two descriptions of the double bond are identical in the molecular-orbital treatment based on s-p hybrids.76 They are not identical... 

All calculations and experimental data support the assumption that the contact term is the dominating coupling mechanism. In the independent electron model of Pople and Santry s molecular orbital treatment [11], the contact term is described by equation (1) for the reduced coupling constant AT(Sn,X) [ (Sn,X)=4ic2y(Sn,X) (/ry" nyX)- ). 

Ab initio A quantum mechanical nonparametrized molecular orbital treatment (Latin from first principles ) for the description of chemical behavior taking into account nuclei and all electrons. In principle, it is the most accurate of the three computational methodologies ab initio, semi-empirical all-valence electron methods, and molecular mechanics. 

The more recent treatment of the covalent bond, based on the application of the principles of wave mechanics, has developed in two distinct forms, usually termed the valence-bond and molecular-orbital theories, respectively. Although ultimately there is no inconsistency between these two theories, they do in fact approach the problem of chemical binding from different points of view, and we shall generally find that for our purposes the valence-bond treatment is the more suitable. This theory starts from concepts already familiar to the chemist and its conclusions can usually be expressed verbally in qualitative terms the molecular-orbital theory, on the other hand, is more mathematical in its approach and lends itself less readily to such an interpretation. We shall, therefore, first discuss the valency-bond theory, and refer only briefly to the molecular-orbital treatment later in the chapter. 

On the other hand, the VB model developed by Pauling was based on a more quantum-mechanical-based model of valence electrons. Instead of simply putting electrons into spatially separated regions (domains), atomic orbitals are involved in the discussion, and all bonding interactions are considered as overlaps between orbitals of different atoms. This approach has been very useful in bridging the Lewis model to the more modem molecular orbital treatment, and similar to VSEPR, the hybridization scheme developed by Pauling has provided an important theoretical underpinning for chemistry over the years. 

Other known acid-catalyzed pentaborane substitution reactions also result in apically substituted pentaboranes (251, 261-263). This is in agreement with the predicted site of electrophilic substitution based on charge distributions, as determined from valence bond and molecular orbital treatments (17,264,265). Furthermore, the position of observed attachment of boron on the carbon skeleton (i.e., the most substituted carbon when unsymmetrical alkenes are used) is consistent with this predicated mechanism (249). The position of boron attachment is kinetically rather than thermodynamically controlled, for basal substituted alkylpentaboranes are found to be about 3 kcal/mole more stable than the corresponding apically substituted pentaboranes (266). 

In our treatment of molecular systems we first show how to determine the energy for a given iva efunction, and then demonstrate how to calculate the wavefunction for a specific nuclear geometry. In the most popular kind of quantum mechanical calculations performed on molecules each molecular spin orbital is expressed as a linear combination of atomic orhilals (the LCAO approach ). Thus each molecular orbital can be written as a summation of the following form ... 

SCF, see Self-consistent field treatment (SCF) Schroedinger equation, 2,4,74 Secular equations, 6,10, 52 solution by matrix diagonalization, 11 computer program for, 31-33 Self-consistent field treatment (SCF), of molecular orbitals, 28 Serine, structure of, 110 Serine proteases, 170-188. See also Subtilisin Trypsin enzyme family comparison of mechanisms for, 182-184, 183... 

There are two principal methods available for the quantum mechanical treatment of molecular structure, the valence bond method and the molecular orbital method. In this paper we shall make use of the latter, since it is simpler in form and is more easily adapted to quantitative calculations.3 We accordingly consider each electron... 

In order to describe the hydrogen molecule by quantum mechanical methods, it is necessary to make use of the principles given in Chapter 2. It was shown that a wave function provided the starting point for application of the methods that permitted the calculation of values for the dynamical variables. It is with a wave function that we must again begin our treatment of the H2 molecule by the molecular orbital method. But what wave function do we need The answer is that we need a wave function for the H2 molecule, and that wave function is constructed from the atomic wave functions. The technique used to construct molecular wave functions is known as the linear combination of atomic orbitals (abbreviated as LCAO-MO). The linear combination of atomic orbitals can be written mathematically as... 

MOPAC is a general-purpose semiempirical molecular orbital program for the study of chemical structures and reactions. It is available in desktop PC running Windows, Macintosh OS, and Unix-based workstation versions. It uses semiempirical quantum mechanical methods that are based on Hartree-Fock (HF) theory with some parameterized functions and empirically determined parameters replacing some sections of the complete HF treatment. The approximations in... 

A rigorous mathematical formalism of chemical bonding is possible only through the quantum mechanical treatment of molecules. However, obtaining analytical solutions for the Schrodinger wave equation is not possible even for the simplest systems with more than one electron and as a result attempts have been made to obtain approximate solutions a series of approximations have been introduced. As a first step, the Bom-Oppenheimer approximation has been invoked, which allows us to treat the electronic and nuclear motions separately. In solving the electronic part, mainly two formalisms, VB and molecular orbital (MO), have been in use and they are described below. Both are wave function-based methods. The wave function T is the fundamental descriptor in quantum mechanics but it is not physically measurable. The squared value of the wave function T 2dT represents probability of finding an electron in the volume element dr. 

Quantum chemistry or molecular electronic structure theory is the application of the principles of quantum mechanics to calculate the stationary states of molecules and the transitions between these states. Today, both computational and experimental groups routinely use ab initio (meaning from first principles ) molecular orbital calculations as a means of understanding structure, bonding, reaction paths between intermediates etc. Explicit treatment of the electrons means that, in principle, one does not make assumptions concerning the bonding of a system. 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

The purpose of this book is to show how the consideration of molecular symmetry can cut short a lot of the work involved in the quantum mechanical treatment of molecules. Of course, all the problems we will be concerned with could be solved by brute force but the use of symmetry is both more expeditious and more elegant. For example, when we come to consider Huckel molecular orbital theory for the trivinylmethyl radical, we will find that if we take account of the molecule s symmetry, we can reduce the problem of solving a 7 x 7 determinantal equation to the much easier one of solving one 3x3 and two 2x2 determinantal equations and this leads to having one cubic and two quadratic equations rather than one seventh-order equation to solve. Symmetry will also allow us immediately to obtain useful qualitative information about the properties of molecules from which their structure can be predicted for example, we will be able to predict the differences in the infra-red and Baman spectra of methane and monodeuteromethane and thereby distinguish between them. 

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