An overview of the MO model

In molecular orbital (MO) theory, we begin by placing the nuclei of a given molecule in their equilibrium positions and then calculate the molecular orbitals (i.e. regions of space spread over the entire molecule) that a single electron might occupy. Each MO arises from interactions between orbitals of atomic centres in the molecule, and such interactions are  

An important ground-rule of MO theory is that the number of MOs that can be formed must equal the number of atomic orbitals of the constituent atoms. 

Each MO has an associated energy and, to derive the electronic ground state of a molecule, the available electrons are placed, according to the aufbau principle, in MOs beginning with that of lowest energy. The sum of the individual energies of the electrons in the orbitals (after correction 

An approximate description of the MOs in H2 can be obtained by considering them as linear combinations of atomic orbitals (LCAOs). Each of the H atoms has one 1 atomic orbital let the two associated wavefunctions be ipi and In Section 1.6, we mentioned the importance of the signs of the wavefunctions with respect to their overlap during bond formation. The sign of the wavefunction associated with the I5 atomic orbital may be either + or —. Just as transverse waves interfere in a constructive (in-phase) or destructive (out-of-phase) manner, so too do orbitals. Mathematically, we represent the possible combinations of the two I5 atomic orbitals by equations 1.27 and 1.28, where N and N are the normalization factors. Whereas V mo is nn in-phase (bonding) interaction, ipuQ is an out-of-phase (antibonding) interaction. 

9 The parity of MOs for a molecule that possesses a centre of inversion 

The bonding and antibonding MOs in H2 are given the symmetry labels a and a ( sigma and sigma-starf or. 

The ground state electronic configuration of H2 may be written using the notation Og(li), indicating that two electrons 

Each MO has an associated energy and, to derive the electronic ground state of a molecule, the available 

The interaction between the H li atomic orbitals on forming H2 may be represented by the energy level diagram in Fig. 2.4. The bonding MO, V mo is stabDized with respect to the Ij atomic orbitals, while the antibonding MO, is destabilized. Each H atom contributes one electron and, by the aufbau principle, the two electrons occupy the lower of the two MOs in the H2 molecule and are spin-paired (Fig. 2.4). It is important to remember that in MO theory 

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This chapter provides an overview of the theory and methods of molecular modeling and molecular simulation, and reviews applications involving soil minerals. The first section includes a review of the basic theory and then describes the mo-... 

The initial contribution to this volume provides a detailed overview of how spectroscopy and computations have been used in concert to probe the canonical members of each pyranopterin Mo enzyme family, as well as the pyranopterin dithiolene ligand itself. The discussion focuses on how a combination of enzyme geometric structure, spectroscopy and biochemical data have been used to arrive at an understanding of electronic structure contributions to reactivity in all of the major pyranopterin Mo enzyme families. A unique aspect of this discussion is that spectroscopic studies on relevant small molecule model compounds have been melded with analogous studies on the enzyme systems to arrive at a sophisticated description of active site electronic structure. As the field moves forward, it will become increasingly important to understand the structure, function and reaction mechanisms for the numerous non-canonical [ie. beyond sulfite oxidase, xanthine oxidase, DMSO reductase) pyranopterin Mo enzymes. 

Contents E. I. Solomon, K. W.Penfield, D.E. Wilcox Active Sites in Copper Proteins. An Electronic Structure Overview. -B.A.Averill Fe-S and Mo-Fe-S Clusters as Models for the Active Site of Nitrogenase. - N.D. Chasteen The Biochemistry of Vanadium. -KKustin, G.C. McLeod, T.R. Gilbert,... 

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