Molecular orbital theory defined

How does each of the three major bonding theories (the Lewis model, valence bond theory, and molecular orbital theory) define a single chemical bond A double bond A triple bond How are these definitions similar How are they... 

Valence bond and molecular orbital theory both incorporate the wave description of an atom s electrons into this picture of H2 but m somewhat different ways Both assume that electron waves behave like more familiar waves such as sound and light waves One important property of waves is called interference m physics Constructive interference occurs when two waves combine so as to reinforce each other (m phase) destructive interference occurs when they oppose each other (out of phase) (Figure 2 2) Recall from Section 1 1 that electron waves m atoms are characterized by their wave function which is the same as an orbital For an electron m the most stable state of a hydrogen atom for example this state is defined by the Is wave function and is often called the Is orbital The valence bond model bases the connection between two atoms on the overlap between half filled orbifals of fhe fwo afoms The molecular orbital model assembles a sef of molecular orbifals by combining fhe afomic orbifals of all of fhe atoms m fhe molecule... 

Energy, geometry, dipole moment, and the electrostatic potential all have a clear relation to experimental values. Calculated atomic charges are a different matter. There are various ways to define atomic charges. HyperChem uses Mulliken atomic charges, which are commonly used in Molecular Orbital theory. These quantities have only an approximate relation to experiment their values are sensitive to the basis set and to the method of calculation. 

At first sight, the molecular orbital description of N2 looks quite different from the Lewis description ( N=N ). However, it is, in fact, very closely related. We can see their similarity by defining the bond order (b) in molecular orbital theory as the net number of bonds, allowing for the cancellation of bonds by antibonds ... 

Topsom, 1976) and to treat them separately. In this review we will be concerned solely with polar or electronic substituent effects. Although it is possible to define a number of different electronic effects (field effects, CT-inductive effects, jt-inductive effects, Jt-field effects, resonance effects), it is customary to use a dual substituent parameter scale, in which one parameter describes the polarity of a substituent and the other the charge transfer (resonance) (Topsom, 1976). In terms of molecular orbital theory, particularly in the form of perturbation theory, this corresponds to a separate evaluation of charge (inductive) and overlap (resonance) effects. This is reflected in the Klopman-Salem theory (Devaquet and Salem, 1969 Klop-man, 1968 Salem, 1968) and in our theory (Sustmann and Binsch, 1971, 1972 Sustmann and Vahrenholt, 1973). A related treatment of substituent effects has been proposed by Godfrey (Duerden and Godfrey, 1980). 

The Fermi surface plays an important role in the theory of metals. It is defined by the reciprocal-space wavevectors of the electrons with largest kinetic energy, and is the highest occupied molecular orbital (HOMO) in molecular orbital theory. For a free electron gas, the Fermi surface is spherical, that is, the kinetic energy of the electrons is only dependent on the magnitude, not on the direction of the wavevector. In a free electron gas the electrons are completely delocalized and will not contribute to the intensity of the Bragg reflections. As a result, an accurate scale factor may not be obtainable from a least-squares refinement with neutral atom scattering factors. 

In this article, we present an ab initio approach, suitable for condensed phase simulations, that combines Hartree-Fock molecular orbital theory and modem valence bond theory which is termed as MOVB to describe the potential energy surface (PES) for reactive systems. We first provide a briefreview of the block-localized wave function (BLW) method that is used to define diabatic electronic states. Then, the MOVB model is presented in association with combined QM/MM simulations. The method is demonstrated by model proton transfer reactions in the gas phase and solution as well as a model Sn2 reaction in water. 

In molecular orbital theory, there is a clear and well defined path to the exact solution of the Schrodinger equation. All we need do is express our wave function as a Unear combination of all possible configurations (full CI) and choose a basis set that is infinite in size, and we have arrived. While such a goal is essentially never practicable, at least the path to it can be followed unambiguously until computational resources fail. 

Resonance integrals of bonds between atoms X and Y, XY, are expressed as defined in Eq. (2), where kXY depends on the bond length. There has been considerable variation in the values taken for the Coulomb and resonance integrals for heterocyclic molecules. One of the best available set of parameters is still that originally suggested by A. Streitwieser (Molecular orbital theory. J. Wiley Sons, Inc., N.Y.-L., 1961) ... 

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... 

From molecular orbital theory, a many-electron wavefunction, may be defined by a determinant of molecular wavefunctions, i/ ,. The i[i, may in turn be expressed as a linear combination of one-electron functions, that is, (fj, = where cM, are the molecular orbital expansion coefficients... 

Earlier in this chapter, you learned the definition of bond order in the valence bond theory. In molecular orbital theory, the bond order is defined as one-half the difference between the number of electrons in bonding orbitals and the number of electrons in antibonding orbitals. Mathematically, this can be expressed as... 

This is the basic equation used to derive normal coordinate analysis [110] as well as to define the vibrational quantities to be calculated using molecular orbital theory [79,94], The coefficients, g , are the forces acting on the nuclei, which are zero at equilibrium geometiy. This leaves the quadratic terms Vs the first term in the change of potential energy with instantaneous vibrational displacement. The quadratic terms Fy, are conveniently ordered as a matrix which is known as the force field or force matrix. These terms correspond to the derivatives of the potential energy V ... 

As it is well known (see, for example, [16,17]), the Hiickel molecular orbital theory is based on a Hamiltonian operator, ff defined by means of the matrix elements... 

The second major obstacle to application of molecular-orbital theory lies in the need to define the electronic state of the ion. Thus, it is possible to calculate groimd- and excited-state properties of molecules and compare the results with experimental observation, but there is no direct knowledge of the electron configimation in an ion produced by electron impact except perhaps immediately after ionization at threshold voltages. The quasi-equilibrium theory can be applied to any state the ion is known to exist in, but this knowledge is usually lacking. Some attempt has been made to define the electronic state of an ion as ground-state or excited-state from the appearance of metastable ions, as is... 

Exponents of molecular-orbital theory treat the subject in two fairly well defined ways. One is to apply the theory in a qualitative or even semi-quantitative manner to aid understanding of chemical processes and the other is concerned more with ab initio calculations of molecular properties. Present ill-defined knowledge of ion structures and reaction mechanisms suggest that the latter approach is unlikely to be rewarding. 

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